Answer:
[tex]x = y = z = 20[/tex]
Step-by-step explanation:
Given
[tex]Volume = 8000cm^3[/tex]
Required
Determine the dimensions that minimizes the surface area.
Surface area of a box is;
[tex]S = 2(xy + xz + yz)[/tex]
Volume of a box is:
[tex]V = xyz[/tex]
Make z the subject
[tex]z = \frac{V}{xy}[/tex]
Substitute 8000 for V
[tex]z = \frac{8000}{xy}[/tex]
Substitute 1000/xy for z in [tex]S = 2(xy + xz + yz)[/tex]
[tex]S = 2(xy + x\frac{8000}{xy}+y\frac{8000}{xy})[/tex]
[tex]S = 2(xy + \frac{8000}{y}+\frac{8000}{x})[/tex]
Expand:
[tex]S = 2xy + \frac{16000}{y}+\frac{16000}{x}[/tex]
[tex]S = 2xy + 16000(\frac{1}{y}+\frac{1}{x})[/tex]
Differentiate S w.r.t x
[tex]\frac{dS}{dx} = 2y - \frac{16000}{x^2}[/tex]
Differentiate S w.r.t y
[tex]\frac{dS}{dy} = 2x - \frac{16000}{y^2}[/tex]
Equate both differentiation to 0
[tex]2x - \frac{16000}{y^2} = 0[/tex]
Multiply through by [tex]y^2[/tex]
[tex]2xy^2 - 16000 = 0[/tex]
[tex]2xy^2 = 16000[/tex]
Divide through by 2
[tex]xy^2 = 8000[/tex] -- (1)
[tex]2y - \frac{16000}{x^2} = 0[/tex]
Multiply through by x^2
[tex]2x^2y - 16000 = 0[/tex]
[tex]2x^2y = 16000[/tex]
Divide through by 2
[tex]x^2y = 8000[/tex] --- (2)
Divide (1) by (2)
[tex]\frac{x^2y = 8000}{xy^2 = 8000}[/tex]
[tex]\frac{x}{y} = 1[/tex]
[tex]x = y[/tex]
Substitute y for x in (1)
[tex]x^2y = 8000[/tex]
[tex]x^2 * x = 8000[/tex]
[tex]x^3 = 8000[/tex]
Take cube roots
[tex]x =20[/tex]
Hence;
[tex]x = y = 20[/tex]
Recall that:
[tex]z = \frac{8000}{xy}[/tex]
[tex]z = \frac{8000}{20 * 20}[/tex]
[tex]z = 20[/tex]
Hence, the dimension of the box that minimizes the surface area of the box is:
[tex]x = y = z = 20[/tex]
Need help asap pllzzz will give brainliest
Answer:
d. $350.00
Step-by-step explanation:
A constant is a number that does not have any variables. The additional cost would depend on the number of persons at attendance so the cost would be $10.00p which is not the constant here. Thus, $350.00 is the only constant in this situation.
Which of the following accurately shows the range of the function defined below? [3, infinity), [2,infinity), [3,6], (-infinity, infinity)
2,infinity
Hope this helps
Answer:[2,♾)
Step-by-step explanation:
Am i right if not plz help me giving brainlist
Answer:
C. 3/4 = 9/12
Step-by-step explanation:
The reason 3/4 = 9/12 is a proportion is because this....
You multiply 3*3 and 4*3 to get 9 and 12 = 9/12
Hope this helps!
Answer
The answer is 3/4 = 9/12.
Step-by-step explanation:
Let u = ln x and v= In y. Write In (x^2y^5)
in terms of u and y.
Answer:
Step-by-step explanation:
u=㏑ x
x=e^u
v=㏑ y
y=e^v[tex]x^{2} y^5 =(e^u)^{2} (e^v)^5=e^{2u}e^{5v}=e^{2u+5v}[/tex]
Answer:
D. 2u + 5v
Step-by-step explanation:
answer on edge
If you are solving the equation 1/(x-4)+1=14/(x+2) by factoring, which of the following equations would you use the zero product property on?
(x - 5)(x + 4) = 0
(x - 5)(x - 10) = 0
(x + 5)(x + 10) = 0
Answer:
The equation that would be used for the zero product property on will be (x-5)(x-10)=0
Option B is correct.
