Answer:
[tex]l = \sqrt[3]{\frac{2V}{7}}[/tex] [tex]b = \sqrt[3]{\frac{2V}{7}}[/tex] [tex]h = \sqrt[3]{\frac{49V}{4}}[/tex]
Step-by-step explanation:
Represent the volume of the box with V and the dimensions with l, b and h.
The volume (V) is:
[tex]V = l * b * h[/tex]
Make h the subject of the formula
[tex]h = \frac{V}{lb}[/tex]
The surface area (S) of the aquarium is:
[tex]S = lb + 2(lh + bh)[/tex]
Where lb represents the area of the base (i.e. slate):
The cost (C) of the surface area is:
[tex]C = 7 * lb + 1 * 2(lh + bh)[/tex]
[tex]C = 7lb + 2(lh + bh)[/tex]
[tex]C = 7lb + 2h(l + b)[/tex]
Substitute [tex]\frac{V}{lb}[/tex] for h in the above equation
[tex]C = 7lb + 2*\frac{V}{lb}(l + b)[/tex]
[tex]C = 7lb + \frac{2V}{lb}(l + b)[/tex]
[tex]C = 7lb + \frac{2V}{b} + \frac{2V}{l}[/tex]
Differentiate with respect to l and with respect to b
[tex]C_l=7b - \frac{2V}{l^2}[/tex] [tex]=0[/tex]
[tex]C_b=7l - \frac{2V}{b^2}[/tex] [tex]=0[/tex]
To solve for b and l, we equate both equations and set l to b (to minimize the cost)
[tex]7b - \frac{2V}{l^2}=7l - \frac{2V}{b^2}[/tex]
[tex]7l - \frac{2V}{l^2}=7b - \frac{2V}{b^2}[/tex]
By comparison:
[tex]l =b[/tex]
[tex]C_l=7b - \frac{2V}{l^2}[/tex] [tex]=0[/tex] becomes
[tex]7l - \frac{2V}{l^2}=0[/tex]
[tex]7l = \frac{2V}{l^2}[/tex]
Cross Multiply
[tex]7l^3 = 2V[/tex]
Solve for l
[tex]l^3 = \frac{2V}{7}[/tex]
[tex]l = \sqrt[3]{\frac{2V}{7}}[/tex]
Recall that: [tex]l =b[/tex]
[tex]b = \sqrt[3]{\frac{2V}{7}}[/tex]
Also recall that:
[tex]h = \frac{V}{lb}[/tex]
[tex]h = \frac{V}{\sqrt[3]{\frac{2V}{7}}*\sqrt[3]{\frac{2V}{7}}}[/tex]
[tex]h = \frac{V}{\sqrt[3]{\frac{4V^2}{49}}}[/tex]
Apply law of indices
[tex]h = \sqrt[3]{\frac{49V^3}{4V^2}}[/tex]
[tex]h = \sqrt[3]{\frac{49V}{4}}[/tex]
The dimension that minimizes the cost of material of the aquarium is:
[tex]l = \sqrt[3]{\frac{2V}{7}}[/tex] [tex]b = \sqrt[3]{\frac{2V}{7}}[/tex] [tex]h = \sqrt[3]{\frac{49V}{4}}[/tex]
40 of the cats at the pet store are black, which is 25% of all cats. How many cats are there at the pet store
Answer:
There are 160 cats at the store.
Step-by-step explanation:
There are 40 black cats, which is 25% of all the cats. You are trying to find all the cats at the store, or 100% of the cats at the store. So:
40 = 25%
40(4) = 25% (4)
160 = 100%
There are 160 cats at the store.
Answer:
160
Step-by-step explanation:
25%=1/4=0.25
=40×4
=160
jessica wondered if elementary school students tend to write more when they are given
full question plsAnswer:
Step-by-step explanation:
40.1 =
С C
+ 3.1
0.1
Answer:
1.876
because I said it was
En una tienda de videojuegos venden, por la mañana, las 3/4 partes de los que tenían. Por la tarde vendieron 4/5 de los que le quedaban. Cuando cerró la tienda quedaron 200 videojuegos sin vender, ¿cuántos había al principio?, ¿cuántos vendieron por la tarde?
al principio había 10
y se vendieron por la tarde150
2 -7
-9
5
Given A=
and B-
6
1
-1
If X-A=B, what is X?
