let V be the volume of a right circular cone of height ℎ=20 whose base is a circle of radius =5. An illustration a right circular cone with horizontal cross sections. The right circular cone has a line segment from the center of the base to a point on the circle of the base is labeled capital R, and the horizontal line from the vertex is labeled h. (a) Use similar triangles to find the area of a horizontal cross section at a height y. Give your answer in terms of y.

a. The equivalent expression for cos(4x) in terms of just x is 8cos⁴x - 8cos²x + 1

b. The equivalent expression for sin(4x) in terms of just x is 4sinxcos³x - 2sinxcosx

To find the trigonometric expression for cos(4x)

cos(4x) = cos[2(2x)]

Now from trigonometric identities

cos2Ф = 2cos²Ф - 1

Let 2x = Ф.

So, cos(4x) = 2cos²2x - 1

Also, cos2x = 2cos²x - 1

So, substituting cos2x into cos4x, we have

cos(4x) = 2cos²2x - 1

cos(4x) = 2[2cos²x - 1]² - 1

cos(4x) = 2[4cos⁴x - 4cos²x + 1] - 1

cos(4x) = 8cos⁴x - 8cos²x + 2 - 1

cos(4x) = 8cos⁴x - 8cos²x + 1

So, the equivalent expression for cos(4x) in terms of just x is 8cos⁴x - 8cos²x + 1

To find the expression for sin(4x)

sin(4x) = sin2(2x)

From trigonometric identities sin2Ф = 2sinФcosФ

Let 2x = Ф

So, sin(4x) = sin2(2x)

= 2sin2xcos2x

Since

Substituting these into the equation, we have

sin(4x) =  2sin2xcos2x

sin(4x) = (2sinxcosx)(2cos²x - 1)

sin(4x) = 4sinxcos³x - 2sinxcosx

So, the equivalent expression for sin(4x) in terms of just x is 4sinxcos³x - 2sinxcosx

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Hello,

y = ax + b where a is the slope ! so here the slope is 6

Answer:

(0,0)

Step-by-step explanation:

The y-intercept (where the graph of the equation crosses the y-axis) occurs where x = 0. If you substitute 0 for x in the equation, y = 0. So the y-intercept is at (0,0).

Answer:

A=3Bz/2

B=2A/3z

Step-by-step explanation:

if you need more explanation you can ask me :)

Answer:

a: (-1,0) , (3/5,0)

b:(-0.2,-3.2). It will be a minimum

c: To graph, you would first find the vertex using (-b/2a) and then plug that back into the equation to find the y coordinate of the vertex. Once you have the vertex plotted, you can then find the x-intercepts. This can be found by factoring the equation and finding the zeros. These 3 points you plot are enough to graph the line.

Step-by-step explanation:

For showing work on part a:

Turn 5x^2+2x-3 into

(5x^2+5x) (-3x-3)

5x(x+1) -3(x+1)

Finally:

(5x-3)(x+1)

The zeros from that are -1 and 3/5

Answer:

Answer C: m = 26, f = 22

there is a typo in answer D.

Step-by-step explanation:

There are 48 vehicles, so m + f = 48.

They have 140 wheels, so 2m+4f = 140.

You can rewrite the first as m = 48-f and then plug it into the second:

2(48-f) + 4f = 140 =>

96 - 2f + 4f = 140 =>

2f = 140 - 96 =>

2f = 44

f = 22

m = 48 - 22 = 26

Answer:

D

Step-by-step explanation:

Let m = motorcycles and c = cars

m + c = 48                 2m + 4c = 140

m + c  = 48  Multiple this equation through by -2

-2m -2c = -96  Add this to the second equation above

2m +4c = 140

        2c = 44  Divide both sides by 2

          c  = 22.  There are 22 cars.  Plug this back into the top equation to find the number of motorcycles.

m + c = 48

m + 22 = 48 Subtract 22 from both sides

m = 26

The expression equivalent to -7(y - 2) is -7y + 14

Given the expression; -7(y - 2)

We expand the expression by multiplying each element inside the parentheses the element out i.e -7

-7(y - 2)

[ -7 × y and -7 × -2 ]

-7y + 14

Therefore, the expression equivalent to -7(y - 2) is -7y + 14.

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The ratio guest to appetizers at the party was 4 guest per appetizer.

An equation is an expression that shows the relationship between two or more variables and numbers.

Ratio of guest to appetizers = 8 guest / 2 appetizers = 4 guest per appetizer.

The ratio guest to appetizers at the party was 4 guest per appetizer.

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Other than translation, the transformation that is used to create this frieze pattern is; B: Vertical Reflection

Now, we see all the Frieze Patterns on top are being transformed using Translation as it is the exact same pattern throughout the top.

Now, for the bottom we see that is is simply a reflection of the one on top and so it is a vertical reflection because it is reflected across the x-axis.

A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis.

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The equation which could be used to find the length of the hypothenuse is; 5 squared + 8 squared = c squared.

It follows from the task content that the equation which could be used to find the length of the third side be determined.

