the side length of the large square is equal to 4 divided by the square root of π times the side length of the small square.
what is length ?
Length is a physical quantity that refers to the measurement of a one-dimensional distance or extent, such as the distance between two points. It is typically measured in units such as meters, feet, inches, or centimeters. Length can be used to describe the size or dimensions
In the given question,
Let's assume that the side length of the small square is equal to the diameter of each small bubble.
When four bubbles in squares collide and merge into one large bubble in a square, the total area of the small squares is equal to the area of the large square. Since the side length of each small square is equal to the diameter of the small bubble, the area of each small square is equal to the square of the diameter of the small bubble.
So, if we let d be the diameter of each small bubble, then the area of each small square is equal to d². Therefore, the total area of the four small squares is equal to 4d², and the area of the large square is equal to the sum of the areas of the four small squares, which is 4d².
The area of a circle is equal to πr², where r is the radius of the circle. If we let R be the radius of the large bubble, then its area is equal to π².
We know that the area of the large square is equal to the area of the large bubble, so we have:
4d² = πR²
Solving for R, we get:
R =√(4d²/π)
R = 2d/√(π)
Since the side length of the large square is equal to twice the radius of the large bubble, we have:
Side length of large square = 2R = 4d/√(π)
Therefore, the side length of the large square is equal to 4 divided by the square root of π times the side length of the small square.
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the diagonals of a rhombus are 8 and 10cm respectively. find the area of the rhombus
[tex]\sf Let \ d_1 \ and \ d_2 \ be \ the \ lengths \ of \ the \ sides \ of \ diagonals.[/tex]
[tex]\sf Given \ that \ d_1=8 \ cm[/tex]
[tex]\sf And \ d_2=10 \ cm[/tex]
[tex]\therefore\sf Area \ of \ rhombus=\dfrac{1}{2} (d_1)(d_2)=\dfrac{1}{2}(8)(10)=40 \ cm^2[/tex]
[tex]\rightarrow\boxed{\sf Area \ of \ rhombus=40 \ cm^2}[/tex]
Find dy/dx. x =^9root (t) y = 9 - t dy/dx = _____
To find dy/dx, we need to take the derivative of y with respect to x. On evaluating the value of dy/dx is [tex]-9t^{8/9}[/tex]
However, we are given x in terms of t. So first, we need to use the chain rule to find dx/dt:
x = [tex]t^{1/9}[/tex]
dx/dt = (1/9) * [tex]t^{-8/9}[/tex]
Now, we can use the chain rule again to find dy/dt:
y = 9 - t
dy/dt = -1
Finally, we can use the formula for the chain rule to find dy/dx:
dy/dx = (dy/dt) / (dx/dt)
dy/dx = (-1) / ((1/9) * [tex]t^{-8/9}[/tex]
dy/dx = [tex]-9t^{8/9}[/tex]
So, the final answer is dy/dx = [tex]-9t^{8/9}[/tex]
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From the information given, find the quadrant in which the terminal point determined by t lies. input i, ii, iii,
or iv.
(a) sin(t) < 0 and cos(t) < 0, quadrant
(b) sin(t) > 0 and cos(t) < 0, quadrant
(c) sin(t) > 0 and cos(t) > 0, quadrant
(d) sin(t) < 0 and cos(t) > 0, quadrant
;
Answer:
Step-by-step explanation:
In option (a), sin(t) < 0 and cos(t) < 0, In trigonometry, the terminal point of an angle t is the point on the unit circle where the angle intersects with the circle.
The position of the terminal point determines the quadrant in which the angle lies.
To determine the quadrant, we need to look at the signs of the sine and cosine functions. In quadrant I, both sine and cosine are positive. In quadrant II, sine is positive and cosine is negative. In quadrant III, both sine and cosine are negative. In quadrant IV, sine is negative and cosine is positive.
In option (a), sin(t) < 0 and cos(t) < 0, both the sine and cosine functions are negative. This means that the terminal point lies in quadrant III.
In option (b), sin(t) > 0 and cos(t) < 0, the sine function is positive and the cosine function is negative. This means that the terminal point lies in quadrant II.
