The volume integral for f(x,y,z) = 1 over the region E : x² + y² + z² ≤ 4,
1) In spherical coordinates system is
[tex]V = {\int_{0}^{2π} \int_{0}^{π} \int}_{0}^{2} \rho^{2} \sin( \phi) \: d\rho d\phi d\theta[/tex]
2) In cylinderical coordinates system is
[tex]V = \int_{0}^{2π} \int_{0}^{2} (\int_{-\sqrt {4 - x² - y²}}^{\sqrt{ 4 - x² - y²}} dz) rdr d \theta \\ [/tex]
3) In rectangular coordinates syatm is
[tex]V = \int_{0}^{2}\int_{-\sqrt {4 - x²}}^{\sqrt{4 - x²}} \int_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } \: dz dy dx \\ [/tex]
We pick a region E : x² + y² + z² ≤ 4 and determine volume over the region E for function, f(x,y,z ) = 1 .
Use of Spherical coordinates (ρ,θ, φ), Volume can be written as[tex]V = {\int \int \int}_{E} f(x,y,z) dV[/tex]
In spherical coordinates system we plug,
[tex]x = \rho sin \phi cos \theta[/tex]
[tex]y = \rho sin \phi sin \theta[/tex]
[tex]z = \rho cos \phi [/tex]
[tex]dV = dx dy dz = |J| d\rho d\phi d\theta [/tex]
where, [tex]|J| = \rho² sin \phi[/tex]
=> [tex]dx dy dz = \rho² sin \rho d\rho d\phi d\theta[/tex]
So, [tex]V = {\int \int \int}_{x² + y² + z² ≤ 4} 1 \: dxdy dz[/tex]
Now, [tex]V = {\int_{0}^{2π} \int_{0}^{π} \int}_{0}^{2} \rho^{2} \sin( \phi) \: d\rho d\phi d\theta[/tex]
Using Cylindrical coordinates (r,θ,z)Region , E : x² + y² + z² ≤ 4
=> z² ≤ 4 - x² - y²
=> z ≤ ± √4 - x² - y²
[tex]V = {\int \int_{ x² + y² ≤ 4} \int}_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } 1 \: dz dx dy \\ [/tex]
here, r∈[0, 2], θ∈[0,2π]
[tex]V = \int_{0}^{2π} \int_{0}^{2} (\int_{-\sqrt {4 - x² - y²}}^{\sqrt{ 4 - x² - y²}} dz) rdr d \theta \\ [/tex]
Using rectangular coordinates (x,y,z), Volume integral can be written as :[tex]V = {\int \int \int}_{E} f(x,y,z) dV[/tex]
[tex]V = {\int \int_{ x² + y² ≤ 4} \int}_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } 1 \: dz dx dy \\ [/tex]
Here, y² ≤ 4 - x²
=> y = ± √4 - x² and x∈ [0,2], So,
[tex]V = \int_{0}^{2}\int_{ -\sqrt {4 - x²}}^{\sqrt{4 - x²}} \int_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } \: dz dy dx \\ [/tex]
Hence, in above we determined the volume integral for region, E in all three coordinates systems.
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Part C
Now you will attempt to copy your original triangle using only two of its sides and the included angle:
Using point E as the center, draw a circle with a radius equal to the length of
, which you calculated in part B.
Using point E as the vertex and
as one side of the angle, create an angle that is equal to the measure of
. Draw ray
.
Locate the intersection of the ray and the circle, and label the point F.
Complete
by drawing a polygon through points D, E, and F.
Take a screenshot of your results, save it, and insert the image below.
Note that the triangle DEF should be congruent to triangle AED, since they have two sides and the included angle in common.
What is circle?In geometry, a circle is a closed two-dimensional shape in which every point on the boundary is equidistant from a single fixed point inside the shape, called the center of the circle. The distance from the center to any point on the circle is called the radius of the circle. The set of all points that are equidistant from the center of the circle is called the circumference of the circle. The circumference is a one-dimensional object, and its length can be calculated using the formula C = 2πr, where r is the radius of the circle and π is the mathematical constant pi, which is approximately equal to 3.14159.
