So, 30 is the perimeter. We are told the table is twice as long as it is wide.
So, we have think of 2 numbers, one being twice as big than the other. So, it is a rectangle The two number represents the length and the width. To find the perimeter we add all the lengths and the widths. Since the pool table is a rectangle we have two lengths and two widths.
So,
the tow numbers be 10 and 5. 5 is half of 10 and, when multiplied by 2 it is 10. So just to make sure the numbers 5 and 10 work out lets do a calculation.
So,
10+5+10+5 = 30feet. This proves that the sides are these two numbers.
a) {-21, -11}
b) {-29,21}
c) {-41,9}
d) {-1,1}
Answer:
pi/3? 2pi/3?
Step-by-step explanation:
Choose exactly two answers that are correct.
A.
Triangle RST was reflected across the x-axis and then rotated 90° clockwise around the origin.
B.
Triangle RST was reflected across the x-axis and then reflected across the y-axis.
C.
Triangle RST was rotated counterclockwise 90° around the origin and then reflected across the x-axis.
D.
Triangle RST was translated 8 units right and then reflected across the x-axis.
Answer:
what they promote? describe each.
b. Use your variables to determine expressions for the volume, surface area, and cost of the can.
c. Determine the total cost function as a function of a single variable. What is the domain on which you should consider this function?
d. Find the absolute minimum cost and the dimensions that produce this value.
Answer:
a) file annex
b) V(c) = π*x²*y
A(x) = 2*π*x² + 32/x
C(x) = 0,1695*x² + 0,48 /x
Domain C(x) = {x/ x >0}
d) C(min) = 0,64 $
x = 1.123 in radius of base
y = 4,04 in height of the can
Step-by-step explanation:
See annex file
Lets:
call x = radius of the base of the cylinder and
y = the height of the cylinder
Then
Volume of the cylinder ⇒ V(c) = π*r²*h ⇒V(c) = π*x²*y
And y = V / ( π*x²) ⇒ V = 16 / ( π*x²)
Area of cylinder = lids area + lateral area
lids area = 2*π*x² ⇒ lateral area = 2*π*x*y
lateral area =2*π*x [16/(π*x²) ] ⇒ lateral area = 32/x
Then
A(x) = 2*π*x² + 32/x
Function cost C(x)
C(x) = 0.027 * 2*π*x² + 0.015 * (32/x)
C(x) = 0,1695*x² + 0,48 /x
Domain C(x) = {x/ x >0}
Now function cost:
C(x) = 0,1695*x² + 0,48 /x
Taking derivative:
C´(x) = 2*0,1695*x - 0.48/x² C´(x) = 0,339*x - 0.48/x²
C´(x) = 0 0.339*x³ - 0.48 = 0 x³ = 0.48/0.339 x³ = 1.42
x = 1.123 in
y = 16/πx² ⇒ y = 4,04 in
C(min) = 0,64 $