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Anna007 [38]
3 years ago
11

Rewrite the product as a sum: 10cos(5x)sin(10x)

Mathematics
1 answer:
mote1985 [20]3 years ago
8 0

Answer:

10cos(5x)sin(10x) =  5[sin (15x) + sin (5x)]

Step-by-step explanation:

In this question, we are tasked with writing the product as a sum.

To do this, we shall be using the sum to product formula below;

cosαsinβ = 1/2[ sin(α + β) - sin(α - β)]

From the question, we can say α= 5x and β= 10x

Plugging these values into the equation, we have

10cos(5x)sin(10x) = (10) × 1/2[sin (5x + 10x) - sin(5x - 10x)]

= 5[sin (15x) - sin (-5x)]

We apply odd identity i.e sin(-x) = -sinx

Thus applying same to sin(-5x)

sin(-5x) = -sin(5x)

Thus;

5[sin (15x) - sin (-5x)] = 5[sin (15x) -(-sin(5x))]

= 5[sin (15x) + sin (5x)]

Hence,  10cos(5x)sin(10x) =  5[sin (15x) + sin (5x)]

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Answer:

\large\boxed{Common\ factors:\ 1,\ 2,\ 4,\ a,\ 2a,\ 4a}

Step-by-step explanation:

16a=2\cdot2\cdot2\cdot2\cdot a\\Factors:\boxed1,\ \boxed2,\ \boxed4,\ 8,\ 16,\ \boxed{a},\ \boxed{2a},\ \boxed{4a},\ 8a,\ 16a\\\\20ab=2\cdot2\cdot5\cdot a\cdot b\\Factors:\boxed1,\ \boxed2,\ \boxed4,\ 5,\ 10,\ 20,\ \boxed{a},\ \boxed{2a},\ \boxed{4a},\ 5a,\ 10a,\ 20a,\\b,\ 2b,\ 4b,\ 5b,\ 10b,\ 20b,\ 2ab,\ 4ab,\ 5ab,\ 10ab,\ 20ab\\\\Common\ factors:\ 1,\ 2,\ 4,\ a,\ 2a,\ 4a

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Answer

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Step-by-step explanation:

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While taking an online pretest for an algebra class, the distance formula was displayed as shown below.
olga_2 [115]

The calculated distance would be in square units instead of linear units.

Answer: Option C.

<u>Explanation:</u>

The Distance Formula itself is actually derived from the Pythagorean Theorem. This is the formula where c is the longest side of a right triangle (also known as the hypotenuse) and a and b are the other shorter sides (known as the legs of a right triangle).

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Answer:

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Step-by-step explanation:

given slope m = \frac{6}{5}

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further you can multiply by 5 to get rid of fraction

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