Answer:
[tex]Radius = 1.997\ in[/tex] and [tex]Height = 7.987\ in[/tex]
[tex]Cost = \$1.05[/tex]
Step-by-step explanation:
Given
[tex]Volume = 100in^3[/tex]
[tex]Cost =\$0.014[/tex] -- Top and Bottom
[tex]Cost =\$0.007[/tex] --- Sides
Required
What dimension of the cylinder minimizes the cost
The volume (V) of a cylinder is:
[tex]V = \pi r^2h[/tex]
Substitute 100 for V
[tex]100 = \pi r^2h[/tex]
Make h the subject
[tex]h = \frac{100 }{\pi r^2}[/tex]
The surface area (A) of a cylinder is:
[tex]A = 2\pi r^2 + 2\pi rh[/tex]
Where
[tex]Top\ and\ bottom = 2\pi r^2[/tex]
[tex]Sides = 2\pi rh[/tex]
So, the cost of the surface area is:
[tex]C = 2\pi r^2 * 0.014+ 2\pi rh * 0.007[/tex]
[tex]C = 2\pi r(r * 0.014+ h * 0.007)[/tex]
[tex]C = 2\pi r(0.014r+ 0.007h)[/tex]
Substitute [tex]h = \frac{100 }{\pi r^2}[/tex]
[tex]C = 2\pi r(0.014r+ 0.007*\frac{100 }{\pi r^2})[/tex]
[tex]C = 2\pi r(0.014r+ \frac{0.007*100 }{\pi r^2})[/tex]
[tex]C = 2\pi r(0.014r+ \frac{0.7}{\pi r^2})[/tex]
[tex]C = 2\pi (0.014r^2+ \frac{0.7}{\pi r})[/tex]
Open bracket
[tex]C = 2\pi *0.014r^2+ 2\pi *\frac{0.7}{\pi r}[/tex]
[tex]C = 0.028\pi *r^2+ \frac{2\pi *0.7}{\pi r}[/tex]
[tex]C = 0.028\pi *r^2+ \frac{2 *0.7}{r}[/tex]
[tex]C = 0.028\pi *r^2+ \frac{1.4}{r}[/tex]
[tex]C = 0.028\pi r^2+ \frac{1.4}{r}[/tex]
To minimize, we differentiate C w.r.t r and set the result to 0
[tex]C' = 0.056\pi r - \frac{1.4}{r^2}[/tex]
Set to 0
[tex]0 = 0.056\pi r - \frac{1.4}{r^2}[/tex]
Collect Like Terms
[tex]0.056\pi r = \frac{1.4}{r^2}[/tex]
Cross Multiply
[tex]0.056\pi r *r^2= 1.4[/tex]
[tex]0.056\pi r^3= 1.4[/tex]
Make [tex]r^3[/tex] the subject
[tex]r^3= \frac{1.4}{0.056\pi }[/tex]
[tex]r^3= \frac{1.4}{0.056 * 3.14}[/tex]
[tex]r^3= \frac{1.4}{0.17584}[/tex]
[tex]r^3= 7.96178343949[/tex]
Take cube roots of both sides
[tex]r= \sqrt[3]{7.96178343949}[/tex]
[tex]r= 1.997[/tex]
Recall that:
[tex]h = \frac{100 }{\pi r^2}[/tex]
[tex]h = \frac{100 }{3.14 * 1.997^2}[/tex]
[tex]h = \frac{100 }{12.52}[/tex]
[tex]h = 7.987[/tex]
Hence, the dimensions that minimizes the cost are:
[tex]Radius = 1.997\ in[/tex] and [tex]Height = 7.987\ in[/tex]
To calculate the cost, we have:
[tex]C = 2\pi r(0.014r+ 0.007h)[/tex]
[tex]C = 2* 3.14 * 1.997 * (0.014*1.997+ 0.007*7.987)[/tex]
[tex]Cost = \$1.05[/tex]
What is 15 didvide 7.35
Answer:
2.04081632653
Step-by-step explanation:
If you wanted to round it, it would be 2 because the 4 isn't enough to bump it up. Hope this helped you!
