Answer:
The dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.
Step-by-step explanation:
A cylindrical can holds 300 cubic centimeters, and we want to find the dimensions that minimize the cost for materials: that is, the dimensions that minimize the surface area.
Recall that the volume for a cylinder is given by:
[tex]\displaystyle V = \pi r^2h[/tex]
Substitute:
[tex]\displaystyle (300) = \pi r^2 h[/tex]
Solve for h:
[tex]\displaystyle \frac{300}{\pi r^2} = h[/tex]
Recall that the surface area of a cylinder is given by:
[tex]\displaystyle A = 2\pi r^2 + 2\pi rh[/tex]
We want to minimize this equation. To do so, we can find its critical points, since extrema (minima and maxima) occur at critical points.
First, substitute for h.
[tex]\displaystyle \begin{aligned} A &= 2\pi r^2 + 2\pi r\left(\frac{300}{\pi r^2}\right) \\ \\ &=2\pi r^2 + \frac{600}{ r} \end{aligned}[/tex]
Find its derivative:
[tex]\displaystyle A' = 4\pi r - \frac{600}{r^2}[/tex]
Solve for its zero(s):
[tex]\displaystyle \begin{aligned} (0) &= 4\pi r - \frac{600}{r^2} \\ \\ 4\pi r - \frac{600}{r^2} &= 0 \\ \\ 4\pi r^3 - 600 &= 0 \\ \\ \pi r^3 &= 150 \\ \\ r &= \sqrt[3]{\frac{150}{\pi}} \approx 3.628\text{ cm}\end{aligned}[/tex]
Hence, the radius that minimizes the surface area will be about 3.628 centimeters.
Then the height will be:
[tex]\displaystyle \begin{aligned} h&= \frac{300}{\pi\left( \sqrt[3]{\dfrac{150}{\pi}}\right)^2} \\ \\ &= \frac{60}{\pi \sqrt[3]{\dfrac{180}{\pi^2}}}\approx 7.25 6\text{ cm} \end{aligned}[/tex]
In conclusion, the dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.
An exponential function contains the points: (2,121) and (3,133.1)
What is the exponential function that contains these points?
y=ab^x
121= ab^2
133.1= ab^3
we divide the 2 equations
[tex] \frac{121}{133.1} = \frac{a {b}^{2} }{a {b}^{3} } [/tex]
0.9 = b^-1
b = 1.1
121 = a (1.1)^2
121 = a × 1.21
a = 100
y=100 × ((1.1)^x) is the function
7-9-0-0-0-0-0-0-0-0-0-0-6-6-6-6--6-6-6-6-6-6-6-6-6-6-6-
Answer:
It is -80
Step-by-step explanation:
u just subtract
What is the sum of 3.6 x 10^-2 and 2.4 x 10^3?
Answer:
2400.036 or 4.875 × 10^5
Step-by-step explanation:
HELP ASAP: I WILL MARK BRAINLIEST SOMEONE PLEASE HELP!!
Answer:
Step-by-step explanation:
Please see the picture below
A test has 20 questions. The test awards 3 points if the answer is correct and takes
away 1 point if the answer is incorrect. A student answered 5 questions incorrectly.
How many points did the student lose?
Show your work.
Answer:
55
Step-by-step explanation:
20 * 3 = 60
60 marks - 5 Incorrect answer (5 marks deducted)
55 Marks
Mike can bind 109 flowers per hour, John can bind 116 flowers
per hour. If they work together for 5 hours, how many flowers
can they bind?
flowers
Hello!
We know that mike can bind 109 flowers per hour.
Lets create an equation to remember this.
Mikes equation:
109x = y
<x is representing per hour in this math problem>
We know that John can bind 116 flowers per hour, here is his equation.
Johns equation:
116x = y
Question: If they work together for 5 hours, how many flowers can they bind?
First, plug in the number five in both equations.
Second, solve the equation by multiplying.
Mikes:
109(5) = y
109 times 5 is 545
y = 545
Johns:
116(5) = y
116 times 5 is 580
y = 580
We want to know how many flowers can they bind if they work together.
This means we need to add the answers of the equations from both mike's and john's together.