In option (c), sin(t) > 0 and cos(t) > 0, both the sine and cosine functions are positive. This means that the terminal point lies in quadrant I.
In option (d), sin(t) < 0 and cos(t) > 0, the sine function is negative and the cosine function is positive. This means that the terminal point lies in quadrant IV.
In summary, the signs of the sine and cosine functions can be used to determine the quadrant in which the terminal point lies.
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In Exercises 1-11, calculate all four second-order partial derivatives and check that fxy = fyx. Assume the variables are restricted to a domain on which the function is defined. 1. f(x,y) = (x + y)2 2. f(x,y) = (x + y) 3. f(x,y) = 3x"y + 5xy! 4. f(x,y) = 2xy 5. f(x,y) = (x + y)ey 6. f(, y) = xe 7. f(x, y) = sin(x/y) 8. f(x,y) = x2 + y2 9. f(x, y) = 5x®y2 - 7xy? + 9x² +11 10. f(x, y) = sin(x2 + y2) 11. f(x, y) = 3 sin 2x cos 5y
For each function, all four second-order partial derivatives are f(x,y) are (x + y)2, (x + y), 3x^2y + 5xy^2, 2xy, (x + y)e^y, xe^y, sin(x/y), x^2 + y^2, 5x^3y^2 - 7xy^3 + 9x^2 +11, sin(x^2 + y^2) and 3 sin(2x) cos(5y). It is proved that f x y is equals to f y x.
f(x,y) = (x + y)2
f x x = 2, f xy = 2, f yx = 2, f y y = 2
Since f x y = fy x, the mixed partial derivatives are equal.
f(x,y) = (x + y)
f x x = 0, f x y = 1, f y x = 1, f y y = 0
Since f x y = f y x, the mixed partial derivatives are equal.
f(x, y) = 3x^2y + 5xy^2
f x x = 6y, f x y = 6x + 10y, f y x = 6x + 10y, f y y = 10x
Since f x y = f y x, the mixed partial derivatives are equal.
f(x, y) = 2 x y
f x x = 0, f x y = 2, f y x = 2, f y y = 0
Since f x y = f y x, the mixed partial derivatives are equal.
f(x,y) = (x + y) * e^y
f x x = e^y, f x y = e^y + e^y, f y x = e^y + e^y, f y y = (x + 2y) * e^y
Since f x y = f y x, the mixed partial derivatives are equal.
f(x,y) = x * e^y
f x x = 0, f x y = e^y, fy x = e^y, f y y = x * e^y
Since fx y = fy x, the mixed partial derivatives are equal.
f(x, y) = sin(x/y)
f x x = -sin(x/y) / y^2, f x y = cos(x/y) / y^2, f y x = cos(x/y) / y^2, f y y = -x * cos(x/y) / y^4 - sin(x/y) / y^2
Since f x y = f y x, the mixed partial derivatives are equal.
f(x, y) = x^2 + y^2
f x x = 2, f x y = 0, f y x = 0, f y y = 2
Since f x y = f y x, the mixed partial derivatives are equal.
f(x, y) = 5x^2y^2 - 7xy + 9x^2 + 11
f x x = 10xy^2 + 18, f x y = 10x^2y - 7, f y x = 10x^2y - 7, fy y = 10x^2y^2
Since fx y = fy x, the mixed partial derivatives are equal.
f(x,y) = sin(x^2 + y^2)
fx x = 2xcos(x^2 + y^2), fx y = 2ycos(x^2 + y^2), fy x = 2ycos(x^2 + y^2), fy y = 2x * cos(x^2 + y^2)
Since fx y = fy x, the mixed partial derivatives are equal.
f(x,y) = 3sin(2x)cos(5y)
fx x = 0, fx y = -30sin(2x)sin(5y), fy x = -30sin(2x)sin(5y), fy y = 0
Since fx y = fy x, the mixed partial derivatives are equal.
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Find the volume of a pyramid with a square base, where the side length of the base is
11. 8 ft and the height of the pyramid is 5. 2 ft. Round your answer to the nearest
tenth of a cubic foot.
The volume of the pyramid with a square base of side length 11.8 ft and a height of 5.2 ft is 240.0 cubic feet.
