The derivative dy/dx for the given functions [tex]y = 6u^-5[/tex] and [tex]u = 2(14x)[/tex]is:
[tex]dy/dx = (-30(28x)^-6) * 28[/tex]
GIven the functions y = f(u) and u = g(x), and we need to find the derivative dy/dx using the chain rule. The given functions are [tex]y = 6u^-5[/tex]and [tex]u = 2(14x).[/tex] Let's begin.
First, let's find the derivative of y with respect to u, which is f'(u). We have:
[tex]y = 6u^-5\\f'(u) = -30u^-6[/tex]
Next, let's find the derivative of u with respect to x, which is g'(x). We have:
u = 2(14x)
g'(x) = 28
Now we can apply the chain rule to find dy/dx:
dy/dx = f'(g(x)) * g'(x)
Substitute the derivatives we found earlier and the function u = g(x):
dy/dx = (-30(2(14x))^-6) * 28
Simplify the expression:
dy/dx = (-30(28x)^-6) * 28
Learn more about derivative here :-
https://brainly.com/question/18722002
#SPJ11
I have to reproduce the rectangle taking into account the instructions
The rectangle is reproduced accordingly. You would note that the other side is the length = 6,3 cm. The other angle is also 28°. This is because of the properties of a rectangle.
What are the properties of a rectangle?Rectangles have the following fundamental properties:
A quadrilateral is a rectangle.Each inner angle is equal to 90 degrees since the opposite sides are parallel and equal.The total of all internal angles equals 360 degrees.Both diagonals are the same length and bisect each other.The perimeter of a rectangle with side lengths a and b is 2a+2b units.The area of a rectangle with side lengths a and b is given by ab sin 90 = ab square units.A rectangle's diagonal is its circumcircle's diameter.The diagonals intersect at various angles. One is sharp, while the other is obtuse.opposites sides are equalIf the two diagonals intersect at right angles, the rectangle is called a square.Learn more about rectangles:
https://brainly.com/question/29123947
#SPJ1
Ross constructs a scatter plot. He realizes that he needs to add one more point, which will be an outlier. Which of the ordered pairs does he still need to plot? Responses (1,3) left parenthesis 1 comma 3 right parentheses (7,6) left parenthesis 7 commas 6 right parentheses (5,9) left parenthesis 5 commas 9 right parentheses (3,6) PLESA HELP I REALLY NEED THIS I WILL GIVE BRANLIST TO ANYONE WHO answers
Answer:
(7, 6)
Step-by-step explanation:
If we look at the graph, there is a line containing (1, 2.5), (3, 3.5), (8, 8.5) roughly. So, the point (7, 6) is the closest to being on this line.
Answer:
(5,9)
Step-by-step explanation:
I just took the quiz and I chose (7,6) and it is incorrect
Is There a Genetic Marker for Dyslexia?A disruption of a gene called DYXC1 on chromosome 15 for humans may be related to an increased risk of developing dyslexia. Researchers1 studied the gene in 109 people diagnosed with dyslexia and in a control group of 195 others who had no learning disorder. The DYXC1 break occurred in 10 of those with dyslexia and in 5 of those in the control group.1Science News, August 30, 2003, p 131.(a) Is this an experiment or an observational study?ExperimentObservational study(b) How many rows and how many columns will the data table have? Assume rows are the cases and columns are the variables. (There might be an extra column for identification purposes; do not count this column in your total.) Number of rows: Enter your answer in accordance to item (b) of thequestion statementNumber of columns: Enter your answer in accordance to item (b) of the question statement (c) Display the results of the study in a two-way table. Gene breakNo breakTotalDyslexia groupEnter your answer in accordance to item (c) of the question statementEnter your answer in accordance to item (c) of the question statementEnter your answer in accordance to item (c) of the question statementControl groupEnter your answer in accordance to item (c) of the question statementEnter your answer in accordance to item (c) of the question statementEnter your answer in accordance to item (c) of the question statementTotalEnter your answer in accordance to item (c) of the question statementEnter your answer in accordance to item (c) of the question statementEnter your answer in accordance to item (c) of the question statement(d) To see if there appears to be a substantial difference between the group with dyslexia and the control group, compare the proportion of each group who have the break on the DYXC1 gene.Round your answers to three decimal places.Proportion for dyslexia group: Enter your answer in accordance to item (d) of the question statementProportion for control group: Enter your answer in accordance to item (d) of the question statement(e) Does there appear to be an association between this genetic marker and dyslexia for the people in this sample?YesNo (f) If the association appears to be strong, can we assume that the gene disruption causes dyslexia?YesNo
(a) Experiment
(b) Number of rows: 304 (109 dyslexia group + 195 control group)
Number of columns: 2 (gene break, no break)
(c)
Gene breakNo breakTotal
Dyslexia group 10 99 109
Control group 5 190 195
Total 15 289 304
(d) Proportion for dyslexia group: 0.092
Proportion for control group: 0.017
(e) Yes, there appears to be an association between this genetic marker and dyslexia for the people in this sample.
