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3 years ago

A circle is centered at (-6,3) and has a radius of 11. Where does the point (3,-3) lie?

Mathematics

1 answer:

makvit [3.9K]3 years ago

8 0

As we can see that the distance of the given point is less than the radius,

The point lies inside the circle

Step-by-step explanation:

We will use the distance formula to find the distance between the centre of the circle and the given point. If the distance is less than the radius, the point lies inside the circle. If the distance is equal to the radius then the point lies on the circle. If the distance is greater than the radius of the circle, then the point will be out of the circle.

Given

(-6,3) = (x1,y1)

(3,-3) = (x2, y2)

The distance formula is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\= \sqrt{(3-(-6))^2+(-3-3)^2}\\=\sqrt{(3+6)^2+(-6)^2}\\=\sqrt{(9)^2+36}\\=\sqrt{81+36}\\=\sqrt{117}\\=10.81$

As we can see that the distance of the given point is less than the radius,

The point lies inside the circle

Keywords: Circle, Equation of circle

Learn more about circle at:

#LearnwithBrainly

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A new gas- and electric-powered hybrid car has recently hit the market. The distance traveled on 1 gallon of fuel is normally di

Doss [256]

Answer:

a) P [ Z > 70 ] = 0.1075 or 10.75 %

b) P [ Z < 60 ] = 0.1038 or 10.38 %

c) P [ 55 ≤ Z ≤ 70 ] = 0.8882 or 88.82 %

Step-by-step explanation:

Normal Distribution μ = 65 and σ = 4

a) The probability of the car travels more than 70 miles per gallon is:

P [ Z > 70 ] = (Z-μ) ÷ σ ⇒ P [ Z > 70 ] = (70-65) ÷4 P [ Z > 70 ] = 1.25

the point 1.25 corresponds at values, from left tail up to 70 so we must go and look for the area for the point 1.24 which is 0.8925. Then we have the area or probability of all cars traveling up to 70 miles therefore we have to subtract 1 -0,8925

P [ Z > 70 ] = 0.1075 or 10.75 %

b)The probability of the car travels less than 60 miles per gallon is:

P [ Z < 60 ] = ( 60 - μ ) ÷ σ ⇒ P [ Z < 60 ] = (60-65)÷ 4 P [ Z < 60 ] = -1.25

Again -1.25 corresponds to 60 miles per gallon threfore we move to the left and find for point -1.26 which area is 0.1038 so

P [ Z < 60 ] = 0.1038 10.38 %

c) P [ 55 ≤ Z ≤ 70]

For point Z = 70 or 1.25 (case a above) P [ Z ≤ 70] = (70-65)÷4

P [ Z ≤ 70] = 1.25

In this case we got the whole area from the left tail up to 1.25

P [ Z ≤ 70] = 0.8944 (includes the area of the point from the left tail up to the point assocciated to 55 miles and for that reason we have to subtract that area)

P [ Z ≥ 55 ] = (55-65) ÷ 4 P [ Z ≥ 55 ] = -2.5 and the area is 0.0062

So P [ 55 ≤ Z ≤ 70 ] = 0.8944 - 0.0062 = 0.8882

8 0

3 years ago

A father is 32 years older than his son. In four years,

sergiy2304 [10]

Answer:

father: 36
son: 4

Step-by-step explanation:

Let s represent the son's age now. Then s+32 is the father's age. In 4 years, we have ...

5(s+4) = (s+32)+4

5s +20 = s +36 . . . . . eliminate parentheses

4s = 16 . . . . . . . . . . . . subtract s+20

s = 4

The son is now 4 years old; the father, 36.

_____

<em>Alternate solution</em>

In 4 years, the ratio of ages is ...

father : son = 5 : 1

The difference of their ages at that time is 5-1 = 4 "ratio units". Since the difference in ages is 32 years, each ratio unit must stand for 32/4 = 8 years. That is, the future age ratio is ...

father : son = 40 : 8

So, now (4 years earlier), the ages must be ...

father: 36; son: 4.

5 0

3 years ago

What is the solution of log(3x − 2)125 = 3?

Reil [10]

$log_{3x - 2}125 = 3 \\ (3x - 2)^3 = 125 \\ \sqrt[3]{(3x - 2)^3} = \sqrt[3]{125} \\ 3x - 2 = 5 \\ 3x = 5 + 2 \\ 3x = 7 \\ x = 7/3$