To find the volume of a pyramid with a square base of side length 11.8 ft and a height of 5.2 ft, you can use the following formula:
Volume = (1/3) × Base Area × Height
1: Find the base area.
The base is a square with a side length of 11.8 ft, so the area of the base is:
Base Area = Side Length × Side Length
Base Area = 11.8 ft × 11.8 ft
Base Area ≈ 139.24 square ft
2: Find the volume.
Now, use the formula to find the volume:
Volume = (1/3) × Base Area × Height
Volume = (1/3) × 139.24 sq ft × 5.2 ft
Volume ≈ 240.0368 cubic ft
3: Round your answer to the nearest tenth.
Volume ≈ 240.0 cubic ft
So, the volume of the pyramid is approximately 240.0 cubic feet.
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Is the expression (x + 18) a factor of x² - 324?
Answer: We can check whether the expression (x + 18) is a factor of x² - 324 by dividing x² - 324 by (x + 18) using polynomial long division or synthetic division.
Using polynomial long division:
x + 18 │x² + 0x - 324
-x² - 18x
----------
18x - 324
18x + 324
----------
0
Since there is no remainder, we can see that (x + 18) is indeed a factor of
x² - 324.
Use spherical coordinates to evaluate the triple integral
∫∫∫E 4x^2 + 3dV = ______
The evaluation of the triple integral ∫∫∫E 4[tex]x^{2}[/tex] + 3dV is (38/15)ππ
To evaluate the triple integral ∫∫∫E 4x^2 + 3dV in spherical coordinates, we need to express the integrand and the volume element dV in terms of the spherical coordinates ρ, θ, and φ.
The volume element dV in spherical coordinates is given by:
dV = sin φ dρ dθ dφ
where ρ is the radial distance, θ is the azimuthal angle, and φ is the polar angle.
The region E in which we are integrating can be defined in spherical coordinates as follows:
0 ≤ ρ ≤ 2
0 ≤ θ ≤ 2π
0 ≤ φ ≤ π/2
Substituting these expressions into the volume element, we have:
dV = sin φ dρ dθ dφ
= (sin φ) dρ dθ dφ
Now, we need to express the integrand 4[tex]x^2[/tex] + 3 in terms of the spherical coordinates.
The variable x can be expressed in terms of the spherical coordinates as:
x = ρ sin φ cos θ
Therefore, 4[tex]x^2[/tex] + 3 can be expressed as:
4[tex]x^2[/tex] + 3 = 4 [tex]sin^2[/tex] φ [tex]cos^2[/tex] θ + 3
Substituting this expression into the triple integral, we have:
∫∫∫E 4[tex]x^2[/tex] + 3dV
Now, we can evaluate the integral by performing the integration in the order φ, θ, ρ.
= (8/15)π + 2π
= (38/15)ππ
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In circle P with m \angle NPQ= 104m∠NPQ=104 and NP=9NP=9 units find area of sector NPQ. Round to the nearest hundredth
Area of sector NPQ ≈ 127.23 square units
To find the area of the sector NPQ, we first need to find the measure of the central angle that defines the sector. We know that the measure of the angle NPQ is 104 degrees, but we need to find the measure of the central angle that includes this arc.
Since NP is a radius of the circle, we know that triangle NQP is an isosceles triangle, with angles NQP and PNQ each measuring (180 - 104)/2 = 38 degrees. Therefore, the measure of the central angle that includes arc NPQ is 2 * 38 + 104 = 180 degrees.
The area of the sector NPQ is then a fraction of the total area of the circle, where the fraction is equal to the ratio of the central angle to the total angle around the circle. Since the total angle around a circle is 360 degrees, the fraction of the circle's area covered by the sector is:
180 degrees / 360 degrees = 1/2
Therefore, the area of the sector NPQ is equal to half the area of the circle with radius 9 units:
Area of sector NPQ = (1/2) * π * 9^2 = 40.5π
Rounding to the nearest hundredth, the area of the sector NPQ is approximately:
Area of sector NPQ ≈ 127.23 square units
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Suppose that a report by a leading medical organization claims that the healthy human heart beats an average of 72 times per minute. Advances in science have led some researchers to question if the healthy human heart beats an entirely different amount of time, on average, per minute. They obtain pulse rate data from a sample of 85 healthy adults and find the average number of heart beats per minute to be 76, with a standard deviation of 13. Before conducting a statistical test of significance, this outcome needs to be converted to a standard score, or a test statistic. What would that test statistic be
The test statistic (or standard score) would be 1.72.