545 + 580 = 1,125
The answer is 1,125
Solve the system by substitution.
y = -9x
y = 2x + 33
Answer:
[tex]y = - 9x \\ theny = 2x + 33 \\ - 9x = 2x + 33 \\ - 9x - 2x = 33 \\ - 11x = 33 \\ x = \frac{ - 33}{11} = - 3 \\ x = - 3 \\
then\\ y=-9×-3=21\\ thank \: you[/tex]
Can anyone help solve this for me ASAP. Thanks!
Answer:
x = 20
y = 26
Step-by-step explanation:
40 and 2x are vertical angles, so they're equal to each other.
40 = 2x
Divide both sides by 2
x = 20
We see that 40 and 5y + 10 are a linear pair, which means they add up to 180.
5y + 10 + 40 = 180
5y + 50 = 180
5y = 130
y = 26
Simplify.
(If an answer is undefined, enter UNDEFINED.)
6/10
Answer:
3/5
Step-by-step explanation:
1.) Find the Greatest Common Factor of 6/10.
2
2.) Divide both the numerator and the denominator by the greatest common factor.
6÷2
10÷2
3.) Simplify 6÷2/10÷2
3/5
The last line of a proof represents
the
given
information.
the argument.
the conclusion.
O the assumptions.
What is 12 X 1 1/2? Can someone explain with step by step?
Answer:
6
Step-by-step explanation:
[tex]12 \times 1 \frac{1}{2} [/tex]
[tex]12 \times \frac{1}{2} [/tex]
[tex] = 6[/tex]
Help!!! A student Is given the rectangle and square shown. The student states that the two figures have the same perimeter. Is this still in correct? Explain your reasoning.
Answer:
yes figures have the same perimeter
Step-by-step explanation:
The opposite sides of the rectangle are equal , then
perimeter = 2(x + 4) + 2x = 2x + 8 + 2x = 4x + 8
The square has 4 equal sides , then
perimeter = 4(x + 2) = 4x + 8
Then the figures have the same perimeter
Please help quickly it is super late rn
Step-by-step explanation:
-4^(-5)/ 2^(-3) =
2³/(-4)^5 =
8/(-1024) =
- 1/128 (d)
The volume of a cube is 27 cubic inches. What is the length of each edge of this cube?
a. 13.5 inches
b. 9 inches
c. 3 inches
Answer:
Option c. 3 inches
Step-by-step explanation:
Volume=27 inches³
By applying the volume formula of cube, we get
L³=27 inches³
L³=(3 inches)³
Hence the cube cancels the opposite side's cube
L=3 inches
P(x) = x^4+ax^3-x^2+bx-12 has factors of (x-2) and (x+1). Solve the equation P(x)=0
Answer:
because P(x) has factors of (x-2) and (x+1) => x = 2 and x = -1 are the solutions of P(x)
so we have:
[tex]\left \{ {{2^{4}+2^{3}a-2^{2}+2b-12 =0} \atop {1-a-1-b-12=0}} \right.\\=>\left \{ {{8a+2b=0} \atop {a+b=-12}} \right.\\<=>\left \{ {{4a+b=0} \atop {a+b=-12}} \right.\\<=>\left \{ {{a=4} \atop {b=-16}} \right.[/tex]
=> [tex]P(x)=x^{4} + 4x^{3}-x^{2} -16x-12[/tex]
With P(x) = 0
=> [tex]x^{4}+4x^{3}-x^{2} -16x-12 = 0[/tex]
=> ........
Step-by-step explanation:
Alice rented bowling shoes for $3.25 and played five games at $2 each write and evaluate an expression for the total cost of bowling? 
Write numerical or algebraic expression
Answer:
The total cost is $13.25
Step-by-step explanation:
x = 3.25 + 5(2)
x = 13.25
Which numbers are irrational?
V81
148
144
V22
Which numbers are irrational? Select all that apply.
OA. V48
B. 181
OC. V22
OD. 144
Click to select your answer(s) and then click Check Answer.
Allarte
can anyone help me plz?
Answer:
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What is the quotient when 8x^3-5x^2+x+2 is divided by x^2
Step-by-step explanation:
[tex]8 {x}^{3} - 5 {x}^{2} + x + 2 \div {x}^{2} [/tex]
[tex]8 {x}^{3} - 5 {x}^{2} + x + \frac{2}{ {x}^{2} } [/tex]
[tex] = \frac{8 {x}^{5} - 5 {x}^{4} + {x}^{3} + 2}{ {x}^{2} } [/tex]
problem in photo 20 characters
Answer:
Step-by-step explanation:
i dont know but work hard
Find two positive numbers whose difference is 30 and whose product is 2584.