Answer:
2.04
Step-by-step explanation:
The lines shown below are parallel If the green line has a slope of -1/2 what is the slope of the red line?
Answer:
-1/2
Step-by-step explanation:
parallel lines have the same slopes
tina completed 2/3 of her homework.George completed 7/8 of his homework. Who completed a greater fraction if homework
Answer:
2/3 = 16/24
7/8 = 21/24
Step-by-step explanation:
Please help and I will give brainlest
Answer:
approx 72 feet
Step-by-step explanation:
the left and bottom sides of the quadrilateral are easy to see that their sum is 15 + 20 or 35
however, from (40, 30) to (45, 40) you can use the distance formula
d = √(y - y)² + (x - x)²
d = √10² + 5²
d = √125 which is approx 11.1
from (20, 40) to (45, 40) you get:
d = √5² + 25²
d = √650 which is approx 25.5
Please help me I’m not good with graphs
Answer:
I'm pretty sure it's 2 and 3
__+ (-4) = -1 what is the missing number
Answer:
3
Step-by-step explanation:
_+(-4) = -1
_-4 = -1
_ = 3
Select the reason why these triangles are
similar. If they are not, select "Not similar".
8
12
5
7
6.25
10
A. AA
B. SAS
C. SSS
D. Not similar
The triangles of the dimensions are not similar by any property of similarity. Thus option D is correct.
Concept of similarity : Two triangles can be similar by AAA, SAS, SSS property .
Given,
Two triangles with different side lengths.
Here,
The two triangles are similar if they have same shape , but can be of different sizes and corresponding sides are of same proportions.
Here,
Triangles are of same shape but the corresponding sides are not in same proportions.
∴ 8/5 = 10/6.25 ≠ 12/7
Therefore the two triangles are not similar.
Know more about similar triangles,
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Need help ASAP
Will make you brainlist
Answer:
y=1.3x-3
or
y=4/3x-3
Step-by-step explanation:
1.3 is the slope (the change in between points)
-3 is the y intercept (the point on the y-axis)
A singles tennis court measures (8x – 2) ft long and (3x – 3) ft wide.Which expression represents the area of the court?
Answer:
The expression that represents the area of the court is: [tex]24x^2 - 30x + 6[/tex]
Step-by-step explanation:
Area of a rectangle:
A rectangle has length l and width w. The area of a rectangle is:
[tex]A = lw[/tex]
A singles tennis court measures (8x – 2) ft long and (3x – 3) ft wide.
This means that [tex]l = 8x - 2, w = 3x - 3[/tex]
Which expression represents the area of the court?
The tennis court is rectangular, so
[tex]A = lw = (8x - 2)(3x - 3) = 24x^2 - 24x - 6x + 6 = 24x^2 - 30x + 6[/tex]
The expression that represents the area of the court is: [tex]24x^2 - 30x + 6[/tex]
Solve the equation 3x-1 = -7
Answer: x = -2
Step-by-step explanation:
first, we move the constant to the right.
3x = -7 + 1
then, we calculate that.
3x = -6
finally, we divide both sides.
x = -2
The solution to the equation 3x - 1 = -7 is x = -2.
To solve the equation 3x - 1 = -7, we need to isolate the variable x on one side of the equation.
Here are the steps to solve it:
Step 1: Start with the given equation: 3x - 1 = -7.
Step 2: To eliminate the constant term (-1) on the left side, we can add 1 to both sides of the equation:
3x - 1 + 1 = -7 + 1.
Simplifying, we get: 3x = -6.
Step 3: Now, we want to isolate x, so we need to get rid of the coefficient 3 in front of x.
We can do this by dividing both sides of the equation by 3:
(3x)/3 = (-6)/3.
Simplifying further, we have: x = -2.
Step 4: We have found the solution to the equation: x = -2.
Therefore, the solution to the equation 3x - 1 = -7 is x = -2.
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Phillip wanted to leave a 15% tip. He thought to himself that 15% = 10% plus half of 10%. Which of the following equations will help Phillip estimate the tip on a $36.00 bill correctly?
