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stepladder [879]

2 years ago

14

10x - 4 = 2 ( ? ) is it a) 5x - 4 b) 5x - 2 c) 10x - 4 d ) 10x - 8

1 answer:

attashe74 [19]2 years ago

3 0

We have that

<span>10x - 4 = 2 ( ? )
</span>I proceed to replace the missing value with the given expression

case a-------------> <span>5x - 4
</span><span>then
</span>10x - 4 = 2 (5x-4 )--------> 10x - 4 = 10x-8--------> is not solution

case b-------------> 5x - 2
then
10x - 4 = 2 (5x-2 )--------> 10x - 4 = 10x-4--------> is solution

case c-------------> <span>10x - 4
</span>then
10x - 4 = 2 (10x - 4 )--------> 10x - 4 = 20x-8--------> is not solution

case d-------------> <span>10x - 8
</span>then
10x - 4 = 2 (10x - 8 )--------> 10x - 4 = 20x-16--------> is not solution

the answer is the option b) 5x - 2

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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

$\Rightarrow y=\sqrt{x^2+100}$

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

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

$=\frac{24\times (-13)}{\sqrt{676}}$

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

= -12 m/s

Negative sign denotes the distance between the car and the person decrease.

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.

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