Answer:
f(4) = 2
Step-by-step explanation:
Step 1: Define
f(x) = 2x - 6
g(x) = x²
Step 2: Find g(-2)
g(-2) = (-2)²
g(-2) = 4
Step 3: Find f(g(-2))
f(g(-2)) = f(4)
f(4) = 2(4) - 6
f(4) = 8 - 6
f(4) = 2
The integral above is definite so we must first calculate for indefinite one.
Rule:
.
Now we apply this rule and get:
Or just simply:
Now we integrate:
look at the screenshot :)
Answer:
Part one: The function rule for the area of the rectangle is A(x) = 3x² - 2x
Part two: The area of the rectangle is 8 feet² when its width is 2 feet
Step-by-step explanation:
Assume that the width of the rectangle is x
∵ The width of the rectangle = x feet
∵ The length of the rectangle is 2 ft less than three times its width
→ That means multiply the width by 3, then subtract 2 from the product
∴ The length of the rectangle = 3(x) - 2
∴ The length of the rectangle = (3x - 2) feet
∵ The area of the rectangle = length × width
∴ A(x) = (3x - 2) × x
→ Multiply each term in the bracket by x
∵ A(x) = x(3x) - x(2)
∴ A(x) = 3x² - 2x
∴ The function rule for the area of the rectangle is A(x) = 3x² - 2x
∵ The rectangle has a width of 2 ft
∵ The width = x
∴ x = 2
→ Substitute x by 2 in A(x)
∵ A(2) = 3(2)² - 2(2)
∴ A(2) = 3(4) - 4
∴ A(2) = 12 - 4
∴ A(2) = 8
∴ The area of the rectangle is 8 feet² when its width is 2 feet
<span>let x be number of bicycles
and y the number of</span> tricycles<span>
So
x + y = 25 equation 1
The number of wheels is
2x + 3y = 63 equation 2
</span>We can multiply the equation 1 by two and subtract from the second one...
2x + 3y = 63
-(2x + 2y = 50)
then
y = 13 trikes and
x = 12 bikes