All categories

3 years ago

This is converting to polar form, I need help and the answer too.

Mathematics

1 answer:

Mila [183]3 years ago

7 0

Answer:

2 cis (7/6 pi)

Step-by-step explanation:

r = sqrt( a^2 + b^2)

r = sqrt (-sqrt(3) )^2 + (-1)^2)

= sqrt(3 +1)

= sqrt(4)

= 2

theta = arctan (b/a)

theta = arctan (-1/-sqrt(3))

theta = 30

but this is in the third quardrant -a and -b

so add 180

theta = 210 degrees

convert this to radians

210 * pi/180 = 210/180 * pi = 21/18 * pi = 7/6 * pi

r cis (theta)

2 cis (7/6 pi)

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NEED HELP I WILL GIVE THE MOST BRAINLIEST TO THE FIRST ONE THAT ANSWERS

vesna_86 [32]

Answer:

Center: (3, -2)

Radius: 4.

Step-by-step explanation:

The equation of a circle is (x - h)^2 + (y - k)^2 = r^2.

In this case, the equation given is (x - 3)^2 + (y + 2)^2 = 16.

That means that h = 3, and k = -2. In other words, the center of the circle is (3, -2).

The radius will be

$\sqrt{16} \\= \sqrt{4 * 4} \\= \sqrt{4^2}$

= 4

Hope this helps!

8 0

3 years ago

The coordinates of the vertices of a polygon are (-2, 1). (-3, 3), (-1, 5), (2, 4), and (2, 1). What is the perimeter of the pol

kobusy [5.1K]

Answer:

$15.2\ units$

Step-by-step explanation:

step 1

Plot the vertices of the polygon to better understand the problem

we have

$A(-2, 1). B(-3, 3), C(-1, 5), D(2, 4),E(2, 1)$

using a graphing tool

The polygon is a pentagon (the number of sides is 5)

see the attached figure

The perimeter is equal to

$P=AB+BC+CD+DE+AE$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 2

Find the distance AB

$A(-2, 1). B(-3, 3)$

substitute in the formula

$d=\sqrt{(3-1)^{2}+(-3+2)^{2}}$

$d=\sqrt{(2)^{2}+(-1)^{2}}$

$d_A_B=\sqrt{5}=2.24\ units$

step 3

Find the distance BC

$B(-3, 3), C(-1, 5)$

substitute in the formula

$d=\sqrt{(5-3)^{2}+(-1+3)^{2}}$

$d=\sqrt{(2)^{2}+(2)^{2}}$

$d_B_C=\sqrt{8}=2.83\ units$

step 4

Find the distance CD

$C(-1, 5), D(2, 4)$

substitute in the formula

$d=\sqrt{(4-5)^{2}+(2+1)^{2}}$

$d=\sqrt{(-1)^{2}+(3)^{2}}$

$d_C_D=\sqrt{10}=3.16\ units$

step 5

Find the distance DE

$D(2, 4),E(2, 1)$

substitute in the formula

$d=\sqrt{(1-4)^{2}+(2-2)^{2}}$

$d=\sqrt{(-3)^{2}+(0)^{2}}$

$d_D_E=\sqrt{9}\ units$

$d_D_E=3\ units$

step 6

Find the distance AE

$A(-2, 1).E(2, 1)$

substitute in the formula

$d=\sqrt{(1-1)^{2}+(2+2)^{2}}$

$d=\sqrt{(0)^{2}+(4)^{2}}$

$d_A_E=\sqrt{16}\ units$

$d_A_E=4\ units$

step 7

Find the perimeter

$P=AB+BC+CD+DE+AE$

substitute the values

$P=2.24+2.83+3.16+3+4=15.23\ units$

Round to the nearest tenth of a unit

$P=15.2\ units$

6 0

3 years ago

Solve, leaving in terms of a logarithm, with steps please! 160(0.4^x) +1=321

ludmilkaskok [199]

Answer:

321

Step-by-step explanation:

4 0

4 years ago

A gasoline pump delivers 4 2/5 gallons of gas per minute. How many minutes will it take to fill a gas tank that holds 17 1/4 gal

Liono4ka [1.6K]

Well if it pumps 4 2/5 per minute that is equal to 4 4/10 in a minute or 4.4 because you multiply the top and bottom of the fraction by two. it’s still the same fraction but it is easy to convert to a decimal now. you could use this fraction but it’s much easier to use decimals. Because the first number is a decimal you should make the second one a decimal too. To do this you need to know that 1/4 of 100 is 25. so now we have these numbers and all you do now is divide 17.25 by 4.4 which could be rounded to 4 because it’s a long decimal

8 0

3 years ago

The coordinate grid below shows triangle ABC and its image after translation, triangle A'B'C':

svetlana [45]

Answer:

+6 B

Step-by-step explanation:

Which of the following completes the rule for this translation, (x, y) + (x + 6, )?

8 0

3 years ago