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Alchen [17]
3 years ago
5

Simplify the given expression. Assume that no variable equals 0. (14x^20y^10 / 28x12y^14)^4

Mathematics
1 answer:
sertanlavr [38]3 years ago
7 0

what does the ^ mean.

i will answer in the comments

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Find the locus of a point such that the sum of its distance from the point ( 0 , 2 ) and ( 0 , -2 ) is 6.
jok3333 [9.3K]

Answer:

\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1

Step-by-step explanation:

We want to find the locus of a point such that the sum of the distance from any point P on the locus to (0, 2) and (0, -2) is 6.

First, we will need the distance formula, given by:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Let the point on the locus be P(x, y).

So, the distance from P to (0, 2) will be:

\begin{aligned} d_1&=\sqrt{(x-0)^2+(y-2)^2}\\\\ &=\sqrt{x^2+(y-2)^2}\end{aligned}

And, the distance from P to (0, -2) will be:

\displaystyle \begin{aligned} d_2&=\sqrt{(x-0)^2+(y-(-2))^2}\\\\ &=\sqrt{x^2+(y+2)^2}\end{aligned}

So sum of the two distances must be 6. Therefore:

d_1+d_2=6

Now, by substitution:

(\sqrt{x^2+(y-2)^2})+(\sqrt{x^2+(y+2)^2})=6

Simplify. We can subtract the second term from the left:

\sqrt{x^2+(y-2)^2}=6-\sqrt{x^2+(y+2)^2}

Square both sides:

(x^2+(y-2)^2)=36-12\sqrt{x^2+(y+2)^2}+(x^2+(y+2)^2)

We can cancel the x² terms and continue squaring:

y^2-4y+4=36-12\sqrt{x^2+(y+2)^2}+y^2+4y+4

We can cancel the y² and 4 from both sides. We can also subtract 4y from both sides. This leaves us with:

-8y=36-12\sqrt{x^2+(y+2)^2}

We can divide both sides by -4:

2y=-9+3\sqrt{x^2+(y+2)^2}

Adding 9 to both sides yields:

2y+9=3\sqrt{x^2+(y+2)^2}

And, we will square both sides one final time.

4y^2+36y+81=9(x^2+(y^2+4y+4))

Distribute:

4y^2+36y+81=9x^2+9y^2+36y+36

The 36y will cancel. So:

4y^2+81=9x^2+9y^2+36

Subtracting 4y² and 36 from both sides yields:

9x^2+5y^2=45

And dividing both sides by 45 produces:

\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1

Therefore, the equation for the locus of a point such that the sum of its distance to (0, 2) and (0, -2) is 6 is given by a vertical ellipse with a major axis length of 3 and a minor axis length of √5, centered on the origin.

5 0
3 years ago
Read 2 more answers
A kite is flying 9.75 feet above a lamp post that is 84 2/3 feet tall. How high is the kitchen flying?
Elden [556K]

The kite is flying at the height of 94 5/2 feet.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.

= 9.75 +84 2/3                                               { 9+0.75 = 9.75   84 2/3}

= 9 + 0.75 +84 2/3                                           { a+b+c+d = a+c+b+d}

= 9 + 84 + 3/4 + 2/3

=93 + 3*3 / 4*3 + 4*2 / 4*3

= 93 + 9/12 + 8/12

= 93 + 17/12

= 93 + (1 + 5/12)

= 94 + 5/12

=94 5/12 feet

{kite height = (post height + the height of the kite above the post)

To learn more about addition from given link

brainly.com/question/24536701

#SPJ9

8 0
1 year ago
How to solve this one step inequality
dem82 [27]

Answer: add 1 to both sides

             -1+r+1≥4+1

              simplify

               x≥5

Step-by-step explanation:

8 0
3 years ago
Please answer this correctly
kotykmax [81]

Answer:

Option C

20 +40g

Step-by-step explanation:

5(4 +8g)

20 +40g

4 0
3 years ago
25 POINTS<br><br> IF U TELL ME THE ANSWER I'LL GIVE U 20 POINTS AND MARK YOU AS BRAINLIEST
choli [55]

I am not sure about this. I am sure that 3 has atleast 1.

6 0
3 years ago
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