The circumference of a circle is 37.68 inches. What is the circle's radius?<br> Use 3.14 for .

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

3 years ago

Which statement is true?

lora16 [44]

4 0

3 years ago

Read 2 more answers

Identify the sequences that have a common difference of 4

cluponka [151]

Answer:

IDK

Step-by-step explanation:

7 0

4 years ago

You plan to go snowboarding this weekend in Pennsylvania. The resort charges $15.75 per hour in addition to a $25 deposit to ren

erica [24]

Answer:

$88 in total

Step-by-step explanation:

x = number of hours

y = total cost to rent the snowboard.

$25 is already guaranteed

25 + 15.75x = y

since it is 4 hours from 8:30 a.m. to 12:30 a.m. you put 4 into x.

25+15.75(4) = y

88 = y

6 0

3 years ago

Thats the question

elixir [45]

Answer:

160 in ^2

Step-by-step explanation:

First we need to find the area of each shape and add them together

1. Triangles:

The formula for a triangle is (base x height)/2, so we can replace them as (5 * 4)/2 * 2( Because there are two triangles), so therefore the two triangles will add up to 20 inches

2. The Rectangles

<u>The Big Rectangle:</u>

The big rectangle is just <em>l x w </em> or 5 * 20 which is 100

<u>The small rectangle:</u>

To find the width of the small rectangle you have to do 20 - (5 + 5) because we are not including the triangles. 20 - (5 + 5) = 10, so that would be 10 * 4 = 40.

3.Add them together

20 + 100 + 40 = 160 inches ^2

Hope this helps!!!

4 0

3 years ago

The circumference of a circle is 37.68 inches. What is the circle's radius? Use 3.14 for ​.

The circumference of a circle is 37.68 inches. What is the circle's radius? Use 3.14 for .