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2 years ago

6

Albreic is building from a rope. He has three ropes. One is 6ft, another is 8ft and and the last is 12 ft. Will he be able to bu

ild his triangle?

1 answer:

Radda [10]2 years ago

7 0

Answer:

Yes. 6+8= 14, thats bigger than 12. 6+12= 18. That's bigger than 8. 8+12=20 and that's bigger than 6.

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you have a large container of olive oil. You have used 22 1/2 quarts of oil. Twenty- five percent of the oil remain. How many qu

Alex Ar [27]

Answer:

7.5 quarts of olive oil remain.

Explanation:

Let

q = quarts of olive oil remain

<span>25%</span> of olive oil remains means that <span>75%</span> has been used.

22<span>12</span> quarts = 22.5 quarts used

<span><span>22.5.75</span>=<span>q.25</span></span>

Multiply both sides by .25 to isolate q.

<span><span>22.5.75</span><span>(.25)</span>=<span>q.25</span><span>(.25)</span></span>

<span><span>5.625.75</span>=q</span>

<span>7.5=<span>q</span></span>

3 0

2 years ago

<img src="https://tex.z-dn.net/?f=%20%5Crm%20%5Cint_%7B0%7D%5E%7B%20%20%5Cpi%20%7D%20%5Ccos%28%20%5Ccot%28x%29%20%20%20%20-%20%2

Nikolay [14]

Replace x with π/2 - x to get the equivalent integral

$\displaystyle \int_{-\frac\pi2}^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx$

but the integrand is even, so this is really just

$\displaystyle 2 \int_0^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx$

Substitute x = 1/2 arccot(u/2), which transforms the integral to

$\displaystyle 2 \int_{-\infty}^\infty \frac{\cos(u)}{u^2+4} \, du$

There are lots of ways to compute this. What I did was to consider the complex contour integral

$\displaystyle \int_\gamma \frac{e^{iz}}{z^2+4} \, dz$

where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be

$\displaystyle \left|\int_{z=Re^{i0}}^{z=Re^{i\pi}} f(z) \, dz\right| \le \frac{\pi R}{|R^2-4|}$

which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit

$\displaystyle \int_{-\infty}^\infty \frac{\cos(x)}{x^2+4} \, dx = 2\pi i {} \mathrm{Res}\left(\frac{e^{iz}}{z^2+4},z=2i\right) = \frac\pi{2e^2}$

and it follows that

$\displaystyle \int_0^\pi \cos(\cot(x)-\tan(x)) \, dx = \boxed{\frac\pi{e^2}}$

7 0

1 year ago

Can u guys help me on #24

lora16 [44]

56.5ft x 17ft x 1ft = 960.5ft^3.

The question wants the answer in ft^3. One of the measurements is given as 13 inches but that converts to 1ft. And with the volume formula for rectangles is widthxlenghtxheight. Plug in the numbers.

7 0

2 years ago

Verify that each of the following transformations preserves congruence and name the congruence transformation

AnnZ [28]

Pentagon A B C D E is reflected across the X-axis to form pentagon A B C D.

6 0

3 years ago

Write the equation of the line that includes the point (1,5) and has a slope of 3 in standard form.

Ymorist [56]

Answer:

-3x + y = 2

Step-by-step explanation:

The slope is 3. So the coefficient of x is 3.

when x = 1, y = 5.

So 3*1 + c = 5

So c is 2.

So y = 3x + 2

Therefore, taking 3x to the LHS, we get,

-3x + y = 2

Hope it helps ;)

7 0

3 years ago

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