-2
O
7
0
-11
12
-2
-5
-7 -12
5
0
11-12
Answer:
it is b furqufhrfhquh quf hqhf
Step-by-step explanation:bfygefy eyfeyfyewfyefwef eqf
\fn qf7f
The value of the matrix X is X = [tex]\left[\begin{array}{ccc}-7&-2\\7&0\\\end{array}\right][/tex].
What are Matrices?Matrices are a set of numbers arranged in such a way that the numbers are arranged in rows and columns.
Each number is called element in a matrix.
Given are two matrices.
A = [tex]\left[\begin{array}{ccc}2&-7\\6&1\\\end{array}\right][/tex] and B = [tex]\left[\begin{array}{ccc}-9&5\\1&-1\\\end{array}\right][/tex]
We have given that, a matrix X exists such that,
X - A = B
We can rearrange this as,
X = A + B
Adding the two matrices,
The entries will be,
2 - 9 = -7
-7 + 5 = -2
6 + 1 = 7
1 - 1 = 0
X = [tex]\left[\begin{array}{ccc}-7&-2\\7&0\\\end{array}\right][/tex]
Hence the X is option A.
Learn more about Matrices here :
https://brainly.com/question/30646566
#SPJ7
Four points A, B, C, and d are on a number line, in some order, so that AB=1, BC=2, CD=3, and DA=4. Which two points are farthest away from each other?
Answer: B or C sorry if its wrong
Step-by-step explanation: have a nice day
Which pair of angles are complementary but not adjacent?
1
N
5
3
4
+
0 21 and 25
0 21 and 23
0 24 and 21
0 24 and 25
HURRY PLEASE
Answer: 1 and 3
Step-by-step explanation:
I got it right on edge 2021
Answer:
1 and 3
Step-by-step explanation:
carry out the following divisions.
Answer:
9a²b²c²
Step-by-step explanation:
72a³b⁴c⁵ / 8ab²c³
= 9a²b²c²
Which equation represents a line which is parallel to the y-axis?
X=-4y
Y=x-3
Y=-7
X=-8
Answer:
x = -8
Step-by-step explanation:
If the line is parallel to the y axis, that means it will be a vertical line.
Vertical lines have an equation of x = , because the line will only go through one x value.
They also will not have a slope, because their slope is undefined.
So, the correct answer is x = -8
Jessica has just purchased a new purse in the shape of a rectangular box to match her favorite shoes. The purse has a length of 15 cm, a width of 6.4 cm, and a height of 8 cm. What is the volume of the purse?
Clara went to a music store and brought some CDs and DVDs. She paid $14 for each CD and $17 for each DVD. Let x represent the number of CDs that she purchased and y represent the number of DVDs.
I think the answer is nine but I’m not sure how to explain how I got my answer
Answer:
ur answer is right it is 9
Step-by-step explanation:
NOTE: divide the number 36 with 4 and u will get 9
GOOD JOB
Please mark as brainliest
Have a great day, be safe and healthy
Thank u
XD
4 = x + 12 PLEASE HELP QUICK
Answer:
x= -8
Step-by-step explanation:
Move the terms
Calculate: -x=12-4 = -x=8
Change the signs
Six more than five times a number
Answer:
? = 5n + 6
Explanation:
Answer:
5x + 6
Step-by-step explanation:
Let the number = x. 5 times x = 5x. So, the equation 5x + 6.
Evaluate 12.3p+11.9r when p=7 and r=8.
Find the errors and correct the following mathematical sentences.
Answer:
Step-by-step explanation:
18). 3x + 2 ÷ 3x = [tex]\frac{2}{3x}[/tex]
Since, 3x + 2 ÷ 3x = 3x + [tex]\frac{2}{3x}[/tex]
Therefore, right hand side of the equation will be = 3x + [tex]\frac{2}{3x}[/tex]
20). [tex]\frac{4x+3}{3}=x+1[/tex]
Since, [tex]\frac{4x+3}{3}=\frac{4x}{3}+\frac{3}{3}[/tex]
= [tex]\frac{4}{3}x+1[/tex]
Therefore, right hand side of the equation should be [tex]\frac{4}{3}x+1[/tex].
Help please!!!
I’m failing math and I need help
Answer:
3.
vertically opposite angles ,
= 30°
4. 50° +30°+2x = 180°
80°+2x=180°
2x=180°-80°
2x=100°
Story Problem:
Avery purchased 4 tacos and 2 burritos and her total cost was $21. Sasha purchased 4 tacos and 3 burritos
and her total cost was $26.50. What is the price of one burrito?