Step-by-step explanation:
We need to solve the equation [tex]\frac{1}{(x-4)}+1=\frac{14}{x+2}[/tex]
Solving the equation:
[tex]\frac{1}{(x-4)}+1=\frac{14}{x+2}\\\frac{1+(x-4)}{x-4}= \frac{14}{x+2}\\\frac{1+x-4}{x-4}= \frac{14}{x+2}\\\frac{x-3}{x-4}= \frac{14}{x+2}\\Cross\: Multiply\\(x-3)(x+2)=14(x-4)\\x(x+2)-3(x+2)=14x-56\\x^2+2x-3x-6=14x-56\\x^2-x-6-14x+56=0\\x^2-x-14x-6+50=0\\x^2-15x+50=0[/tex]
Now, we would factorise to find value of x
[tex]x^2-15x+50=0\\x^2-5x-10x+50=0\\x(x-5)-10(x-5)=0\\(x-5)(x-10)=0[/tex]
So, the equation that would be used for the zero product property on will be (x-5)(x-10)=0
Option B is correct.
Answer:
So, the equation that would be used for the zero product property on will be (x-5)(x-10)=0
Option B is correct.
Step-by-step explanation:
Sean tried to drink a slushy as fast as he could. He drank 5 milliliters of slushy each second and finished all
the slushy after 50 seconds.
Graph the relationship between the amount of slushy left in the cup (in milliters) and time (in seconds).
Answer:
graph like this:
Step-by-step explanation:
First, in 5 seconds, we know that he drinks 25 mL of slushy. We know this because 1 second is 5 mL, so 5 seconds is 25 mL. So, your graph should be going from the 5 second to 25 mL mark, then the 10 second and 50 mL mark, then the 15 mL and 75 mL mark, and so on.
A board 30 metres long is to be divided into 2pieces so that the larger piece is 3 metres longer than twice the shorter piece. How long will the pieces be?
Answer: 9 and 21
Step-by-step explanation:
board=30m
divide by 2 pieces
one piece, we call it a
b, the other piece is b= 2a+3
a+b=30
a+2a+3=30
3a=30-3
3a=27
a=9
b=21
If ris the radius of a circle and dis its diameter, which of the following is an
equivalent formula for the circumference C= 2?
Answer:
D is the answer.
Step-by-step explanation:
The equivalent formula for the circumference C is,
⇒ C = πd
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
r is the radius of a circle and d is its diameter,
We know that;
The circumference of circle is,
C = 2πr
Where, 'r' is radius of circle
Now, We know that;
⇒ r = d / 2
Hence, We get;
The equivalent formula for the circumference C is,
⇒ C = 2π × d/2
⇒ C = πd
Thus, The equivalent formula for the circumference C is,
⇒ C = πd
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please pleas help me!!
Solve the system using elimination.
6x + 14y = 32
6x - 14y = 4
The solution is ___ ( simplify your answer. Type an ordered pair.)
Answer:
x = 3 and y = 1
Step-by-step explanation:
The given equations are :
6x + 14y = 32 ...(1)
6x - 14y = 4 .....(2)
Add equation (1) and (2) :
6x + 14y + 6x - 14y = 32 + 4
12x = 36
x = 3
Put the value of x in equation (1)
6(3) + 14y = 32
18 + 14y = 32
14y = 32-18
14y = 14
y = 1
Hence, the value of x is 3 and y is 1.
What is 7/12 plus 1/4 simplest form
Answer:
i think its 1/3 sorry if im wrong
Question
Tim has an investment account that compounds interest continuously at a rate of 1.6%. After 5 years, he has $2400 in the
account.
How much money did he initially place in the account?
Round your answer to the nearest dollar.
Answer:
$2215
Step-by-step explanation:
The formula for continuous compound interest is P(t) = P₀[tex]e^{rt}[/tex].
