An initial investment of $60.00 increases in value by 15% each year. Which of the following statements are true? Select all that apply.Select answers;
This function can be represented by the quadratic equation f(x)=0.15(x+60)^2
This situation can be represented by the exponential function f(x)=60 x 1.15^x
This function has no x-intercept
After 4 years the value of the investment will be $120.00
After 6 years the value of the investment will be $653.00
After 7.86 years the value of the investment will be 3 times the initial value
After 8 years the value of the investment will be $184.00

9514 1404 393

Answer:

  area = 50π ≈ 157.08 square units

Step-by-step explanation:

The parameter t is the angle in the polar form equation of the curve. The square of the radius is the sum of squares of x and y. The area of a differential sector is ...

  dA = (1/2)r²·dt

The figure has 6-fold symmetry, so we only need to find the area of the first lobe of the curve. The integral is shown in the attachment, which evaluates it numerically.

The epicycloid encloses an area of 50π square units.

Final answer:

To calculate the area enclosed by an epicycloid curve defined by given parametric equations, use the area formula for a plane curve and integrate from 0 to 2π. Calculations involve derivatives and integration.

Explanation:

The area that the epicycloid encloses can be calculated using the formula for the area of a plane curve that is parameterized by the equations you provided: x = 7 cos t − cos 7t, y = 7 sin t − sin 7t. This area can be computed by integrating the expression x dy - y dx from 0 to 2π. In the case of these parametric equations, dx and dy are the derivatives of x and y with respect to t (the parameter), which can be calculated as: dx/dt = -7 sin t + 7 sin 7t, dy/dt = 7 cos t - 7 cos 7t. After calculating these derivatives, substitute them into the aforementioned integral, and perform the integration. The result should be the area that the epicycloid encloses.

Learn more about Calculation of the area of the epicycloid here:

brainly.com/question/35361017

#SPJ3

Answer:

$525

Step-by-step explanation:

Edgar Anderson earns in a week = $300

He also earns commission on the sales he makes after his first $1,000 = 15%

Mr. Anderson's sales for one week are = $2,500

His commission is on his sale = 2,500 - 1,000 = 1,500

He earns commission = 15% of 1,500

                                     = 0.15 × 1,500

                                     = $225

His gross pay for that week = $225 + $300 = $525

Mr. Anderson's gross pay for that week is $525.

The volume generated by rotating the region in the first quadrant bounded by y = ex and the x-axis from x = 0 to x = ln(3) about the y-axis is (πln(3)3)/3.

To find the volume generated by rotating the region in the first quadrant bounded by y = ex and the x-axis from x = 0 to x = ln(3) about the y-axis, we can use the disk method. The disk method involves slicing the region into thin disks and adding up their volumes.

The volume of each disk is πr2h, where r is the radius of the disk and h is the thickness of the disk. In this case, the radius of each disk is x and the thickness is dx.

So, the volume of the region is:

V = ∫0ln(3)πx2dx

We can use the power rule for integration to solve this integral:

V = π∫0ln(3)x2dx = π[(x3)/3]0ln(3) = π[(ln(3)3)/3 - (03)/3] = (πln(3)3)/3

Therefore, the volume generated by rotating the region in the first quadrant bounded by y = ex and the x-axis from x = 0 to x = ln(3) about the y-axis is (πln(3)3)/3. This is the exact form of the volume.

To know more about disk method refer here:

brainly.com/question/28184352#

#SPJ11

The distance an object falls in 4 seconds is 256 feet.

Given,

The expression 16t² models the distance in feet that an object falls during t seconds after being dropped.

We need to find out what distance will an object fall in 4 seconds.

What is a function?

A function has an input and an output.

Example:

f(x) = x + 1

x = 1

f(1) = 1 + 1 = 2

Input = 1

Output = 2

Find the expression that describes the distance at t seconds.

= 16t²

Find the distance at t = 4.

We have,

= 16t²

= 16 x 4²

= 16 x 16

= 256

Thus the distance an object fall in 4 seconds is 256 feet.

Learn more about finding distance at 2 seconds from a given expression here:

brainly.com/question/11260574

#SPJ2

1. it fell in 2 seconds so plug the "t" with 2

2. 16*4²  ⇒   4² = 16

3. 16*16 = 256