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Setler [38]
3 years ago
8

Jane left the school and started to bike along the road at a rate of 12 mph. Her friend Sally left the school 10 minutes after J

ane, biking on the same road at a rate of 15 mph. How long will it take Sally to catch up with Jane?
Mathematics
1 answer:
Artyom0805 [142]3 years ago
3 0

Answer:

8 minutes if Jane was assumed to be stationary

Step-by-step explanation:

The question is on relative speed

First find the distance covered by Jane when Sally left school

Speed=Distance/Time ⇒⇒ Distance=Time×Speed

Time=10minute=10/60 hrs

Jane's speed= 12mph

Distance covered by Jane when Sally left school was= 12 ×10/60 = 2miles

So, when Sally left school, Jane was 2 miles away. To find the time Sally requires to catch up with Jane;

Time=Distance/speed

Time of meeting =2/15 hrs ⇒⇒ 2/15 × 60 =8minutes

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Solve 4x-5/5=3<br> thankyou
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x = 1

Step-by-step explanation:

4x - 5/5 = 3

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add 1 to each side of the equation:

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A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per
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Answer:

The total revenue is TR=580x-10x^2.

The marginal revenue is MR=580-20x.

The fixed cost is $900.

The marginal cost function is MC=50x+300.

Step-by-step explanation:

The Total Revenue (TR) received from the sale of x goods at price p is given by

                                                         TR=p\cdot x

The Marginal Revenue (MR) is the derivative of total revenue with respect to demand and is given by

                                                       MR=\frac{d(TR)}{dx}

From the information given we know that the price they can sell cakes is given by the function p=580-10x, where x is the number of cakes sold per day.

So, the total revenue is

TR=(580-10x)\cdot x\\TR=580x-10x^2

And the marginal revenue is

MR=\frac{d}{dx}(580x-10x^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\MR=\frac{d}{dx}\left(580x\right)-\frac{d}{dx}\left(10x^2\right)\\\\MR=580-20x

The Fixed Cost (FC) is the amount of money you have to spend regardless of how many items you produce.

The Marginal Cost (MC) function is the derivative of the cost function and is given by

                                                   MC=\frac{d(TC)}{dx}

We know that the total cost function of the company is given by C=(30+5x)^2, which it is equal to

\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\a=30,\:\:b=5x\\\\\left(30+5x\right)^2=30^2+2\cdot \:30\cdot \:5x+\left(5x\right)^2=25x^2+300x+900\\\\C=25x^2+300x+900

From the total cost function and applying the definition of fixed cost, the fixed cost is $900.

And the marginal cost function is

MC=\frac{d}{\:dx}\left(25x^2+300x+900\right)\\\\MC=\frac{d}{dx}\left(25x^2\right)+\frac{d}{dx}\left(300x\right)+\frac{d}{dx}\left(900\right)\\\\MC=50x+300+0=50x+300

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A hot tub that holds 300 gallons of water drains at a rate of 8 gallons write an equation that represents how many gallons of wa
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A hot tub that holds 300 gallons of water drains at a rate of 8 gallons.

Let x represent the number of minutes for which the hot tub has drained water.

If the hot tub drains 8 gallons of water per minute, it means that in x minutes, the number of gallons of water that the hot tub would have drained is 8x

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