The value of a car t years after it is purchased is given by the decreasing function V, where V(t) is measured in dollars. The r

Response:

B. 255 m

Detailed breakdown:

utilize similar triangles

L / 60 = 85 / 20

L = (85 * 60) / 20

L = 255 m

Answer:

Part 1) The equation is

Part 2) When x=40 m, the area of the schoolyard is A=2,800 m^2

Part 3) The valid domain consists of all real numbers exceeding zero and below 75 meters

Step-by-step explanation:

Part 1) Formulate an expression for A(x)

Let

x -----> the length of the rectangular school yard

y ---> the width of the rectangular school yard

It is known that

The perimeter for the fencing (taking the school wall as one side) is

thus

-----> this is equation A

The area of the rectangular school yard is

----> this is equation B

Substituting equation A into equation B yields

Change to function notation

Part 2) What is the area when x=40?

With x equal to 40 m

substitute the value into the expression from Part 1 to determine A

Part 3) What would be a suitable domain for A(x) in this scenario?

We understand that

A signifies the area of the rectangular school yard

x characterizes the length of the rectangular school yard

It follows that

This forms a vertical parabola opening downwards

The vertex indicates a maximum point

The x-coordinate of the vertex corresponds to the length that maximizes the area

The y-coordinate of the vertex denotes the maximum area

The vertex corresponds to (37.5, 2812.5)

Refer to the accompanying figure

Consequently,

The peak area achieved is 2,812.5 m^2

The x-intercepts are located at x=0 m and x=75 m

The domain for A is the range -----> (0, 75)

All real numbers greater than zero and less than 75 meters

Answer:

(value - mean)/standard deviation.

Now substitute 78 for the value, 84.5 for the mean, and 3.1 for the standard deviation.

Step-by-step explanation:

Answer:

The rotation angle measures 2.11 °

Step-by-step explanation:

Stated as follows:

The radius of the circular path = r = 18 feet

The distance rolled by the wheel = l = 38 feet

Let us denote the angle of rotation as Ф

Now, according to the problem:

∵ the length of an arc at the center corresponds to an angle Ф

Thus,

distance rolled by the wheel = π × radius ×

As 180° represents π radians

And π approximates to 3.14

Thus, distance rolled by the wheel = 180 °× radius ×

That is l = r × Ф

So, Ф =

Consequently, Ф =

Therefore, Ф = 2.11 °

Thus, the rotation angle is Ф = 2.11 °

Hence, the rotation angle is 2.11 ° Answer