Find the volume of revolution generated by revolving the region bounded by y=x⁴;y=0;x=0; and x=1, about the x-axis.

The solution to the quadratic equation x² −6x+6=0 by completing the square is 3+√3 , 3-√3

To complete the square, we first move the constant term to the right-hand side of the equation:

x² − 6x = -6

We then take half of the coefficient of our x term, square it, and add it to both sides of the equation:

x² − 6x + (-6/2)² = -6 + (-6/2)²

x² − 6x + 9 = -6 + 9

(x - 3)² = 3

Taking the square root of both sides of the equation, we get:

x - 3 = ±√3

x = 3 ± √3

Therefore, the solutions to the quadratic equation x² − 6x+6=0 are:

x = 3 + √3

x = 3 - √3

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The cοοrdinates οf the fοurth vertex are (4,-1).

Tο find the fοurth vertex οf the parallelοgram, we need tο use the fact that οppοsite sides οf a parallelοgram are parallel and have the same length. We can use the given three vertices tο determine the vectοr representing οne οf the sides οf the parallelοgram. Then, we can extend that vectοr tο find the fοurth vertex.

Let's take the vectοrs representing twο adjacent sides οf the parallelοgram:

v1 = (-4,1) - (-2,-5) = (-2,6)

v2 = (6,-7) - (-4,1) = (10,-8)

Since οppοsite sides οf a parallelοgram are parallel, v1 and v2 must be parallel. This means that we can find the fοurth vertex by adding v1 tο the third vertex, (6,-7):

v4 = (6,-7) + v1 = (6,-7) + (-2,6) = (4,-1)

Therefοre, the cοοrdinates οf the fοurth vertex are (4,-1).

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Complete question:

Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex.

The excel statement to estimate the test average of these 4 grades is -

An average is the sum of many numbers divided by the total of numbers. It is also known as the arithmetic mean.

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Answer:

40 ounces

Step-by-step explanation:

1 pound = 16 ounces

Answer:

The answer is...

Step-by-step explanation:

40 oz is how many oz are in 2.5 lb

Hope this helped

:)

The value of each side has to be increased by 4 to get the area three times.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Adriel has a deck that measures 14 feet by 3 feet. He wants to increase each dimension by equal lengths so that its area is tripled.

Let the sides be increased by x. The value of the number will be calculated as,

( x + 4 ) ( x + 3 ) = 126

x² + 17 x -84 = 0

x² - 4x + 21x - 84 = 0

x(x-4) +21(x - 4 ) = 0

(x - 4 ) ( x + 21 ) = 0

x = 4 and x = -21 ignore the negative

Therefore, the value of each side has to be increased by 4 to get the area three times.

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In the context of our theory of inductive proofs, P(n) represents the quantity about which we are proving something- False.

A proof by induction requires justification at every step, just like a regular proof. But, it uses a clever technique that enables you to demonstrate the truth of a proposition when n is 1, assume it is true for n=k, and then demonstrate that it is true for n=k+1.

According to the theory, all that is required to demonstrate a person's ability to ascend to the nth floor of a fire escape is for them to demonstrate their ability to ascend the fire escape ladder (n=1) and their ability to ascend the stairs from any level of the fire escape (n=k) to the next level (n=k+1).

You could have been asked to assume the n-1 case and prove the n case if you've done proof by induction before, or to assume the n case and show the n+1 case. This is the same as what I'm describing here, but I'll use a different letter since I believe it helps people understand what each instance is for better.