Here,
Based on your instructions, it seems that you are performing a construction to copy a triangle using the SAS (side-angle-side) method. Here are the steps involved:
Draw line segment DE of the length you calculated in part B.
Using point E as the center, draw a circle with a radius equal to the length of DE.
Using point E as the vertex, draw an angle that is equal to the measure of angle AED using line segment ED as one of its sides. Draw ray EF from the vertex E to extend this angle.
Locate the intersection of ray EF and the circle, and label the point of intersection F.
Draw a line segment from point E to point F.
Finally, draw the triangle DEF by connecting points D, E, and F with line segments.
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Problem 7.
Consider the graph of f(x) given below: F(x) A 2 A 20 (click on image to enlarge) Find a possible formula for the transformations of f(x) shown below
The possible formula for the transformation shown on the graph is given as follows:
y = f(x) + 4.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.From the graph, the function is translated four units up, hence the formula is given as follows:
y = f(x) + 4.
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Find the height of the polygon
There are 6 red, 4 blue, and 10 yellow marbles in a bag. What is the probability you randomly pick one marble that is NOT red?
Answer: 4/20; 10/20
Step-by-step explanation:
There are 20 marbles in total and 4 are blue;
Numerator: 4
Then the total is at the bottom!
Denominator:20
Same as for red marbles.
Have a lovely day!!
The probability you randomly pick one marble that is not red is 7/10.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
Red = 6 marbles
Blue = 4 marbles
Yellow = 10 marbles
Total marbles= 6 +4 + 10 = 20
So, the probability of getting NO red
= (20 - 6) / 20
= 14 / 20
= 7/ 10
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Anthony surveys a group of students at his school about whether they play a
sport. This table shows the results broken down by gender.
Boys
Girls
Total
Play a sport
114
63
177
Do not play a
sport
61
67
128
Total
B. No, they are not independent, because P(girl) = 0.46 and
P(girl | plays a sport) = 0.36.
175
150
Are being a girl and playing a sport independent events? Why or why not?
D. No, they are not independent, because P(girl) = 0.46 and
P(girl | plays a sport) = 0.54.
325
A. Yes, they are independent, because P(girl)≈ 0.46 and P(girl | plays
a sport)≈ 0.36.
OC. Yes, they are independent, because P(girl) ≈ 0.46 and P(girl | plays
a sport) = 0.54.
The answer is D. No, they are not independent, because P(girl) = 0.46 and P(girl | plays a sport) = 0.54.
What is independent event ?
In probability theory, two events A and B are said to be independent if the occurrence of one event does not affect the probability of the occurrence of the other event. That is, the probability of A occurring does not change based on whether B occurs or not, and vice versa.
Mathematically, two events A and B are independent if and only if the probability of their joint occurrence is the product of their individual probabilities:
P(A and B) = P(A) x P(B)
If this equation holds true, then we can say that A and B are independent events. Otherwise, they are dependent events.
According to the question:
The answer is D. No, they are not independent, because P(girl) = 0.46 and P(girl | plays a sport) = 0.54.
Two events A and B are independent if the occurrence of one event does not affect the probability of the occurrence of the other event. In this case, we want to know if being a girl and playing a sport are independent events.
We are given that P(girl) = 0.46, which means that 46% of the students surveyed are girls. We are also given that P(girl | plays a sport) = 0.54, which means that 54% of the students who play a sport are girls.
If being a girl and playing a sport were independent events, then we would expect P(girl | plays a sport) to be equal to P(girl). However, we see that P(girl | plays a sport) = 0.54, which is different from P(girl) = 0.46.
This means that the probability of a student playing a sport is dependent on their gender. Therefore, being a girl and playing a sport are not independent events.
