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2 years ago

Solve this system of equations using substitution:

Mathematics

1 answer:

yanalaym [24]2 years ago

4 0

I’m thinking your r in the first equation is actually an x.

X + 2(2x -4) =10

X +4x -8 =10

5x = 18

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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

In-s [12.5K]

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.

8 0

2 years ago

Write out the following proportions in words. a. 7 :28 = 2 : 8 b. 3⁄1 = 18⁄6 c. 9 : 72 = 2 : 16 d. 81⁄9 = 45⁄5

Lerok [7]

1) Proportion a.

7 : 28 = 2 : 8

That means that the ratio 7 / 28 is equal to the ratio 2 : 8.

You can verify the equality by simplifying to the simplest form:

 7 : 28 = 1 / 4 simplest form
 2 : 8 = 1 / 4 simplest form, then the proportion is right.

In words that is 7 is to 28 as 1 is to 4 ← answer

2) Proportion b.. 3⁄1 = 18⁄6


In words: 3 is to q as 18 is to 6 ← answer


You can verify the proportion by simplifiying the second fraction:


 18 / 6 = [18 / 6] / [ 6 / 6] = 3 / 1


3) Proportion c. 9 : 72 = 2 : 16


In words: 9 is to 72 as 2 is to 16 ← answer


Proove the proportion:


 9 / 72 = 1 / 8


 2 / 16 = 1 / 8


4) Proportion d. 81⁄9 = 45⁄5

In words: 81 is to 9 as 45 is to 5 ← answer

Proove it:
 81 / 9 = 9
 45 / 9 = 9

8 0

3 years ago

Read 2 more answers

I NEED help ASAP!!!!!!!

horsena [70]

Step-by-step explanation:

Step 1: Plot the points

L(1,2)

M(0,-1)

J(1,-2)

K(2,-1)

Step 2: Multiply each point by 5.

and record thise points so we have

L(5,10)

M(0,-5)

J(5,-10)

K(10,-5)

Step 3: Plot those points.

3 0

2 years ago

Read 2 more answers

Twenty percent of what number is 9?

vampirchik [111]

Answer:

Step-by-step explanation:

There are 100%. When divided by 5 you get twenty percent. 9 times 5 equals 45.

3 0

3 years ago

Help pls it’s easy I’m just slow lol

IgorLugansk [536]

Answer:

12.65

Step-by-step explanation:

4 0

2 years ago