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ad-work [718]
4 years ago
10

4. Determine the center and radius of each circle.

Mathematics
1 answer:
Vladimir79 [104]4 years ago
8 0
<h2>a) Center (0,0) and radius 5</h2><h2>b) Center (-1,-2) and radius 2.236</h2><h2>c) Center (2,9) and radius 4     </h2>

Step-by-step explanation:

Equation of circle with (h,k) as center and radius r is given by,

          (x-h)²+(y-k)² = r²

a) 3x²+3y²=75

   Dividing by 3

                    x²+y²=25

                    (x-0)²+(y-0)² = 5²  

          Center (0,0) and radius 5

b) 2(x+1)²+2(y+2)²=10

 Dividing by 2

        (x+1)²+(y+2)²=5

        (x-(-1))²+(y-(-2))²= 2.236²

          Center (-1,-2) and radius 2.236

c)  4(x−2)²+4(y−9)²−64=0  

           4(x−2)²+4(y−9)²= 64

 Dividing by 4

          (x−2)²+(y−9)²= 16

          (x−2)²+(y−9)²= 4²

          Center (2,9) and radius 4                                  

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Solve the quadratic equation<br> HINT: Answers will be a decimals<br> 2x2 - 12x+8 = 3
Oduvanchick [21]

Answer:

x= 5.55 and 0.45

Step-by-step explanation:

Quadratic Equation = (-b±√b²-4(a)(c))÷2(a)

Get equation = to 0 by subtracting the 3 on the right side of the = sign

2x² - 12x + 5

Identify the variables

a=2

b=-12

c=5

Put them into the quadratic equation

(-(-12)± √-12² - 4(2)(5))÷2(2)

Simplify

(12 ±√144 - 40)÷4

(12±√104)÷4

Now split into 2 equations (one with addition one with subtraction) because of the ± then continue simplifying

(12 - √104)÷4                  (12 + √104)÷4

(12 - 10.198039)/4          (12 + 10.198039)/4

5.54950975                  0.45049025

Round

5.55                               0.45

6 0
3 years ago
Suppose a football is kicked with an initial velocity of 82 ft/sec., at an angle of
satela [25.4K]

Answer:

The position P is:

P = 87\^x + 75\^y ft     <u><em> Remember that the position is a vector. Observe the attached image</em></u>

Step-by-step explanation:

The equation that describes the height as a function of time of an object that moves in a parabolic trajectory with an initial velocity s_0 is:

y(t) = y_0 + s_0t -16t ^ 2

Where y_0 is the initial height = 0 for this case

We know that the initial velocity is:

82 ft/sec at an angle of 58 ° with respect to the ground.

So:

s_0 = 82sin(58\°) ft/sec

s_0 = 69.54 ft/sec

Thus

y(t) = 69.54t -16t ^ 2

The height after 2 sec is:

y(2) = 69.54 (2) -16 (2) ^ 2

y(2) = 75\ ft

Then the equation that describes the horizontal position of the ball is

X(t) = X_0 + s_0t

Where

X_ 0 = 0 for this case

s_0 = 82cos(58\°) ft / sec

s_0 = 43.45 ft/sec

So

X(t) = 43.45t

After 2 seconds the horizontal distance reached by the ball is:

X (2) = 43.45(2)\\\\X (2) = 87\ ft

Finally the vector position P is:

P = 87\^x + 75\^y ft

6 0
3 years ago
Is the figure on the right congruent to the sample figure? EXPLAIN.
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he can either send one half or the other half.

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A polygraph (lie detector) is an instrument used to determine if the individual is telling the truth. These tests are considered
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Answer:

Step-by-step explanation:

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Therefore,

P(Type-I) = 0.07

Therefore 0.07 is the required probability here.

b) The probability of a Type II error in a lie detection test would be the probability that the lie detection machine incorrectly detected truth for the the people who are actually liars. This is thus 1 - reliability.

P(Type-II) = 1 - Reliability = 1- 0.86 = 0.14

Therefore 0.14 is the required probability here.

7 0
3 years ago
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