Answer:
x = 2 + sqrt(5) or x = 2 - sqrt(5)
Step-by-step explanation using the quadratic formula:
Solve for x over the real numbers:
7 (x^2 - 4 x - 1) = 0
Divide both sides by 7:
x^2 - 4 x - 1 = 0
Add 1 to both sides:
x^2 - 4 x = 1
Add 4 to both sides:
x^2 - 4 x + 4 = 5
Write the left hand side as a square:
(x - 2)^2 = 5
Take the square root of both sides:
x - 2 = sqrt(5) or x - 2 = -sqrt(5)
Add 2 to both sides:
x = 2 + sqrt(5) or x - 2 = -sqrt(5)
Add 2 to both sides:
Answer: x = 2 + sqrt(5) or x = 2 - sqrt(5)
Answer:
31x^2-2 is the answer....
Step-by-step explanation:
The base of a parallelogram is 28.4 cm.
The height is one fourth of the base.
28.4 ÷ 4 = 7.1, so the height is 7.1 cm.
What the area of the parallelogram?
The area of any parallelogram is the base times the height.
28.4 cm × 7.1 cm = 201.64 cm²
12(3w+8)=25
36w+96=25 ( I used the distributive property)
-96 . -96
36w=-71
w=-1.972222.... ( I divided both sides by 36)
The cone equation gives

which means that the intersection of the cone and sphere occurs at

i.e. along the vertical cylinder of radius

when

.
We can parameterize the spherical cap in spherical coordinates by

where

and

, which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is

. So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is

Now the surface area of the cap is given by the surface integral,



