Answer:
[tex]Width = 4ft[/tex]
[tex]Height = 4ft[/tex]
[tex]Length = 8ft[/tex]
Step-by-step explanation:
Given
[tex]Volume = 128ft^3[/tex]
[tex]L = 2W[/tex]
[tex]Base\ Cost = \$9/ft^2[/tex]
[tex]Sides\ Cost = \$6/ft^2[/tex]
Required
The dimension that minimizes the cost
The volume is:
[tex]Volume = LWH[/tex]
This gives:
[tex]128 = LWH[/tex]
Substitute [tex]L = 2W[/tex]
[tex]128 = 2W * WH[/tex]
[tex]128 = 2W^2H[/tex]
Make H the subject
[tex]H = \frac{128}{2W^2}[/tex]
[tex]H = \frac{64}{W^2}[/tex]
The surface area is:
Area = Area of Bottom + Area of Sides
So, we have:
[tex]A = LW + 2(WH + LH)[/tex]
The cost is:
[tex]Cost = 9 * LW + 6 * 2(WH + LH)[/tex]
[tex]Cost = 9 * LW + 12(WH + LH)[/tex]
[tex]Cost = 9 * LW + 12H(W + L)[/tex]
Substitute: [tex]H = \frac{64}{W^2}[/tex] and [tex]L = 2W[/tex]
[tex]Cost =9*2W*W + 12 * \frac{64}{W^2}(W + 2W)[/tex]
[tex]Cost =18W^2 + \frac{768}{W^2}*3W[/tex]
[tex]Cost =18W^2 + \frac{2304}{W}[/tex]
To minimize the cost, we differentiate
[tex]C' =2*18W + -1 * 2304W^{-2}[/tex]
Then set to 0
[tex]2*18W + -1 * 2304W^{-2} =0[/tex]
[tex]36W - 2304W^{-2} =0[/tex]
Rewrite as:
[tex]36W = 2304W^{-2}[/tex]
Divide both sides by W
[tex]36 = 2304W^{-3}[/tex]
Rewrite as:
[tex]36 = \frac{2304}{W^3}[/tex]
Solve for [tex]W^3[/tex]
[tex]W^3 = \frac{2304}{36}[/tex]
[tex]W^3 = 64[/tex]
Take cube roots
[tex]W = 4[/tex]
Recall that:
[tex]L = 2W[/tex]
[tex]L = 2 * 4[/tex]
[tex]L = 8[/tex]
[tex]H = \frac{64}{W^2}[/tex]
[tex]H = \frac{64}{4^2}[/tex]
[tex]H = \frac{64}{16}[/tex]
[tex]H = 4[/tex]
Hence, the dimension that minimizes the cost is:
[tex]Width = 4ft[/tex]
[tex]Height = 4ft[/tex]
[tex]Length = 8ft[/tex]
PLEASE HELP MATH QUESTION 99 POINTS ASAP
Function A and Function B are linear functions. Compare the two functions and choose all that are correct.
Answer:
2 .The slope of Function A is less than the slope of Function B
A graph of Function A shows it has a y-intercept of 4, the same as that of Function B. (Statements 3 and 4 are not correct.)
The slope of Function A is 2, which is less than the slope of 3 that Function B has. (Statement 2 is correct; statement 1 is not.)
_____
More detailed working
The slope of Function A can be figured easily between the points with x-values that differ by 1:
m = (y3 -y2)/(x3 -x2) = (24-22)/(10-9) = 2/1 = 2 . . . . . Fun A has slope of 2.
The slope of Function B is the coefficient of x in the equation: 3.
__
The y-intercept of Function A can be found starting with point-slope form:
y -22 = 2(x -9)
y = 2x -18 +22
y = 2x +4 . . . . . . . slope-intercept form
The intercept of +4 is the same as that of Function B.
Step-by-step explanation:
mrk me brainliest plz
Answer:
2 .The slope of Function A is less than the slope of Function B
A graph of Function A shows it has a y-intercept of 4, the same as that of Function B. (Statements 3 and 4 are not correct.)
The slope of Function A is 2, which is less than the slope of 3 that Function B has. (Statement 2 is correct; statement 1 is not.)
_____
More detailed working
The slope of Function A can be figured easily between the points with x-values that differ by 1:
m = (y3 -y2)/(x3 -x2) = (24-22)/(10-9) = 2/1 = 2 . . . . . Fun A has slope of 2.
The slope of Function B is the coefficient of x in the equation: 3.
__
The y-intercept of Function A can be found starting with point-slope form:
y -22 = 2(x -9)
y = 2x -18 +22
y = 2x +4 . . . . . . . slope-intercept form
The intercept of +4 is the same as that of Function B.
