Answer:
i believe its 376ft
Step-by-step explanation:
4y^2 - 8y + 25x^2 +150x - 171 = 0
4y^2 - 8y + 25x^2 +150x - 171 = 0 Rearrange and regroup.
(25x^2 + 150x) + (4y^2 - 8y) = 0+171. Group the xs together and the ys together.
25(X^2 + 6x) + 4(y^2-2y) = 171. Factorising.
We are going to use completing the square method.
Coefficient of x in the first expression = 6.
Half of it = 1/2 * 6 = 3. (Note this value)
Square it = 3^2 = 9. (Note this value)
Coefficient of y in the second expression = -2.
Half of it = 1/2 * -2 = -1. (Note this value)
Square it = (-1)^2 = 1. (Note this value)
We are going to carry out a manipulation of completing the square with the values
9 and 1. By adding and substracting it.
25(X^2 + 6x) + 4(y^2-2y) = 171.
25(X^2 + 6x + 9 -9) + 4(y^2-2y + 1 -1) = 171
Note that +9 - 9 = 0. +1 -1 = 0. So the equation is not altered.
25(X^2 + 6x + 9) -25(9) + 4(y^2-2y + 1) -4(1) = 171
25(X^2 + 6x + 9) + 4(y^2-2y + 1) = 171+25(9) +4(1) Transferring the terms -25(9) and -4(1)
to other side of equation.
25(X^2 + 6x + 9) + 4(y^2-2y + 1) = 171+25(9) +4(1)
25(X^2 + 6x + 9) + 4(y^2-2y + 1) = 400
We now complete the square by using the value when coefficient was halved.
25(x+3)^2 + 4(y-1)^2 = 400
Divide both sides of the equation by 400
(25(x+3)^2)/400 + (4(y-1)^2)/400 = 400/400 Note also that, 16*25 = 400.
((x+3)^2)/16 + ((y-1)^2)/100 = 1
((x+3)^2)/(5^2) + ((y-1)^2)/(10^2) = 1
Comparing to the general format of an ellipse.
((x-h)^2)/(a^2) + ((y-k)^2)/(b^2) = 1
Coordinates of the center = (h,k).
Comparing with above (x+3) = (x - h) , h = -3.
Comparing with above (y-1) = (y - k) , k = 1.
Therefore center = (h,k) = (-3, 1).
You can easily draw the ellipse...Cheers.
Answer:
C; About 100 in².
Step-by-step explanation:
This problem may seem confusing because they talk about tabletops, but that is just their choice of representing circumference of a circle.
<u>The formula for finding the circumference of a circle is 2πr:</u>
In that case, we can substitute 16 for our r.
Likewise, the tabletop will be if we were to multiply it by π.
Thusly, the table top's circumference can be estimated as .
Hope this helps! ((:
Answer:
Step-by-step explanation:
<u><em>The complete question is</em></u>
How do you calculate the mass of a solid copper cuboid with a density of 9.86 g/cm^3. The dimensions of the cuboid are 10 cm by 3 cm by 5 cm
step 1
Find the volume of the cuboid
step 2
Find the mass
we know that
To find out the mass multiply the density of the solid by its volume
so
First, I would find the difference of 82 and 26: 82 - 26 = 56.
Since there are 7 days in a week, I'd divide 56 by 7: 56/7 = 8.
Therefore, the average weekly change is $8.