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viktelen [127]
3 years ago
7

Which conic section does the equation below describe? (y-1)^2=8(x+3)

Mathematics
1 answer:
AURORKA [14]3 years ago
3 0

Answer:

parabola

Step-by-step explanation:

This is the equation of a parabola, notice that only one of the variables (in this case the variable y) appears squared in the equation, and it satisfies the general form of a parabola with branches pointing horizontally.

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What is the maximum volume in cubic inches of an open box to be made from a 12-inch by 16-inch piece of cardboard by cutting out
Romashka-Z-Leto [24]

If you start with a 12x16 rectangle and cut square with side length x, when you bend the sides you'll have an inner rectangle with sides 12-2x and 16-2x, and a height of x.

So, the volume will be given by the product of the dimensions, i.e.

(12-2x)(16-2x)x = 4x^3-56x^2+192x

The derivative of this function is

12x^2-112x+192

and it equals zero if and only if

12x^2-112x+192=0 \iff x = \dfrac{14\pm 2\sqrt{13}}{3}

If we evaluate the volume function at these points, we have

f\left(\dfrac{14-2\sqrt{13}}{3}\right) = \dfrac{64}{27}(35+13\sqrt{13})> f\left(\dfrac{14-2\sqrt{13}}{3}\right) = -\dfrac{64}{27}(13\sqrt{13}-35)

So, the maximum volume is given if you cut a square with side length

x=\dfrac{14-2\sqrt{13}}{3}\approx 2.7

5 0
3 years ago
How to write a slope equation using y intercept as 6 and the slope as -2
Bingel [31]
The slope equation is y=mx+b where m is the slope and b is the y intercept. After plugging the numbers into the equation you should get y=-2x+6. Hope this helps!
4 0
3 years ago
Six plus -2 times a number is the same as 26 plus six times the same number.
aleksandr82 [10.1K]

Step-by-step explanation:

let the number be x

and according to question,

six + 2 times a number = 2x + 6

26 + 6 times a number = 6x + 26

→ 2x + 6 = 6x + 26

→ -6x + 2x = 26 - 6

→ -4x = 20

→ x = 20/4 = 5

→ x = 5

therefore, the number is 5.

hope this answer helps you dear...take care and may u have a great day ahead!

7 0
3 years ago
Expanded -8(-2x-5)<br> please give answer
nika2105 [10]

Answer:

-80

Step-by-step explanation:

We have to do the parentheses first because it's part of PEDMAS.

-2x-5= 10

Next, we take 10 times -8

-8 x 10= -80

There you go! Hope this helps!

8 0
3 years ago
Read 2 more answers
Find the measure of angle C in the triangle below. (The figure is not drawn to scale.)
alisha [4.7K]
2x+4x-4=80
6x-4=80
6x=84
84/6=14
Angle c = 4 x 14= 56 - 4 = 52

Hope this helps.
6 0
2 years ago
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