Step-by-step explanation:
MARK ME BRAINLEIST PLZ PLZ PLZ
write the equation for a parabola with a focus at (-3,-5) and a directrix at x=-7
x=
Answer:
hope this helps
Step-by-step explanation:
equation for a parabola is:
What is parabola?The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus.
Given: focus= (3,-5), directrix at x =-7.
To find equation of parabola we will use distance formula,
√(x+7)²=√(x+3)² + (y+5)²
(x+7)²=(x+3)² + (y+5)²
x²+14x+49= x²+9+6x + (y+5)²
8x + 40 = (y+5)²
x= (y+5)²/8 -5
Hence, the equation of parabola is x= (y+5)²/8 -5
Learn more about equation of parabola here:
https://brainly.com/question/4025891
#SPJ2
PLEASE HELP MATH QUESTION 99 POINTS HELP ASAP PLEASE
LOOK AT LINKED IMAGE FOR QUESTION.
Answer:
Graph A. not a function
Graph B. is a function
Mapping A. is a function
Mapping B. not a function
Table A. not a function
Table B. is a function
Answer:
a graph. not a function
b graph.function
a table. not a function
b table. function
maaping a. function
mapping b. not a function
Step-by-step explanatio n:
mark me brainelst plz
From the equation below, where is the center of the circle located and what is the radius?
(x – 4)2 + (y + 8)2 = 16
A) Center: (4, -8) Radius = 4
B) Center: (-4, 8) Radius = 4
C) Center: (4, -8) Radius = 16
D) Center: (-4, 8) Radius = 16
Answer:
B Center: (-4, 8) Radius = 4
Step-by-step explanation:
The local weather forecast has been accurate for 24 of the past 30 days. Based on this fact what is the relative frequency probability that the forecast for tomorrow will be accurate
Step-by-step explanation:
the empirical probability is 24/30, or 4/5. this is also the desired probability.
What is the measure of angle L
Answer:
90-15 and you have your answer
Answer:
75
Step-by-step explanation: it is a right angle so you do 90-15 which is 75 degrees.
Can anyone help me out
Answer:
14.49 people per square mile
Step-by-step explanation:
Divide to find the answer:
836,109/57,714 = 14.49
plzzzzzzzz help for a brainly
Answer:
246
Step-by-step explanation:
Can someone please help me I will mark u brilliant for both
Answer:
1. 1/2
2. 4
Step-by-step explanation:
2. 14x = 56
56 / 14
x = 4
1.) Apply the distributive property and simplify the expression : 4(2x + y)
Your answer
Answer:
8x + 28
Step-by-step explanation:
Mira uses the mapping rule to find the coordinate of a point that had been rotated 90° clockwise about the origin. Examine Mira’s solution to determine which step has an error.
M(–5, –6) is rotated 90° clockwise.
Step 1. Use the rule (x, y)g(y, –x).
Step 2. Switch x and y coordinates:
(–6, –5)
Step 3. Multiply the new x-coordinate by –1:
((–1)–6, –5)
Step 4. Simplify:
(6, –5)
Mira made an error in Step
Answer:
3
Step-by-step explanation:
Answer: You multiply the old x coordinate by negative 1, so the error is at step 3.
It should give (-6, (-1)-5).
Step-by-step explanation:
1) A farmer has sheep and cattle in the ratio 8:3.
a) How many sheep has the farmer if he has 180 cattle?
b) Find the ratio of the number of sheep to the total number of animals.
c) Find the ratio of the total number of animals to the number of cattle.
2)My fortune of $ 810 000 is to be divided in the ratio 4:3:2. How much does each person receive?
Good
Answer:
Q 1)
a) No of sheep = 480
b) 8 : 11
c) 11 : 3
Q 2)
Each person will receive: $360,000, $270,000 and $180,000
Step-by-step explanation:
Ratio of sheep to cattle = 8 : 3
Let the number of sheep be 8x
And number of cattle be 3x
a)
No of cattle = 180 (Given)
Therefore,
3x = 180
x = 180/3
x = 60
Therefore, 8x = 8*60 = 480
No of sheep = 480
b)
Total animals = 180 + 480 = 660
Ratio of sheep to the total number of animals
= 480 : 660
= 8 : 11
c)
Ratio of total animals to the number of cattle
= 660 : 180
= 11 : 3
Q 2) Let each person will receive 4x, 3x and 2x dollars.
Therefore,
4x + 3x + 2x = 810,000
9x = 810000
x = 810000/9
x = 90,000
Therefore,
4x = 4*90,000 = $360,000
3x = 3*90,000 = $270,000
2x = 2*90,000 = $180,000
So, each person will receive $360,000, $270,000 and $180,000.