(f) No, we cannot assume that the gene disruption causes dyslexia solely based on this study. Further research and experimentation would be needed to establish a causal relationship.
(a) This is an observational study.
(b) Number of rows: 2
Number of columns: 2
(c) Two-way table:
| | Gene break | No break | Total |
|----------------|------------|----------|-------|
| Dyslexia group | 10 | 99 | 109 |
| Control group | 5 | 190 | 195 |
| Total | 15 | 289 | 304 |
(d) Proportion for dyslexia group: 10/109 = 0.092
Proportion for control group: 5/195 = 0.026
(e) Yes, there appears to be an association between this genetic marker and dyslexia for the people in this sample.
(f) No, even if the association appears to be strong, we cannot assume that the gene disruption causes dyslexia.
Visit here to learn more about dyslexia brainly.com/question/14294569
#SPJ11
Which letter answer is it? I'm so confused!
The percentage of the total number of bottles sold in June, July and August that was sold in July is given as follows:
C. 40%.
How to calculate the percentage?The bar graph gives the number of bottles of suntan sold each month, as follows:
June: 1200 bottles.July: 1500 bottles.August: 1050 bottles.The total amount of bottles is given as follows:
1200 + 1500 + 1050 = 3750 bottles.
There were 1500 bottles sold in July, hence the percentage is given as follows:
p = 1500/3750 x 100%
p = 40%.
More can be learned about percentages at https://brainly.com/question/24877689
#SPJ1
find the macluaring series for both f(x)( and g(x) using the definition of maclaurin series. use basis of your solution ln(1 2x)
The Maclaurin series for g(x) is ln(1+2x)[tex].^{2}[/tex] = -8[tex]x^2[/tex] - 128ln(2)[tex].^{2}[/tex][tex]x^{4}[/tex]
To find the Maclaurin series for a function f(x) using the definition of Maclaurin series, we need to express f(x) as a power series centered at x=0, which is given by:
f(x) = Σ[ n=0 to infinity ] ([tex]n^{2}[/tex](0)/n!) * [tex]x^{n}[/tex]
where [tex]f^n[/tex](0) is the nth derivative of f(x) evaluated at x=0.
Using the definition of Maclaurin series, we can find the Maclaurin series for f(x) and g(x) as follows:
f(x) = ln(1+2x)
First, we find the derivatives of f(x) with respect to x:
f'(x) = 2 / (1+2x)
f''(x) = -4 / (1+2x)
f'''(x) = 16 / (1+2x)
f''''(x) = -64 / (1+2x)
Next,
We evaluate the derivatives at x=0 to find the coefficients of the Maclaurin series:
f(0) = ln(1) = 0
f'(0) = 2
f''(0) = -4
f'''(0) = 16
f''''(0) = -64
Substituting these coefficients into the formula for the Maclaurin series, we get:
f(x) = 2x - 2x + (8/3)x - (32/3)x + ...
Therefore, the Maclaurin series for f(x) is:
ln(1+2x) = 2x - 2x + (8/3) - (32/3) + ...
