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2 years ago

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If linda has borrowed 8 more books than susan from school library. Richard has borrowed half as many books as Linda has. If Rich

ard has borrowed 17 books from library. How many books has susan borrowed

1 answer:

Mumz [18]2 years ago

4 0

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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

In the diagram below what is the relationship between the number of rectangles in the perimeter of the figure they form?

Wewaii [24]

Answer:

the correct answer is the third one. (1, 16), (2, 20), (3, 24)

Step-by-step explanation:

A perimeter is a path that surrounds a two-dimensional shape.

In the first case, 1 rectangle, the perimeter is the sum of all the sides:

Perimeter = 6 + 2 + 6 + 2 = 16

In the second case, 2 rectangles, the perimeter is the sum of all external sides:

Perimeter = 6 + 2 + 2 + 6 + 2 + 2 = 20

In the third case, three rectangles, the perimeter is the sum of all external sides:

Perimeter = 6 + 2 + 2 + 2 + 6 + 2 + 2 + 2 = 24

In none of the cases, you take into consideration the interal sides. Just the external sides, so the correct answer is the third one.

8 0

3 years ago

If a circle has a radius of 16,and an arc length of 12x, what is the angle measure of the central angle that matches that arc?

GREYUIT [131]

Answer:

135°

Step-by-step explanation:

Using S = rA, where S is arc length, r is radius and A is angle(in radians).

Comparing:

=> 12 = 16A

=> 12/16 = A

=> 3/4 = A

Required radian is 3/4 which is 3/4 * 180° = 135°

4 0

2 years ago

96=-8k solve <br> Show work

larisa86 [58]

Answer:

$k = -12$

Step-by-step explanation:

<u>Step 1: Divide both sides by -8</u>

<u /> $96 / -8 = -8k / -8$

$-12 = k$

Answer: $k = -12$

3 0

3 years ago

Read 2 more answers

GCF of the numbers 15 and 27

balandron [24]

Three would be your answer :)

6 0

3 years ago

Read 2 more answers