Hence, since it follows from Pythagoras theorem that the square of the hypothenuse is equivalent to the sum of the squares of the two other sides of a right triangle.

Hence, the required equation is; 5 squared + 8 squared = c squared.

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Answer:

The answer is A
5 squared + 8 squared = c squared

Step-by-step explanation:

Answer:

17√3

Step-by-step explanation:

In a 45-45-90 triangle, the hypotenuse is √3 times larger than the legs.

17*√3 = 17√3

The equation that describes the new function is y' = x^2 + 5

The function is given as:

y = x^2

Shifting the function up by 5 units, the rule is

(x, y) = (x, y + 5)

So, we have:

y' = x^2 + 5

Hence, the equation that describes the new function is y' = x^2 + 5

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Answer:

patient A has the greater weight

The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).

First, we find the vector between the two points by vector sum:

[tex]\vec r = (-8, -9, - 11) - (- 3, 0, -7)[/tex]

[tex]\vec r = (- 5, - 9, - 4)[/tex]

The distance between the two points is found by the following Pythagorean expression:

[tex]d = \sqrt{(-5)^{2}+(-9)^{2}+(-4)^{2}}[/tex]

d ≈ 11.1

And the midpoint is found by linear algebra:

[tex]\vec m = 0.5\cdot (-3, 0, -7) + 0.5 \cdot (-8, -9, - 11)[/tex]

[tex]\vec m = (- 1.5, 0, - 3.5) + (- 4, - 4.5, -5.5)[/tex]

[tex]\vec m = (- 5.5, - 4.5, - 9)[/tex]

The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).

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Answer: 98

Step-by-step explanation: 180 - 82 = 98

180 - 80 = 100, and 100 - 2 is 98.

There will be total 14 hard centred and 14 soft centred choclates in the box.

The ratio is the division of the two numbers.

For example, a/b where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that in the question hard-centred and soft-centred chocolates in the ratio 5 : 2

Hard centred/ Soft centred = 5/2

And total

Hard centred + Soft centred = 49

Now let say hard centred is H and soft centred S

H/S = 5/2 and H + S = 49

Now H = (5/2)S put into second equation

(5/2)S + S = 49

S(7/2) = 49

S = 14 now put into second equation

H + 14 = 49 = 35 hence hard centred will be 35 and soft centred will be 14.

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The factored form of the equation that has the zeros 4 and -7 is y = ( x - 4)( x + 7 ).

Roots are simply the points where the graph intercepts with the x-axis. ( y = 0 )
That is, y = 0 the roots

Given the roots of the equation;

Now, at x = 4,

x = 4

x - 4 = 0

y = ( x - 4)

Also, at x = -7,

x = -7

x - ( - 7 ) = 0

x + 7 = 0

y = ( x + 7 )

Hence; for the equation with the given roots; 4 and -7 will be;

y = ( x - 4)( x + 7 ).

The factored form of the equation that has the zeros 4 and -7 is y = ( x - 4)( x + 7 ).

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A confidence interval is an interval estimate of an individual y value, given values of the independent variables.

According to statement

we have to find a interval which give an estimate of an individual y value, given values of the independent variables.

Confidence interval tells that more than just the possible range around the estimate. It also tells about how stable the estimate is. A stable estimate is one that would be close to the same value if the survey were repeated.

So, A confidence interval is an interval estimate of an individual y value, given values of the independent variables.

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The surface area of the oblique prism is equal to 485 square units.

In this question we have an oblique prism with seven faces, consistiting in two regular hexagons and five parallelograms. The surface areas is the sum of these seven faces:

A = 2 · 50 + 5 · 11 · 7

A = 485

The surface area of the oblique prism is equal to 485 square units.

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The upper quartile for NFC is 3 points higher than that of AFC.

A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%

On the box, the third line on the box represents the upper quartile. 75% of the scores represents the upper quartile.

Upper quartile for AFC : 26

Upper quartile for NFC : 23

Difference = 26 - 23 = 3

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The missing height is 65.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

Missing height = (mean x total number of students) - sum of existing heights

Sum of existing heights = (54 + 55 + 56 + 61 + 63 + 64 + 70 ) = 423

Missing height = (8 x 61) - 423 = 64

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The correct answer is  8.5 in.

we know that

The formula of area of triangle is equal to

             [tex]A = \frac{1}{2} (b) (h)[/tex]

We have

b = BC = 6 in

h = AD = x in

substitute

[tex]A = \frac{1}{2} (6) (x)[/tex]

[tex]A = 3x^{2} in^{2} ..................(1)[/tex]

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.  

Let  a,b,c be the lengths of the sides of a triangle.  