g(x) = ln(1+2x)
Using the chain rule, we can find the derivatives of g(x) as:
g'(x) = 4ln(1+2x) / (1+2x)
g''(x) = -8[ln(1+2x) + 1] / (1+2x)
g'''(x) = 32[ln(1+2x) + 2] / (1+2x)
g''''(x) = -128[ln(1+2x) + 3] / (1+2x)
Evaluating these derivatives at x=0, we get:
g(0) = ln(1)[tex].^{2}[/tex] = 0
g'(0) = 0
g''(0) = -8
g'''(0) = 0
g''''(0) = -128*ln(2)[tex].^{2}[/tex]
Therefore, the Maclaurin series for g(x) is:
ln(1+2x)[tex].^{2}[/tex] = -8[tex]x^2[/tex] - 128ln(2)[tex].^{2}[/tex][tex]x^{4}[/tex]
For similar question on Maclaurin series:
https://brainly.com/question/31388111
#SPJ11
Consider the series M: 3 + 4 + 3 Evaluate the the following limit. If it is infinite, type "infinity" or "int". If it does not exist type "DNE" lim Val = 1 Answer: - What can you say about the series using the Root Test? Answer "Convergent", "Divergent", or "Inconclusive Answer choose one o Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Answer "Absolutely Convergent", "Conditionally Convergent", or "Divergent". Answer: choose one
The limit of the series M is infinity, Using the Root Test, we can say that the series is convergent, To determine whether the series is absolutely convergent, conditionally convergent, or divergent, we need to look at the individual terms of the series.
Since the series M contains both positive and negative terms, we need to consider both the series of positive terms and the series of negative terms separately, The series of positive terms is 3 + 4 + 3 + ... which is clearly divergent since it is an increasing sequence that goes to infinity.
The series of negative terms is -4 - 3 - 4 - 3 - ... which is also divergent for the same reason, Since neither the series of positive terms nor the series of negative terms is convergent, the original series M is divergent. Therefore, we can say that the series M is divergent, The series M consists of three terms: 3 + 4 + 3.
Since the series M is a finite series, it is absolutely convergent. It is not conditionally convergent or divergent, as those terms only apply to infinite series.
Answer:
1. Limit: DNE (Does Not Exist)
2. Root Test: Inconclusive
3. Series Type: Absolutely Convergent
To know more about negative terms:- https://brainly.com/question/21959954
#SPJ11
An envelope measures 33 centimeters by 44 centimeters. A pencil is placed in the envelope at a diagonal. What is the maximum possible length of the pencil?
Answer:
The maximum possible length of the pencil is 55 centimeters (cm).
Step-by-step explanation:
We know that the Pythagorean Theorem states that a² + b² = c² in a right triangle.
a = the altitude (the vertical line of a right triangle)
b= the base (the horizontal line of a right triangle)
c= the hypotenuse (the diagonal line of a right triangle)
1. substitute 33 for a and 44 for b
33² + 44² = c²
2. simplify the expression
1089 + 1936 = c²
3. combine like terms
3025 = c²
4. square root both sides
√3025 = √c²
55 = c
c = 55
This means that the maximum possible length of the pencil is 55 centimeters (cm).
Calculate how many roofs trusses would be needed to frame the roof if the ridgeline runs parallel to the longest side of the shed
22 roofs trusses would be needed to frame the roof if the ridgeline runs parallel to the longest side of the shed
The longest side of the roof is 28ft
Each roof is 16 inches apart
S0 28×12/16
We get 21
It means that there are 21 aparts for the roof trusses
So there are 21+1 =22 roof trusses are needed
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
Find the value for x.
Area of the rectangle=
24 m^2
(2x -9) m
(x + 2) m
The value for x is 6.
We are given that area of a rectangle is 24 and the length and breadth are (x + 2) and (2x - 9).
Area of a rectangle = length * width
Substituting the values, we get
24 = (x+2) (2x-9)
24 = [tex]2x^2-5x-18[/tex]
[tex]2x^2-5x-42 = 0[/tex]
0 = (2x+7) (x-6)
0 = (2x+7) or 0 = (x-6)
x = -7/2 or x = 6
if we consider the value of x as -7/2 and substitute this value of x in the equation of the side of a rectangle (x + 2), we get -7/2 + 2 = -3/2 and a side cannot be negative. Therefore, we will reject this value of x.
Therefore, our answer is 6.
To learn more about the area of a rectangle;
https://brainly.com/question/2607596
#SPJ4
The complete question is "Find the value for x.
Area of the rectangle = 24 m^2 and the length and breadth are (2x -9) m
and (x + 2) m."
Explain the rules of multiplication and division to convert units . How do you know when to multiply and when to divide to convert units of measurement?
Write three to four sentences
When converting a larger unit to a smaller one, we multiply; when we convert a smaller unit to a larger one, we divide
The built-in functions for multiply, divide, and subtract can also be used to specify arithmetic operations.
If we need to go from a bigger to a smaller unit, multiply. If we need to get from a smaller to a larger unit, we should divide. We will do so since division is all about bringing down numbers, as we well know.