To convert the outcome of the pulse rate data to a standard score, we would need to calculate the z-score. The formula for the z-score is: (sample mean - population mean) / (standard deviation / square root of sample size).
In this case, the sample mean is 76, the population mean (according to the report) is 72, the standard deviation is 13, and the sample size is 85. Plugging these values into the formula, we get:
(76 - 72) / (13 / sqrt(85)) = 1.72.
Therefore, the test statistic (or standard score) is 1.72. This indicates that the sample mean of 76 is 1.72 standard deviations above the population mean of 72. This information can be used to conduct a statistical test of significance and determine whether the difference between the sample mean and population mean is statistically significant.
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Eddie's dog weighs 31. 8 kilograms. How many grams are equivalent to 31. 8 kilograms?
A). 0318 grams
B) 318 grams
() 3,180 grams
D) 31,800 grams
31.8 kilograms is equivalent to 31,800 grams.
What is the weight in grams of Eddie's 31.8 kg dog?The correct answer is (D) 31,800 grams.
To convert kilograms to grams, we multiply the number of kilograms by 1000. So, to convert 31.8 kilograms to grams, we can use the following formula:
31.8 kilograms x 1000 grams/kilogram = 31,800 grams
Therefore, 31.8 kilograms is equivalent to 31,800 grams.
To convert kilograms to grams, we need to multiply the number of kilograms by 1000 because there are 1000 grams in one kilogram. In this case, Eddie's dog weighs 31.8 kilograms. To find out how many grams this is, we simply multiply 31.8 by 1000, which gives us 31,800 grams. Therefore, 31.8 kilograms is equivalent to 31,800 grams. It's important to understand the basic metric system conversions, like kilograms to grams, as they are commonly used in everyday life, particularly when it comes to measuring weight. Knowing how to make these conversions can be helpful in many different situations, from cooking and baking to medical and scientific contexts.
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A parabola has a focus of (22, 3) and a directrix of y 5 1. answer each question about the parabola, and explain your reasoning.
a. what is the axis of symmetry?
b. what is the vertex?
c. in which direction does the parabola open?
The parabola has an axis of symmetry x=22, vertex at (22, 2), and opens downward.
Given the focus (22, 3) and directrix y=1, we can determine the following:
a. Axis of symmetry: Since the parabola is vertical (directrix is horizontal), the axis of symmetry will be a vertical line passing through the focus. So, x=22 is the axis of symmetry.
b. Vertex: The vertex is the midpoint between the focus and the directrix. To find the vertex, average the y-coordinates of the focus and the directrix. Vertex = (22, (3+1)/2) = (22, 2).
c. Direction: If the focus is above the directrix, the parabola opens upward. If the focus is below the directrix, the parabola opens downward. In this case, the focus (22, 3) is above the directrix y=1, so the parabola opens downward.
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The food company is now designing soup boxes. The largest box of soup will be a dilation of the smallest box using a scale factor of 2. The Smallest box hold 8 fl oz or about 15 cubic inches of soup find a set of dimensions for the largest box? round your answer to the nearest tenth if necessary
The largest box of soup will hold about 120 ounces or 221 cubic inches of soup.
Since the scale factor is 2, the volume of the largest box will be 2^3 = 8 times the volume of the smallest box. Therefore, the volume of the largest box will be 8 x 15 cubic inches = 120 cubic inches. To find the dimensions of the largest box, we need to find the cube root of 120 cubic inches, which is approximately 5.87 inches.
Since the smallest box has no shape restrictions, we can assume that the largest box will also have a rectangular shape. Therefore, a set of dimensions for the largest box could be 5.87 inches x 5.87 inches x 5.87 inches, or rounded to the nearest tenth, 5.9 inches x 5.9 inches x 5.9 inches.
This would result in a volume of approximately 221 cubic inches, which is about 120 ounces of soup.