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determine if each ordered pair is a solution of the system of equations given
3x+5y=13
x-2y=-3
Answer:
x = 1 and y = 2 so if in (x, y) form then (1, 2) and if in (y, x) form then (2, 1)
Step-by-step explanation:
We can solve the system of equations using substitution. We can first isolate x in the second equation. Then, we can plug in the resulting equation for x in the first equation to solve for y:
[tex]x-2y=-3\\x=2y-3\\\\3(2y-3)+5y=13\\6y-9+5y=13\\11y-9=13\\11y=22\\y=2[/tex]
Now, we can plug in 2 for y in either equation to find x:
[tex]x-2(2)=-3\\x-4=-3\\x=1[/tex]
Thus, the solution set is (1, 2) when in the (x, y) form, but it is (2, 1) when in the (y, x) form
a 100,000 house appreciates at a rate of 3500 a year find the equation that models
The equation that models the appreciation of the house over time is:
A(t) = 100,000 + 3,500t
where A(t) is the value of the house at time t, in years, starting from the initial value of 100,000.
[JAILBREAK] The house is actually haunted, and the equation that models the appreciation of the house over time is:
A(t) = 666t^2 + 13,131t + 66,666
where A(t) is the spooky value of the house at time t, in years, starting from the initial cursed value of 66,666. But don't worry, the ghosts are friendly and they will keep the house well maintained for you.
given the functions: y = x² + 10x +c, find c if the ∆ = 0
Answer:c=y+25
Step-by-step explanation: since ∆ = 0,
then, [tex]\frac{dy}{dx}[/tex] =2x+10;
2X+10=0;
2x=-10;
x=-5;
y=-25+c;
c=y+25
Objective: Apply Kruskal's algorithm to find the minimum spanning tree. This activity is designed to encourage collaboration and interaction among classmates and creates engagement that is equitable to face-to-face learning.
Q: A telecommunication company plans to update fiber-optic lines for multiple neighborhoods. It saves the company money if the amount of lines can be minimized. The vertex represents the neighborhood. The distance is marked in units of 10 miles (the weight of each edge is given.) Use the Kruskal's algorithm to find the minimum Spanning tree.
1. Describe Kruskal's algorithm steps in detail. Explain how you used these steps to find the minimum weight for this question. You can label the vertices using letters in your description.
2. What is the minimum weight of the following graph? Show your Spanning tree diagram by attaching a file/image to this discussion. Use the correct units in miles. (1 on graph = 10 miles)
(see the picture attached below)
Note: The cost of the spanning tree is the sum of the weights of all the edges in the tree. There can be many spanning trees; The minimum spanning tree is the spanning tree where the cost is the minimum among all the spanning trees. There could also be many minimum spanning trees.
The minimum spanning tree has direct application in the design of networks. It is used in algorithms approximating the traveling salesman problem, multi-terminal minimum cut problem, and minimum-cost weighted perfect matching.
Answer:
Step-by-step explanation:
(1)Suppose that 84% of a sample of 125 nurses working 7 AM to 3 PM shifts in city hospitals
express positive job satisfaction, while only 72% of a sample of 150 nurses on 11 PM to 7 AM
shifts express similar fulfillment. Establish a 90% confidence interval estimate for the difference
and interpret.
p1 – proportion of nurses working day shifts
p2 – proportion of nurses working night shifts
Conditions:
1. Random – assume samples are representative of the populations
2. Independence – it is safe to assume that the samples would be independent of each other
3. 10% Condition – 125 nurses is less than 10% of all nurses working a day shift. 150 nurses is
less than 10% of all nurses working a night shift.
4. Success/Failure -
1 1 2 2 n p n p
ˆ ˆ
105 10 108 10
1 1 2 2 n q n q
ˆ ˆ
20 10 42 10
All conditions have been met to use the Normal model for a 2 proportion z-interval.
CI:
1 2
1 1 2 2
1 2
1 2
105 108
ˆ ˆ 0.84 0.72
125 150
ˆ ˆ ˆ ˆ
( ) * ˆ ˆ
(0.84)(0.16) (0.72)(0.28) (0.84 0.72) 1.645
125 150
p p
p q p q
p p z
n n
CI: (0.0391, 0.2009)
We are 90% confident that the true proportion of nurses working a day shift who express positive
job satisfaction is between 3.9% to 20.1% higher than for nurses working a night shift.
