Answer:
<em>Your answer will be </em>
<em> cups of popcorn.</em>
Step-by-step explanation:
To find out how much the new bags hold, you need to find out the discount.
<em>We know that the discount is </em>
<em>.</em>
<em>To figure out how much the new bags hold, subtract by the old bags.</em>
<em>The new bags hold 12 cups of popcorn. </em>
First integral
Since 
is a linear function, its graph is a line. This means that you can decompose the area under its graph as the sum of a right triangle and a rectangle, as shown in the attached image.
All the dimensions are fairly easy to deduce: we have
So, the area of the triangle is
For the rectangle, we have
So, the total area is 
Second integral
We have
So, this function is the upper half of the unit circle (the two halves are the functions 
)
Since the area of the unit circle is 
, the value of the integral is 
Third integral
It follows the exact same logic as the first one, you only have to adjust the numbers.
Answer:
2m^7n^4/3
Step-by-step explanation:
Applying the area of a rectangle, the width of the walkway (x) is: 4 feet.
<h3>What is the Area of a Rectangle?</h3>
Area of a rectangle = (length)(width)
Total area of the pool and walkway = 300 sq. ft
Length of the pool and walkway = 12 + 2x
Width of the pool and walkway = 7 + 2x
Thus, we will have the equation of the total area as:
(12 + 2x)(7 + 2x) = 300
4x² + 38x + 84 = 300
4x² + 38x + 84 - 300 = 0
4x² + 38x - 216 = 0
Factorize
(x - 4)(2x + 27) = 0
x = 4
or
x = -27/2
The width, x, cannot be negative, so, the width of the walkway (x) would be 4 feet.
Learn more about the area of a rectangle on:
brainly.com/question/25292087
#SPJ1
Answer:
100 - 4q²
Step-by-step explanation:
(10 - 2q)(10 + 2q)
each term in the second factor is multiplied by each term in the first factor.
10(10 + 2q) - 2q(10 + 2q) ← distribute parenthesis
= 100 + 20q - 20q - 4q² ← collect like terms
= 100 - 4q²