As a result, we multiply when translating a larger unit to a smaller one and divide when converting a smaller unit to a larger one.
Learn more about unit conversion here:
brainly.com/question/4736731
#SPJ1
In this problem we consider a differential equation in the form Mdx + Ndy =0.
(3x^(2)y+e^y)dx+(x^3+xe^y-2y)dy=0
Find: My
Nx
Is the equation (1) Exact or (2) Not Exact?
If the problem is exact then the solution is given as f(x,y)=C
where C is an arbitrary constant. In this case enter f(x,y)below.
To find My, we need to take the partial derivative of N with respect to y: My = ∂N/∂y = x(e^y - 2). the potential function f(x, y) is: f(x, y) = x^3y + xe^y - y^2. The solution to the exact differential equation is: f(x, y) = C, where C is an arbitrary constant. In this case, the solution is: f(x, y) = x^3y + xe^y - y^2 = C.
To determine whether the equation is exact or not, we need to check if M and N satisfy the condition:
∂M/∂y = ∂N/∂x
1.)Taking the partial derivative of M with respect to y:
∂M/∂y = 3x^2 + e^y
2.)Taking the partial derivative of N with respect to x:
∂N/∂x = 3x^2 + e^y
Since ∂M/∂y = ∂N/∂x, the equation is exact.
To find the solution, we need to integrate M with respect to x and N with respect to y, then equate them to a constant C:
∫M dx = ∫(3x^2y + e^y) dx = x^3y + xe^y + g(y)
∫N dy = ∫(x^3 + xe^y - 2y) dy = x^3y + ye^y - y^2 + h(x)
Equating them:
x^3y + xe^y + g(y) = x^3y + ye^y - y^2 + h(x)
Simplifying:
xe^y + y^2 - h(x) = -g(y)
Since both sides are functions of different variables, they must be equal to a constant C:
xe^y + y^2 - h(x) = -g(y) = C
Therefore, the solution is:
f(x,y) = x^e^y + y^2 - C = x^e^y + y^2 - (xe^y + y^2 - h(x)) = h(x) + x^e^y - xe^y - C
Learn more about partial derivative here: brainly.com/question/31397807
#SPJ11
A solid cube has a density of 3 ounces per cubic inch. Which is closest to the side length (in inches) of the cube if its mass is 80 ounces?
Closest to the side length (in inches) of the cube if its mass is 80 ounces is any side as the cube has equal sides. So The side length of the cube is approximately 4.3 inches.
To solve the problem, we can use the formula for density:
Density = Mass / Volume
We are given the density (3 ounces per cubic inch) and the mass (80 ounces), so we can rearrange the formula to solve for the volume:
Volume = Mass / Density
Volume = 80 / 3
Volume = 26.67 cubic inches
Since the cube is a regular solid, all of its sides are equal in length. Therefore, we can use the formula for the volume of a cube to solve for the side length:
Volume = Side length³
26.67 = Side length³
Side length ≈ 4.3 inches (rounded to one decimal place)
Learn more about cube:
https://brainly.com/question/28776132
#SPJ4
A teacher asks students to identity their favorite reality television show. What type of measurement scale do the different television shows make up? tof Select one: a. Nominal b. Ordinal c. Ratio d. Interval 12 Given the following bivariate data, compute the sum of squares out of to one decimal place. х 2 4 у 3 5 8 6 8 15 18 10 12 21 VOIPILUL UNION A regression between foot length (response variable in cm) and height (explanatory variable in inches) for 33 students resulted in the following regression equation: 9 = 10.9 +0.23x. One student in the sample was 73 inches tall with a foot length of 29 cm. What is the residual for this student? Select one: a. 1.31 cm b. -1.31 cm c. 0.00 cm d. 29.00 cm A regression equation for left palm length (y variable) and right palm length (x variable) for 55 college students gave an error sum of squares (SSE) of 10.7 and a total sum of squares (SSTO) of 85.2. The proportion of variation explained by x, Rº, is Select one: a. 87.4% b. 11.2% c. 12.696 d. 88.8%
The answer to the first question is a. Nominal. The answer to the second and third questions are option a -1.31 cm and option a 87.5%, respectively
To compute the sum of squares, we need the mean of the data.
