the zeros and the x-intercepts are the same with different names
x -intercepts are (- 7, 0 ) and (2, 0 )
if x = a is a zero then (x - a ) is a factor
thus (x + 7 ) and (x - 2 ) are the factors
Recall that a circle of radius 2 centered at the origin has equation
where the positive root gives the top half of the circle in the x-y plane. The definite integral corresponds to the area of the right half of this top half. Since the area of a circle with radius
is
, it follows that the area of a quarter-circle would be
.
You have
, so the definite integral is equal to
.
Another way to verify this is to actually compute the integral. Let
, so that
. Now
Recall the half-angle identity for cosine:
This means the integral is equivalent to
Answer:
806 meters
Step-by-step explanation:
This is a number you will have memorized in grade school. If not, you can always perform long division of 2 by 3 to find it---or ask your calculator.
2/3 = 0.6666_6 . . . . . . repeating 6s indefinitely
____
Most folks get tired of writing 6s after a couple million of them, so they round it off to 0.67 or 0.667. These rounded values are NOT exactly 2/3.
Answer:
We know that:
She needs 9/10 grams of flour for the cake (this quantity does not make a lot of sense, maybe is written incorrectly, but is the only info we have, so let's solve the problem with this)
She only has 1/3 of the amount she needs.
How much flour does she have?
Well, she needs 9/10 grams, and she has one-third of that.
Then she has (1/3) times (9/10) grams, this is:
F = (1/3)*(9/10) grams
F = (1*9)/(3*10) grams
F = 9/30 grams
That is the amount of flour that she has.