A system has two identical components, and requires both the components for system success. If one component fails, the other cannot fail while the failed component is being repaired. The component failure rates and repair rates are 0.1 failures/year and 365 repairs/year respectively. If a similar component is carried as a spare with an average installation time of 1 hour, evaluate the probability of failure, frequency of failure and the average down time of the system.
Answer:
Step-by-step explanation:
We are given that:
The failure rate = 0.1 failure/year
i.e. = [tex]\dfrac{0.1}{365\times 24}= 0.00001 \ failure /hour[/tex]
The repair rate = 365 repair/year, if we convert this to repair/hour; we get:
[tex]= \dfrac{365}{365\times 24} \\ \\ = 0.04 \ repair/ hour[/tex]
Time (t) = 1 hour
P(failure) = 1 - R ; if (t=1)
where:
[tex]Reliability (R ) = e^{-\lambda t}(1+ \lambda t) \\ \\ = e^{-0.00001*1}(1+0.00001 *1) \\ \\ \simeq 0.9999[/tex]
P (failure) = 1 - R
= 1 - 0.9999
= 0.0001
≅ 0
The frequency meantime of failure = [tex]\dfrac{1}{\lambda}[/tex]
[tex]\dfrac{1}{0.00001}[/tex]
= 100000
The average downtime of repair for the system = [tex]\dfrac{1}{\mu}[/tex]
[tex]=\dfrac{1}{0.04}[/tex]
= 25
a loaf of bread has 12 slice. micky ate 1/4 of the loaf. write the fraction of the loaf micky ate in twelfths
Answer:
3/12
Step-by-step explanation:
1/4*3/3=3/12
This graph shows the altitude of an airplane over time. Which story matches the graph?
A.)The aircraft rose quickly into the air at takeoff, and then it continued at a constant altitude.
B.)The aircraft rose steadily over the entire flight.
C.)The aircraft rose quickly to its maximum height, and then it immediately began going back down toward the grou
D.)The aircraft rose quickly into the air at takeoff, and then it rose slowly for the rest of the flight.
SHOW HINT
Answer:
A.) The aircraft rose quickly into the air at takeoff, and then continued at a constant altitude.:)
Answer:
Omg, thank u so much I am on this question rn on Edulatic and I have 100 Q's and I'm only on Q 45, This Question rly helped me a lot bc it came with the answer. God Bless you!!
#11. The space occupied by a wooden block is 4cm × 2cm × 2cm=_____cm 3 Which is equivalent to_______mililiters
Write in the equation for the slope intercept form and please no links or I will report you
Answer:
y = 3/2x + 8
Step-by-step explanation:
using points (-2,5) and (0,8),
we find slope, by using rise/run aka the y's/x's. so 8-5/0--2= 3/2 for slope. (8,0) is an intercept, so b out y=mx +b has been found!
Sequences:
Determine the first five terms of the following sequences:
A. [tex]a_{n} = \frac{2n+3}{4}[/tex]
B. [tex]a_{n} = \frac{n-3}{n-2}[/tex]
Answer:
A.
aₙ = (2n + 3)/4The first 5 terms:
a₁ = (2*1 + 3) / 4 = 5/4a₂ = (2*2 + 3) / 4 = 7/4a₃ = (2*3 + 3)/ 4 = 9/4a₄ = (2*4 + 3) / 4 = 11/4a₅ = (2*5 + 3) / 4 = 13/4B.
aₙ = (n - 3)/(n - 2)The first 5 terms:
a₁ = (1 - 3) / (1 - 2) = 2a₂ = (2 - 3) / (2 - 2) = undefineda₃ = (3 - 3)/ (3 - 2) = 0a₄ = (4 - 3) / (4 - 2) = 1 / 2a₅ = (5 - 3) / (5 - 2) = 2 / 3(x-4)2 + 3x at the value x = 7
Answer:
30
Step-by-step explanation:
x = 7
( x - 4 )^2 + 3x
= ( 7 - 4 )^2 + 3 ( 7 )
= 3^2 + 21
= 9 + 21
= 30
Answer:
The answer is 27
Step-by-step explanation:
(X-4)2 + 3x
x is equal to 7
first substitute the values.
(7-4)2 + 3 x 7
solve-
(3)2 + 21
=27
Find the missing side. Round to the nearest tenth
Answer:
We know Cot51 = x/17
=> 0.809784 × 17 = x
=> 13.753 = ×
.°. The value of x = 13.753 ~~ 14.000 (Ans)
My faces are not all
congruent.
I contain 12 edges.
I contain 6 faces.
Answer:
its a rectangle
Step-by-step explanation:
Assume a bank loan requires an interest payment of $85 per year and a principal payment of $1,000 at the end of the loan's eight-year life. What would be the present value of this loan if it carried an 8.5 percent interest rate?
