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N76 [4]
3 years ago
13

A. Show

Mathematics
1 answer:
nydimaria [60]3 years ago
8 0

a. Recall the double angle identities:

\sin^2x=\dfrac{1-\cos2x}2

\cos^2x=\dfrac{1+\cos2x}2

Then

\sin^2x\cos^2x=\dfrac{(1-\cos2x)(1+\cos2x)}4=\dfrac{1-\cos^22x}4

Applying the identity again, we have

\sin^2x\cos^2x=\dfrac{1-\frac{1+\cos4x}2}4=\dfrac{2-(1+\cos4x)}8=\dfrac{1-\cos4x}8

as required.

b. Using the result from part (a),

\sin^2x\cos^2x=\dfrac{1-\cos4x}8=\dfrac{2-\sqrt2}{16}

\implies\cos4x=\dfrac1{\sqrt2}

\implies4x=\dfrac\pi4+2n\pi\text{ or }4x=-\dfrac\pi4+2n\pi

(where n is any integer)

\implies\boxed{x=\pm\dfrac\pi{16}+\dfrac{n\pi}2}

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A contemporary building has a window in the shape of a parallelogram with a base of 90 in and an adjacent side of 40 in. How man
BaLLatris [955]

260 inches of trim are needed to surround the​ window.

<h3 /><h3>What is the surface area?</h3>

The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.

Actually, all we need is a trim that is the same size as our window and equal to the parallelogram's circumference, which is

The sum of the side is;

⇒Length of lower side + Length of the upper side

⇒ 90+90

⇒180 inches

The sum of adjacent sides;

Sum of adjacent sides  =  40+40

Sum of adjacent sides  = 80 inches

The length you should trim is needed to surround the​ window is found as;

⇒ 180 inches + 80 inches

⇒260 inches

Hence,260 inches of trim are needed to surround the​ window.

To learn more about the surface area, refer to the link;

brainly.com/question/2835293

#SPJ1

7 0
2 years ago
Question 6
oee [108]

Answer:

The answer is 200km

Step-by-step explanation:

250\5=50,50×4=200

7 0
3 years ago
You are an office manager and you need to order supplies for your office. you need 3 boxes of computer diskettes at $8.99 per bo
DENIUS [597]
3 boxes of computer diskettes at $8.99 per box = (3 * 8.99 = 26.97 ) 
2 packages of pens at $ 2.50 per package = (2 * 2.50 = 5.00 ) 
6 boxes of paper at $ 22.95 per box = (6 * 22.95 = 137.70) 
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5 0
3 years ago
Help Please<br> Find The Surface Area Of The Prism
snow_lady [41]

Answer:

360 cm^2

Step-by-step explanation:

Find the area of each face of the triangular prism.

Imagine the triangular prism as its net, it is composed with 2 triangular faces (these are tye bases of the prism) and 3 rectangular faces.

Areas of the 2 triangular bases (they are similar triangles):

1/2 x 8 cm x 6 cm = 24 cm^2

24 x 2 = 48 cm^2

Area of the rectangular face:

8 x 13 = 104 cm^2

Area of another rectangular face:

6 cm x 13 cm = 78 cm^2

Area of another rectangular face:

13 cm x 10 cm = 130 cm^2

Add up all the areas of all faces:

48 + 104 + 78 + 130 = 360

So the SA is 360 cm^2

8 0
2 years ago
200 divided by 5.50 is what because if one hour is 5.50 and you need 200 how many hours do you work
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Answer:

if you divided 200 by 5.50 the answer will be 36.3636363636

8 0
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