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3 years ago

F(x) = x4/5(x − 6)2 find the critical numbers of the function

1 answer:

5 0

You can find the critical numbers by finding the derivative of the function and solving for 0.

F(x) = x(4/5)(x-6)(2) = x(8/5)(x-6) = (8/5)(x^2 - 6x)

Taking the derivative:
F'(x) = (8/5)(2x - 6)
F'(x) = 0 at x = 3,

critical number = 3

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A figure is composed of a rectangle and a right triangle. What is the area of the figure?

strojnjashka [21]

QUESTION 1

The figure is a tra-pezoid.

The area of a trapezoid is given by the formula;

$A=\frac{1}{2}(Sum\:of\:parallel\:sides)\times h$

We substitute the values to obtain;

$Area=\frac{1}{2}(13.2cm+8.4cm)\times 6cm$

$Area=\frac{1}{2}(21.6cm)\times 6cm$

$Area=64.8cm^2$

QUESTION 2

The approximate length of the ribbon is equal to the circumference of the circular table cloth.

We can find this by using the formula for calculating the circumference of a circle.

$C=2\pi r$

where $r=3.5ft$ is the radius of the circular table cloth.

We substitute this value and $\pi=3.14$ into the formula to get;

$C=2(3.14)(3.5)ft$

$C=21.98ft$

The approximate length of the ribbon is 22.0ft to the nearest tenth.

QUESTION 3

Type of quadrilateral:Rectangle

Explanation: A rectangle has 4 angles that are right angles.

The two pairs of opposite sides of a rectangle are also congruent.

QUESTION 4.

The circumference of a semi circle is calculated using the formula;

$C=\pi r$

where $r=12.5cm$ is the radius of the semicircle.

$C=3.14\times 12.5cm$

$C=39.25cm$

QUESTION 5

The area of the entire figure is the area of the semicircle plus the area of the isosceles triangle.

$Area=\frac{1}{2}\pi r^2+\frac{1}{2}bh$

$Area=\frac{1}{2}\times3.14\times12.5^2+\frac{1}{2}\times25\times 24$

$Area=345.3125+300$

$Area=645.3125cm^2$

$Area\approx645cm^2$

QUESTION 6

The area of the parallelogram is given by the formula;

$A=bh$

From the diagram, $b=y\:in.,h=3in.$ .

Given, A=23.7 inches squared.

We substitute the values to obtain;

$23.7=3y$

$y=\frac{23.7}{3}$

$y=7.9in.$

QUESTION 7

The area of a rectangle is given by the formula;

$Area=l\times b$

The area of the bigger rectangle $=9\times15=135in^2$

The area of the smaller rectangle $=8\times 13=104in^2$

The area of the shaded region $=135-104=31in^2$

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3 years ago

A water sprinkler has a range of 5 meters as shown. The jet of water from the sprinkler sweeps out at an angle of 85° as the noz

telo118 [61]

I found the image that accompanied this problem.
We need to solve for the area of the sector.

A = n/360 * π * r²
A = 85/360 * 3.14 * 5²
A = 0.2361 * 3.14 * 25
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Answer is C. 18.5 square meters.

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3 years ago

Read 2 more answers

I need help with part b and c

Vikki [24]

I am not sure about b cut I think C is 10

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3 years ago

Given the parent function f(x)=x^3 calculate f(-3) and f(3)

777dan777 [17]

Answer: f(-3) = -27 & f(3) = 27

Step-by-step explanation:

(-3)^3

-27

(3)^3

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3 years ago

What are the coordinates of the foci of the conic section shown below?

Naddik [55]

Answer:

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3 years ago