Patsy has cheerleading practice every fourth day. She wants to be in the school play but they have practice every sixth day

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

Mi padre compró un radio por cierta suma de dinero, un televisor que costó 10 veces más que el radio y un reproductor cuyo preci

Maru [420]

Answer:

For radio = $40.43

Television = $444.73

Player = $364.73

Step-by-step explanation:

The computation of the each device cost is shown below:

let us assume the following things

radio be x

television x + 10x

player x + 10x - $80

Now the equation is

x + x + 10x + x + 10x - $80 = $850

3x + 20x - $80 = $850

23x = $930

x = $40.43

For radio = $40.43

Television = $40.43 + 10(40.43)

= $40.43 + $404.3

= $444.73

and, the player would be

= $444.73 - $80

= $364.73

7 0

3 years ago

Complete the sentence.<br> In the formula C=2r. C stands for

AleksAgata [21]

Answer:

Circumference

3 0

3 years ago

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I NEED HELP: So this question came on a quiz I'm taking and the answer I got was $1,723.45 but it says its incorrect can someone

Olin [163]

Answer: the answer is right, try putting a $ in front of it, sometimes those programs mess up if you aren't specific

5 0

3 years ago

An electronics store makes a profit of $72 for every television sold and $90 for every computer sold. The manager’s target is to

exis [7]

the complete question in the attached figure

we have

$72 ------------------------------------ > for every television sold

$90 ------------------------------------ > for every computer sold.

let

x--------------------- > numbers of television sold

y--------------------- > numbers of computer sold

then

72x+90y >= $360 ----------- >72x/72+90y/72 >= $360 /72---- >x+1.25y >= $5

y >= (5-x)/1.25--------------see the graph in attached figure

case A---------- > (5,2) (3,3) (1,4)

72x+90y --------- > 72*5+90*2=540 >= 360----- > is solution

72x+90y --------- > 72*3+90*3=486 >= 360----- > is solution

72x+90y --------- > 72*1+90*4=432 >= 360----- > is solution

case B------------ > (4,0) (2,2) (1,1)

72x+90y --------- > 72*4+90*0=288 < 360----- > is not solution

72x+90y --------- > 72*2+90*2=324 < 360----- > is not solution

72x+90y --------- > 72*1+90*1=162 < 360----- > is not solution

case C------------ > (3,1) (2,2) (1,0)

72x+90y --------- > 72*3+90*1=306 < 360----- > is not solution

72x+90y --------- > 72*2+90*2=324 < 360----- > is not solution

72x+90y --------- > 72*1+90*0=72 < 360----- > is not solution

case D------------ > (4,0) (3,3) (1,4)

72x+90y --------- > 72*4+90*0=288 < 360----- > is not solution

72x+90y --------- > 72*3+90*3=486 >= 360----- > is solution

72x+90y --------- > 72*1+90*4=432 >= 360----- > is solution

<span>the answer is case A </span>

4 0

4 years ago

Read 2 more answers