a box is constructed out of two different types of metal. the metal for the top and bottom, which are both square, costs 1/ft2 and the metal for teh sides costs 2 ft find the dimensions that minimize cost if the box has a volume of 20 ft 3
Answers
The cost function of the box is C(x) = 2. x² + 160/x and the dimension that lead to the minimum cost is length = ∛40 ft., width = ∛40 ft., height = ∛5 ft.
Let:
x = the bottom's side length
h = the height of the box
Then, the surface area of top and bottom:
A1 = 2. x²
The surface area of vertical sides:
A2 = 4 x. h
The cost function is:
C(x) = 2. x² . 1 + 4 x. h . 2
C(x) = 2. x² + 8 x. h
The volume of the box is:
V = x² . h
20 = x² . h
h = 20 / x²
Substitute h = 20 / x² into the cost function:
C(x) = 2. x² + 8 x. h
C(x) = 2. x² + 8 x. 20 / x²
C(x) = 2. x² + 160/x
At the minimum point, the derivative of a function is equal to zero. Hence,
C'(x) = 4x -160 / x² = 0
x³ = 40
x = ∛40
Substitute x = ∛40 to find the height:
h = 20 / x²
= 2 . 10 / (∛4² . ∛10²)
= ∛10 / ∛2 = ∛5
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Related Questions
d = 12 cm42°Find the area of the green sector.
Answers
We will determine the area of the green section as follows:
[tex]A=r^2\cdot\frac{\alpha}{2}[/tex]Here alpha is the angle [In radians] and r is the radius-
*First: We determine the angle:
[tex]\alpha=360-42-180\Rightarrow\alpha=138[/tex]Now, we transform it to radians:
[tex]138\cdot\frac{\pi}{180}=\frac{23}{30}\pi[/tex]*Second: We replace on the equation:
[tex]A=(6)^2\cdot\frac{(\frac{23}{30}\pi)}{2}\Rightarrow A=\frac{69}{5}\pi[/tex]So, the area of the green sector is 69pi/5 square centimeters. [Approximately 43.4 square centimeters]
Answer:
A ≈ 43.4 cm²
Step-by-step explanation:
the area (A) of the green sector is calculated as
A = area of circle × fraction of circle
given d = 12 then r = 12 ÷ 2 = 6 cm
the central angle of the green sector = 180° - 42° = 138°
then
A = πr² × [tex]\frac{138}{360}[/tex] ( simplify fraction by dividing numerator/denominator by 6 )
= π × 6² × [tex]\frac{23}{60}[/tex]
= 36π × [tex]\frac{23}{60}[/tex]
= [tex]\frac{36\\pi (23) }{60}[/tex]
≈ 43.4 cm² ( to the nearest tenth )
Add or subtract the following mixed numbers. First change each mixed number to an equivalent improper fraction. Then find a common denominator, and proceed as before. Leave your answer as an improper fraction. Be sure your answers are reduced to lowest terms. 3 1/4 + 6 1/2
Answers
In terms of the calculation, the answer is 39/4 in improper fraction.
What is an improper fraction?An improper fraction has a denominator that is greater than or equal to the numerator. Based on the numerator and denominator values, proper fractions and improper fractions are the two main types of fractions in mathematics.
What is a mixed fraction?A mixed fraction is a fraction formed by combining a natural number and a proper fraction. It is a shortened version of an improper fraction.
The given equation is [tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] .
Taking 4 as LCM from the above equation.
[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = (13/4) + (13/2)
[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = (13+26)/4
[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = 39/4
Now, since the solution must be proffered in an improper fraction.
Therefore, the obtained improper fraction is 39/4.
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classify in as many ways possible
Answers
The figure above is a rectangle
The classifications of a rectangle are:
1. A rectangle has 4 sides and angles, therefore, it is a quadrilateral.
2. Each interior angle is a right-angle, that is 90⁰
3. The sum of the interior angles equals 360
4. The opposite sides are parallel
5. The opposite sides are equal
6. The diagonals bisect each other
7. The diagonals have the same length
HELP ASAP PLSSSPLSPSLSPLSSSSSS
Graph g(x) = |x + 3|.
Answers
Answer:
Hope this helps!!
determine the equation of line from the graph
Answers
Answer:
y=2x+0
Step-by-step explanation:
This is slope intercept form. The slope is 2 you can tell by the two points on the graph at (0,0) and (1,2). The points move up 2 and over 1. That makes the slope 2/1 but since the bottom half is just a one it can be simplified to 2.
And the +0 just means that its y intercept is 0,0
however it is not required to put +0 at the end
Answer:y=2x+0
Step-by-step explanation:
Simplify by dividing
Answers
Answer: -27/40
Step-by-step explanation:
ANSWER ASAPDonna received a $70 gift card for a coffee store. She used it in buying some coffee that cost $8.36 per pound after buying a coffee she had $26.85 left on your card how many pounds of coffee did she buy
Answers
The amount of coffee she bought is 5.16 pounds.
How to find the pounds of coffee she bought?She received a $70 gift card for a coffee store.
She used it in buying some coffee that cost $8.36 per pound after buying a coffee she had $26.85 left.
Therefore, base on the card, the number of pounds of coffee she bought can be calculated as follows;
Hence,
let
the amount of coffee she bought in pounds = x
Hence,
70 = 8.36x + 26.85
70 - 26.85 = 8.36x
43.15 = 8.36x
divide both sides by 8.36
43.15 / 8.36 = x
x = 5.16148325359
Therefore, the amount in pounds is 5.16 pounds.
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7) 5x - 125 5x-:5 OTROW VOITA U Name Samantha Date 3/3 Kuta Software - Infinite Algebra 2 Graphing Linear Inequalities Sketch the graph of each linear inequality. 1) yz-2x-2 9) y 25 *2=5 2) ys-*+1 Yst
Answers
It is not possible to write a linear inequality such that the solution contains only positive values of x and y.
This happens because every line on the coordinate plane must have a y-intercept and/or an x-intercept. When the line crosses an axis, either the variable x or y changes its sign.
given that tank=8 and sinx is negative determine sin(2x) cos(2x) and tan(2x)
Answers
Answer:
sin2x = 16/65
cos2x = -63/65
tan2x = -16/63
Explanation:
the tangent of an angle is equal to the opposite side over the adjacent side. So, if the tan(x) = 8, we can represent this as the following diagram:
Therefore, we can calculate the value of the hypotenuse as:
[tex]\text{Hypotenuse = }\sqrt[]{8^2+1^2}=\sqrt[]{64+1}=\sqrt[]{65}[/tex]With the hypotenuse, we can calculate sin(x) and cos(x) as follows:
[tex]\begin{gathered} \sin x=\frac{Opposite}{hypotenuse}=-\frac{8}{\sqrt[]{65}} \\ \cos x=\frac{\text{Adjacent}}{\text{hypotenuse}}=-\frac{1}{\sqrt[]{65}} \end{gathered}[/tex]We type the negative sign because the question says that sin(x) is negative.
Now, we will use the following trigonometric identities to find sin(2x), cos(2x) and tan(2x)
[tex]\begin{gathered} \sin 2x=2\sin x\cos x \\ \cos 2x=1-2\sin ^2x \\ \tan 2x=\frac{2\tan x}{1-\tan ^2x} \end{gathered}[/tex]Therefore, replacing the values, we get:
[tex]\sin 2x=2(\frac{-8}{\sqrt[]{65}})(\frac{-1}{\sqrt[]{65}})=\frac{16}{65}[/tex][tex]\cos 2x=1-2(\frac{-8}{\sqrt[]{65}})^2=1-2(\frac{64}{65})=-\frac{63}{65}[/tex][tex]\tan 2x=\frac{2(8)}{1-8^2}=-\frac{16}{63}[/tex]So, the answers are:
sin2x = 16/65
cos2x = -63/65
tan2x = -16/63
Select the correct answer.
Which of the following represents a function?
A. The first graph
B. The second graph
C. {(0,1), (3,2), (-8,3), (-7,2), (3,4)}
D.
x -5 -1 9 8 -1
y 1 7 23 17 1
Answers
The relation that represents a function is given as follows:
B. The second graph.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.
For a point in the standard format (x,y), we have that:
x is the input.y is the output.The meaning is that the input given by the x-coordinate is mapped to the output given by the y-coordinate.In a graph, the equivalent to this is that there can be no vertically aligned points.
Then, for the options in this problem, we have that:
a does not represent a function, as the input -1 is mapped to two outputs, meaning that there are vertically aligned points.b represents a function, as each input value(-4, 9, 13 and -7) is mapped to only one output.c does not represent a function, as the input 3 is mapped to two outputs.d does not represent a function, as the input -1 is mapped to two outputs.More can be learned about relations and functions at https://brainly.com/question/12463448
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What’s the answer plsss
Answers
Answer:
option a is the right answer .
