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3 years ago

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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At a gas station during a road trip, Gerard has $32.00 to spend on fuel and windshield washer fluid for his car. Fuel costs $2.7

Lemur [1.5K]

Answer:

Step-by-step explanation:

Total amount with Gerald = $32

Cost of fuel per gallon = $2.75

Cost of each bottle of windshield = $3

38 miles per gallon. If Gerard must fill his car with enough fuel to drive 250 miles,

Total gallons of fuel = 250 miles / 38 miles

= 6.5789473684210 gallons

Total cost of fuel = Total gallons of fuel × cost per gallon

= 6.5789473684210 × $2.75

= $18.1

Amount left for windshield = Total amount with Gerald - Total cost of fuel

= $32 - $18.1

= $13.9

what is the maximum number of bottles of windshield washer fluid Gerard can buy?

= Amount left for windshield / Cost of each bottle of windshield

= $13.9 / $3

= 4.6333333333333 bottles

Maximum number of bottles =

4 bottles

5 0

3 years ago

Solve each inequality. <br> 1. 5x + 2 <17

butalik [34]

Answer:

x<3

Step-by-step explanation:

5x+2<17

Subtract 2 from both sides.

5x<17−2

Subtract 2 from 17 to get 15.

5x<15

Divide both sides by 5. Since 5 is positive, the inequality direction remains the same.

x=15/5

Divide 15 by 5 to get 3.

x<3

8 0

3 years ago

What is the equation of the line that passes through the point (−4,−8) and has an undefined slope?

Masja [62]

Answer:

x = -4

Step-by-step explanation:

An undefined slope would look like a vertical line, up and down. This is shown using an x equals equation instead of a y equals equation.

Since the line goes vertically, you only need to look at the x-value to make the equation, since after doing x = -4 the line would keep going down until it touched (-4, -8).

The line would touch everything in the y-value but stay at x = -4.

Therefore the answer to this problem is x = -4. I've attached a picture (from desmos) showing what the graph of x = -4 would look like and how it touches the point (-4, -8).