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3 years ago

7

Decide if each is a measurement of length, area, volume, or weight. How many gallons of gas in a gas tank (would this be weight

or volume?)

1 answer:

patriot [66]3 years ago

5 0

Answer:

Volume

Step-by-step explanation:

This would be volume as gallons is the measurement of how much liquid there is in a container.

This would be volume.

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Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

torisob [31]

Answer:

32.66 units

Step-by-step explanation:

We are given that

$y=6x^2+14x$

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

$\frac{dy}{dx}=12x+14$

We know that length of curve

$s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx$

We have a=-2 and b=1

Using the formula

Length of curve= $s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx$

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

$dt=12dx$

$dx=\frac{1}{12}dt$

Length of curve= $s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt$

We know that

$\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C$

By using the formula

Length of curve= $s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}$

Length of curve= $s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})$

Length of curve= $s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})$

Length of curve= $s=32.66$

5 0

3 years ago

At a sale this week, a sofa is being sold for $527. This is a 32% discount from the original price. What is the original price?

sashaice [31]

The answer is: $695.64

527 times 0.32 then add that to 527

4 0

2 years ago

8 is what percent of 24?

Irina18 [472]

Answer:

1, 33.3

2, 81.9

3, 240

4, the farmer sold 33.3 of his crops

5, 750 students are enrolled.

5 0

3 years ago

Read 2 more answers

A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)? Determine t

Greeley [361]

Answer:

The answer is 660.4 millimeters in diameter.

Step-by-step explanation:

The wheel is 26 inches in diameter. An inch is 25.4 millimeters. 26 * 25.4 = 660.4

3 1

3 years ago

PLZ HELP WILL MAKR BRAINLIEST

lions [1.4K]

Answer:

It will be 0.2

Step-by-step explanation:

Hope this Helped

5 0

3 years ago