x: 2, 4, 6, 8, 10, 12, 18, 21
y: 3, 5, 8, 6, 8, 15, 10, 12
Mean of x = (2+4+6+8+10+12+18+21)/8 = 9.375
Mean of y = (3+5+8+6+8+15+10+12)/8 = 8.5
SSE = Σ(yi - ŷi)²
= (3 - 8.525)² + (5 - 9.002)² + (8 - 11.48)² + (6 - 10.336)²
+ (8 - 11.48)² + (15 - 19.556)² + (10 - 12.962)² + (12 - 15.898)²
= 127.98
The residual is given by:
residual = observed y value - predicted y value
= 29 - (10.9 + 0.23*73)
= -1.31 cm
The proportion of variation explained by x is:
R² = 1 - (SSE/SSTO) = 1 - (10.7/85.2) = 0.875 or 87.5% (approx.)
The answer to the first question is a, the second and third questions are option a and option a respectively.
To know more about mean refer to-
https://brainly.com/question/30112112
#SPJ11
Find an equation of the tangent plane to the given surface at the specified point. z = 5(x - 1)^2 + 4(y + 3)^2 + 4, (2, -2, 13) z = ______
The equation of the tangent plane to the given surface at the specified point is z = 10x + 8y + 6.
To find an equation of the tangent plane to the given surface at the specified point (2, -2, 13), we need to first take partial derivatives of the given function.
Taking partial derivatives with respect to x and y, we get:
∂z/∂x = 10(x-1)
∂z/∂y = 8(y+3)
Next, we plug in the given point (2, -2, 13) into the partial derivatives to find the slope of the tangent plane:
∂z/∂x = 10(2-1) = 10
∂z/∂y = 8(-2+3) = 8
So the slope of the tangent plane at the given point is (10, 8).
Now we need to find the intercept of the tangent plane by plugging in the point (2, -2, 13) into the original function:
z = 5(2-1)^2 + 4(-2+3)^2 + 4 = 13
Therefore, the equation of the tangent plane is:
10(x-2) + 8(y+2) = z-13
Or rearranging,
10x + 8y - z = -6
For more about tangent plane:
https://brainly.com/question/31397815
#SPJ11
Please help! Suppose Jasmine earns $3000 per month after taxes. She spends $1000 on rent, between $80 and $100 on groceries, her electricity and water cost between $120 and $160, car insurance $80, car payment $150 and gas is $40 to $50 per month. Which of these expenses are fixed expenses?
rent
groceries
electricity
water
car insurance
car payment
gas
Answer:
Fixed:
Rent
Car insurance
Car payment
Step-by-step explanation:
This is because they are not variable in the question and only give one value
the probability is 52% that the sample mean will be between what two values symmetrically distributed around the population mean?
We don't have enough data to provide specific values in this situation for the population mean and standard error.
However, using the 52% probability provided, you can now discover the two values that are symmetrically distributed around the population mean using the Z-score of 0.75 and the standard error.
To determine the two values symmetrically distributed around the population mean, we need to use the concept of a confidence interval.
Given a probability of 52%, we can calculate the confidence interval as follows:
Convert the probability to a confidence level: 100% - 52% = 48%.
So, we have a 48% confidence level.
Divide the remaining probability by 2 to find the percentage of values in each tail: (100% - 48%) / 2 = 26%.
This means 26% of the values lie in each tail.
Use a Z-table or online calculator to find the corresponding Z-score for 26%.
The Z-score represents the number of standard deviations away from the mean. In this case, the Z-score is approximately ±0.75.
Apply the Z-score to the standard error formula:
Confidence interval = population mean ± (Z-score * standard error)
However, we don't have enough information about the population mean and standard error to provide the exact values in this case.
But with the given probability of 52%, you can now use the Z-score of ±0.75 and the standard error to find the two values symmetrically distributed around the population mean.
For similar question on standard deviations.
https://brainly.com/question/30802727
#SPJ11
(-3.1)+(-4.9)-{(-2.7-[(-0.2-(-0.8]}
Answer:
-4.3
Step-by-step explanation:
1. Simplify the expression
-3.1+-4.9--2.7--0.2--0.8
Calculate any addition or subtraction, from left to right.
-3.1+-4.9--2.7--0.2--0.8
-3.1-4.9--2.7--0.2--0.8
-8--2.7--0.2--0.8
-8+2.7--0.2--0.8
-5.3--0.2--0.8
-5.3+0.2--0.8
-5.1--0.8
-5.1+0.8
-4.3
A corner offset is a bend consisting of two offsets turned at a 45º angle from each other.Select one:TrueFalse
True. A corner offset is a bend that consists of two offsets turned at a 45-degree angle from each other.