The area is given by:-

[tex]A = \sqrt{p(p-a) (p-b) (p-c)}[/tex]                     where p is half the perimeter

[tex]p = \frac{a +b+ c}{2}[/tex]

a = 9 in , b= 9 in, c = 6 in

[tex]p = \frac{9 + 9 + 6}{2} = 12 in[/tex]

Find the area

[tex]A = \sqrt{12( 12 - 9) (12-9) (12 - 6)}[/tex]

[tex]A = \sqrt{12 (3)(3)(6)}[/tex]

[tex]A = \sqrt{648}[/tex]

[tex]A = 25.46 in^{2}[/tex]

Substitute the value of the area in the equation 1 and solve for x

[tex]A = 3x in^{2}[/tex]

25.46 = 3x

x = 25.46/3

x = 8.5 in

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The complete question is -

HELP PLEASE! Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.

A. 8 in.

B. 11.3 in.

C. 8.5 in.

D. 6.2 in.

Answer:

76.25

Step-by-step explanation:

The probability is 1/5.

There are 3 red marbles and 3 white marbles, for a total of 6.

The probability that the first marble is red is:

P(red) = 3/6

The probability that the second marble is also red is:

P(red') = 2/5 (because now there are 2 red marbles and a total of 5).

The joint probability is:

P = (3/6)*(2/5) = 1/5

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The period of simple harmonic motion is T = 4.19 seconds:

For given question,

A mass weighing 16 pounds is attached to a spring whose spring constant is 36 lb/ft.

So, we have mass (m) = 16 pounds

spring constant (k) = 36 lb/ft.

Let T be the period of simple harmonic motion.

Using the formula for the period of simple harmonic motion,

⇒ T = 2π√(m/k)

⇒ T = 2 × π × √(16/36)

⇒ T = 2 × π × √(0.444)

⇒ T = 2 × π × 0.666

⇒ T = 1.333 × π

⇒ T = 4.19 seconds

Therefore, the period of simple harmonic motion is T = 4.19 seconds

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Answer:

Step-by-step explanation:

Let Kevin have x dollars. Then Latoya has x - 9 dollars and Milan has 4(x - 9) dollars.

x + (x-9) + 4(x-9) = 177

7x - 40 = 177

7x = 217

x = 31

Kevin has $31

Latoya has 31 - 9= $22

Milan has 4*24 = $96

By Pythagorean theorem we find that the length of the hypotenuse is [tex]r = \sqrt{2}\cdot l[/tex].

In the image attached we have a right triangle with two legs of same length. The hypotenuse of right triangles can be found by Pythagorean theorem, whose form is:

[tex]r = \sqrt{l^{2}+l^{2}}[/tex]

[tex]r = \sqrt{2}\cdot l[/tex], where l is the length of the legs.

By Pythagorean theorem we find that the length of the hypotenuse is [tex]r = \sqrt{2}\cdot l[/tex].

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The steps in evaluating each of the following expressions is shown below.

An expression can be defined as a mathematical equation which shows the relationship existing between two or more numerical quantities or variables.

15 - 35/7 - 2 + 3 - 4

15 - (35/7) - 2 + 3 - 4 (bracket and division)

15 - 5 - 2 + 3 - 4 (regroup)

15 + 3 - 5 - 2 - 4 (subtract and add)

18 - 11 = 7.

10 + 2(9 - 5) - 16/18

10 + (2 × 4) - 8/9 (bracket and division)

10 + 8 - 8/9 (add)

18 - 8/9 (subtract)

162/9 - 8/9 = 17 1/9 or 154/9.

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Complete Question:

Show your steps in evaluating each of the following expressions. The steps count 4 points each, the answer is 1 point.

A. 15 - 35/7 - 2 + 3 - 4

B. 10 + 2(9 - 5) - 16/18

Answer:27 < AB < 81

Step-by-step explanation:

Answer:

27 < AB < 81

Step-by-step explanation:

in a triangle the sum of any 2 sides must be larger than the third side.

that must be true for every pair of sides you pick.

simply because, if that is not fulfilled, the third side would be too long, and the other 2 sides cannot connect to the endpoints of the third side.

so,

AC + CB = 81 must be longer than AB. otherwise the triangle cannot "close".

AC + AB = 27 + AB must be longer than CB = 54.

so, AB must be longer than 27.

CB + AB = 54 + AB must be longer than AC = 27. but that is always true, as CB alone is already larger.

so only the other 2 conditions need to be true.

hence the answer.

Answer:

Step-by-step explanation:

The ys have to have the same value. That allows you to equate the right side of each y to each other.

-x^2 + 4 = 2x + 1                             Subtract the right side from the left side.

-x^2 + 4 - 2x - 1 = 2x-2x +1 - 1        Combine

-x^2 - 2x + 3 = 0                            Multiply both sides by - 1

-1(-x^2 -  2x + 3) = 0*-1                    Remove the brackets

x^2 + 2x - 3                                   Factor

(x - 1)(x + 3 )

x - 1 = 0

x =   1

x + 3 = 0

x = - 3

So the line goes through x = 1 or x = - 3

x = 1

y = 2x + 1

y = 2(1) + 1

y = 3

x = - 3

y = 2(-3) + 1

y = - 6 + 1

y = - 5

Does the graph confirm this? See below.

red: y = -x^2 + 4

green: y = 2x + 1

Yes the graph is in agreement.