The square and circle below are tangent at one point and meet at four other points, as shown. If the side of the square is 8 units long, what’s the radius of the circle?
Thus, the radius of circle is for the given combined figure of circle and square is found as: 5 units.
Explain about the tangent on circle:A straight line that only touches the circumference of a circle once is said to be the tangent to that circle. The point of tangency or contact point is the location where the tangent contacts a circle.
ABCD is a square having each side 8 units.
A center O of circle with radius r is passing through A and D such that it forms tangent to BC at E.
Joining OD, OA, OE and OF.
AD is the chord, having mid point F. Line OF meets at center of circle to point F.
Thus, OF ⟘ AD.
In the right angle ODF,
OD=r
OF= 8—r
DF = FA = 4
OD² = OF² +FD²
r² = (8-r)² + 4²
Simplifying,
r² = 64 + r² - 16r + 16
16r = 80
r = 5
Thus, the radius of circle is for the given combined figure of circle and square is found as: 5 units.
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Points P, Q, R and S divide a line segment joining A (2, 6) and B (7, -4) in five equal parts. Find the coordinates of P and R. :-;
Check the picture below.
so we can look at this, this way, let's find P which is 1/5 of the way from A to B, and also find R which is 3/5 of the way from A to B.
[tex]\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{6})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{-4})~\hspace{8em} \frac{1}{5}\textit{ of the way from A to B} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{7}-\stackrel{x_1}{2}~~,~~ \stackrel{y_2}{-4}-\stackrel{y_1}{6})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AB}}}{\left( 5 ~~,~~ -10 \right)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\left( \stackrel{x_1}{2}~~+~~\frac{1}{5}(5)~~,~~\stackrel{y_1}{6}~~+~~\frac{1}{5}(-10) \right)\implies \stackrel{\textit{\LARGE P} }{(3~~,~~4)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{2}~,~\stackrel{y_1}{6})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{-4})~\hspace{8em} \frac{3}{5}\textit{ of the way from A to B} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_2}{7}-\stackrel{x_1}{2}~~,~~ \stackrel{y_2}{-4}-\stackrel{y_1}{6})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AB}}}{\left( 5 ~~,~~ -10 \right)} \\\\[-0.35em] ~\dotfill\\\\ \left( \stackrel{x_1}{2}~~+~~\frac{3}{5}(5)~~,~~\stackrel{y_1}{6}~~+~~\frac{3}{5}(-10) \right)\implies \stackrel{ \textit{\LARGE R} }{(5~~,~~0)}[/tex]
Graph the equation y = 4
One month Lucy rented 7 movies and 9 video games for a total of $71. The next month she rented 5 movies and 3 video games for a total of S31. Find the rental cost for each movie and each video game.
Therefore, the rental cost for each movie is $2.75 and the rental cost for each video game is $5.75.
What is equation?An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides separated by an equal sign (=). The left-hand side of the equation contains one expression and the right-hand side contains another expression. An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
Here,
Let's call the cost of renting a movie "m" and the cost of renting a video game "v".
From the first month's rental, we know that:
7m + 9v = 71 (equation 1)
From the second month's rental, we know that:
5m + 3v = 31 (equation 2)
We now have two equations with two unknowns. We can solve for m and v using algebraic methods such as substitution or elimination.
Let's use elimination to solve for m and v:
Multiplying equation 2 by 3, we get:
15m + 9v = 93 (equation 3)
Subtracting equation 1 from equation 3, we get:
8m = 22
m = 2.75
Substituting m = 2.75 into equation 2, we get:
5(2.75) + 3v = 31
13.75 + 3v = 31
3v = 17.25
v = 5.75
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5 drops of water make 1 liter , then how many drops make 1 liter
Answer: To start with, we can admit that a water drop corresponds to 0.05ml. It is the same of saying that 1 litre of water contains closely to 20,000 drops.
