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3 years ago

What is true of an adjustable rate mortgage?

Mathematics

1 answer:

Varvara68 [4.7K]3 years ago

5 0

Answer: B. the interest rate may change depending on the condition of the economy.

Step-by-step explanation:

By definition, in a adjustable-rate mortgage (which can be identified as ARM), the interest rates can fluctuates, this means that it can change periodically.

Therefore, the interest rate is fixed for a period of time and then it varies based on the index it is tied to. This index is set by market situation.

Then, keeping this on mind, the correct answer is the option B, which is: The interest rate may change depending on the condition of the economy.

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Find the length and width of a rectangle that has the given area and a minimum perimeter. Area: 162 square feet

Gnom [1K]

Answer:

The width and length of rectangle is 12.728 m

Step-by-step explanation:

Let the length of the rectangle = L

let the width of the rectangle = W

The subjective function is given by;

F(p) = 2(L + W)

F = 2L + 2W

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A = LW

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L = 162 / W

Substitute in the value of L into subjective function;

$f = 2l + 2w\\\\f = 2(\frac{162}{w} )+2w\\\\f = \frac{324}{w} + 2w\\\\\frac{df}{dw} = \frac{-324}{w^2} +2\\\\$

Take the second derivative of the function, to check if it will given a minimum perimeter

$\frac{d^2f}{dw^2}= \frac{648}{w^3} \\\\Thus, \frac{d^2f}{dw^2}>0, \ since,\frac{648}{w^3} >0 \ (minimum \ function \ verified)$

Determine the critical points of the first derivative;

df/dw = 0

$\frac{-324}{w^2} +2 = 0\\\\-324 + 2w^2=0\\\\2w^2 = 324\\\\w^2 = \frac{324}{2} \\\\w^2 = 162\\\\w= \sqrt{162}\\\\w = 12.728 \ m$

L = 162 / 12.728

L = 12.728 m

Therefore, the width and length of rectangle is 12.728 m

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Step-by-step explanation:

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