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iren [92.7K]
3 years ago
15

Calculate the volume of a square-based pyramid with a slant height of 5 ft and base edges of 6 ft.

Mathematics
1 answer:
Ostrovityanka [42]3 years ago
6 0

Answer:

Volume is 60ft³

Step-by-step explanation:

b²h/3

b=6

h=5

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Lim x->pi/3 ((2cosx-1)/(tan^2x-3))
beks73 [17]

You can check that the limit comes in an undefined form:

\displaystyle \lim_{x\to\frac{\pi}{3}} \frac{2\cos(x)-1}{\tan^2(x)-3}=\dfrac{0}{0}

In these cases, we can use de l'Hospital rule, and evaluate the limit of the ratio of the derivatives. We have:

\dfrac{\text{d}}{\text{d}x}2\cos(x)-1 = -2\sin(x)

and

\dfrac{\text{d}}{\text{d}x}\tan^2(x)-3 = 2\dfrac{\tan(x)}{\cos^2(x)}=\dfrac{2\sin(x)}{\cos^3(x)}

So, we have

\displaystyle \lim_{x\to\frac{\pi}{3}} \frac{2\cos(x)-1}{\tan^2(x)-3}=\lim_{x\to\frac{\pi}{3}} \dfrac{-2\sin(x)}{\frac{2\sin(x)}{\cos^3(x)}}=\lim_{x\to\frac{\pi}{3}}-\cos^3(x)=-\cos^3\left(\dfrac{\pi}{3}\right)

6 0
3 years ago
Algebra two graph problem!
Paladinen [302]
It has no real solutions. To be precise, no real zeros (or roots).

The zeros (here called "solutions", I guess) are the points where the function intersects the x-axis: at those points the value of the function is zero. So they are solutions to the equation f(x)=0.

This function does not intersect the x-axis. Hence, no solutions.
5 0
3 years ago
Damian plans to do a lot of babysitting this summer. He charges $6.50 per hour and babysits for 3 hours. He has agreed to babysi
RoseWind [281]

Answer:

$195

Step-by-step explanation:

multiplying 6.50*3*10 = 195

7 0
3 years ago
Read 2 more answers
Ten minutes after he left his home, Gerald was 40 miles from his grandmother’s house. Then, 22 minutes after he left, he was 34
Svetlanka [38]
After 10 minutes, he's 40 miles away. After 22 minute, he's 34 miles away. Therefore, in those 12 minutes between, he covered 6 miles. We can make a ratio out of this: 6/12 = 0.5, so he is walking at a rate of 0.5 mi/min (miles per minute). Finally, we can set x/90 equal to 0.5/1 because he is walking at the same rate the entire time. Cross multiply to solve for x. Finally, you get that he had to travel 45 miles in 90 minutes, so his home is 45 miles away from his grandmother's.

3 0
3 years ago
Whats 48.5438 x 16 1/7 divided by 8?
Vlad1618 [11]

Answer:

97.95

Step-by-step explanation:

48.5438 x 16 1/7 = 783.6356286

783.6356286 ÷ 8 =97.95445357

round- 97.95

6 0
3 years ago
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