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3 years ago

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A bridge is built in the shape of a semielliptical arch. The bridge has a span of 60 feet and a maximum height of 10 feet. Choos

e a suitable rectangular coordinate system and find the height of the arch at a distance of 10 feet from the center.

1 answer:

Dennis_Churaev [7]3 years ago

6 0

Is there a way you can send me a picture of what your copying your answer from ?

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Work out the circumference of a circle with diameter 1.8

dalvyx [7]

5.66 (3 significant figures)

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3 years ago

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What is the antiderivative of 3x/((x-1)^2)

Maslowich

Answer:

$\int \:3\cdot \frac{x}{\left(x-1\right)^2}dx=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C$

Step-by-step explanation:

Given

$\int \:\:3\cdot \frac{x}{\left(x-1\right)^2}dx$

$\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx$

$=3\cdot \int \frac{x}{\left(x-1\right)^2}dx$

$\mathrm{Apply\:u-substitution:}\:u=x-1$

$=3\cdot \int \frac{u+1}{u^2}du$

$\mathrm{Expand}\:\frac{u+1}{u^2}:\quad \frac{1}{u}+\frac{1}{u^2}$

$=3\cdot \int \frac{1}{u}+\frac{1}{u^2}du$

$\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx$

$=3\left(\int \frac{1}{u}du+\int \frac{1}{u^2}du\right)$

as

$\int \frac{1}{u}du=\ln \left|u\right|$ ∵ $\mathrm{Use\:the\:common\:integral}:\quad \int \frac{1}{u}du=\ln \left(\left|u\right|\right)$

$\int \frac{1}{u^2}du=-\frac{1}{u}$ ∵ $\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1$

so

$=3\left(\ln \left|u\right|-\frac{1}{u}\right)$

$\mathrm{Substitute\:back}\:u=x-1$

$=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)$

$\mathrm{Add\:a\:constant\:to\:the\:solution}$

$=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C$

Therefore,

$\int \:3\cdot \frac{x}{\left(x-1\right)^2}dx=3\left(\ln \left|x-1\right|-\frac{1}{x-1}\right)+C$

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3 years ago

a man has a garden measuring 84 metre by 56 he want to divide them equally into the minimum number of square plot what is the le

maw [93]

Answer:

6

Step-by-step explanation:

84 = 3 x 28

56 = 2 x 28

Minimum number of square plot, each square is 28 x 28

the number is 3 x 2 = 6

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2 years ago

Tom had $56. He bought a soda for $2 and 2 cookies for $3. Which expression correctly shows the total money Tom has left? A. $56

deff fn [24]

C ($56) - ($2) - ($3)

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3 years ago

A Ferris wheel has a diameter of 140 ft. There are 40 cars for riders, and they are placed at even intervals around the Ferris w

max2010maxim [7]

The circumference of a Ferris wheel:
C = 2 r π
C = 2 · 70 · 3.14
C = 439.6 ft
439.6 : 40 = 10.99 ≈ 11 ft
Answer:
The cars are placed approximately 11 ft apart.

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3 years ago

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