we are given

Firstly, we will find all possible factors of 144

we can also write as

now, we can put exponent to over entire term

now, we can replace 144

now, sqrt will get cancelled with square
and we get

now, we can simplify it

.............Answer
Given:
The shaded sector above covers
of the circle.
Radius of the circle = 3 cm
To find:
The area of the sector in terms of π.
Solution:
The area of a circle is

Substituting
, we get


It is given that the shaded sector above covers
of the circle.
The area of shaded sector 


Therefore, the area of shaded sector is 3π sq. cm.
Answer:
Initial height or what the ball was originally bounced from a height of 9 feet
Step-by-step explanation:
9 represents the height that the ball was originally bounced from.
If you plug in 0 for
into
, you get:
.
9 feet is the initial height since that is what happens at time zero.
3.) An extreme value refers to a point on the graph that is possibly a maximum or minimum. At these points, the instantaneous rate of change (slope) of the graph is 0 because the line tangent to the point is horizontal. We can find the rate of change by taking the derivative of the function.
y' = 2ax + b
Now that we where the derivative, we can set it equal to 0.
2ax + b = 0
We also know that at the extreme value, x = -1/2. We can plug that in as well.

The 2 and one-half cancel each other out.


Now we know that a and b are the same number, and that ax^2 + bx + 10 = 0 at x = -1/2. So let's plug -1/2 in for x in the original function, and solve for a/b.
a(-0.5)^2 + a(-0.5) + 10 = 0
0.25a - 0.5a + 10 = 0
-0.25a = -10
a = 40
b = 40
To determine if the extrema is a minima or maxima, we need to go back to the derivative and plug in a/b.
80x + 40
Our critical number is x = -1/2. We need to plug a number that is less than -1/2 and a number that is greater than -1/2 into the derivative.
LESS THAN:
80(-1) + 40 = -40
GREATER THAN:
80(0) + 40 = 40
The rate of change of the graph changes from negative to positive at x = -1/2, therefore the extreme value is a minimum.
4.) If the quadratic function is symmetrical about x = 3, that means that the minimum or maximum must be at x = 3.
y' = 2ax + 1
2a(3) + 1 = 0
6a = -1
a = -1/6
So now plug the a value and x=3 into the original function to find the extreme value.
(-1/6)(3)^2 + 3 + 3 = 4.5
The extreme value is 4.5
Answer:
StartFraction 9 Over 64 EndFraction
Step-by-step explanation:
He must add the square of half the x coefficient. That coefficient is 3/4, so half of it is 3/8 and the square of that is ...
(3/8)^2 = 9/64
Brian mus add 9/64 to boths sides of the equation.