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4 years ago

13

You purchase a new guitar and take out a loan for $450. You have 18 equal monthly payments of $28 each. What is the simple inter

est rate for the loan? Round to the nearest tenth of a percent, if necessary.

1 answer:

Daniel [21]4 years ago

8 0

18*28/450=1.12
(1.12-1)*100=12%
Simple interest rate of the loan is 12%

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A person stands 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 meters

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Answer:

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

Step-by-step explanation:

Given that,

A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.

From Pythagorean Theorem,

(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+

Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.

∴y²= x²+10²

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Differentiating with respect to t

$\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}$

$\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}$

Since the car driving towards the intersection at 13 m/s.

so, $\frac{dx}{dt}=-13$

$\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)$

Now

$\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)$

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$=\frac{24\times (-13)}{26}$

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