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2 years ago

12

How many inches are in a marathon (26.2 miles)?

1 answer:

storchak [24]2 years ago

7 0

Answer:

1660032

Step-by-step explanation:

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Evaluate the line integral, where C is the given curve. (x + 4y) dx + x2 dy, C C consists of line segments from (0, 0) to (4, 1)

zubka84 [21]

Parameterize the line segments (call them $C_1$ and $C_2$ , respectively, by

$\vec r_1(t)=(1-t)(0,0)+t(4,1)=(4t,t)$

$\vec r_2(t)=(1-t)(4,1)+t(5,0)=(4+t,1-t)$

both with $0\le t\le1$ . Then

$\displaystyle\int_C(x+4y)\,\mathrm dx+x^2\,\mathrm dy$

$=\displaystyle\int_0^1\bigg((4t+4t)(4)+(4t)^2(1)\bigg)\,\mathrm dt+\int_0^1\bigg((4+t+4(1-t))(1)+(4+t)^2(-1)\bigg)\,\mathrm dt$

$=\displaystyle\int_0^115t^2+21t-8\,\mathrm dt=\boxed{\frac{15}2}$

6 0

2 years ago

A dairy wishes to mix together 1,000 pints of milk that contains 8% butterfat.If the mixture is to be made from milk containing

3241004551 [841]

Answer:

<u>800 pints</u> of 5% butterfat and <u>200 pints</u> of 20% butterfat is needed.

Step-by-step explanation:

Given:

A dairy wishes to mix together 1,000 pints of milk that contains 8% butterfat.

If the mixture is to be made from milk containing 5% butterfat, and cream

containing 20% butterfat.

Now, to find the pints of each is needed.

Let the pints of 5% butterfat be $x.$

And the pints of 20% butterfat be $y.$

<em>So, the total pints of milk:</em>

$x+y=1000$

$x=1000-y$ ......(1)

<em>As, given:</em>

<em>1,000 pints of milk that contains 8% butterfat.</em>

<em>The mixture of milk containing 5% butterfat, and cream containing 20% butterfat.</em>

According to question:

$5(x)+20(y)=8(1000)$

$5x+20y=8000$

Substituting the value of $x$ from equation (1):

$5(1000-y)+20y=8000$

$5000-5y+20y=8000$

$5000+15y=8000$

<em>Subtracting both sides by 5000 we get:</em>

$15y=3000$

<em>Dividing both sides by 15 we get:</em>

$y=200.$

<em>The pints of 20% butterfat = 200 pints.</em>

Now, to get the pints of 5% butterfat we put the value of $y$ in equation (1):

$x=1000-y$

$x=1000-200$

$x=800.$

<em>The pints of 5% butterfat = 800 pints.</em>

Therefore, 800 pints of 5% butterfat and 200 pints of 20% butterfat is needed.

8 0

2 years ago

What is x to the power of two plus 3x plus 5

AlexFokin [52]

Answer:

4x+5

Step-by-step explanation:

4 0

3 years ago

What is all the answers to a 2 × problem

nalin [4]

Double the number like 2 x5 would be 5+5

8 0

3 years ago

Read 2 more answers

Anyone know how to do this?

Lera25 [3.4K]

Answer:

Part A) 25

Part B) 225

Step-by-step explanation:

Part A

The slope of the graph gives us the mile per gallon of the car.

Recall that the slope of the graph is rise over run.

$m = \frac{200}{8} = 25$

Therefore car gets 25 miles per gallon

Part B) Since we know the slope of the direct variation line, we substitute into y=kx to get:

$y = 25x$

To find the number of miles the car travels using 9 gallons, we substitute x=9 to get:

$y = 25 \times 9$

This gives us 225 miles

8 0

2 years ago