Answer: 7
Step-by-step explanation:
7•4=28 therefor 28\4= 7
Find the dimensions of the box with volume 8000 cm3 that has minimal surface area. (Let x, y, and z be the dimensions of the box.)
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]
In the phrase rise over run
what does rise indicate
Answer:
how far a line goes up
Step-by-step explanation:
rise/run gives the slope of the line
What is |9|?
-18
-9
9
18
Answer:
the true answer is 9
Step-by-step explanation:
Because the product of the absolute value is the same number and positive
A rectangle measures 54 feet by 72 feet. What is the length, in feet, of
the diagonal of the rectangle?
a. 48 ft
b. 90 ft
c. 110 ft
d. 2268 ft
e. 8100 ft
length (l) =54
breath (b) =72
l²+b²= diagonal²..........(Pythagoras theorem) and (all sides of rectangle are 90degree)
(54)²+(72)²=diagonal²
2916+5184=diagonal²
8100=diagonal²
90= diagonal.............(taking square root)
length of diagonal is 90ft
i hope it helps
have a nice day and thanks for asking this question
find the length of side x in simplest radical denominator
Answer:
324352
Step-by-step explanation:
Given `∆QRS≅∆TUV,` QS = 5v + 2, and TV = 8v - 7, find the length of QS
Answer:
3
Step-by-step explanation:
You have to equate them so...
5v+2=8v-7
I hope this helps you!
There are 3 cups of blue paint and 2 cups of red paint. Whats the ratio?
Answer:
3:2
Step-by-step explanation:
can also be written as 3/2 as a fraction!
Answer:
Blue paint to red paint - 3:2
Red paint to blue paint 2:3
Step-by-step explanation:
For every 3 cups of blue paint there is 2 cups of red paint
For every 2 cups of red paint there is 3 cups of blue paint
Fraction Mode: 3/2 or 2/3
Subtract. Write the answer in lowest terms.
6 1/6 - 2 5/6
Answer:
61/6_25/6=61_25/6=36/6 we divide =6The answer is 6Step-by-step explanation:
Please mark my answer as a brainliest. Please follow me. ❤❤❤Answer:
3 1/6
Step-by-step explanation:
look on the attachment i sent
multiple choice question
The function f(x) is graphed on the coordinate plane?
Which equation represents the function graphed on the coordinate plane? ~
answer options below~
a. g(x)=|x+1|+3?
b. g(x)=|x+3|-1?
c. g(x)=|x-1|+3?
d. g(x)=|x+3|+1?
Answer:
b. g(x)=|x+3|-1
Step-by-step explanation:
An election for favorite lunch snack is between Apples, Beets, and Carrots. Students voted for their top three from best to least. The results are: ABC : 41 BAC : 26 CAB : 42 How many votes will A have in total after B is eliminated due to the Hare method
Answer: after eliminating B due to Hare Method, A will have a total of 67 VOTES
Step-by-step explanation:
Given that;
The results are
ABC : 41
BAC : 26
CAB : 42
NOW
A>B>C = 41 ⇒ A has 41 votes
B>A>C = 26 ⇒ B has 26 votes
C>A>B = 42 ⇒ C has 42 votes
According to Hare method, least votes gainers will be eliminated and once eliminated, his/her/its votes will be transferred to the next choice of person/thing.
based on the question; B will be eliminated
so we have;
A>B>C = 41 ⇒ A has 41 votes
B>A>C = 26 ⇒ B has 26 votes
we eliminate B, the votes are transferred to the next (A)
A>C = 26 ⇒ A has 26 votes
C>A>B = 42 ⇒ C has 42 votes
SO in total
A votes = 41 + 26 = 67 VOTES
Therefore after eliminating B due to Hare Method, A will have a total of 67 VOTES
After eliminating B due to Hare Method, A will have a total of 67 votes
We have given that,the results are
ABC : 41
BAC : 26
CAB : 42
A>B>C = 41 ⇒ A has 41 votes
B>A>C = 26 ⇒ B has 26 votes
C>A>B = 42 ⇒ C has 42 votes
What is the Hare method?
The Hare method is least votes gainers will be eliminated and once eliminated,The votes will be transferred to the next choice of person/thing.
From the given question we have B will be eliminated
Therefore we have
A>B>C = 41 ⇒ A has 41 votes
B>A>C = 26 ⇒ B has 26 votes
We eliminate B, the votes are transferred to the next (A)
A>C = 26 ⇒ A has 26 votes
C>A>B = 42 ⇒ C has 42 votes
Therefore the total votes are
A votes = 41 + 26 = 67 votes
Therefore after eliminating B due to Hare Method, A will have a total of 67 votes.
To learn more about the votes visit:
https://brainly.com/question/3710029
A school carnival is having a dunk tank. The graph shows the temperature, t, in Fahrenheit after h hours.
Tank Temperature
Which linear function does the graph represent?
Each dairy cow in the U.S. produces an average
of 25 quarts of milk per day. Given that there are
quarts in a gallon, how many gallons of milk does a
cow produce?
Help I have like 10 minutes
Answer:
Option C
Step-by-step explanation:
please mark me brainliest and 5 star
Help plz Translate this sentence into an equation.
The product of Jenny's savings and 2 is 36.
Use the variableſ to represent Jenny's savings.
Answer:
2j = 36
Step-by-step explanation:
First, look for keywords.
"Product" means you multiply, and when you multiply a number by a variable you set it up by putting them together as demonstrated. 36 is the product so it's your total.
4x-(12 divided 3) +2x=20
Answer:
4
Step-by-step explanation:
f(x)=5x-3
f(5)=????