This type of bend is commonly used in plumbing and electrical installations to change the direction of pipes or conduit around corners while maintaining a constant flow of materials. Corner offsets can be made using various tools and techniques, including hand benders, hydraulic benders, or mechanical benders, depending on the specific requirements of the job.
It's important to follow safety guidelines and use appropriate protective gear when performing any bending or installation work to avoid accidents and ensure high-quality results.
To learn more about degree angle click here
brainly.com/question/17106565
#SPJ11
Find the expected value of the winnings
from a game that has the following payout
probability distribution:
Payout ($) -1 1
3
5
7
Probability 0.70 0.15 0.10 0.04 0.01
Expected Value = [?
Round to the nearest hundredth.
Enter
The expected value of the winnings from the game is $0.02.
To find the expected value of the winnings from the game, we need to multiply each possible payout by its corresponding probability, and then sum these products.
The expected value, denoted by E(X), can be calculated using the formula:
E(X) = ∑(xi × pi)
where:
xi is the possible payout
pi is the probability of receiving that payout
E(X) = (-1) × 0.70 + 1 × 0.15 + 3 × 0.10 + 5 × 0.04 + 7 × 0.01
= -0.70 + 0.15 + 0.30 + 0.20 + 0.07
= 0.02
Therefore, the expected value of the winnings from the game is $0.02.
To learn more on probability click:
https://brainly.com/question/11234923
#SPJ1
Derivatives polys expRecall the definition of |x| as a piece-wise function: if x > 0 | 20 | if x < 0 Suppose = { - h(x) = (x – 2] + x – 5). - Find a formula for h' (x) Hint: h(a) may not be differentiable at x = = 2 o
To find a formula for h'(x), the derivative of h(x), we need to consider the two parts of the piece-wise function separately.
1. For x > 2:
In this case, h(x) = (x - 2) + x - 5.
To find h'(x), we can differentiate each term separately:
h'(x) = (d/dx)(x - 2) + (d/dx)(x - 5)
Since the derivative of a constant is zero, we have:
h'(x) = 1 + 1 = 2
So, for x > 2, h'(x) = 2.
2. For x < 2:
In this case, h(x) = |x| = -x.
The derivative of -x is simply -1:
h'(x) = -1
So, for x < 2, h'(x) = -1.
Note: At x = 2, the function h(x) has a corner or "kink" due to the absolute value function. The left and right derivatives are not equal, so h(a) is not differentiable at x = 2. Therefore, we cannot find a formula for h'(x) at x = 2.
In summary, the formula for h'(x) is:
h'(x) =
2 if x > 2
-1 if x < 2
At x = 2, h(a) is not differentiable.
To know more about derivative refer here
https://brainly.com/question/29990226#
#SPJ11
find integral form 0 to 5 sqrt 25 x^2?
To find the integral of √(25 - x²) from of limits x = 0 to x = 5, the integral of √(25 - x²) from x = 0 to x = 5 is 25π/4.
To find the integral of √(25 - x²) from x = 0 to x = 5, we can use trigonometric substitution. Let x = 5sinθ, then dx = 5cosθdθ.
When x = 0, θ = 0, and when x = 5, θ = π/2. Substituting these limits, we get:
∫[0,5] √(25 - x²) dx = ∫[0,π/2] √(25 - 25sin²θ) (5cosθ) dθ
= 25 ∫[0,π/2] cos²θ dθ
Using the identity cos²θ = (1 + cos2θ)/2, we get:
25 ∫[0,π/2] cos²θ dθ = 25/2 ∫[0,π/2] (1 + cos2θ) dθ
= 25/2 [θ + (sin2θ)/2] [0,π/2]
= 25/2 [(π/2) + (sinπ)/2 - (0 + sin0)/2]
= 25π/4
Therefore, the integral of √(25 - x²) from x = 0 to x = 5 is 25π/4.
For more details regarding integral, visit:
https://brainly.com/question/18125359
#SPJ1
State the five-number summary of the data used to construct the box-and-whisker plot.
The angles in a quadrilateral are in the ratio 6:2:7:3.
Work out the size of the smallest angle in this quadrilateral.
The value of the smallest angle of the quadrilateral will be 40 degrees.
The angles in a quadrilateral are in the ratio 6:2:7:3.
Let the canceling number be 'x'.
