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3 years ago

Find all solutions in the interval (0,2pi) you should get kpi and pi/4 but how do you get there

Mathematics

1 answer:

Ket [755]3 years ago

4 0

Add sin(x) to both sides

tan(x)sin(x)=sin(x)

Divide sin(x) from both sides

tan(x)=1

now you just have to figure out where tan(x)=1. you can figure this out from there by looking at the unit circle.

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Solve the following system of equations for a and for b:

viktelen [127]

Answer:

$a=3\\b=1$

Step-by-step explanation:

$9a+3b=30\\8a+4b=28$

Let's solve the second equation for a to later on replace it in the first equation.

$8a+4b=28\\8a=28-4b\\a=\frac{28-4b}{8}$

Now plug this into the first equation.

$9a+3b=30\\9(\frac{28-4b}{8})+3b=30$

Distribute the 9

$(\frac{252-36b}{8}) +3b=30$

Break down the fraction.

$\frac{252}{8}-\frac{36b}{8}+3b=30$

Simplify.

$\frac{63}{2}-\frac{9}{2}b+3b=30$

Subtract $\frac{63}{2}$

$-\frac{9}{2}b+3b=30-\frac{63}{2}$

Combine like terms.

$\frac{-9+2*3}{2}b=\frac{30*2-63}{2}$

$\frac{-9+6}{2}b=\frac{60-63}{2}$

$\frac{-3}{2}b=\frac{-3}{2}$

Muliply by the reciprocal or inverted fraction next to b.

$(-\frac{2}{3})(-\frac{3}{2}) b=-\frac{3}{2}(-\frac{2}{3})$

$b=1$

Now plug this value into any of the equations to find the value of a.

$8a+4b=28\\8a+4(1)=28\\8a+4=28\\8a=28-4\\8a=24\\a=\frac{24}{8}\\ a=3$

5 0

3 years ago

Write the equation of the line that passes through the points (-6,1) and (-2,5). Put your answer in fully reduced point-slope fo

irinina [24]

(-6,1)
(-2,5)

Slope:-

$\\ \sf\longmapsto m=\dfrac{5-1}{-2+6}=\dfrac{4}{4}=1$

Point-Slope form

$\\ \sf\longmapsto y-y_1=m(x-x_1)$

$\\ \sf\longmapsto y-1=1(x+6)$

$\\ \sf\longmapsto y-1=x+6$

$\\ \sf\longmapsto x-y+7=0$

3 0

3 years ago

Explain the difference between observed frequency and expected frequency as it relates to Chi-Square test.

emmasim [6.3K]

Answer:

Step-by-step explanation:

A Chi-square test is used to test the test of independence between rows and columns, contingency tables. It is a test related to frequencies. The observed frequency is a given statistical frequency known as the actual frequency, the expected frequency is known as the theoretical frequency is derived from the study by using the sum total of the row and total in the column divided by their corresponding sample size.

5 0

3 years ago

Write an equation of the perpendicular bisector of the line segment whose endpoints are (−1,1) and (7,−5)

icang [17]

The equation is $y = \frac{3}{2} x - \frac{11}{2}$

<u>Explanation:</u>

We have to first find the mid-point of the segment, the formula for which is

$(\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )$

So, the midpoint will be $(\frac{-1+7}{2} , \frac{1-5}{2} )\\\\$

= $(3,-2)$

It is the point at which the segment will be bisected.

Since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment. To determine the segment's slope, we use the slope formula $\frac{y_2-y_1}{x_2-x_1}$