$2,400 = P₀e⁽¹⁻⁰¹⁶⁾⁽⁵⁾
Divide both sides by (e⁽¹⁻⁰¹⁶⁾⁽⁵⁾) to isolate the initial amount:
($2,400) ÷ e⁽¹⁻⁰¹⁶⁾⁽⁵⁾ = (P₀e⁽¹⁻⁰¹⁶⁾⁽⁵⁾) ÷ e⁽¹⁻⁰¹⁶⁾⁽⁵⁾
$2,400 ÷ e⁽¹⁻⁰¹⁶⁾⁽⁵⁾ = P₀
Solve:
$2,400 ÷ e⁽¹⁻⁰¹⁶⁾⁽⁵⁾ = $2215.48
P₀ = $2215.48
P₀ = $2215
Hope this helps!
1. Find the value of 3x -2x^2 ; when x = -3. ^ means "power of" *
Answer:
27
Step-by-step explanation:
3x - 2x²
3 × -3 = -9
2 × -3 = -6
-9 - (-6²)
-9 - (-36)
-9 + 36
36 - 9
36 - 9 = 27
5x + y = 13
3(x + y) =12+ y
Solve the system of Equations
Answer:
the other persons answer is correct
Step-by-step explanation:
Ms. Thomas buys a new computer for $659. She plans to pay it off in 8 monthly payments. If she pays the same amount each month, which is the best estimate of her monthly payments?
Answer:
$82.38
Step-by-step explanation:
What you have to do is divide. $659 divided by 8 equals 82.375 so then you round so then it will be money. This would equal $82.38. There you go. Hope that answered your question. Mark me brainliest please!
A family went out to dinner and their meal cost $45.50. They left a 20% tip. How much tip did they leave?
Answer:
45.5*0.2 which is 9.1
Step-by-step explanation:
Hope this helps plz hit the crown :D
Jerome wants to rent a car for 8 days, and he's interested in the collision damage waiver but not the loss damage waiver. If the daily rate is $60 and CDW is $66, what is his total rental cost?
A$588
B$480
C$546
D$1008
Answer:
c?
Step-by-step explanation:
Answer:
C.546
Step-by-step explanation:
60×8=480+ 66=546
Three times a number is the same as the difference of twice the number and four. Find the number. Round your answer to the nearest integer, if necessary.
The number is .
Answer:
-4
Step-by-step explanation:
3x = 2x - 4 Subtract 2x from both sides
x = -4
Please help me out I’m lost
Given:
The function is
[tex]f(x)=2x^4-4x^3+20x-100[/tex]
To find:
The remainder if f(x) is divided by (x+11).
Solution:
According to the remainder theorem, if a function f(x) is divided by (x-c), then the remainder is f(c).
On comparing (x+11) and (x-c), we get c=-11.
Using remainder theorem, if a function f(x) is divided by (x+11), then the remainder is f(-11).
Putting x=-11 in the given function.
[tex]f(-11)=2(-11)^4-4(-11)^3+20(-11)-100[/tex]
[tex]f(-11)=29282+5324-220-100[/tex]
[tex]f(-11)=34606-320[/tex]
[tex]f(-11)=34286[/tex]
Therefore, the remainder is 34286 when f(x) is divided by (x+11).
PLEASE HELP :) 20 POINTS FOR IT IF U JUST ANSWER LIKE IDK OR SUM IMMA REPORT
Answer:
BC = [tex] 1.8 [/tex]
Step-by-step explanation:
∆ABC is an equilateral ∆ because all three angles are equal. Therefore, all its sides would be equal also. This means AB = BC = AC
Thus, let's find the value of x.
[tex] \frac{7}{4}x - 1 = \frac{9}{3}x - 3 [/tex]
Collect like terms
[tex] \frac{7}{4}x - \frac{9}{3}x = 1 - 3 [/tex]
[tex] \frac{7x}{4} - 3x = -2 [/tex]
[tex] \frac{7x - 12x}{4} = -2 [/tex]
[tex] \frac{-5x}{4} = -2 [/tex]
Multiply both sides by 4
[tex] \frac{-5x}{4}*4 = -2*4 [/tex]
[tex] -5x = -8 [/tex]
Divide both sides by -5
[tex] x = \frac{8}{5} [/tex]
AB = BC = AC
Therefore,
BC = [tex] \frac{7}{4}x - 1 [/tex]
Plug in the value of x
BC = [tex] \frac{7}{4}*\frac{8}{5} - 1 [/tex]
BC = [tex] \frac{56}{20} - 1 [/tex]
BC = [tex] 2.8 - 1 [/tex]
BC = [tex] 1.8 [/tex]
30 POINTS! PLEASE GRAPH AND ANSWER THE QUESTION WILL MARK BRANLIEST
Answer:
Step-by-step explanation:
put a point on -5 and put a point on -4 then write the equation on the top to show what you did, name the points then put a point on -9
Answer:
x ≥ 1
Step-by-step explanation:
Move all terms not containing x to the right side of the inequality.