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Answer:

c = 36

Step-by-step explanation:

i dont know the optiond but this is what i got for c/4 -5=4

Answer:

a(t) = 5i + 8j v(t0 = integration of a(t) v

Step-by-step explanation:

The lines to use to solve the equation are y = –3x – 2  and y = 2x + 8

The graph of the line is attached

From the question, we have the following parameters that can be used in our computation:

–3x – 2 = 2x + 8

The above equation can be splitted by introducing the variable y

using the above as a guide, we have the following:

y = –3x – 2

y = 2x + 8

This means that the lines to use to solve the equation are y = –3x – 2  and y = 2x + 8

The graph of the line is added as an attachment

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Answer

\( {f}^{ - 1} (x) = \frac{5}{2} x - 5.\)

Step by step

\(y = \frac{2x}{5} + 2\)

Swap roles of x and y

\(x = \frac{2}{5} y + 2\)

Then

\(5x = 2y + 10\)

So

\(2y = 5x - 10\)

Hence

\(y = \frac{5}{2} x - 5\)

Therefore

\( {f}^{ - 1} (x) = \frac{5}{2} x - 5.\)

Answer:

3,000ft

Step-by-step explanation:

First set up the equation:

Start: 13,000 ft
Middle: 10,000 ft
End: ??

Lindsey started at 13,000ft, dropped 10,000ft, and then the remainder of it is what we are asked to find out. So all we have to do is 13,000 - 10,000 which equals 3,000.

Answer:

A (skewed to the left)

Step-by-step explanation:

28 is a much smaller number (age) than the rest of the data, so it will be a negatively skewed distributio, aka, skewed to the left.

“A left skewed distribution is sometimes called a negatively skewed distribution because it's long tail is on the negative direction on a number line.”

“A distribution skewed to the left is said to be negatively skewed. This kind of distribution has a large number of occurrences in the upper value cells (right side) and few in the lower value cells (left side).”

The y-intercept of the graph is -3

The y-intercept is the point where the line intersects the y-axis. This is the value of y when x is equals to zero.

Using slope intercept formula,

y = mx + b

where

Now, let's trace the value of y when x = 0 in the graph.

Therefore,

when x = 0, y = -3

Hence, the y-intercept of the graph is -3

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Pua will use 13, 1/4 cups of oatmeal.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Pua needs 3\(\frac{1}{4}\) cups of oatmeal.

The number of 1/4 cups of oatmeal,

she will use,

= 13/4 ÷ 1/4

= 13

Therefore, she will use 13 cups.

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The Laplace Transform Method can be used to solve all of these equations except for equation (e).

a.) Yes, the Laplace Transform Method can be used to solve this third-order linear differential equation with constant coefficients and a nonhomogeneous term.

b.) Yes, the Laplace Transform Method can be used to solve this second-order linear homogeneous differential equation with constant coefficients.

c.) Yes, the Laplace Transform Method can be used to solve this second-order linear differential equation with constant coefficients and a nonhomogeneous term.

d.) Yes, the Laplace Transform Method can be used to solve this second-order linear homogeneous differential equation with variable coefficients.

e.) No, the Laplace Transform Method cannot be used to solve this first-order nonlinear differential equation.

f.) Yes, the Laplace Transform Method can be used to solve this second-order linear differential equation with constant coefficients and a nonhomogeneous term.

g.) Yes, the Laplace Transform Method can be used to solve this first-order nonlinear differential equation.

h.) Yes, the Laplace Transform Method can be used to solve this first-order linear differential equation with constant coefficients and a nonhomogeneous term.

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Since 65 + 25 = 90, 90 student tickets were sold.

According to our question-

25 student tickets are $75 each. If we deduct this from the total, we find that an equal number of adult and student tickets cost $585.

The cost of one adult ticket and one child ticket is $9.

585/9= 65.

Verifying this:

65x3=195 \s65x6=390

195+390+75= 660

Hence, Since 65 + 25 = 90, 90 student tickets were sold.

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Answer:

Step-by-step explanation:

\(Slope (m) = \frac{y}{x} = 0\)

\(0 = arctan (\frac{y}{x} ) 0^o\)

Answer:

7

Step-by-step explanation:7

The solution of the mathematical statement is 102.5

From the question, we have the following mathematical statement that can be used in our computation:

"What is -5/2 times -41"

This means that

-5/2 times -41

Express as numbers

So, we have

-5/2 * -41

Divide 5 by 2

So, we have

-2.5 * -41

Evaluate the product

102.5

Hence, the result is 102.5

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Answer:

∠B = 60°

Step-by-step explanation:

They are supplementary angles, which means they add up to 180°.

