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Semenov [28]
3 years ago
5

Find+the+positive+value+for+α+if+the+radius+of+the+circle+3x^2+3y-6αx+12y-3α=0+is+4

Mathematics
1 answer:
Alik [6]3 years ago
8 0

Answer:

\alpha=3

Step-by-step explanation:

<u>Equation of a Circle</u>

A circle of radius r and centered on the point (h,k) can be expressed by the equation

(x-h)^2+(y-k)^2=r^2

We are given the equation of a circle as

3x^2+3y^2-6\alpha x+12y-3\alpha=0

Note we have corrected it by adding the square to the y. Simplify by 3

x^2+y^2-2\alpha x+4y-\alpha=0

Complete squares and rearrange:

x^2-2\alpha x+y^2+4y=\alpha

x^2-2\alpha x+\alpha^2+y^2+4y+4=\alpha+\alpha^2+4

(x-\alpha)^2+(y+2)^2=r^2

We can see that, if r=4, then

\alpha+\alpha^2+4=16

Or, equivalently

\alpha^2+\alpha-12=0

There are two solutions for \alpha:

\alpha=-4,\ \alpha=3

Keeping the positive solution, as required:

\boxed{\alpha=3}

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allochka39001 [22]

Answer:

420,000 J/Kg

Step-by-step explanation:

energy= temperature change* mass* specific heat capacity

energy= 20*5*4200

energy= 420,000

7 0
2 years ago
Conrad had $110 to spend on 9 cheese pizzas for a party. After buying them, he had $8.75 left. How much did each pizza cost? Sho
Igoryamba
Subtract 110 and 8.75 and you get 101.25 then divide that by 9 and you get 11.25

3 0
3 years ago
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Yakvenalex [24]
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8 0
2 years ago
BRAINLIEST ANSWER!! ASAP<br><br> 3(x+1)+6=-9<br> PLEASE EXPLAIN HOW YOU GOT THE ANSWER
Kryger [21]

Answer:

x=-6

Step-by-step explanation:

use distributive property on the () and times x and 1 by three

then you subtract 6 from both sides

then subtract three from both sides

then divide both sides by 3

your work would look like this:

3(x+1)+6=-9

3x+3+6=-9

3x+3=-15

3x=-18

x=-6

Hope this helps!

8 0
3 years ago
Read 2 more answers
Choose the correct response​
lilavasa [31]

Answer:

f(2) = 9

Step-by-step explanation:

It's give in the question,

Two different functions are,

f(x) = 4x + 1

g(x) = -2x

Then we have to find the output value of function 'f' for the input value x = 2.

By substituting the value of x in the function 'f',

f(2) = 4(2) + 1

     = 9

f(2) = 9

5 0
2 years ago
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