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The coiling dragon cliff skywalk in china is $128$ feet longer than the length $x$ (in feet) of the tianmen skywalk in china. The world's longest glass-bottom bridge, located in china's zhangjiaji national park, is about $4. 3$ times longer than the coiling dragon cliff skywalk. Write and simplify an expression that represents the length (in feet) of the world's longest glass-bottom bridge
The expression that represents the length (in feet) of the world's longest glass-bottom bridge is 4.3x+550.4.
Let's denote the length of the Coiling Dragon Cliff Skywalk as y (in feet). According to the given information, we have:
y = x + 128
The length of the world's longest glass-bottom bridge is 4.3 times longer than the Coiling Dragon Cliff Skywalk, so we can write an expression for it as:
Length of the longest glass-bottom bridge = 4.3 * y
Now, we can substitute the expression for y from the first equation:
Length of the longest glass-bottom bridge = 4.3 * (x + 128)
To simplify, distribute the 4.3:
Length of the longest glass-bottom bridge = 4.3x + 550.4
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PLEASE HELP WITH 4 AND 5
1. The area of the shaded region is
2. percentage of the shaded part is 89.6%
What is area of shape?The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.
The area of the shaded part = area of the rectangle - area of unshaded part
Area of rectangle = 7× 11 = 77 unit²
area of rectangle = 1/2 bh
= 1/2 × 4 × 4
= 1/2 × 8
= 4 unit²
area of second triangle = 4 units²
area of unshaded part = 4+4 = 8 units²
area of shaded part = 77-8 = 69units²
2. percentage of the rectangle shaded = 69/77 × 100
= 6900/77 = 89.6%
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Triangle ABC has vertices A(-1,1), B(1,3) and C(4,1). The image of ABC after the transformation matrix T=
The coordinates of transforming image of the vertices of the triangle ABC are A' (1, -1) ,B' (3, 1) , and C' (1, 4).
In triangle ABC,
Coordinates of the vertices of triangle ABC are,
A(-1,1), B(1,3) and C(4,1)
The transformation T y=x reflects the points across the line y=x.
The image of each point, we simply swap the x and y coordinates of each point.
So, applying the transformation T y=x to the vertices of triangle ABC, we get,
A' = (-1, 1) → (1, -1)
B' = (1, 3) → (3, 1)
C' = (4, 1) → (1, 4)
This implies,
The image of triangle ABC under the transformation T y=x is triangle A'B'C', where,
A' is located at (1, -1)
B' is located at (3, 1)
C' is located at (1, 4)
Therefore, in triangle ABC labeling the coordinates of the vertices of A'B'C' after transformation are as follows,
A' (1, -1)
B' (3, 1)
C' (1, 4)
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The above question is incomplete, the complete question is:
Triangle ABC has vertices A(-1,1), B(1,3) and C(4,1). The image of ABC after the transformation T y=x is A’ B’ C’. State and label the coordinates of A’ B’ C’.
A museum groundskeeper is creating a simicircular stauary garden with a diameter of 38 feet there will be a fence around the garden the fencing cost $9.25 per linear foot . About how much will the fencing cost although? Round to the nearest hundredth use 3.14 for n the fencing will cost about $
The amount for the fencing cost is $903. 36
How to determine the valueFrom the information given, we have that the shape of the garden is semi -circle.
Now, the formula that is used for calculating the circumference of a semicircle is expressed as;
C = πr + 2r
Given that the parameters of the equation are;
C is the circumference of the semicircler is the radius of the semicircleFrom the information given,
Substitute the values, we have;
Circumference = 3.14(19) + 2(19)
expand the bracket
Circumference = 59. 66 + 38
Add the values
Circumference = 97. 66 feet
Then,
if 1 feet = $9.25
Then, 97. 66 feet = x
x = $903. 36
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(4y + z)^2 what is the a value and what is the b value
Answer:
a = 16
b = 8z
Step-by-step explanation:
Expanding the given expression, we get:
(4y + z)^2 = (4y + z) × (4y + z)
= 16y^2 + 8yz + z^2
Comparing this with the general form of a quadratic expression, ax^2 + bx + c, we can see that:
a = 16
b = 8z
Therefore, the value of a is 16 and the value of b is 8z.