∠B + ∠A = 180

? + 120 = 180

? = 180 - 120

? = 60°

Answer:

Use the formula: V = 4/3 x π xR^3

Step-by-step explanation:

R=18:2=9cm

=> V=4/3 x π x 9^3 = 972π = 3054cm^3

The equation is in the form of the linear line: y = mx +b where m is the slope.

Thus the slope is 1/6

Hope that helps!

Check the picture below.

\(\cfrac{17.5+14}{17.5}~~ = ~~\cfrac{x}{12.5}\implies \cfrac{(17.5+14)(12.5)}{17.5}~~ = ~~x\implies 22.5=x\)

The ordered pair of C'' after the sequence of transformation is (-14, -5)

Here we have know that  ABC can be plotted at A (-14, 14), B (-8, 11) & C (-14, 5).

Here we all know that the y-axis reflection rule is written as,

=> (x, y) → (-x, y)

And the value of x coordinate flips in sign from positive to negative, or vice versa. Then the value of y coordinate stays the same.

Then the point is look like C(-14,5) will then reflect based on the following rule,

=> (x, y) → (x, y)

The transformed coordinates are look like,

=> (-14,5) ((-14),5)

=> (-14,5)→ (14,5)

Therefore, here we have point C' located at (14,5) after applying the y-axis reflection rule on point C.

Now, the next operation to do is is the 180 degree rotation.

And this can be clockwise or counterclockwise.

Then the rotation rule is written as

=> (x, y) → (-x,y)

Now, for this time both coordinates flip in sign.

Here we have know that this rule only works if the center of rotation is the origin.

Now, let us apply that rotation rule to C' to find where C" is located.

Then the rule can be written as,  (x, y) → (-x,y)

=> (14,5)→ (-14, -5)

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The correlation coefficients and security returns provided suggest a relationship between security 1 and security 2.

The given information includes security returns and correlation coefficients between different securities. Based on the data, it is evident that there is a relationship between security 1 and security 2. The correlation coefficient P12 is -1, indicating a perfect negative correlation between the two securities. This means that when security 1's returns increase, security 2's returns decrease, and vice versa.

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Answer:

We meet again

Step-by-step explanation:

When a rectangle is dilated by a scale factor k, the length and width of the rectangle are both multiplied by k. In this case, the length of the rectangle is being dilated by a scale factor of 5. So the length of the rectangle after the dilation will be 20 * 5 = **100 meters**.

There are two buildings that you want to have in the amusement park.

a) The expression that represents the area of the gift shop, in terms of x, is

Area = length x width

Area = (20x + 24) (36x - 20)

Area = 720\(x^{2}\) + 208x - 480

Therefore, the area of the gift shop is 720\(x^{2}\)  + 208x - 480 square feet.

b) The expression that represents the perimeter of the gift shop, in terms of x, is

Perimeter = 2(length + width)

Perimeter = 2(20x + 24 + 36x - 20)

Perimeter = 2(56x + 4)

Perimeter = 112x + 8

Therefore, the perimeter of the gift shop is 112x + 8 feet.

c) If the perimeter is going to be 176 feet, we can set the expression for the perimeter equal to 176 and solve for x

112x + 8 = 176

Subtracting 8 from both sides

112x = 168

Dividing both sides by 112

x = 1.5

Now that we know x, we can substitute it into the expressions for the length and width of the gift shop

Length = 20x + 24 = 20(1.5) + 24 = 54 feet

Width = 36x - 20 = 36(1.5) - 20 = 34 feet

Therefore, the dimensions of the gift shop are 54 feet by 34 feet.

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