The sum of the angle of the quadrilateral is 360 degrees. Then the equation is given as,
6x + 2x + 7x + 3x = 360
18x = 360
x = 20
The value of the smallest angle is calculated as,
2x = 2(20)
2x = 40 degrees
More about the quadrilateral link is given below.
https://brainly.com/question/29934291
#SPJ1
Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(-1,9, -3), C(1, 12, -10), D(3, 4, -4)
The area of the parallelogram is |AB x BC| = sqrt(3088) square units. To verify that the given points are the vertices of a parallelogram, we need to check if the opposite sides are parallel.
Using vector notation, we can find the vectors AB, BC, CD, and DA as follows:
AB = < -2, 8, -6 >
BC = < 2, 3, -7 >
CD = < 2, -8, 6 >
DA = < -2, -8, 6 >
We can see that AB is parallel to CD, and BC is parallel to DA, since they have the same direction (but possibly different magnitudes). Therefore, the given points are the vertices of a parallelogram.
To find the area of the parallelogram, we can use the cross-product of AB and BC (or CD and DA, since they have the same magnitude and direction):
AB x BC = < -54, 8, 28 >
|AB x BC| = sqrt(54^2 + 8^2 + 28^2) = sqrt(3088)
Therefore, the area of the parallelogram is |AB x BC| = sqrt(3088) square units.
Learn more about parallelograms here: brainly.com/question/29147156
#SPJ11
Complete parts (a) through (h) for the data below 2 3 4 6 7 3 6 11 15 18 y 0 10 20 10 10 (b) Find the equation of the line containing the points (2,3) and (7,18) 3 y = 3 x+ - (Type integers or simplified fractions.) (c) Graph the line found in part (b) on the scatter diagram. Choose the correct graph below B. Ay 10- Ay 20- 20- 10- X 0 0- 0- 0 10 10 10 (d) By hand, determine the least-squares regression line. y x + (Round to three decimal places as needed.) f) Compute the sum of the squared residuals for the line found in part (b).
G) Compute the sum of the squared residuals for the least-squares regression line found in part (d).
need help with this
Mr. Bond is riding his bike. The graph represents the distance Mr. Bond travels from his house over time.
He traveled 80 meters in 4 minutes.
For two minutes the bike was stationary.
He was traveling at the greatest speed from 6 minutes to 8 minutes.
The car's greatest speed is 50 m/s.
We have,
We are assuming from the graph that,
The x-values are in minutes and the y-values are the distance in meters.
Now,
The orders pairs from the graph are:
(4, 80)
This means,
In 4 minutes, 80 meters were traveled.
And,
(4, 80) and (6, 80)
This means,
From 4 minutes to 6 minutes, the distance traveled is 80 meters.
So,
The bike was stationary from 4 minutes to 6 minutes.
And,
(0, 0) and (4, 80)
Speed = (80 - 0) / (4 - 0) = 80/4 = 20m/s
(4, 80) and (6, 80)
Speed = (80 - 80) / (6 - 4) = 0 = constant speed
(6, 80) and (8, 180)
Speed = (180 - 80) / (8 - 6) = 100/2 = 50 m/s
(8, 180) and (10, 220)
Speed = (220 - 180) / (10 - 8) = 40/2 = 20 m/s
This means,
From 6 minutes to 8 minutes, the distance traveled is (180 - 80) meters.
This is the greatest speed.
Thus,
He traveled 80 meters in 4 minutes.
For two minutes the bike was stationary.
He was traveling at the greatest speed from 6 minutes to 8 minutes.
The car's greatest speed is 50 m/s.
Learn more about speed here:
https://brainly.com/question/7359669
#SPJ1
Consider the following. (If an answer does not exist, enter DNE.)
f(x) = x^6e^-x (a) Find the interval(s) on which f is increasing. (Enter your answer using interval
notation.
f is increasing on the interval (0,6). To find the interval(s) on which f is increasing, we need to find the derivative of f and determine where it is positive.
f'(x) = 6x^5e^-x - x^6e^-x = x^5e^-x(6-x)
Now, we need to determine when f'(x) > 0.
x^5e^-x(6-x) > 0
x^5 is always positive, so we just need to consider e^-x(6-x).
When x < 0, e^-x is positive and (6-x) is negative, so the product is negative.
When 0 < x < 6, both e^-x and (6-x) are positive, so the product is positive.