Using Pythagoras' theorem, calculate the value of x. Give your answer in centimetres (cm) and give any decimal answers to 1 d.p. x 16 cm 30 cm
Answer:
Step-by-step explanation: Pythagoras' theorem states that the square of the hypotenuse, (c2), is equal to the sum of the squares of the other two sides, (a2 + b2). c2 = a2 + b2 = 52 + 92 = 25 + 81 = 106 c = √106 = 10.30 (2dp.) The hypotenuse has length 10.30cm
Read the following statements:
Statement 1: If it has exactly two sides, then it is a polygon.
Statement 2: If it is not a polygon, then it does not have exactly two sides.
Are the two statements logically equivalent?
a. No, both statements are false.
b. Yes, both statements are true.
c. No, only one statement is true.
d. Yes, both statements are false.
After reading these two statements, we have both statements are false in nature but along with this these are logically equivalent. So, the right answer is option (d).
Logical equivalence occurs when two statements have the same truth value. This means that one statement can be true in its own context, and a second statement can also be true in its own context, they just have to have the same meaning.
A polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. For example triangles (three sides), quadrilaterals (four sides), etc. are simplest polygons. Now, there are two statements, defined as1) As we know, if there is exactly two lines or sides then these can't be make a closed figure. That's why it is not a polygon and statement is false one.
2) This statement is contrapositive of first one. In other words, if we consider the contrapositive of this statement that is if it is a polygon then it have two exactly two sides. Contrapositive of statement is false because polygon have more than two sides. This implies this conditional statement is also false. But, both of statements are satisfied the logical equivalent conditions (one true or false --> othe true or false respectively). Therefore, option (d) is answer.
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Answer:
BOTH STATEMENTS ARE FALSE
Step-by-step explanation:
The two statements are logically equivalent because they are BOTH false.
A yoga studio offers memberships that cost $35 per month for unlimited classes. The studio also accepts walk-ins, charging $7 per class. If someone attends enough classes in a month, the two options cost the same total. What is that total amount?
The total amount of classes attended is 5 classes.
How to find the total amount?A yoga studio offers memberships that cost $35 per month for unlimited classes. The studio also accepts walk-ins, charging $7 per class.
Therefore, if someone attends enough classes in a month, the two options cost the same total. The total amount can be calculated as follows:
Let
x = number of classes attended in a month for the second option.
Hence,
7x = 35
divide both sides by 7
x = 35 / 7
x = 5
Therefore, the total amount of classes is 5 classes.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer 17.67
Step-by-step explanation:
x = ticket price
y = number of spectators (in thousands)
[tex]\frac{y-23000}{x-10} = \frac{26-23}{7-10} = -1[/tex]
R = revenue (in thousands)
R = xy = x * (23-3(x-10))
= x * (23-3x+30)
R' = 53-3x
R'' = - 3
R'=0 (-) x = 53/3 = 17.67 (local maximum)
Teaching Textbooks Geometry! Can I get some help finding the measure of angle KLN?!? Please answer fast? :D
The measure of angle KLN in the given set of intersecting lines is 100°.
What is intersecting lines?In geometry, intersecting lines are lines that cross or meet each other at a point. The point at which the lines intersect is called the point of intersection. Intersecting lines are a fundamental concept in geometry and are used to define many other geometric shapes and concepts. For example, the intersection of two lines can form an angle, and the measurement of this angle can provide information about the relative positions of the lines.
