All categories

3 years ago

Let sin(2x)-sin(x)=0, where 0 ≤ x < 2pi. What are the possible solutions for x?

Mathematics

1 answer:

Dominik [7]3 years ago

4 0

Step-by-step explanation:

sin2x - sinx = 0

2sinxcosx - sinx = 0

(Double Angle Formula)

sinx(2cosx - 1) = 0

Either sinx = 0 or cosx = 1/2.

When sinx = 0,

x = 0 or x = π.

When cosx = 1/2,

x = π/3 or x = 5π/3.

Hence the solutions are

x = 0, x = π/3, x = π or x = 5π/3.

You might be interested in

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 500

kolezko [41]

Answer:

The 35-week gestation period baby has a z-score of 0.7.

The 41-week gestation period baby has a z-score of 0.89

Since the 41-week gestation period baby has a higher z-score, he weighs more relatively to his gestation period.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Which baby weighs more relative to the gestation period?

The baby with the higher z-score.

35-week gestation period baby weighs 2850 grams

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 500 grams

This means that Z is found when $X = 2850, \mu = 2500, \sigma = 500$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{2850 - 2500}{500}$

$Z = 0.7$

The 35-week gestation period baby has a z-score of 0.7.

41-week gestation period baby weighs 3150 grams.

Babies born after a gestation period of 40 weeks have a mean weight of 2800 grams and a standard deviation of 395 grams.

This means that Z is found when $X = 3150, X = 2800, \mu = 395$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{3150 - 2800}{395}$

$Z = 0.89$

The 41-week gestation period baby has a z-score of 0.89

Since the 41-week gestation period baby has a higher z-score, he weighs more relatively to his gestation period.

5 0

3 years ago

Eliza started her savings account with $100. Each month she deposits $25 into her account. Determine the average rate of change

Afina-wow [57]

First, lets create a equation for our situation. Let $x$ be the months. We know four our problem that Eliza started her savings account with $100, and each month she deposits $25 into her account. We can use that information to create a model as follows:
 $f(x)=25x+100$

We want to find the average value of that function from the 2nd month to the 10th month, so its average value in the interval [2,10]. Remember that the formula for finding the average of a function over an interval is: $\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1} }$ . So lets replace the values in our formula to find the average of our function:
$\frac{25(10)+100-[25(2)+100]}{10-2}$
$\frac{350-150}{8}$
$\frac{200}{8}$
$25$

We can conclude that the average rate of change in Eliza's account from the 2nd month to the 10th month is $25.

6 0

3 years ago

Using powers of 10, which would be the best choice for the first number to subtract in the division problem 956 ÷ 87?

dlinn [17]

Answer:

870 as it is the only number in the list which closest and lesser then 956.

(if you divide, then you get 10 as quotient and 86 as remainder)

we can also take 87 but the question mentions with multiples of 10.

Step-by-step explanation:

6 0

3 years ago

Mr.Chen left $45,000 to his aunt when he died. This was 5% of his total worth. a) how much was Mr.Chen worth when he died? Show

marysya [2.9K]

A) Mr Chen was worth:

45,000/5 = 9,000

9,000 x 100 = 900,000

The answer is 900,00

You can also write this as an equation.

3 0

3 years ago

How do i find the sum

djverab [1.8K]

Answer:

To find the sum of two numbers add them together C:

Step-by-step explanation:

example: the sum of 3 and 4 is 7

the sum means its addition

6 0

3 years ago

Read 2 more answers