Which equation matches the given graph?

Simplify using trigonometric identities<br> 2sinθ - sin2θ cosθ

Anit [1.1K]

Double angle identity for sine:

$\sin(2x) = 2 \sin(x) \cos(x)$

$\implies 2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta)$

Factorize the left side.

$2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta) = 2 \sin(\theta) \left(1 - \cos^2(\theta)\right)$

Pythagorean identity:

$\cos^2(x) + \sin^2(x) = 1$

$\implies 2 \sin(\theta) \left(1 - \cos^2(\theta)\right) = 2 \sin^3(\theta)$

so that

$\boxed{2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin^3(\theta)}$

8 0

2 years ago

Write words to match the expression 3+(4×12)

Airida [17]

3 more than the produce of 12 and 4.

3 0

4 years ago

Read 2 more answers

A rocket is traveling at 283 miles per minute. How far will the rocket travel in 15 minutes?

Eddi Din [679]

Answer:

4,245 miles

Step-by-step explanation:

Hello there,

the reason the answer is 4245 is because its says per minute therefore each minute of the rocket is going 283 miles and when it ask how miles did it travel in 15 minutes u just multiply 283 and 15 which gets you the answer 4245 miles

Hope dis helps.

8 0

3 years ago

Read 2 more answers

A sphere is inscribed in a cube with a volume of 64 cubic inches. What is the volume of the sphere? Round your answer to the nea

erma4kov [3.2K]

Answer:

the volume of the sphere is

$33.51 in^{3}$

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, sphere and cube.

Given data

Volume of cube v = 64 cubic inches

since we are dealing with a cube the height and the radius of the sphere is same as the sides of the cube,

we know that volume of cube is expressed as

$v= l*b*h$

$v=l^{3}$

$64= l^{3}$

$l= \sqrt[3]{64}$

$l= 4 in$

also diameter d=length l

Diameter d= $4in$

Radius r = $\frac{d}{2}$ = $\frac{4}{2}$ = ${2 in}$

Height h= $4in$

we know that the volume of a sphere is given by

$v= \frac{4}{3} \pi r^{3}$

substituting into the formula we have

$v= \frac{4}{3} \ *3.142*2^{3} \\v=\frac{4*3.142*8}3} \\v= \frac{100.54}{3} \\v= 33.52in^{3}$

8 0

3 years ago

Ice Cold Creamery will give a free ice cream maker to anyone who spends at least $100 on buckets of ice cream and frozen yogurt.

kotykmax [81]

Given:

Free ice cream maker to anyone who spends at least $100 on buckets of ice cream and frozen yogurt.

Each bucket of ice cream costs $7.28

Each bucket of frozen yogurt costs $8.21.

To find:

The inequality represents number of ice cream and frozen yogurt that she may buy in addition to get a free ice cream maker.

Solution:

Let i be the number of buckets of ice cream and y be the number of buckets of frozen yogurt.

According to the question, total amount spend on both must be greater than or equal to $100 to get a free ice cream maker.

$7.28i+8.21y\geq 100$

$8.21y\geq 100-7.28i$

Divide both sides by 8.21.

$y\geq \dfrac{100-7.28i}{8.21}$

Therefore, the required inequality is $y\geq \dfrac{100-7.28i}{8.21}$ .

8 0

3 years ago