Answer:
$36.00
Step-by-step explanation:
A scuba diver dives 10 meters below the surface of the ocean, and then dives down another 8 meters. How many meters down does the diver dive? Show an absolute value equation that can be used to find your answer.
HELP GEOMETRY PROOFS
Step-by-step explanation:
See the attached for the proof
You have a loan for $200,000 at 8.5% annual simple interest.what is your monthly interest payment
Answer:
~1467
Step-by-step explanation:
$200,000 x 8.5% or .085 = $17,000 Annualy
$17,000 / 12 Months out of the year = $1466 2/3 Monthly Payments
Answer is $1467 Rounded
The monthly interest payment is $1,467.
Given that,
The loan amount is $200,000.The rate of interest is 8.5%.We need to find out the monthly interest payment.Based on the above information, the calculation is as follows:
[tex]= (\$200,000 \times 8.5\%) \div 12[/tex]
= $1,467
Therefore we can conclude that the monthly interest payment is $1,467.
Learn more: brainly.com/question/13324776
how much water must be added to a 6-liter solution that contains 7% extract of baneberry to get a solution that contains 5% extract of baneberry
Answer:
the water to be added is 0.2 L
Step-by-step explanation:
The computation of the water to be added is given below:
The banberry amount is
= 7% of 6 Liters
= 0. 42L
Now
Let us assume the amount of water added be x L
So, the total solution is
= 6+ x L
Now percentage of banberry is
= 0.42 × 100 ÷ (6+x)
5 = 0.42 × 100 ÷ (9 + x)
9 + x = 9.2
x = 0.2 L
hence, the water to be added is 0.2 L
PLEASE HELP I’LL GIVE BRAINLIEST TO WHO EVER ANSWERS FIRST CORRECTLY
Use the rational zeros theorem to list all possible rational zeros of the following.
h(x)=-3x^4+5x^3-8x^2-3x+2
Be sure that no value in your list appears more than once.
Answer:
Step-by-step explanation:
[tex]h(x)=-3x^{4} +5x^{3}-8x^{2} -3x+2[/tex]
roots:±1, ±[tex]\frac{1}{3}[/tex], ±2, ±[tex]\frac{2}{3}[/tex]
Please help will give a 100 points
Answer:
The answers are 0 and -1
Step-by-step explanation:
Answer:
0 and -1
Step-by-step explanation:
how many months are in y years and m months?
Answer:
Step-by-step explanation:
There are 12 months in one year, so there would be 12*y in y years.
Answer:
there 12 months in one 1 year
Step-by-step explanation:
For each statement below, determine whether the statement is a decision variable or not.
* Number of Aqua-Spa Produced.
* Number of Hydro-Lux Produced.
* Number of Pumps Purchased.
* Amount of Available Labor Hours.
* Amount of Available Tubing Available.
* Profit of Aqua-Spa.
* Profit of Hydro-Lux.
Answer and explanation:
Decision variables are variables that are independent(indeoendent variables) and can be controlled by the decision maker. Decision variables influence outcome or result of a solution, usually denoted x in linear programming.
Decision variables above include:
Number of Aqua-Spa Produced.
* Number of Hydro-Lux Produced.
* Number of Pumps Purchased.
* Amount of Available Labor Hours.
* Amount of Available Tubing Available
Pls help with this math problem
Answer:
y=1/4x+6
Step-by-step explanation:
The formula for writing a slope equation is y=mx+b. The slope is 1/4, or m, and the y-intercept is 6, or b. Don't worry about the x or y, leave them as variables.
Five girls in a homeroom class of 20 students have blonde hair. If there are 120 students in the school, how many would you predict are blonde haired girls?
Step-by-step explanation: To find how many girls are blonde-haired, we'll have to subtract.
120 - 20 =
1. Subtract 0 by 0.
0 - 0 = 0
2. Subtract 2 by 2.
2 - 2 = 0
3. Since there isn't a number in the hundred's place, bring the 1 down.
Therefore, your answer is: 100. There are 100 blonde-haired girls.
help pls? If mF= 109*, mQ=122*, mR=44, find mJ
Answer:
∠J=85°
Step-by-step explanation:
Theory to know when answering this question:
1. The sum of the angles in a quadrilateral (shape with four sides) is 360°
2. Similar shapes have the same angles
Point 1 tells us that ∠P+∠Q+∠S+∠R=360
Point 2 tells us that ∠F=∠P, ∠G=∠Q, ∠J=∠S, and ∠H=∠R.