Write the explicit formula for the following sequence, then generate the first five terms. A1 = 256, r = 0. 25
The explicit formula for the given sequence is An = 256 * (0.25)ⁿ⁻¹, where n is the term number. Using this formula, we can generate the first five terms of the sequence as follows:
A1 = 256 * (0.25)¹⁻¹ = 256 * 1 = 256
A2 = 256 * (0.25)²⁻¹ = 256 * 0.25 = 64
A3 = 256 * (0.25)³⁻¹ = 256 * 0.0625 = 16
A4 = 256 * (0.25)⁴⁻¹ = 256 * 0.015625 = 4
A5 = 256 * (0.25)⁵⁻¹ = 256 * 0.00390625 = 1
In simpler terms, the explicit formula for the given sequence is found by multiplying the first term by the common ratio raised to the power of n-1, where n is the term number. This results in a decreasing sequence as the common ratio is less than 1. The first five terms of the sequence are 256, 64, 16, 4, and 1, respectively.
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The school assembly is being held over the lunch hour in the school gym. All the teachers and students are there by noon and the assembly begins. About 45 minutes after the assembly begins, the temperature within the gym remains a steady 77 degrees Fahrenheit for a few minutes. As the students leave after the assembly ends at the end of the hour, the gym begins to slowly cool down
1 hour =60 minutes
Step-by-step explanation:
Let M be the time in minutes . T be temperature in Farhenheit. From 45th min to end of the hour there remains a steady temperature. after that gyms starts to cools down . For time 45≤M≤60, Temperature T=77oF.To find a) Is M a function of T ? we know that Temperature changes with respect to time . So M is independent variable and T is dependent variable . so M cannot be a function of T .
The table shows transactions from a bank account. fill in the missing number for box a.
transaction amount
account balance
transaction 1
150 150
transaction 2
50 100
transaction 3
90 a
transaction 4
-200 b
transaction 5
c 0
btw this is integers
The missing number for box a transaction amount account balance are a = 10, b = 210, c = 210.
Using the information provided in the table, we can fill in the missing numbers as follows:
For transaction 3: The account balance after transaction 2 was $100, and transaction 3 had an amount of $90. Therefore, the account balance after transaction 3 is $190. Hence, the missing number in box a is 190.
For transaction 4: The account balance after transaction 3 was $190, and transaction 4 had an amount of -$200. Therefore, the account balance after transaction 4 is -$10. Hence, the missing number in box b is -10.
For transaction 5: The account balance after transaction 4 was -$10, and transaction 5 had an amount of $c. Therefore, the account balance after transaction 5 is 0. Hence, the missing number in box c is 10.
Therefore, the completed table is:
transaction amount account balance
1 150 150
2 50 100
3 90 190
4 -200-10
5 10 0
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answer options:
x= 3, -4
x= 5, -1
x= 0, 5
x= 1, 5
From the given graph, the roots of the quadratic equation, 0 = x² - 6x + 5, is 1 and 5. The correct option is the last option x= 1, 5
Determining the roots of a quadratic function from the graphFrom the question, we are to determine the roots of the quadratic equation from the provided graph.
From the given information,
The given quadratic equation is
0 = x² - 6x + 5
The roots of a quadratic function are the values of x where the function equals zero. On a graph, this corresponds to the points where the graph intersects the x-axis.
From the graph, we will read the x-coordinates of the points where the graph intersects the x-axis.
From the given graph, the x-coordinates of the points where the graph intersects the x-axis are 1 and 5
Hence, the roots of the quadratic equation is 1 and 5
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The double dot plot shows the values in two data sets. express the difference in the measures of center as a multiple of the measure of variation.
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The difference in measures of center as a multiple of the measure of variation can be expressed using the coefficient of variation.
How to express difference in data?To express the difference in measures of center as a multiple of the measure of variation, you can use the coefficient of variation (CV).
The CV is calculated by dividing the standard deviation (measure of variation) by the mean (measure of center), and then multiplying by 100 to express the result as a percentage.
For example, if the standard deviation of one dataset is 5 and the mean is 10, the CV would be 50%. If the standard deviation of another dataset is 2 and the mean is 8, the CV would be 25%.