When x > 6, e^-x is very small and (6-x) is negative, so the product is negative.
Therefore, f is increasing on the interval (0,6).
Learn more about derivatives here: brainly.com/question/23847661
#SPJ11
how many ways can a license plate be made with 2 letters followed by 3 numbers if no repetition is allowed
The total number of possible ways to create a license plate with 2 letters followed by 3 numbers if no repetition is 4,680,00.
To calculate the number of ways to create a license plate with 2 letters followed by 3 numbers, we need to consider two separate parts: the number of ways to choose the two letters, and the number of ways to choose the three numbers. Since no repetition is allowed, we have to take this into account in both parts.
For the first part, we have 26 choices for the first letter and 25 choices for the second letter, since we cannot choose the same letter twice.
For the second part, we have 10 choices for each of the three numbers. Again, we cannot choose the same number twice, so we have to decrease the number of choices by 1 for each subsequent number.
Thus, the total number of ways to create a license plate with 2 letters followed by 3 numbers is:
26 x 25 x 10 x 9 x 8 = 468,000
If no repetition of characters is allowed, then the number of possible ways to create a license plate with 2 letters followed by 3 numbers can be calculated as follows:
There are 26 choices for the first letter (A-Z).
There are 25 choices for the second letter (since no repetition is allowed).
There are 10 choices for the first number (0-9).
There are 9 choices for the second number (since no repetition is allowed).
There are 8 choices for the third number (since no repetition is allowed).
Therefore, the total number of possible ways to create a license plate with 2 letters followed by 3 numbers if no repetition is allowed is:
26 x 25 x 10 x 9 x 8 = 4,680,00
To learn more about license plate visit:
https://brainly.com/question/15143769
#spj4
use the chain rule to find dz/dt. z = x2 + y2 + xy, x = sin(t), y = 4et
The derivative dz/dt can be found using the chain rule. By differentiating each term with respect to t and applying the chain rule, we can calculate dz/dt as follows:
[tex]dz/dt = 2sin(t)cos(t) + 4e^tcos(t) + 4e^tsin(t) + 4e^t + 4sin(t)e^t.[/tex]
How can we use the chain rule to find the derivative of z with respect to t ?By applying the chain rule, we can find dz/dt as follows: differentiate z with respect to x, then multiply it by dx/dt, and finally differentiate z with respect to y and multiply it by dy/dt.
The function z = x² + y² + xy can be rewritten as z = (sin(t))² + (4e^t)² + (sin(t))[tex](4e^t)[/tex].
To find dz/dt, we need to find the partial derivatives of z with respect to x and y and multiply them by dx/dt and dy/dt, respectively.
The partial derivative of z with respect to x is (2x + y), and the partial derivative of z with respect to y is (2y + x).
Next, we differentiate x = sin(t) with respect to t, giving us dx/dt = cos(t).
Similarly, differentiating[tex]y = 4e^t[/tex] with respect to t yields [tex]dy/dt = 4e^t.[/tex]
Now we can apply the chain rule:
dz/dt = (2x + y) * dx/dt + (2y + x) * dy/dt
Substituting the expressions for x, y, dx/dt, and dy/dt:
[tex]dz/dt = (2sin(t) + 4e^t) * cos(t) + (2(4e^t) + sin(t)) * (4e^t)[/tex]
Simplifying this expression will yield the final result.
Learn more about chain rule
brainly.com/question/24898810
#SPJ11
1) Mrs. Morris's kids will go trick-or-treating at more than 100 houses on
Halloween.
The inequality that represents the number of houses that the kids will go on Halloween is given as follows:
n > 100.
What are the inequality symbols?The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:
> x: the amount is greater than x -> the number is to the right of x with an open dot at the number line. -> points above the dashed horizontal line y = x on the coordinate plane.< x: the amount is less than x. -> the number is to the left of x with an open dot at the number line. -> points below the dashed horizontal line y = x on the coordinate plane.≥ x: the amount is at least x. -> the number is to the right of x with a closed dot at the number line. -> points above the solid vertical line y = x on the coordinate plane.≤ the amount is at most x. -> the number is to the left of x with a closed dot at the number line. -> points above the dashed vertical line y = x on the coordinate plane.The inequality that represents more than 100 houses on Halloween is given as follows:
n > 100.
Missing InformationThe problem asks for the inequality that models the situation.
More can be learned about inequalities at brainly.com/question/25275758
#SPJ1