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Cerrena [4.2K]
3 years ago
7

shonna skateboards for some number of minutes on Monday, On Tuesday, dshe skateboards for twice as many minutes as she did on mo

nday, and on Wednesday, she skateboards for half the sum of minutes from Monday and Tuesday. Altogether , she skateboard for a total of three hours. how many minutes did she skateboard each day?
Mathematics
1 answer:
Paha777 [63]3 years ago
8 0

Shonna skateboarded 40 minutes on Monday, 80 minutes on Tuesday and 60 minutes on Wednesday.

Step-by-step explanation:

Given,

Total time spent on skate boarding = 3 hours

1 hour = 60 minutes

3 hours = 60*3 = 180 minutes

Time spent on skate boarding = 180 minutes

Let,

Time spent on skate boarding on Monday = x

Time spent on Tuesday = 2x

Time spent on Wednesday = \frac{x+2x}{2} = \frac{3x}{2}

According to given statement;

x+2x+\frac{3}{2}=180

Taking LCM on left side;

\frac{2x+4x+3x}{2}=180\\\frac{9x}{2}=180

Multiplying both sides by 2

2*\frac{9x}{2}=180*2\\9x=360

Dividing both sides by 9

\frac{9x}{9}=\frac{360}{9}\\x=40

Time spent on Monday = x = 40 minutes

Time spent on Tuesday = 2x = 2(40) = 80 minutes

Time spent on Wednesday = \frac{3x}{2} = \frac{3(40)}{2} =\frac{120}{2} = 60\ minutes

Shonna skateboarded 40 minutes on Monday, 80 minutes on Tuesday and 60 minutes on Wednesday.

Keywords: linear equation, variable

Learn more about variables at:

  • brainly.com/question/8301701
  • brainly.com/question/8358304

#LearnwithBrainly

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Hope this helps :)

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Chase has 3 gallons of a solution that is 30% antifeeze that he wants to use to winterize his car. How much pure antifreeze shou
makvit [3.9K]

Let  x gallons be the amount of pure antifreeze that should be added to the 30% solution to produce a solution that is 65% antifreeze. Then the total amount of antifreeze solution will be x+3 gallons.

There are 30% of pure antifreeze in 3 gallons of solution, then

3 gallons - 100%,

a gallons - 30%,

where a gallons is the amount of pure antifreeze in given solution.

Mathematically,

\dfrac{3}{a}=\dfrac{100}{30},\\ \\a=\dfrac{3\cdot 30}{100}=0.9\ gallons.

Now in new solution there will be x+0.9 gallons of pure antefreeze.

x+3 gallons - 100%,

x+0.9 - 65%

or

\dfrac{x+3}{x+0.9}=\dfrac{100}{65},\\ \\65(x+3)=100(x+0.9),\\ \\65x+195=100x+90,\\ \\35x=105,\\ \\x=3\ gallons.

Answer: he should add 3 gallons of pure antifreeze.

8 0
3 years ago
Can someone help please
myrzilka [38]
<h3>Answer:   15x^(7/3) - 8x^(7/4) + x + 9000</h3>

=========================================================

Explanation:

If you know the cost function C(x), to find the marginal cost, we apply the derivative.

Marginal cost = derivative of cost function

Marginal cost = C ' (x)

Since we're given the marginal cost, we'll apply the antiderivative (aka integral) to figure out what C(x) is. This reverses the process described above.

\text{Cost} = \text{antiderivative of marginal cost}\\\\\displaystyle C(x) = \int \left(35x^{4/3} - 14x^{3/4} + 1\right)dx\\\\

C(x) = \frac{1}{1+4/3}*35x^{4/3+1} - \frac{1}{1+3/4}*14x^{3/4+1} + x + D\\\\C(x) = \frac{1}{7/3}*35x^{7/3} - \frac{1}{7/4}*14x^{7/4} + x + D\\\\C(x) = \frac{3}{7}*35x^{7/3} - \frac{4}{7}*14x^{7/4} + x + D\\\\C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\

D represents a fixed constant. I would have used C as the constant of integration, but it's already taken by the cost function C(x).

To determine the value of D, we plug in x = 0 and C(x) = 9000. This is because we're told the fixed costs are $9000. This means that when x = 0 units are made, you still have $9000 in costs to pay. This is the initial value. You'll find that all of this leads to D = 9000 because everything else zeros out.

Therefore, we go from this

C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\

to this

C(x) = 15x^{7/3} - 8x^{7/4} + x + 9000\\\\

which is the final answer.

3 0
2 years ago
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