First let's move change the coordinate system so that the rotation axis becomes y
then f(x)=`16x becomes f(x)=16(x-2)=16x-32, y=0 stays as it is but x=1 becomes x=3
then we apply the formula for cyl shells method:
V=integral 2 to 3 (2pi*x*f(x))dx = int 2-3 (2pi*x*16x-2pi*x*32)dx=
int 2-3 32pi*x^2 dx - int 2-3 64pi*x dx = 2-3| 32pi*x^3/3 - 32pi*x^2 =
32pi*27/3 - 32pi*9 - 32pi*8/3+ 32pi*4 = 32pi*(9-9-8/3+4) = 32pi*4/3 = 128pi/3
Answer:
5.6
Step-by-step explanation:
Mrs. Sanchez gets 36 miles per gallon
Mr. White gets 30.4 miles per gallon (76 ÷ 2.5)
Answer:
The answer to this question is s n= 3.
Answer:
<h3>5 seccs</h3>
Step-by-step explanation:
Given the modeled function of the height expressed as;
h(t)=-16t^2+64t+80
The ball hits the ground when h(t) = 0 (when the height is zero)
Substitute into the function and find t;
0 =-16t^2+64t+80
divide through by -16
0 = t²-4t-5
Factorize;
t²-4t-5 = 0
t²-5t+t-5 = 0
t(t-5)+1(t-5) = 0
(t+1)(t-5) = 0
t + 1 = 0 and t-5 = 0
t = -1 and t = 5
Time can't be negative
Hence it will take the ball 5secs before it hits the ground
Answer:
x = - 4
Step-by-step explanation:
Given
3 - 2 |0.5x + 1.5 | = 2 ( subtract 3 from both sides )
- 2 |0.5x + 1.5 | = - 1 ( divide both sides by - 2 )
|0.5x + 1.5 | = 0.5
The absolute value function always gives a positive value, however, the expression inside can be positive or negative, thus
0.5x + 1.5 = 0.5 ( subtract 1.5 from both sides )
0.5x = - 1 ( divide both sides by 0.5 )
x = - 2 ← solution Manuela obtained
OR
-(0.5x + 1.5) = 0.5 ← distribute parenthesis on left side by - 1
- 0.5x - 1.5 = 0.5 ( add 1.5 to both sides )
- 0.5x = 2 ( divide both sides by - 0.5 )
x = - 4 ← other solution to the equation