To express the difference in measures of center as a multiple of the measure of variation between these two datasets, you would calculate the difference in their means (10-8=2) and divide it by the CV of the combined dataset ((5/10 + 2/8)/2 = 47.5%).
Therefore, the difference in measures of center is approximately 0.042 times the measure of variation (2/47.5%).
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Classify triangle ABD by its sides and then by its angles.
Select the correct terms from the drop-down menus.
Image shows a triangle ABD having three sides of unequal length and one angle larger than 90 degrees.
Triangle ABD is
and
.
.
Triangle ABD is scalene and obtuse.
How to classify the triangle?The triangle has three sides of unequal length, hence it is classified as an scalene triangle.
(it would be equilateral if all had the same length, and isosceles if two sides have the same length).
The triangle has one angle larger than 90º, hence it is classified as an obtuse triangle.
(acute with no angles of 90º or greater, right with one angle of exactly 90º).
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Suppose z = x+ sin(y) , x = 2t = - 482, y = 6st. - 1 A. Use the chain rule to find дz as and Oz as functions of дz Ət X, Y, s and t. - az მs/Əz as/Əz B. Find the numerical values of and o"
The numerical value of Oz is approximately -1819.86.
Using the chain rule, we have:
[tex]dz/dt = dz/dx * dx/dt + dz/dy * dy/dt\\dz/ds = dz/dy * dy/ds[/tex]
We can calculate each term using the given equations:
dz/dx = 1
dx/dt = 2
dy/dt = 0
dz/dy = cos(y)
dy/ds = 6t
Substituting these values, we get:
[tex]dz/dt = dz/dx * dx/dt + dz/dy * dy/dt = 1 * 2 + cos(y) * 0 = 2\\dz/ds = dz/dy * dy/ds = cos(y) * 6t = 6t * cos(6st)[/tex]
To find дz as/Əz, we need to solve for as in terms of z and s:
z = x + sin(y) = 2t + sin(6st)
x = 2t
y = 6st - 1
Solving for s in terms of t, we get:
s = (y + 1)/(6t)
Substituting this into the equation for z, we get:
z = 2t + [tex]sin(6t(y+1)/(6t)) = 2t + sin(y+1)[/tex]
Taking the partial derivative of z with respect to as, we get:
[tex]дz/Əz = 1[/tex]
B. To find the numerical values of дz and Oz, we need to plug in the given values of x, y, s, and t into our equations. Using the given values, we get:
x = 2t = -964
y = 6st - 1 = -3617
z = x + sin(y) = -964 + sin(-3617) ≈ -964.73
Using the values of s and t, we can find:
s = (y + 1)/(6t) ≈ -0.9985
t = x/2 ≈ -482
Substituting these values into our equation for дz as/Əz, we get:
дz/Əz = 1
Therefore, the numerical value of дz is 1.
Substituting these values into our equation for dz/ds, we get:
dz/ds = 6t * cos(6st) ≈ -1819.86
Therefore, the numerical value of Oz is approximately -1819.86.
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Find the limit of (7x3)/(4x2-2x+10) as x approaches infinity."
To find the limit of (7x3)/(4x2-2x+10) as x approaches infinity, we need to divide the highest power of x in the numerator and denominator, which is x3, by the highest power of x in the denominator, which is x2. This gives us: (7x3)/(4x2-2x+10) = (7/4)x
As x approaches infinity, the value of (7/4)x also approaches infinity. Therefore, the limit of (7x3)/(4x2-2x+10) as x approaches infinity is infinity.
To find the limit of (7x^3)/(4x^2-2x+10) as x approaches infinity, we'll first look at the highest powers of x in the numerator and denominator.
In this case, the highest power of x in the numerator is x^3, and in the denominator, it's x^2. Since the highest power of x in the numerator is greater than that in the denominator, the limit will go to infinity (or -infinity) depending on the coefficients of the highest powers.
For this function, the coefficients are positive (7 for x^3 and 4 for x^2), so the limit as x approaches infinity will be positive infinity.
Your answer: The limit of (7x^3)/(4x^2-2x+10) as x approaches infinity is positive infinity.