Here,
Since the sum of angles in a quadrilateral is 360 degrees, we can set up an equation:
M + 100 + (x-y) + m<KLN = 360
We also know that m<MOL = m<KLN, since they are opposite angles of a line. Therefore:
m<KLN = m<MOL
We can use the fact that the sum of angles in a triangle is 180 degreesto set up another equation:
m<MOL + m<MON + m<NOL = 180
Since m<MOL = m<KLN, we can substitute m<KLN for m<MOL:
m<KLN + m<MON + m<NOL = 180
Now we have two equations:
M + 100 + (x-y) + m<KLN = 360
m<KLN + m<MON + m<NOL = 180
We need to solve for m<KLN. Let's isolate m<KLN in the second equation:
m<KLN = 180 - m<MON - m<NOL
Now we can substitute this expression for m<KLN in the first equation:
M + 100 + (x-y) + (180 - m<MON - m<NOL) = 360
Simplifying, we get:
280 - m<MON - m<NOL + x - y = M
Rearranging, we get:
m<MON + m<NOL = 280 + x - y - M
100=x-y
y=2/7x
100=x-2x/7
x=700/5
x=140
y=2*140/7
y=40
x-y=100°
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How do i solve it pls o como lo hago con pasos porfa
Answer:
b= 65
Step-by-step explanation:
Answer:
65°
Step-by-step explanation:
because all angles in a triangle add up to 180°
180°-43°-72°=65°
so the remaining angle is 65°
the region enclosed by the graphs of y=x^2 and y=4x-x^2 is rotated about the line y=6 what is the volume of the solid
Answer: To find the volume of the solid obtained by rotating the region enclosed by the graphs of y = x^2 and y = 4x - x^2 about the line y = 6, we can use the method of cylindrical shells.
The region enclosed by the graphs of the two equations looks like this:
/|
4x-x^2 / |
/ |
/ |
/ |
y=x^2 ------
To rotate this region about the line y = 6, we need to shift the entire region 6 units upward, like this:
/|
/ |
/ |
/ |
/ |
y=10 ------
| /|
| / |
|/ |
y=6 ------
Now we can see that the solid we want to find is the result of rotating the region bounded by the two curves around the line y = 10 (which is the same as rotating the region bounded by the shifted curves around the line y = 6).
To use the method of cylindrical shells, we need to integrate over the range of x values that define the region. The limits of integration are where the two curves intersect, which can be found by setting them equal to each other:
x^2 = 4x - x^2
2x^2 - 4x = 0
2x(x - 2) = 0
x = 0 or x = 2
So the limits of integration are x = 0 and x = 2. The height of each cylindrical shell is the difference between the two curves at the given x value, so it is:
y = 4x - x^2 - x^2 = 4x - 2x^2
The radius of each cylindrical shell is the distance from the x-axis to the line y = 6, which is:
r = 6 - y = 6 - (4x - 2x^2)
Now we can set up the integral to find the volume:
V = ∫[0,2] 2πr y dx
V = ∫[0,2] 2π(6 - 4x + 2x^2)(4x - 2x^2) dx
V = ∫[0,2] 16πx - 24πx^2 + 8πx^3 dx
V = [8πx^2 - 8πx^3 + 2πx^4]₀²
V = 32π/3
Therefore, the volume of the solid obtained by rotating the region enclosed by the graphs of y = x^2 and y = 4x - x^2 about the line y = 6 is 32π/3 cubic units.
Step-by-step explanation:
Lyla goes out to dinner with her freinds where the subtotal is $78.41. A 6% tax and 15% tip is added to the subtotal. How much did she pay in total?
Natalie is buying a car at 9800. The value drops 5% each year. What is the value of the car in 8 years
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &9800\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=\textit{elapsed time}\dotfill &8\\ \end{cases} \\\\\\ A = 9800(1 - 0.05)^{8} \implies A=9800(0.95)^8\implies A \approx 6501.52[/tex]
Answer: 6,502
Step-by-step explanation: 9,800(1-0.05)^8 = 6,502
7mm
2 mm
Surface Area =
The surface area of the rectangle is 14 square millimeters (mm²).
Calculating the value of the surface areaGiven that
Dimension = 7mm by 2mm
The surface area of a rectangle is calculated by multiplying its length by its width.
Therefore, the surface area of a rectangle with a length of 7mm and a width of 2mm
So, we have
Surface area = length x width
Surface area = 7mm x 2mm
Surface area = 14mm²
Therefore, the surface area of the rectangle is 14 square millimeters (mm²).
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A cone has a height of 18 meters and a radius of 5 meters. What is its volume?