Please give me the answer
Answer:
f(5) = 22
Step-by-step explanation:
Plug in 5 as x into the function:
f(x) = 5x - 3
f(5) = 5(5) - 3
f(5) = 25 - 3
f(5) = 22
1 and 1/4 - 1/3=
please give the right answer
Answer:
11/12
Step-by-step explanation:
15/12-4/12= 11/12
Answer:
11/12
Step-by-step explanation:
5/4 -1/3 first make the equation easier to look at so take the 1 and add it as 4/4
15/12-4/12 then make the bottom the same with multipulcation and tops are multiples as well
11/12 subtract
4. Mrs. Dion decided to go out to dinner. She
spent $15.40 on her meal. She tipped the waiter
$4.25. How much did she pay all together?
Answer:
$19.65
Step-by-step explanation:
Adding decimals is the same as simple addition just line up the point in the numbers and add.
Patrick graphed a square with the area of 50 square units on a coordinate plane. one of the verticles of the square is located at (5,10). which could the other three vertice of the square
Answer:
The other 3 vertices would be (10,5) , (5,0) , and (0,5)
Step-by-step explanation:
2 + x to the power of 3= 18 what is x
Answer:
2.5198421
Step-by-step explanation:
Of the following sets, which represents a function?
Situation A = {student's name, all the colors that the student likes}
Situation B = {student's name, names of all of the student's teachers}
Answer:
what
Step-by-step explanation:
The gas tank on the back of a tanker truck can be equated to a cylinder with a diameter of 8 feet and a length of 19 feet. A gallon of gas is approximately 231 cubic inches. The density of the gasoline is .0262 pounds per cubic inch. The driver has stopped at a local farm to fill a tank that has linear dimensions that are 2/3 the size of his tank. If the driver's tank was full and the farmer's tank was empty, what is the mass of the gasoline in each of the tanks after the smaller tank is full?
9514 1404 393
Answer:
driver's tank: 30,427 lbfarmer's tank: 12,811 lbStep-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr^2·h . . . radius r, height h
The radius of the driver's tank is half its diameter, so is (8 ft)/2 = 4 ft. Then the volume of that tank is ...
V = π(4 ft)^2·(19 ft) = 304π ft^3
Each cubic foot of gasoline has a mass of ...
(1728 in^3/ft^3)(0.0262 lb/in^3) = 45.2736 lb/ft^3
Then the total mass in the driver's full tank is ...
(304π ft^3)(45.2736 lb/ft^3) ≈ 43,238.3 lb
__
The farmer's tank is a scaled-down version of the driver's tank. It's volume will be scaled by the cube of the linear scale factor, so will be (2/3)^3 = 8/27 of the volume of the driver's tank.
The farmer's tank will hold a mass of (43,238.3 lb)(8/27) ≈ 12,811 lb.
The amount remaining in the driver's tank is 43,238 -12,811 = 30,427 lb.
Help please due soon
Answer:
1. H=6
2. Y= -1
3. T= 2
4. D= 2.1
5. K= 0
6. -13 1/3
Step-by-step explanation:
Omar’s watch shows that he takes 642 steps to walk a lap around his school’s track. If he takes a total of 12,198 steps while walking the track, how many laps does Omar walk? It is one of these.
a)18
b)19
c)20
d)21
Answer:
B. 19
12,198÷642 so the final answer will be 19.
Kareem is flying two kites. He has 104 feet of string out to one kite and 120 feet out to the other kite. The angle formed by the two strings is 36° as shown in
the figure below. Find the distance between the kites.
120
104
36 degrees
Carry your intermediate computations to at least four decimal places.
Round your answer to the nearest tenth of a foot.
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Answer: Manuel is flying two kites. He has
102
feet of string out to one kite and
111
feet out to the other kite. The angle between the strings is
36°
as shown in the figure below. Find the distance between the kites
Please help me this is 7th grade math all you have to do is find the slope for the graph if it is right i will give you brianliest
Answer:
-10/2 or -5 for the slope
Step-by-step explanation:
rise over run: it's going down 10 and over 2 or
for every 5 down it goes 1 over
Identify the underlined place in 131.572. Then round the number to that place
The 5 is underlined
Can someone please help??
Answer:
The 5 is in the tenths place.
Step-by-step explanation:
:)
Answer:
131.6
Step-by-step explanation:
Since the 5 in 131.572 is underlined, we need to round the number to the nearest tenth. When rounding numbers, we need to look at the digit next to the rounded digit. The digit after 5 is 7.
If the digit after that is 1-4, we round down the 5. If the digit after that is 5-9, we round up the 5. Since 7 is between 5 and 9, we round the digit 5 to 6.
Thus, the rounded number would be: 131.6
Find the scale factor of trapezoid QRST if it’s dilated to Q’R’S’T’. Type your result in the empty box provided below. HELPP PLEASE!!!!!!
Answer:
5 units
Step-by-step explanation:
its hard to tell but i think it dilated 5 units
We want to find the scale factor at which QRST is dilated to form Q'R'S'T'
We will find that the scale factor is 2.
In a general dilation, we will see that all the measures change in the same way, by the scale factor.
This means that:
QR*k = Q'R'
RS*k = R'S'
And so on, where k is the scale factor.
Then we can just find one of the equivalent measures in both trapezoids and find the value of k.
For example, we have:
Q'R' = 8
QR = 4
Replacing these on the above equation we get:
4*k = 8
k = 8/4 = 2
k = 2
The scale factor of dilation is 2.
If you want to learn more, you can read:
https://brainly.com/question/14793702
The expression on the left side of an equation is shown below.
3(x+1)+9=0
If the equation has no solution, which expression can be written in the box on the other side of the equation?
O 3(x+4)
0 24x+6) + x
O 4(x - 3) - x
O 3(x+1)+9x
Which fraction shoes unit rate that is equal to the ratio 18:2
Answer: 9/1
Step-by-step explanation: