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3 years ago

The circumference of a circle is 11 pi ft. find its diameter, in feet

Mathematics

1 answer:

nexus9112 [7]3 years ago

7 0

Answer:

11 feet

Step-by-step explanation:

Use the circumference formula, C = $\pi$ d

Plug in 11 $\pi$ as C, and solve for d:

C = $\pi$ d

11 $\pi$ = $\pi$ d

11 = d

So, the diameter is 11 feet

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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= $s=32.66$

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Answer:

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Arada [10]

Answer:

3,500 km

Step-by-step explanation:

Assuming that 1:500000 is meters you would have to convert to kilometers.

7 * 500000 / 1000 = 3500

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scZoUnD [109]

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3 years ago

a certain triangle has a perimeter of 3067 mi. the shortest side measures 71 mi less than the middle side and the longest side m

UkoKoshka [18]

Answer:

The measure of the shortest side is 851 miles

Step-by-step explanation:

Let

x ----> the measure of the shortest side

y ---> the measure of the middle side

z ---> the measure of the longest side

we know that