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3 years ago

Which is an equation of a circle with center (-10, 6) and radius 8?

1 answer:

8 0

An equation of a circle:

(x - a)² + (y - b)² = r²

(a; b) - a coordinates of a center
r - a radius

r = 8; (-10; 6) ⇒ a = -10 and b = 6

subtitute

(x - (-10))² + (y - 6)² = 8²

Answer: (x + 10)² + (y - 6)² = 64

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Simplify the following expression below:

IrinaK [193]

So, 4/3 - 2i

4/3 - 2i = 12/13 + i8/13

multiply by the conjugate:
3 + 2i/3 + 2i
= 4(3 + 2i)/(3 - 2i) (3 + 2i)
(3 - 2i) (3 + 2i) = 13

(3 - 2i) (3 + 2i)

apply complex arithmetic rule: (a + bi) (a - bi) = a^2 + b^2
a = 3, b = - 2
= 3^2 + (- 2)^2

refine: = 13
= 4(3 + 2i)/13

distribute parentheses:
a(b + c) = ab + ac
a = 4, b = 3, c = 2i
= 4(3) + 4(2i)

Simplify:
4(3) + 4(2i)
12 + 8i

4(3) + 4(2i)
Multiply the numbers: 4(3) = 12
= 12 + 2(4i)

Multiply the numbers: 4(2) = 8
= 12 + 8i

12 + 8i
= 12 + 8i/13

Group the real par, and the imaginary part of the complex numbers:

Your answer is: 12/13 + 8i/13

Hope that helps!!!

7 0

3 years ago

Help please explain

MatroZZZ [7]

Given:

$\sin^{-1}\left(\dfrac{5}{8}\right)=A$

To find:

The correct equivalent equation.

Solution:

We have,

$\sin^{-1}\left(\dfrac{5}{8}\right)=A$

Taking sin on both sides, we get

$\sin \sin^{-1}\left(\dfrac{5}{8}\right)=\sin A$

$\dfrac{5}{8}=\sin A$ $[\because \sin (\sin^{-1}\theta )=\theta]$

Interchanging the sides, we get

$\sin A=\dfrac{5}{8}$

Therefore, the correct option is 4.

8 0

3 years ago

What's the difference between radius and diameter?

Andreas93 [3]

Diameter is from one side of the circle to the other through the middle
and the radius the from the middle to the edge of the circle
so radius is half the diameter

7 0

3 years ago

Read 2 more answers

If a police officer pulls over someone for speeding, the police officer can either give a ticket or a warning, so it is impossib

babymother [125]

Answer:

0.49

Step-by-step explanation:

P(warning or ticket) = P(warning) + P(ticket) − P(warning and ticket)

0.52 = 0.03 + P(ticket) − 0

P(ticket) = 0.49

3 0

3 years ago

SHOE COLLECTION: Marquise, Bron'Tavious, and JayDarius each have a shoe collection of Nike Air Vapor Max shoes. Marquise has two

Natasha_Volkova [10]

Answer:

(a) The number of shoes that Marquise has is 40 pairs of shoes

(b) The number of pairs of shoes that Bron'Tavious has is 20 pairs of shoes

Step-by-step explanation:

The given information are;

The number of shoes that Marquise has = 2 × The number of pairs of shoes that Bron'Tavious

The number of pairs of shoes that JayDarius has = The number of pairs of shoes that Bron'Tavious + 15

The total number of pairs of shoes they have all together = 95 pairs of shoes

Let the number of pairs of shoes that Bron'Tavious has = X. Therefore, we have;

The number of shoes that Marquise has = 2 × X

The number of pairs of shoes that JayDarius has = X + 15

The total number of pairs of shoes they have all together = X + X + 15 + 2 × X = 95

X + X + 15 + 2 × X = 95

4 × X + 15 = 95

4 × X = 95 - 15 = 80

X = 80/4 = 20

∴ X = 20

(a) The number of shoes that Marquise has = 2 × X = 2 × 20 = 40

The number of shoes that Marquise has = 40 pairs of shoes

(b) The number of pairs of shoes that Bron'Tavious has = X = 20

The number of pairs of shoes that Bron'Tavious has = 20 pairs of shoes

The number of pairs of shoes that JayDarius has = 35 pairs of shoes.

5 0

3 years ago