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3 years ago

12

A car travels 60 miles due north then makes a turn due west. It travels 72 miles west. How far is the car from ils starting poin

t?

2 answers:

Svet_ta [14]3 years ago

7 0

Answer: the answer is 93.7 miles

Greeley [361]3 years ago

6 0

Answer:

132 miles

Step-by-step explanation:

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Find the trigonometric integral. (Use C for the constant of integration.)

Olin [163]

Suppose we let $u=\sin\theta+\cos\theta$ , so that $\mathrm du=(\cos\theta-\sin\theta)\,\mathrm d\theta$ .

Also, recall the double angle identity for cosine:

$\cos(2\theta)=\cos^2\theta-\sin^2\theta=(\cos\theta-\sin\theta)(\cos\theta+\sin\theta)$

So, we can rewrite and compute the integral using the substitution, as

$\displaystyle\int\cos(2\theta)(\sin\theta+\cos\theta)^3\,\mathrm d\theta$

$=\displaystyle\int u\cdot u^3\,\mathrm du$

$=\displaystyle\int u^4\,\mathrm du$

$=\dfrac{u^5}5+C$

$=\boxed{\dfrac{(\cos\theta+\sin\theta)^5}5+C}$

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3 years ago

Which equation can be used to solve for the rate, r, for Sam to change all the light bulbs in the office building by himself?

Bad White [126]

Answer:

$\frac{3}{r}+\frac{3}{8}=1$

Step-by-step explanation:

Given question is incomplete; here is the complete question.

Working together, Sam and Charlie can change all light bulbs in the office building in 3 hours. It would have taken Charlie 8 hours to do the job alone. Which equation can be be used to solve for the rate 'r', for Sam to change all the light bulbs in the office building by himself.

Let Sam can change the bulbs in the office alone in 'r' hours

Per hour work done by Sam alone = $\frac{1}{r}$

Let Sam takes he time to change the same bulbs in the office alone = 8 hours

Per hour work done by Sam = $\frac{1}{8}$

Since, Sam and Charlie complete the work together in time = 3 hours

Therefore, per hour work done by both = $\frac{1}{3}$

Equation for per work done by both will be,

Per hour work done by both = Per hour work done by Sam alone + Per hour work done by Charlie

$\frac{1}{r}+\frac{1}{8}=\frac{1}{3}$

Therefore, equation for the rate 'r' will be,

$\frac{1}{r}+\frac{1}{8}=\frac{1}{3}$

$\frac{3}{r}+\frac{3}{8}=1$

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3 years ago

Read 2 more answers

Evaluate the line integral using the fundamental theorem of line integrals. use a computer algebra system to verify your results

mario62 [17]

$\dfrac{\partial f}{\partial x}=\cos x\sin y\implies f(x,y)=\sin x\sin y+g(y)$

$\dfrac{\partial f}{\partial y}=\sin x\cos y=\sin x\cos y+\dfrac{\mathrm dg}{\mathrm dy}$
$\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=C$

$f(x,y)=\sin x\sin y+C$

$\displaystyle\int_{\mathcal C}\cos x\sin y\,\mathrm dx+\sin x\cos y\,\mathrm dy=\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f\left(\frac{3\pi}2,\frac\pi2\right)-f(0,-\pi)=-1$

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3 years ago

A bag contains 26 tiles, each with a different letter of the alphabet written on it. You choose 3 tiles from the bag without loo

blagie [28]

Answer:

1/26

Step-by-step explanation:

Total no. of tiles = 26

In each tile , a different alphabet is written.

And we need 3 tiles (in which A , B & C are written in it) in one try.

So the probability of choosing tiles with letters A , B & C ( in one try ) = 1/26

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3 years ago

Find the zeros of the function (x+3)^2(x-5)^6 and state the multiplicity

nikklg [1K]

Find the zeros<span> of Function (</span>x)= (x+3)^2(x-5)^6 and state the multiplicity. ... (x--5)^6<span> = 0=> </span>x--5<span>= 0 => </span>x<span> = </span>5<span>. Therefore real </span>zero's of the function<span> are --</span>3<span>,5.</span><span />

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3 years ago