Solve sin^2 2θ=-1-cos^2θ on the interval 0<θ<2pi

Find all the points having an x-coordinate of 4 whose distance from the point (-2,-1) is 10

Marta_Voda [28]

$A(x_1;\ y_1);\ B(x_2;\ y_2)\\\\the\ distance\ between\ A\ and\ B:\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\A(-2;-1);\ B(4;\ y);\ d=10\\\\subtitute\\\\\sqrt{(4-(-2))^2+(y-(-1))^2}=10\\\\\sqrt{(4+2)^2+(y+1)^2}=10\\\\\sqrt{6^2+(y+1)^2}=10\\\\\sqrt{36+(y+1)^2}=10\ \ \ |square\ both\ sides\\\\36+(y+1)^2=10^2\\\\36+(y+1)^2=100\ \ \ |subtract\ 36\ from\ both\ sides\\\\(y+1)^2=64\iff y+1=-\sqrt{64}\ or\ y+1=\sqrt{64}\\\\y+1=-8\ or\ y+1=8\ \ \ \ |subtract\ 1\ from\ both\ sides\\\\y=-9\ or\ y=7$

$Answer:{\boxed{(4;-9)\ or\ (4;\ 7)}$

4 0

3 years ago

Peggy had four times as many quarters as nickels. She had $2.10 in all. How many nickels and how many quarters did she have?

Oksanka [162]

I think the answer is 4n!

8 0

4 years ago

Read 2 more answers

The measures of complementary angles have a sum of 90 degrees.Angle A and angle B are complimentary, and their measures have a d

777dan777 [17]

Answer:

The measure of the angles are 55° and 35°

Step-by-step explanation:

Sum of two angles that are complement of each other are 90.

The angles are A and B, so we can write:

A + B = 90

Also,

The difference is 20. Let A be the greater of them, so we can write equation 2 as:

A - B = 20

Now, we add up both equations, eliminate B and solve for A first:

A + B = 90

A - B = 20

---------------

2A = 90 + 20

2A = 110

A = 110/2

A = 55

And now the measure of B:

A + B = 90

55 + B = 90

B = 90 - 55

B = 35

5 0

4 years ago

Need help with this math problem

ladessa [460]

Answer:

m<1: 51

m<2: 61

m<3: 29

Step-by-step explanation:

m<1 = 51, because to find the 3rd angle, you need to add the other two angles and then subtract 180 from that answer.

61 + 68 = 129

180 - 129 = 51

m<2 = 61, because it's a vertical angle, meaning that the angle that's opposite to it exactly, is the same. So since the angle opposite to m<2 is 61, that's what the answer would be.

m<3 = 29, because all you need to do is add 90 and 61, and then subtract 180 by the answer. I got 90 as one of the angle measurements because there's a right triangle, meaning it's 90. Then since we already know what angle 2 is (61) then all you need to do is add:

90 + 61 = 151

Then subtract:

180 - 151 = 29

8 0

4 years ago

Examine the data below for a stalk of corn. Logarithmic regression Use logarithmic regression to find an equation of the form y

masya89 [10]

The value of a and b for the data values of stalk of corn using the logarithmic regression is -76.2038 and 37.6735 respectively.

<h3>What is logarithmic regression?</h3>

Logarithmic regression is a type of regression which is used to model the statement in which the growth or decay initially at rapid rate, and then slow down with respect to time.

The data of the table for the day and height of the stalk of corn is listed below.

Day (x) 9 12 22 40

Height (y) in 5 17 45 60

Mean of x values,

$m_x=\dfrac{9+12+22+40}{4}\\m_x=17.5581$

Mean of y values,

$m_y=\dfrac{5+17+45+60}{4}\\m_y=31.75$

For the above table, the value of correlation coefficient is 0.99133. For these values, the logarithmic regression can be given as,

$y = -76.2038+37.6735\ln(x)$

Compare it with the following logarithmic regression equation, we get

$y = a+b\ln(x)$

$a=-76.2038\\b=37.6735$

Hence, the value of a and b for the data values of stalk of corn using the logarithmic regression is -76.2038 and 37.6735 respectively.

Learn more about the logarithmic regression here;

brainly.com/question/25226042

5 0

2 years ago