All categories

3 years ago

Write the product as a sum. 17 sin (x/2)cos(x/4)

Mathematics

1 answer:

Korolek [52]3 years ago

4 0

Answer:

$\dfrac{17}{2}\sin{\dfrac{3x}{4}}+\dfrac{17}{2}\sin{\dfrac{x}{4}}$

Step-by-step explanation:

The appropriate identity is ...

$\sin{\alpha}\cos{\beta}=\dfrac{1}{2}(\sin{(\alpha+\beta)}+\sin{(\alpha-\beta)})$

Filling in α=x/2 and β=x/4, we get ...

$17\sin{(x/2)}\cos{(x/4)}=\dfrac{17}{2}(\sin{(x/2+x/4)}+\sin{(x/2-x/4)})\\\\=\dfrac{17}{2}\sin{\dfrac{3x}{4}}+\dfrac{17}{2}\sin{\dfrac{x}{4}}$

You might be interested in

2. What type of sequence is this? 4,0-4,-8, -12,... Arthimetic Geometric Neither

lora16 [44]

Answer:

Arithmetic

Step-by-step explanation:

Arithmetic is additive and geometric is multiplicative, and the numbers aren''t multiplying, they're adding.

8 0

3 years ago

Geometry Help? Plz I Beg Of You!! *pic inside*

Natalija [7]

1a) if all the angles are perpendicular, they all =90°

7 0

3 years ago

Adult men have heights that a normally distributed with a mean of 69.5 inches and a standard deviation of 2.4 inches. Adult wome

Aliun [14]

Answer:

Step-by-step explanation:

From the information given:

For Adult Men

Mean $\mu$ = 69.5

Standard deviation $\sigma$ = 2.4

observed value X = 74

For Adult Women

Mean $\mu$ = 63.8

Standard deviation $\sigma$ = 2.6

observed value X = 70

Therefore ; the values for their z scores can be obtained in order to determine who is more unusually tall within his or her respective sex

For Adult Men :

$z = \dfrac{X- \mu}{\sigma}$

$z = \dfrac{74- 69.5}{2.4}$

$z = \dfrac{4.5}{2.4}$

z = 1.875

For Adult Women :

$z = \dfrac{X- \mu}{\sigma}$

$z = \dfrac{70- 63.8}{2.6}$

$z = \dfrac{6.2}{2.6}$

z = 2.3846

Thus; we can conclude that , the women is more unusually tall within his or her respective sex

5 0

3 years ago

Solve |p + 2| = 10Solve |p + 2| = 10 {-12} {-8, 8} {-12, 8}

valentinak56 [21]

By definition, we have

$|p+2| = \begin{cases} p+2 &\text{ if } p+2 \geq 0 \\-p-2 &\text{ if } p+2 < 0 \end{cases}$

So, we have to solve two different equations, depending of the possible range for the variable. We have to remember about these ranges when we decide to accept or discard the solutions:

Suppose that $p+2\geq 0 \iff p \geq -2$

In this case, the absolute value doesn't do anything: the equation is

$p+2 = 10 \iff p = 10-2 = 8$

We are supposing $p \geq -2$ , so we can accept this solution.

Now, suppose that $p+2 < 0 \iff p < -2$ . Now the sign of the expression is flipped by the absolute value, and the equation becomes

$-p-2 = 10 \iff -p = 12 \iff p = -12$

Again, the solution is coherent with the assumption, so we can accept this value as well.

3 0

3 years ago

Dale drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took hours. When Dale drove hom

IrinaK [193]

Dale drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 7 hours. when dale drove home, there was no traffic and the trip only took 5 hours. if his average rate was 18 miles per hour faster on the trip home, how far away does dale live from the mountains? do not do any rounding.

Answer:

Dale live 315 miles from the mountains

Step-by-step explanation:

Let y be the speed of Dale to the mountains

Time taken by Dale to the mountains=7 hrs

Therefore distance covered by dale to the mountain = speed × time = 7y ......eqn 1

Time taken by Dale back home = 5hours

Since it speed increased by 18 miles per hour back home it speed = y+18

So distance traveled home =speed × time = (y+18)5 ...... eqn 2

Since distance cover is same in both the eqn 1 and eqn 2.

Eqn 1 = eqn 2

7y = (y+18)5

7y = 5y + 90

7y - 5y = 90 (collection like terms)

2y = 90

Y = 45

Substitute for y in eqn 1 to get distance away from mountain

= 7y eqn 1

= 7×45

= 315 miles.

∴ Dale leave 315 miles from the mountains

4 0

3 years ago