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Trevor is comparing two mortgage options from two different banks for his 20 year $120,000 mortgage. He thinks both mortgages are pretty much the same and is having a hard time deciding which bank to partner with. Bank A: 5% with monthly payments of $791. 95 Bank B: 4. 75% with monthly payments of $775. 47
Bank B is offering a lower interest rate and will result in a lower total cost over the 20-year period. Even though the monthly payment is slightly lower with Bank B, Trevor should choose Bank B because he will save money in the long run due to the lower interest rate.
Which bank should Taravar choose? in which he will save money in the long run due to the lower interest rate.To compare the two mortgage options, Trevor needs to consider both the interest rate and the monthly payment amount.
Bank A offers a 5% interest rate with a monthly payment of $791.95. The total amount he will pay over 20 years is:
$791.95 x 12 months/year x 20 years = $190,068
Bank B offers a 4.75% interest rate with a monthly payment of $775.47. The total amount he will pay over 20 years is:
$775.47 x 12 months/year x 20 years = $186,113.60
So, in this case, Bank B is offering a lower interest rate and will result in a lower total cost over the 20-year period. Even though the monthly payment is slightly lower with Bank B, Trevor should choose Bank B because he will save money in the long run due to the lower interest rate.
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Just the answer is fine:)
If C is the parabola y = x? from (1, 1) to (-1,1) then Sc(x - y)dx + (y sin y?)dy equals to: Select one: O a. 12 뮤 Ob O b. 124 7 O c. None of these O d. 5 7 O e. 2 7 Check
The correct answer is e. 2/7.
How to evaluate this line integral?To evaluate this line integral, we need to parameterize the curve given by the parabola y = x from (1, 1) to (-1, 1).
Let's let x = t and y = t, where t goes from 1 to -1. Then we can rewrite the integral as follows:
[tex]\int\ C (x - y)\dx + (y \sin y)\dy[/tex]
[tex]= \int\limits^1_{-1} {[(t - t)dt + (t sin t)}\,dt}[/tex]
[tex]= \int\limits^1_{-1} { (t \sin t)} \, dt[/tex]
We can evaluate this integral using integration by parts:
Let u = t and [tex]dv = sin t\ dt[/tex]. Then [tex]du/dt = 1[/tex] and v = -cos t.
Using the formula for integration by parts, we have:
[tex]\int\limits^1_{-1} { (t \sin t)}\, dt = -t \cos t |_{-1}^{1} + \int\limits^1_{-1} { cos t}\, dt[/tex]
= -cos(-1) + cos(1) + sin(-1) - sin(1)
= 2sin(1) - 2cos(1)
Therefore, the value of the line integral is:
[tex]S_c(x - y)dx + (y \sin y)dy = 2\sin(1) - 2\cos(1)[/tex]
Hence, the correct answer is e. 2/7.
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WALK THE PATH SHOWN WHAT IS THE DISTANCE
Answer:
D. 4π
Step-by-step explanation:
Circumference: C = 2πr = 2π(8) = 16π
The distance = 1/4 circumference (angle is 90 degrees)
=> distance = 16π/4 = 4π
What is the maximum height of Anna’s golf ball? The equation is y=x-0. 04x^2.
The maximum height is____ feet
The maximum height of Anna's golf ball is 6.25 feet.
To find the maximum height of Anna's golf ball, we need to determine the vertex of the parabolic equation y = x - 0.04x^2. The x-coordinate of the vertex can be found using the formula:
x = -b / (2a)
In this case, the coefficients a and b are:
a = -0.04
b = 1
Substituting the values into the formula:
x = -1 / (2 * -0.04)
x = -1 / (-0.08)
x = 12.5
Now, we need to find the y-coordinate of the vertex by plugging the x-coordinate back into the equation:
y = 12.5 - 0.04(12.5)^2
y = 12.5 - 0.04(156.25)
y = 12.5 - 6.25
y = 6.25
So, the maximum height of Anna's golf ball is 6.25 feet.
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Kevin works 3z hours each day from Monday to Friday. He works (4z-7) on Saturday. Kevin does not work on Sunday. Find the number of hours Kevin works in one week in terms of z
Answer:
im gooder like that
Step-by-step explanation:
3z*5=15z
15z+4z-7
19z-7