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Advocard [28]
2 years ago
13

The limit of tan4x/6x as x approaches 0

Mathematics
1 answer:
AleksandrR [38]2 years ago
5 0
\displaystyle\lim_{x\to0}\frac{\tan4x}{6x}=\lim_{x\to0}\frac{\sin4x}{4x}\times\frac{4x}{6x\cos4x}=\dfrac23\lim_{x\to0}\sec4x=\dfrac23
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Answer:

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Step-by-step explanation:

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2 years ago
The design for the palladium window shown includes a semicircular shape at the top. The bottom is formed by squares of equal siz
9966 [12]

Answer:

(a)\ Area = 3765.32

(b)\ Area = 4773

Step-by-step explanation:

Given

A_1 = 169in^2 --- area of each square

Shade = 4in

See attachment for window

Solving (a): Area of the window

First, we calculate the dimension of each square

Let the length be L;

So:

L^2 = A_1

L^2 = 169

L = \sqrt{169

L=13

The length of two squares make up the radius of the semicircle.

So:

r = 2 * L

r = 2*13

r = 26

The window is made up of a larger square and a semi-circle

Next, calculate the area of the larger square.

16 small squares made up the larger square.

So, the area is:

A_2 = 16 * 169

A_2 = 2704

The area of the semicircle is:

A_3 = \frac{\pi r^2}{2}

A_3 = \frac{3.14 * 26^2}{2}

A_3 = 1061.32

So, the area of the window is:

Area = A_2 + A_3

Area = 2704 + 1061.32

Area = 3765.32

Solving (b): Area of the shade

The shade extends 4 inches beyond the window.

This means that;

The bottom length is now; Initial length + 8

And the height is: Initial height + 4

In (a), the length of each square is calculated as: 13in

4 squares make up the length and the height.

So, the new dimension is:

Length = 4 * 13 + 8

Length = 60

Height = 4*13 + 4

Height = 56

The area is:

A_1 = 60 * 56 = 3360

The radius of the semicircle becomes initial radius + 4

r = 26 + 4 = 30

The area is:

A_2 = \frac{3.14 * 30^2}{2} = 1413

The area of the shade is:

Area = A_1 + A_2

Area = 3360 + 1413

Area = 4773

7 0
2 years ago
Sasha went shopping and decided to purchase a set of bracelets for 5% off the regular price ($44.00). If Sasha buys the bracelet
scZoUnD [109]

Answer:

answer should be #31.35

hope this helps :)

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3 years ago
Solve for x using the triangle sun theorem.
Alexeev081 [22]

Answer:

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2 years ago
The measurement of an acute angle is (5w+8) solve for w​
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Answer:

w < 82/5

Step-by-step explanation:

5w + 8 < 90

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