Step-by-step explanation:
Cos theta = B/h = 8/21
theta = 67.6 °
Step-by-step explanation:
imagine the triangle being flipped upwards around DE, so that F is on top instead of on the bottom.
then you see clearly that
DF (21) is the radius of the trigonometric circle,
DE is cos(angle D)×radius,
EF (8) is sin(angle D)×radius.
so,
8 = sin(angle D)×21
sin(angle D) = 8/21 = 0.380952381...
angle D = 22.39268781...° ≈ 22.4°
and so, something is wrong with your problem definition.
the answer options seem to aim for angle F, for which EF (8) is the cosine × radius.
but for angle D EF is clearly the sine × radius.
and for answer option b (20.9°) EF would have to be about 7.5 units long (with the radius DF still being 21). that is all too much off.
your teacher made a mistake. send him/ her my regards.
In Mr. Patterson’s class, the average score among students who studied for an exam was 78. The average among students who did not study was 54. The overall class average was 70. What portion of the class did not study? Express your answer as a common fraction.
Answers
if the value of the response variable is uniquely determined by the values of the predictor variables, we say that the relationship between the variables is: (choose the correct response)
Answers
Deterministic.
The relationship between the variables is deterministic. A deterministic relationship refers to a relationship in which the dependent variable does not depend on other elements (variables) other than the independent element classified in the relationship. The independent variable (element) in the relationship possesses an exact value. Hence deterministic relationship is also named as the exact relationship between variables.
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The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?.
Answers
Percentage of the student body exists at least 21 years old exists 50%.
What is meant by normal distribution?A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
As one moves away from the center, values start to taper off and the majority of values are concentrated in this area. In a normal distribution, the mean, mode, and median are identical measures of central tendency.
When given a normal or Symmetric distribution, the mean of the distribution exists at the center with 0.5 or 50% of the distribution to either side (right and left) of the distribution.
Therefore, if the mean = 21 ; then the percentage of student body with at least 21 years is the percentage to the left of the distribution, which exists 50%.
P(x ≤ 21) = 0.5 = 50%
Therefore, 50 percentage of the student body exists at least 21 years old
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Gwen says that the sum of -1 3/4 and 2 1/2 is the same as the difference between 2 1/2 and 1 3/4 is Gwen correct explain why or why not
Answers
The sum of -1 and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.
First we will convert the mixed fractions into improper fractions.
-1 and 3/4 = -7/4
2 and 1/2 = 5/2
Sum of -1 and 3/4 and 2 and 1/2 = -7/4 + 5/2 = -7/4 + 10/4 = 3/4
Difference between 2 and 1/2 and 1 and 3/4 = 5/2 - 7/4 = 10/4 - 7/4 = 3/4
As both the values equal to 3/4 , we can say that the sum of -1 and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.
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Help This is due at the end of class
Answers
The coordinates of the vertices of the image of the square are S'(x, y) = (- 1, - 4), T'(x, y) = (- 1, 1), U'(x, y) = (4, 1) and V'(x, y) = (4, - 4).
How to translate a geometric locus set on a Cartesian plane
In this problem we need to make use of a translation on a geometric locus on a Cartesian plane, which is generated by four points representing the vertices of the square. The translation is a kind of rigid transformation, whose formula is shown below:
P'(x, y) = P(x, y) + t(x, y)
Where:
P(x, y) - Original pointt(x, y) - Translation vector.P'(x, y) - Resulting pointIf we know that S(x, y) = (- 6, - 5), T(x, y) = (- 6, 0), U(x, y) = (- 1, 0) and V(x, y) = (- 1, - 5) and t(x, y) = (5, 1), then the locations of the vertices of the triangle are:
S'(x, y) = (- 6, - 5) + (5, 1)
S'(x, y) = (- 1, - 4)
T'(x, y) = (- 6, 0) + (5, 1)
T'(x, y) = (- 1, 1)
U'(x, y) = (- 1, 0) + (5, 1)
U'(x, y) = (4, 1)
V'(x, y) = (- 1, - 5) + (5, 1)
V'(x, y) = (4, - 4)
The location of the image of the square is shown below.
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Find the midpoint of the segment below and enter its coordinates as anordered pair. If necessary, express coordinates as fractions, using the slashmark (/) for the fraction bar.
