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Dimas [21]
3 years ago
8

If Sin 3x= Cos (x-60), find the value of x​

Mathematics
1 answer:
Kamila [148]3 years ago
4 0

Answer:

x = 15

Step-by-step explanation:

Assuming 3x and x-60 are in degrees, you can use:

cos(a) = sin(a+90)

To rewrite the equation as:

sin(3x) = sin(x-60+90)

sin(3x) = sin(x+30)

3x = x+30

2x = 30

x = 15

But, solving 3x = x+30 which simplifies to x=15 is not the only solution to this equation, as you can see in below picture. Finding all solutions is a bit more work, but maybe that is not required in your case.

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How many solutions exist for the system of equations graphed below?
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Considering the given graph, the number of solutions for the system of equations is given by:

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A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

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3 years ago
Let us suppose we have data on the absorbency of paper towels that were produced by two different manufacturing processes. From
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Answer:

The 95% CI for the difference of means is:

-155.45 \leq \mu_1-\mu_2 \leq -44.55

Step-by-step explanation:

<em>The question is incomplete:</em>

<em>"Find a 95% confidence interval on the difference of the towels mean absorbency produced by the two processes. Assumed that the standard deviations are estimated from the data. Round to two decimals places."</em>

Process 1:

- Sample size: 10

- Mean: 200

- S.D.: 15

Process 2:

- Sample size:  4

- Mean: 300

- S.D.: 50

The difference of the sample means is:

M_d=M_1-M_2=200-300=-100

The standard deviation can be estimated as:

\sigma_d=\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}\\\\\sigma_d=\sqrt{\frac{15^2}{10}+\frac{50^2}{4}} =\sqrt{22.5+625}=\sqrt{647.5}=25.45

The degrees of freedom are:

df=n_1+n_2-2=10+4-2=12

The t-value for a 95% confidence interval and 12 degrees of freedom is t=±2.179.

Then, the confidence interval can be written as:

M_d-t\cdot \sigma_d\leq \mu_1-\mu_2 \leq M_d+t\cdot \sigma_d\\\\-100-2.179*25.45\leq \mu_1-\mu_2 \leq -100+2.179*25.45\\\\-100-55.45 \leq \mu_1-\mu_2 \leq -100+55.45\\\\ -155.45 \leq \mu_1-\mu_2 \leq -44.55

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