∴∠F+∠Q+∠J+∠R=360
109+122+∠J+44=360
∠J=360-275=85°
PLEASE HELP ASAP!!! awarding a lot of points!
Exact Form:
x=5/4
Decimal Form:
x=1.25
Mixed Number Form:
x= 1 1/4
The correct answer is,
[tex]x = \frac{5}{2} [/tex]
which of the following can be a Pythagorean triplets?:
a) 2cm 2cm ,4cm b) 5cm, 12cm ,13cm c) 3cm ,5cm ,6cm d) 7cm, 4cm 5 cm.
need full solution
or I'll report
As we know that,
Pythagoras triplet
1) a² + b² = c²
Let
[tex]\sf \: {2}^{2} + {2}^{2} = {4}^{2}[/tex]
[tex]\sf \: 4 + 4 = 16[/tex]
8 ≠ 16Hence, A can't be Pythagoras triplet2) a² + b² = c²
[tex]\sf \:5 {}^{2} + {12}^{2} = {13}^{2}[/tex]
[tex]\sf \: 25 + 144 = 169[/tex]
169 = 169Therefore, B can be Pythagoras triplet3)a² + b² = c²
[tex]\sf {3}^{2} + {5}^{2} = {6}^{2}[/tex]
[tex]\sf 9 + 25 = 36[/tex]
34 ≠ 36Hence, C can't be Pythagoras triplet4) a² + b² = c²
[tex]\sf {5}^{2} + {4}^{2} = {7}^{2}[/tex]
[tex]\sf \: 25 + 16 = 49[/tex]
41 ≠ 49Hence, D can't be Pythagoras tripletTherefore :-Only B can be Pythagoras triplet.
Pls help me ASAP I’ll brainlest for the right answer
Answer:
I would say the answer is 13.5
Step-by-step explanation:
Times 7.5 (hours) and $1.80 (dollars).
The reason why this works:
It is $1.80 per hour so if you multiply it by 7.5 the amount of hours that would make it so you'd get the answer $13.5
DO NOT TAKE POINTS!!! Answer this question with what it is asked for. If you have a comment put it in the comment section.
Please explain your thinking and complete the question
Answer:
See the attached
Step-by-step explanation:
The answer is in the attached picture
graph y-2=-3(x-4). please help me
mr chowdhary purchased a house for rs 6.1 lakh and spent 30000 on its repairs. he then sold it rs 8 lakh. find his gain percent
Given:
Purchasing price = 6.1 lakh
Amount spent of repair = 30000
Selling price = 8 lakh
To find:
The gain percentage.
Solution:
We have,
Purchasing price = 6.1 lakh
Amount spent of repair = 30000 = 0.3 lakh
So, total cost price is
[tex]C.P.=6.1+0.3[/tex]
[tex]C.P.=6.4[/tex]
The total cost price is 6.4.
Selling price(S.P.) = 8 lakh
Now,
[tex]Gain\%=\dfrac{S.P.-C.P.}{C.P.}\times 100[/tex]
[tex]Gain\%=\dfrac{8.0-6.4}{6.4}\times 100[/tex]
[tex]Gain\%=\dfrac{1.6}{6.4}\times 100[/tex]
[tex]Gain\%=\dfrac{1}{4}\times 100[/tex]
[tex]Gain\%=25\%[/tex]
Therefore, the gain percent is 25%.
Because you want to prepare and serve the healthiest food possible you monitor the fat and calorie continent of items on your menu some of the menu items are included in the graph below. Is the trend line linear if so write a linear equation that represents the trend line
If there's a graph, maybe I could help...?
Sketch and shade the region in the xy-plane defined by the equation or inequalities.
|x| < 7 and |y| < 3 g
Answer:
attached below is the solution
Step-by-step explanation:
|x| < 7
= -7 < x < 7
| y | < 3
= -3< y < 3
attached below is the shaded region in the xy-plane