$389 is divided between A and B. If A receives $144 more than B, how much does each receives

Solve using algebraic equation: 5sin2x=3cosx (No exponents)

DaniilM [7]

$5\sin2x=3\cos x\iff10\sin x\cos x=3\cos x$

by the double angle identity for sine. Move everything to one side and factor out the cosine term.

$10\sin x\cos x=3\cos x\iff10\sin x\cos x-3\cos x=\cos x(10\sin x-3)=0$

Now the zero product property tells us that there are two cases where this is true,

$\begin{cases}\cos x=0\\10\sin x-3=0\end{cases}$

In the first equation, cosine becomes zero whenever its argument is an odd integer multiple of $\dfrac\pi2$ , so $x=\dfrac{(2n+1)\pi}2$ where $n[/tex ]is any integer.\\Meanwhile,\\[tex]10\sin x-3=0\implies\sin x=\dfrac3{10}$

which occurs twice in the interval $[0,2\pi)$ for $x=\arcsin\dfrac3{10}$ and $x=\pi-\arcsin\dfrac3{10}$ . More generally, if you think of $x$ as a point on the unit circle, this occurs whenever $x$ also completes a full revolution about the origin. This means for any integer $n$ , the general solution in this case would be $x=\arcsin\dfrac3{10}+2n\pi$ and $x=\pi-\arcsin\dfrac3{10}+2n\pi$ .

6 0

3 years ago

Find two numbers whos diffrence is 16 and the product is 720

antiseptic1488 [7]

Answer:

the numbers who's difference is 16 and the product is 720 is

36 &20

Explanation:

to finding numbers you have to express the equation in a quadratic equation then Factor it.

since the two numbers have a difference of 16 you can say that the first number is x and the second number is x -16 then their product is 720.

x(x-16)=720

x²-16x=720

x²-16x-720=0

(x-36)(x+20)

there are two possible value of x but since you are looking for the positive value of x, choose the positive value of x the first number is 20.

To find the second number

x-16=20

x=20+16

x=36

the second number is 36

Now to check

36-20=16

20*36=720

8 0

2 years ago

American households increasingly rely on cell phones as their exclusive telephone service. It is reported that 50.4% of American

OLga [1]

The variance of the binomial distribution of the number of households with landline service is 2.

<h3>What is the binomial probability distribution?</h3>

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The variance of the distribution is given by:

V(X) = np(1 - p)

In this problem, the parameters are given as follows:

n = 8, p = 0.504.

Hence the variance is given by:

V(X) = 8 x 0.504 x 0.496 = 2.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

5 0

1 year ago

A stadium holds 50,000 people.The stadium is divided into 250 different seating sections.How many seats are in each section?

worty [1.4K]

50,000 ÷ 250 = 200

This means that there are 200 seats in each section.

8 0

2 years ago

Read 2 more answers

How many grams must be adde to 970g to make 1 and a half kg

madam [21]

Answer:

530 grams

Step-by-step explanation:

970 grams = 0.970 kg

1 kg = 1000 grams

Thus: 500+30 = 530 grams

3 0

2 years ago

$389 is divided between A and B. If A receives $144 more than B, how much does each receives​

$389 is divided between A and B. If A receives $144 more than B, how much does each receives