Answers
Each midpoint's coordinate is given by the mean of the respective coordinates of the two endpoints of the segment. Then, if we say M is the midpoint of that segment, we have:
Mx = (-4 + 4)/2 = 0/2 = 0
My = [6 + (-2)]/2 = (6 - 2)/2 = 4/2 = 2
Therefore, writing those coordinates as an ordered pair, we have:
M = (0, 2)
The cost of mailing a package is proportional to the weight of the package. The proportional relationship can be represented with the equation c = 0.4w, where c represents the total cost and w represents weight in ounces. A graph for the equation is shown.
graph with x axis labeled weight in ounces and y axis labeled cost in dollars, with a line from 0 comma 0 going through 2 comma 0.8
Which of the following statements is true about the graph shown?
The graph is incorrect and the line should go through the point (0.4, 1).
The equation c = 0.4w is correctly represented by the graph.
The x-axis and y-axis are labeled incorrectly.
The graph does not show a proportional relationship.
Answers
Among the given statements The equation c = 0.4w is correctly represented by the graph is correct.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same.
By given the equation c = 0.4w, where c represents the total cost and w represents weight in ounces.
Given that graph with x axis labeled weight in ounces and y axis labeled cost
Let us construct a table
Weight(x) 1 2
Cost (Y) 0.4 0.8
As given graph with x axis labeled weight in ounces and y axis labeled cost in dollars, with a line from 0 comma 0 going through 2 comma 0.8
The equation c = 0.4w is correctly represented by the graph.
Hence among the given statements The equation c = 0.4w is correctly represented by the graph is correct.
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Evelyn sells beauty supplies. She gets 5% commission for selling beauty products. How much commission will she receive if she sells 1,648 worth of beauty products?
Answers
Given:
Evelyn sells beauty supplies. She gets 5% commission for selling beauty products.
Required:
To find the commission she receive if she sells $1,648 worth of beauty products.
Explanation:
The commission she receive if she sells $1,648 worth of beauty products is
[tex]\begin{gathered} =\frac{5}{100}\times1648 \\ \\ =82.4 \end{gathered}[/tex]Final Answer:
$82.4
You have to write an equation then solve.
Answers
you can ride 7 rides.
The coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4). What are the coordinates of the image if the quadrilateral is translated 4 units down and 3 units right
Answers
If the coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4) and it is translated 4 units down and 3 units right, then the coordinates of the image is A'(-3,-2), B'(-2,-1), C'(10,-1) and D'(3,0)
The coordinates of the quadrilateral ABCD is
A (-6,2) , B(-5,3), C(7,3) and D(0,4)
The quadrilateral is translated 4 units down and 3 units right
After translation
A(x, y)⇒ A(x + a, y +b)
The value of a and b will be positive if the shift is right and up.
The value of a and b will be negative if the shift is left and down.
Therefore
a = 3, b = -4
The coordinates of A' =(-6+3,2-4)=(-3,-2)
The coordinates of B' =(-5+3,3-4)=(-2,-1)
The coordinates of C' =(7+3,3-4)=(10,-1)
The coordinates of D' =(0+3,4-4)=(3,0)
Hence, If the coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4) and it is translated 4 units down and 3 units right, then the coordinates of the image is A'(-3, -2), B'(-2, -1), C'(10, -1) and D'(3, 0)
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Find (3.0x10^15) over (5.0x10^6)(2.4x10^3), expressed in scientific notation.
Answers
The result of 3.0×[tex]10^{15}[/tex] over 5.0×[tex]10^6[/tex] in scientific notation is 6×[tex]10^8[/tex]
The first number = 3.0×[tex]10^{15}[/tex]
The second number = 5.0×[tex]10^6[/tex]
3.0×[tex]10^{15}[/tex] over 5.0×[tex]10^6[/tex] means we have to divide the first number by the second number
The scientific notation is the a method of representing the a very large number or a very small number in a simple way. The general from of the scientific notation is when a number from 1 to 10 is multiplied by the power of 10.
Here we have to divide 3.0×[tex]10^{15}[/tex] by 5.0×[tex]10^6[/tex]
3.0×[tex]10^{15}[/tex] ÷ 5.0×[tex]10^6[/tex] = (3/5) × [tex]10^{15-6}[/tex]
= 0.6×[tex]10^9[/tex]
= 6×[tex]10^8[/tex]
Hence, the result of 3.0×[tex]10^{15}[/tex] over 5.0×[tex]10^6[/tex] in scientific notation is 6×[tex]10^8[/tex]
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Peter says,
"If you subtract 18 from my number and multiply the difference by -6, the result is -84."