Answer:
[tex]38[/tex] and [tex]68[/tex].
Step-by-step explanation:
Let [tex]x[/tex] be the smaller one of the two number.
[tex]x[/tex] must be a positive integer. The other number would be [tex](x + 30)[/tex].
The question states that the product of the two numbers is [tex]2584[/tex]. In other words:
[tex]x\, (x + 30) = 2584[/tex].
Rearrange this equation and solve for [tex]x[/tex]:
[tex]x^{2} + 30\, x - 2584 = 0[/tex].
The first root of this quadratic equation would be:
[tex]\begin{aligned}x_{1} &= \frac{(-30) + \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= \frac{(-30) + \sqrt{900 + 10336}}{2} \\ &= \frac{(-30) + \sqrt{11236}}{2} \\ &= \frac{(-30)}{2} + \sqrt{\frac{11236}{2^{2}}} \\ &= (-15) + \sqrt{2809} \\ &= (-15) + 53 \\ &= 38 \end{aligned}[/tex].
Similarly, the second root of this quadratic equation would be:
[tex]\begin{aligned}x_{1} &= \frac{(-30) - \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= (-15) - 53 \\ &= -68\end{aligned}[/tex].
Since the question requires that both numbers should be positive, [tex]x > 0[/tex]. Therefore, only [tex]x = 38[/tex] is valid.
Hence, the two numbers would be [tex]38[/tex] and [tex](38 + 30)[/tex], which is [tex]68[/tex].
9514 1404 393
Answer:
38 and 68
Step-by-step explanation:
Let x represent the average of the two numbers. Then their product is ...
(x -15)(x +15) = 2584
x^2 = 2584 +225 = 2809 . . . . . . use relation (x -a)(x +a) = x^2 -a^2; add a^2
x = √2809 = 53
Then the two numbers are ...
53 +15 = 68
and
68 -30 = 38
The two numbers are 38 and 68.
_____
Additional comment
Solving the problem in this way is equivalent to writing the quadratic equation for the smallest (or largest) number and solving that by completing the square. The "solution" x = -53 is not relevant in this problem.
(x^4+1)(y'-x^5-3x)=4x^3.y
Answer:
vvvhnxjdhshdhrgrgdrhhdfehfhfh
Step-by-step explanation:
f jfbdhdnrbdjgmt
WHY NOBODY WANT TO HELP ME?
Answer:
X = 111°
I hope it's helps you
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!helpppppppp
Answer:
2W + 56 = 78 , W = 10
Step-by-step explanation:
perimeter of rectangle = 2*the Length + 2*the Width
A case of 8 items costs $14.88 at costco. What is the price of each item
Thank you for your time
Answer:
m∠5= 130°
Explanation:
If lines A and B are parallel we can assume that the angles in the same locations are equal
Answer:
130 is the answer
Step-by-step explanation:
Well it's definitely obtuse (look at the photo)
I hope I helped!
I hope you get the green tick.
Please mark Brainliest if you do!
A cake shop can make 240 boxes of cakes for 8 days. How many cakes can the shop make in 12 days?
Answer:
360 cakesStep-by-step explanation:
soln:onecake =240\8=30then 12 cakes =30×12=360Answer:
360
Step-by-step explanation:
240÷8days=30
30×12days=360
Why do we study statistics?
A. Because technological advances have introduced massive amounts of data into the world
B. Because statistics can be applied to every field of study
C. Because many of the statistical stories told in the media are misleading
D. All of the above
help me please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please
Answer:
B. Because statistics can be applied to every field of study
n!
Use:
n 'k k!(n-k)!
to solve the combination.
After a band parent meeting, each of
the ten members shook hands with
each other once. How many
handshakes were there in all?
Hint: Remember that one handshake involves
two people.
[?] handshakes
What factors of -24 has the sum of 5
Answer:
8 and -3
Step-by-step explanation:
We need to list several factors of -24 that add up to 5.
After trying several possibilities we ge
8 x (-3) =24 and
8 + (-3) = 5
