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MaRussiya [10]
3 years ago
11

Verify the identity sin^2(x)cos^2(x)=1/8(1-cos(4x))

Mathematics
1 answer:
bixtya [17]3 years ago
5 0

cos^2(x) = 1/2 + (1/2)cos(2x)

sin^2(x) = 1 - cos^2(x) = 1/2 - (1/2)cos(2x)

sin^2(x)cos^2(x)

= [1/2 - (1/2)cos(2x)][1/2 + (1/2)cos(2x)]

(a - b)(a + b) = a^2 - b^2

= (1/2)^2 - (1/2)^2[cos^2(2x)]

= 1/4 - (1/4)cos^2(2x)

= (1/4)[1 - cos^2(2x)]

= (1/4)[sin^2(2x)]

= (1/4)[1/2 - (1/2)cos(4x)]

= (1/4)(1/2)[1 - cos(4x)]

= (1/8)[1 - cos(4x)]

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Identify each pair of angles as corresponding, alternate interior, alternate exterior, or consecutive interior.
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Answer:

1. The answer for this question is corresponding angles.

2. The answer for this question is alternate interior

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NO LINKS!!! Part 2: Find the Lateral Area, Total Surface Area, and Volume. Round your answer to two decimal places.​
slava [35]

Answer:

<h3><u>Question 7</u></h3>

<u>Lateral Surface Area</u>

The bases of a triangular prism are the triangles.

Therefore, the Lateral Surface Area (L.A.) is the total surface area excluding the areas of the triangles (bases).

\implies \sf L.A.=2(10 \times 6)+(3 \times 6)=138\:\:m^2

<u>Total Surface Area</u>

Area of the isosceles triangle:

\implies \sf A=\dfrac{1}{2}\times base \times height=\dfrac{1}{2}\cdot3 \cdot \sqrt{10^2-1.5^2}=\dfrac{3\sqrt{391}}{4}\:m^2

Total surface area:

\implies \sf T.A.=2\:bases+L.A.=2\left(\dfrac{3\sqrt{391}}{4}\right)+138=167.66\:\:m^2\:(2\:d.p.)

<u>Volume</u>

\sf \implies Vol.=area\:of\:base \times height=\left(\dfrac{3\sqrt{391}}{4}\right) \times 6=88.98\:\:m^3\:(2\:d.p.)

<h3><u>Question 8</u></h3>

<u>Lateral Surface Area</u>

The bases of a hexagonal prism are the pentagons.

Therefore, the Lateral Surface Area (L.A.) is the total surface area excluding the areas of the pentagons (bases).

\implies \sf L.A.=5(5 \times 6)=150\:\:cm^2

<u>Total Surface Area</u>

Area of a pentagon:

\sf A=\dfrac{1}{4}\sqrt{5(5+2\sqrt{5})}a^2

where a is the side length.

Therefore:

\implies \sf A=\dfrac{1}{4}\sqrt{5(5+2\sqrt{5})}\cdot 5^2=43.01\:\:cm^2\:(2\:d.p.)

Total surface area:

\sf \implies T.A.=2\:bases+L.A.=2(43.01)+150=236.02\:\:cm^2\:(2\:d.p.)

<u>Volume</u>

\sf \implies Vol.=area\:of\:base \times height=43.011193... \times 6=258.07\:\:cm^3\:(2\:d.p.)

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Answer:

a

Step-by-step explanation:

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4 0
3 years ago
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Andre says 10x + 6 and 5x + 11 are equivalent because they both equal 16 when x is 1. Do you agree with Andre?​
Serga [27]

Answer:

No, They are not equivalent

Step-by-step explanation:

The two expressions are only said to be equivalent if they are the same regardless of whatever value the variable(s) is.

The variable in this question is x.

To prove this, we equate both expressions:

10x + 6 = 5x + 11

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This shows that they have the same value ONLY when x is 1.

This is why Andre says that they are equivalent, but they are not.

8 0
3 years ago
Find a factor of 3x^2- 16x - 12​
Greeley [361]

Answer:

x= -2/3 and 6

Step-by-step explanation:

3x²-16x-12

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(3x²-18x)+(2x-12)

3x(x-6)+2(x-6)

(3x+2)(x-6)

x= -2/3 and 6

8 0
2 years ago
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