−x ≤ −1
Divide each term in −x ≤ −1 by −1 and simplify.
x ≥ 1
Hope this helps! :)
HELPPP ASAP!!!!!!! PLZZZ
Answer:
8/12
Step-by-step explanation:
A group of 32 students raised money to pay for a field trip to the Outer Banks Research Park. The trip will cost $3,200 and they have raised $2,156. The students have to pay for the remaining cost of the trip. How much will each student have to pay? (Round to the nearest hundredths).
Answer: 32.63
Step-by-step explanation:
they will have to pay 3200-2156=1044
each student will need to pay
1044/32= 32.625 but this number rounded to the nearest hundredths is 32.63
Answer:
each student would have to pay 32.63
Step-by-step explanation:
3200-2156=1044
1044 divided bye the number of students is 32.625
32.625 rounded to the rearest hundreth is 32.63
Which fraction is less than 3/6
Answer:
The fraction [tex]\frac{3}{6}[/tex] is equavilent to [tex]\frac{1}{2}[/tex].
Step-by-step explanation:
Any fraction less than [tex]\frac{1}{2}[/tex] Is the answer to your question.
Examples: [tex]\frac{1}{4}[/tex], [tex]\frac{2}{8}[/tex], [tex]\frac{1}{9}[/tex], [tex]\frac{4}{9}[/tex], etc.
There is a wide variety of fractions that could be the answer to this question, like I said before, Any fraction less than [tex]\frac{1}{2}[/tex]. I did not see any answer choices so I did my best to answer this properly for you. Hope this helps you.
there is a graph with 36 possible outcomes. What is the probability of rolling a sum of 10 when rolling 2 number cubes.
A. 1/12
B. 1/9
C. 1/3
D. 5/12
Answer: A
Step-by-step explanation:
Answer:
A. 1/12
Step-by-step explanation:
Which of the following is equal to the absolute value of 7?
o the distance between 7 and zero on a number line
o the distance between -3 and -4 on a number line
o the distance between -7 and 7 on a number line
the distance between 1 and 7 on a number line
Which of the
following equations can be used with x + y = 60 to solve for x and y
Answer:
What are "the following equations" supposed to be?
Step-by-step explanation:
:)
- Isabel has a mother dog and her puppy that look
exactly alike. The puppy wcighs 6 pounds, and the
mother weighs 48 pounds. Assuming the two dogs are
similar, what is the scale factor of the dilation?
Answer:
8
Step-by-step explanation:
Classify √3
√3 means the nonnegative square root of 3
√ 3 can be classified as a non negative square root of the number 3 which is also a real and irrational number.
We are given a number √ 3.
We need to classify the number.
First we can see that, this is the non negative square root of the number 3.
That is when we multiply √ 3 two times, we get the number 3.
Also, we can see that, it will be an irrational number as it will be non terminating and non repeating number.
That is it will be a real irrational number.
Therefore, we get that, √ 3 can be classified as a non negative square root of the number 3 which is also a real and irrational number.
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Zinnia and Ruby earn $58 per week for delivering pizzas. Zinnia worked for x weeks and earned an additional total bonus of $13. Ruby worked for y weeks. Which expression shows the total money, in dollars, that Zinnia and Ruby earned for delivering pizzas?
The following equations are set up for each person
Zinnia: 58x+13
Ruby: 58y
If you need the total of both the equation is:
58x+13+58y
Hopefully this helped :) Have a great day
Answer:
I believe your answer is D, 58x+13+58y.
Step-by-step explanation:
Please help
Find the equation of this line
Write it in the form y=mx+b
Y=?
y=1/5x because it passes through the origin