Answer:
Step-by-step explanation:
Let tacos be x and burritos be y
So, Avery purchased 4x+2y = 21
Sasha purchased 4x+3y = 26.5
Solving the 2 eqns:
4x+2y=21
-4x-3y=-26.5
-y=-5.5
The cost of one burrito is $5.5
The question is in the graph. Please help.
Answer:
A I think
Step-by-step explanation:
because if you add them up.
Answer:
Aprox. 216 days
Step-by-step explanation:
Add the counts of the green bar(5-10mm) and the brown bar (0-5mm).
The brown is roughly 130 and the green is roughly 80, which is approx 216 days.
If i helped, a brainliest answer would be greatly appreciated!
Which of the following ratios is not equivalent to the other two? * 1 1/2, 1:2, or 2 to 1
Answer:
1 1/2
Step-by-step explanation:
giving brainliest *easy*
Answer:
pi
Step-by-step explanation:
to convert angles to radians you must multiply the angle measurement by the formula pi/180
180 x pi/180
the 180s cancel out and you are left with pi
Answer:
3.14159 Radian
Step-by-step explanation:
3.142rad × 180/π = 180°
PLEASE PLEASE HELP!!!
These tables of values represent continuous functions. In which table do the
values represent an exponential function?
Question 7 (5 points)
(06.04 LC)
The equation of the line of best fit of a scatter plot is y = 8x - 1. What is the slope of
the equation? (5 points)
1)-8
2-1
3) 1
4) 8
Answer:
4) 8
Step-by-step explanation:
In the formula y = mx + b, m is the slope and b is the y-intercept
m = 8
b = -1
If m = 8 and m is the slope, then the slope is 8
Finley's pumpkin had a mass of 6.5 kilograms (kg) before he carved it. After carving it, the pumpkin had a mass of 3.9 kg
Answer:
[tex]\%Change = -40\%[/tex]
Step-by-step explanation:
Given
[tex]Initial = 6.5kg[/tex]
[tex]Final = 3.9kg[/tex]
Required
Determine the percentage change --- Missing from the question
This is calculated as
[tex]\%Change = \frac{Final - Initial}{Initial} * 100\%[/tex]
[tex]\%Change = \frac{3.9kg - 6.5kg}{6.5kg} * 100\%[/tex]
[tex]\%Change = \frac{-2.6kg}{6.5kg} * 100\%[/tex]
[tex]\%Change = \frac{-260}{6.5}\%[/tex]
[tex]\%Change = -40\%[/tex]
5/6 + (-4/9) - (-2), is this right??
Answer:
YES SIR OR I MEANT YES MAM
how many 5 digits numbers can be created using digits 1,2,3,7, and 6 without repeating any digits within that 5-digit number?
There are 5 numbers that can be used.
The first digit can be 1 of 5
The second digit can be 1 of 4
The third digit is 1 of 3
The fourth digit is 1 of 2
The fifth digit is 1 of 1
Total digits that can be created = 5 x 4 x 3 x 2 x1 = 120
HELP ME PLEASE
bsjsudhdhehe
What is the solution to the following system of equations?
3x + 2y = 30
y = x + 5
Answer:
D
Step-by-step explanation:
Answer:
I think this one is C
Step-by-step explanation:
It seems like its counting by 5's and the answer to the first equation
Hey guys I need help asap
A salesman earns 15% commission on each household appliance he sells. If he sells 6 toasters at $32 each, what is the commission that he earned?
Answer:
$28.8
Step-by-step explanation:
6x32=192
15% of 192 is 28.8
2X-5<9 solve inequality
Step-by-step explanation:
2x<9+5
2x<14
2x/2<14/2
x<7
Answer:
[tex]\boxed {\boxed {\sf x <7}}[/tex]
Step-by-step explanation:
To solve the inequality you must isolate the variable, which is x.
[tex]2x-5 < 9[/tex]
5 is being subtracted from 2x. The inverse of subtraction is addition, so add 5 to both sides of the equation.
[tex]2x-5+5 < 9+5[/tex]
[tex]2x < 14[/tex]
x is being multiplied by 2. The inverse of multiplication is division, so divide both sides by 2.
[tex]\frac {2x}{2} < \frac {14}{2}[/tex]
[tex]x <7[/tex]
The solution to this inequality is x <7