Answer:
radius r = 47/π in
length l = 23.5 in
Step-by-step explanation:
Let us recall that:
Volume of a cylinder = 
--- (1)
The girth g = 
----- (2)
Given that:
height (h) + girth (g) = 141
Then g = 141 - h ----- (3)
Equating equation (2) and (3), we have:
141 - h = 2πr + h
2h = 141 - 2πr
h = 70.5 - πr ------ (4)
From, here now, we can now replace the value of h into equation (1)
i.e.
V = πr²(70.5 - πr)
V = 70.5πr² - π²r³
Taking the differential of the above equation with respect to r, we have:
By further differentiation:
Let set 
, Then:
141πr - 3π²r² = 0
141πr = 3π²r²
Divide both sides by πr
141 = 3πr
r = 141/3π
r = 47/π in
Replacing the value of r = 47/π into equation (4), we have:
h = 70.5 - πr
h = 70.5 - π(47/π)
h = 70.5 - 47
h = 23.5 in
From equation (3);
h + g = 141
23.5 + g = 141
g = 141 - 23.5
g = 117.5 in
Volume = πr²h
V = π × (47/π )² × 23.5
V = 16523.94 in³
-18.5 = -2 (7f + 7.5)
-18.5 = -2×7f + (-2)×7.5
-18.5 = -14f + (-15)
-18.5 = -14f - 15
add 15 to both sides
-18.5 +15 = -14f - 15 + 15
-3.5 = -14f
f = -3.5/-14 = 0.25
Answer:
The total payment is thus $35.75 plus $7.11, or $42.86
Step-by-step explanation:
Note that the sales tax doesn't affect the tip. The sales tax is 5% of the cost and the tip is 15% of the before tax cost. We calculate the tax and the tip separately, then add them together and finally add this sum to the cost.
Sales tax: 5% of $35.75: $1.75
Tip: 15% of $35.75: $5.36
Adding these two quantities results in $7.11.
The total payment is thus $35.75 plus $7.11, or $42.86
First....we need to do inverse operation
Subtract 7 from both sides.
2x+7=1
-7 -7
2x=-6
Now, we need to divide 2 by both sides to isolate x.
2x=-6
2x/2=-6/2
x=-3
Our final answer is that x= -3
Answer:
1st and last one
Step-by-step explanation:
the first and the last one are the only ones that represent a function because for each value of x there is only one corresponding value of y.
