SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
Step-by-step explanation:
Given :
At the state fair, admission at the gate is $9.
In addition, the cost of each ride is $3.
Suppose that Sam will go on x rides.
Then, cost of x rides ( in dollars) = Cost per ride x Number of rides
=3x
Total cost ( in dollars) : Admission fee + cost of x rides
= 9+3x
Sam wants the total number of dollars he spends on admission and rides to be at most t ( less than or equal to t )

CONCLUSION:
The final answer is:
Using the values and variables given, write an inequality describing this.

Answer:
a) 8π
b) 8/3 π
c) 32/5 π
d) 176/15 π
Step-by-step explanation:
Given lines : y = √x, y = 2, x = 0.
<u>a) The x-axis </u>
using the shell method
y = √x = , x = y^2
h = y^2 , p = y
vol = ( 2π ) 
=
∴ Vol = 8π
<u>b) The line y = 2 ( using the shell method )</u>
p = 2 - y
h = y^2
vol = ( 2π )
= 
= ( 2π ) * [ 2/3 * y^3 - y^4 / 4 ] ²₀
∴ Vol = 8/3 π
<u>c) The y-axis ( using shell method )</u>
h = 2-y = h = 2 - √x
p = x
vol = 
= 
= ( 2π ) [x^2 - 2/5*x^5/2 ]⁴₀
vol = ( 2π ) ( 16/5 ) = 32/5 π
<u>d) The line x = -1 (using shell method )</u>
p = 1 + x
h = 2√x
vol = 
Hence vol = 176/15 π
attached below is the graphical representation of P and h
Answer:
x <= 0 or 1 = < x <= 5.
Step-by-step explanation:
First we find the critical points:
x(x - 1)(x - 5) = 0
gives x = 0, x = 1 and x = 5.
Construct a Table of values:
<u> x < 0 </u> <u>x = 0 </u> 0<u>< x < 1</u> <u>1 =< x <= 5</u> <u>x = 5</u>
x <0 0 >0 <0 0
x - 1 <0 -1 >0 <0 0
x - 5 < 0 0 > 0 <0 0
x(x-1)(x-5) < 0 0 >0 <0 0
So the answers are x =< 0 or 1 =< x <= 5.
Answer:
525 x 1,050
A = 551,250 m²
Step-by-step explanation:
Let 'L' be the length parallel to the river and 'S' be the length of each of the other two sides.
The length of the three sides is given by:

The area of the rectangular plot is given by:

The value of 'S' for which the area's derivate is zero, yields the maximum total area:

Solving for 'L':

The largest area enclosed is given by dimension of 525 m x 1,050 and is:

The solution to any system graphically can be found where the 2 graphs intersect. These two graphs intersect at the point (0, 2).