Arthur drops a ball from a height of 81 feet above the ground. Its height, h, is given by the equation h = –16t2 + 81, where t i

Answer:

Step-by-step explanation:

Denote the rectangular prism's volume as VR and the volume of the right triangular prism as VT. Given that the rectangular prism's volume exceeds that of the triangular prism by 32 cubic feet, we establish that VR = 32 + VT.

Calculating VR: VR = length * width * height = 6*x*3.

This simplifies to VR = 18x ft³.

For the triangular prism, VT can be calculated as Length * width * Height / 2, yielding VT = (7 * x * 4) / 2.

Thus, VT = 28x / 2, which simplifies to VT = 14x ft³.

Equating VR to 32 + VT allows the substitution: 18x = 32 + (14x).

Now, simplify the equation:

Combine like terms: 18x - 14x = 32.

This results in 4x = 32.

Dividing both sides by 4:

x = 8.

The volume for the rectangular prism comes to 18x, which equals 18*8.

The volume of the rectangular prism calculates to 144 ft³.

The volume for the right triangular prism calculates to 14x, which equals 14*8.

The volume of the right triangular prism calculates to 112 ft³.

2.8y + 6 + 0.2y = 5y – 14

Start by simplifying the left side:

3y + 6 = 5y - 14

Next, deduct 3y from both sides:

6 = 2y - 14

Add 14 to both sides:

2y = 20

Now, divide by 2:

y = 20 / 2

y = 10

= -4/2 Step-by-step explanation: xp=x1 +k (x2-x1) = -3+1/3 (2- -3) = -3 + 1/3  (5/1) = -3 + 5/3 = -9/3 +5/3 = -4/2 Sorry, it doesn't look the best:)

Response:

C. 50.24 inches

Detailed explanation:

The area of a circle can be expressed with . To determine the circumference, knowing the radius is essential; thereafter, we can substitute that value into the circumference formula . Hence, to ascertain the radius, we observe that:

As a result, the circumference is:

, which approximates the choice C) 50.24 inches.

Hope this was beneficial!:)