What is Peter's number?
I already made the equation, I just am struggling solving it
-6(x-18)=-84
Answers
Answer:
x = 32
Step-by-step explanation:
-6(x-18) = -84
Divide both sides by -6
x - 18 = 14
Add 18 to both sides
x = 32
Hi can someone help me with this?Writing the algebraic equation for the phrase below.. 1. The sum of X and 96 equals half of X .
Answers
Given:
1. The sum of X and 96 equals half of X.
To determine the algebraic equation, we note that the sum of x and 96 would be:
x+96
Next, half of x must be like this:
x/2
Then, the phrase equals means we set x+96 equals to x/2.
Therefore, the answer is:
[tex]x+96=\frac{x}{2}[/tex]Rewrite the following equation as a function of x.
1+ 3y - 29 = 0
O A. f(x)
f(x) = 9,2808 2
OB. f(x) = -9,280 +
O c. f(x) = -9,280 + 20
O D. f(x) = 9,280
1
20x
Answers
Name the line(s) through
point A that appear
perpendicular to GH.
Answers
Answer:
AD
Step-by-step explanation:
Consider the calculation x - y + (- z) where x and z are positive real numbers and y is a negative real number. i) What are the directions of motion for this calculation ? ii) Is the final answer positive , negative , or undetermined ? i) Right, left , left ii) Undetermined i) Right , right , left ii) Undetermined i) Right , left , left ii) Negative i) Right right , left ii) Positive
Answers
Given
x - y + (- z) where x and z are positive real numbers and y is a negative real number.
Find
i) What are the directions of motion for this calculation ?
ii) Is the final answer positive , negative , or undetermined ?
Explanation
i) as we have given
x - y + (- z)
x - y - z
(x - y) - z
right -left - left
ii) for this we take examples
let x = 2 , y = -1 and z = 2
2- (- 1) + (- 2) = 1 , positive
now
let x = 2 , y = -1 and z = 5
2 - (- 1) + (- 5) = 3 - 5 = -2 , negative
so , it is both negative or positive
hence it is undetermined
Final Answer
Hence , the correct option is
i) Right, left , left
ii) Undetermined
Which property is demonstrated below?
a(b+c)=(a.b)+(a.c)
O Inverse property
O Distributive property
O Communitive property
O Identity property
( and 15 points for this and will make brainliest to best answer) Please be fast!
Answers
Which property is demonstrated below?
a(b + c) = (a*b) + (a*c)
O Inverse property
O Distributive property
O Communitive property
O Identity property
Tyee has $720 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. He buys a new bicycle for $401.83. He buys 4 bicycle reflectors for $12.85 each and a pair of bike gloves for $23.83. He plans to spend some or all of the money he has left to buy new biking outfits for $40.49 each. Use the drop-down menu below to write an inequality representing oo, the number of outfits he can buy while staying within his budget.
Answers
The inequality that represents the number of outfits he can buy while staying within his budget is M ≤ 6.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
Total amount to spend = $720
Cost of bicycle = $401.83
Cost of bicycle reflector = $12.85 ( 4 reflector bought )
Cost of bike cloves = $23.83
Cost of biking outfits = $40.49
The number of possible biking outfits:
401.83 + 4 x 12.85 + 23.83 + M40.49 ≤ 720
401.83 + 51.4 + 23.83 + M40.49 ≤ 720
477.06 + M40.49 ≤ 720
M40.49 ≤ 720 - 477.06
M40.49 ≤ 242.94
M ≤ 242.94 / 40.49
M ≤ 6
M = Number of possible outfits
Thus,
The inequality that represents the number of outfits he can buy while staying within his budget is M ≤ 6.
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20) g(a) = a² - 2
h(a) = -3a
Find g(a) + h(a)
Answers
The value of g(a) + h(a) is a²-3a-2 or (a-2)(a-1) using addition of functions.
What is the Function?Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where x belongs to X and y belongs to Y, with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y
Adding two functions-
g(a) = a²- 2
h(a) = -3a
Let h(a) be g(a) + h(a)
So h(a) = a² - 2 - 3a.
We can factorize the function into (a-2)(a-1).
So we get h(a) = (a-2)(a-1).
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