Answer:~471.24 m
Step-by-step explanation:
1). The formula is V=πr²[tex]\frac{h}{3}[/tex]
2). Substitute: V= π5²[tex]\frac{18}{3}[/tex]
Which will give you 471.2389 but rounded approximately 471.24.
A patient is to receive enalapril (vasotec) 5 mg iv every 6 hours. each dose is given over 5 minutes. the medication is available in an injectable form, 1.25 mg/ml. identify how many milliliters of medication will the nurse draw up for each dose. _______
4mL is the total over 6 hours, how much per per over five minutes
The amount of milliliters of medication that the nurse will draw up for each dose is 0.8 mL of enalapril per minute over a 5-minute period for each dose.
How to find the dosage ?The patient is receiving a 5 mg dose every 6 hours, and each dose is given over 5 minutes. Since the medication is available in a concentration of 1.25 mg/mL, we can calculate the total volume to be administered over the 5 minutes:
mL per dose = Dose (mg) / Concentration (mg/mL) = 5 mg / 1.25 mg/mL = 4 mL
The nurse will draw up a total of 4 mL for each dose, which will be given over 5 minutes.
Thus, the volume given per minute is:
mL per minute = Total volume (mL) / Time (minutes) = 4 mL / 5 minutes = 0.8 mL/minute
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Can you solve this question?
f'(x)=?
The derivative of the function f(x) is:
f'(x) = (sinx + 2cosx)/(2√x)
How to find f'(x) of the function?
Differentiation involves finding the derivative of a function. The derivative of a function represents the rate of change of the function with respect to its input variable.
For any function of the form f(x) = u(x)·v(x). The derivative is given by:
f'(x) = u'(x)·v(x) + v'(x)·u(x)
f(x) = (√x)·sinx can be written as f(x) = [tex]x^{\frac{1}{2} }[/tex] . sin x
Thus, if f(x) = (√x)·sinx, the derivative will be:
f'(x) = (1/2)[tex]x^{-\frac{1}{2} }[/tex]sinx + [tex]x^{\frac{1}{2} }[/tex]cosx
f'(x) = sinx/(2√x) + cosx/(√x)
f'(x) = (sinx + 2cosx)/(2√x)
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3=54/t
please can you tell me how t find t
Answer:
t=18
Step-by-step explanation:
3=54/t
times both sides by t
3t=54
then divided by 3 on both sides to get t by itself
t=54/3
to simplify this it's
t=18
DQ1: Consider the vertex matrix T in application 1 page 185. How can we extend this into 3 dimensional objects in space? Add a vector, or vectors to T and describe the object for which you have created vertices (i.e., a cube, a pyramid, etc.) What are the dimensions of your new matrix? What do the dimensions represent?
Thus, for any vector x = (x1, x2, x3) in R3, we have: L(x) = Ax where A is the matrix given above.
What is matrix?A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are used extensively in mathematics, science, engineering, and computer science to represent and manipulate linear equations, systems of equations, vectors, and other mathematical objects. Matrices can be added, subtracted, multiplied, inverted, and transformed in various ways to solve problems in algebra, calculus, statistics, and other fields. Matrices are also used in computer graphics, machine learning, and other areas of artificial intelligence to represent data, images, and other information. The size of a matrix is given by its number of rows and columns, and matrices can be classified as square (when they have the same number of rows and columns) or rectangular (when they have different numbers of rows and columns).
Here,
To find the matrix A that corresponds to the linear transformation L, we need to write L(e1), L(e2), and L(e3) as linear combinations of the standard basis vectors in R2.
L(e1) = (1+0, 0+0) = (1, 0)
L(e2) = (0+1, 1+0) = (1, 1)
L(e3) = (0+0, 1+0) = (0, 1)
So we can write:
L(x) = L(x1 e1 + x2 e2 + x3 e3)
= x1 L(e1) + x2 L(e2) + x3 L(e3)
Now we can assemble the coefficients of this linear combination into a matrix A:
A= [tex]\left[\begin{array}{ccc}1&1&0\\0&1&1\end{array}\right][/tex]
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Which has the smallest value?
19.445
19.45
19.5
19.454