Hannah G.

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Geometry

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Question:

You have 162 square feet of grass that you must plant in a rectangular garden. If the length of the garden is twice the width, how much fencing do you need to create a perimeter around the grass?

Hannah G.

Answer:

In order to solve this problem, you must first find the values for the length and width of the garden. We known that the formula for area is length times width (A = L*W). The problem tells us that the length of the garden is twice the width. So the following formula represents the area: 162 = (x)(2x). x = 9 so the width of the garden is 9 feet and the length is 18 feet. The problem is asking for us to solve for perimeter and we know that the formula for perimeter of a rectangle is twice the width plus twice the length (P = 2L + 2W). Plug in the values you found for length and width to get the length of fence needed to surround the garden: P = 2(9) + 2(18) = 54 feet of fencing

Calculus

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Question:

A car is traveling at the following velocity: v(t) = 4t + 6. Find the position of the car at t = 2. (the car is at rest at t = 0)

Hannah G.

Answer:

We know that position is the integral of the velocity so the first step to solve this problem is to solve the integral. Using the power rule (integral of x^n is x^(n+)/(n+1)), we know that the equation for position is x(t) = 2t^2 + 6t + C. We can solve for the constant by plugging in the initial condition and we find that C = 0. Now that we have the equation, we can solve for the position at time t = 2: x(2) = 2(2)^2 + 6(2) = 20.

Algebra

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Question:

Hannah wanted to buy a blouse that cost $24, but the store was having a sale and she only paid $19.20 (excluding tax). What was the sale?

Hannah G.

Answer:

Every word problem has an unknown number. In this problem, it is the reduction in cost of the blouse do to the sale. In order to solve this problem, you must set up the following equation: 24(1-x)=19.2. Keep in mind that in order to solve this problem, you must convert the value of the sale to be a decimal number. By subtracting x from 1, you will receive the percentage of the cost of the item after the sale is considered. The answer is x = 0.2 which can be multiplied by 100 to give 20%.

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