Answer:
the answer 57.8
85 x 8 x 8.5% = 57.8
Step-by-step explanation:
brainliest pls
What is the degree measure of FEG?
A 20°
B 31°
C 56°
D
124°
Answer:
C) 56
Step-by-step explanation:
DEG and FEG are on a straight line forming 180 degree.
Set your formula up as
180 = (3x+31)+(2x-6)
180 = 3x +2x +31 - 6
180 - 31 + 6 = 5x
155 = 5x
155/5 = x
31 = x
Now substitute 31 in place of x
FEG = (2*31-6)
FEG = 56
HELP ASAP WILL GIVE MOST BRANILIST
the spinner below is spun twice. What is the probability of the arrow landing on a 3 and then an odd number?
Please help
Answer:
4/3
Step-by-step explanation:
NEED HELP ASAP WILL GIVE BRAINLIEST REAL ANSWERS ONLY PLZ WILL REPORT FAKE ANSWERS
Answer:
The graph has a domain of {x|0 < x < infinite} and approaches 0 as x decreases
The graph has a domain of {y| -infinite < y < infinite} and decreases as x approaches 0.
Step-by-step explanation:
I was confused at first because I was like "There is 2 answers" and I reread the question again and found my mistake.
And sorry for the wait because "I am in class"
The X and Y coordinates (in feet) for station Shore are 2058.97 and 6980.06, respectively, and those for station Rock are 1408.03 and 6980.06, respectively. What are the azimuth, bearing, and length of the line connecting station Shore to station Rock
Answer:
Hence, the azimuth, bearing, and length of the line connecting station Shore to station Rock are [tex]270^{\circ},90^{\circ}[/tex] and [tex]650.94[/tex] feet.
Given :
The shore station point [tex](X_1,Y_1)[/tex] in feet,
[tex](X_1,Y_1)=(2058.97, 6980.06)[/tex]
The Rock station point [tex](X_2,Y_2)[/tex] in feet
[tex](X_2,Y_2)=(1408.03,6980.06)[/tex]
From the figure
[tex]x=2058.97-1408.03=650.94[/tex] feet
[tex]y=6980.06-6980.06=0\\[/tex] feet
Length of the line [tex]L=\sqrt{x^2+y^2}[/tex]
[tex]\Rightarrow L=\sqrt{(650.94)^2+0}=650.94[/tex]
[tex]\Rightarrow L=650.94[/tex] feet
[tex]\because[/tex] [tex]\tan \theta=\frac{y}{x}=\frac{0}{x}=0[/tex]
[tex]\Rightarrow \theta=\tan^{-1}(0)=0[/tex]
Azimuth of line[tex]=270^{\circ}+\theta[/tex]
[tex]=270^{\circ}+0[/tex]
[tex]=270^{\circ}[/tex]
[tex]\therefore[/tex] Bearing [tex]=360^{\circ}-\text{Azimuth}[/tex]
[tex]=360^{\circ}-270^{\circ}[/tex]
[tex]=90^{\circ}[/tex]
Please help!! Timed assignment
Arrange the figures in increasing order of their volumes. Use Pi =22/7
Answer:
see the list below
Step-by-step explanation:
did all the formulas for each and I believe the order is from (smallest to biggest)
1. The half sphere or hemisphere (3rd in the picture)
2.The pyramid
3.slanted cone
4.cone
5.slanted cylinder
6.and finally the cylinder
15) Find the product. Show all your work.
Reduce all your answers into simplest
form
3 - x
5
л |N
Answer:
[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
3 [tex]\frac{3}{4}[/tex] x [tex]\frac{2}{5}[/tex]
[tex]\frac{15}{4}[/tex] x [tex]\frac{2}{5}[/tex]
[tex]\frac{30}{20}[/tex] = [tex]\frac{3}{2}[/tex]
or another way
[tex]\frac{15}{4}[/tex] x [tex]\frac{2}{5}[/tex]
[tex]\frac{3}{2}[/tex] x [tex]\frac{1}{1}[/tex] = [tex]\frac{3}{2}[/tex]
WHATS THE ANSWER? MULTIPLE CHOICE 50 PTS
Answer:
D
Step-by-step explanation:
Seventeen less than p infers that the number is p minus 17. This number is then divided by 8, which requires us to put parenthesis in order to properly divide the number after doing p - 17
Please give brainliest thank you
[tex]\boxed{\underline{\bf \: ANSWER}}[/tex]
The quotient when 17 less than p is divided by 8.
Well, let's first take 17 less than p. That'll be :-
[tex] \sf \: p - 17[/tex]
Note :- 'p' comes first as the question has the words - less than p.
Now, we have the remaining -> 'is divided by 8'.
The equation will become :-
[tex] \sf \:( p - 17) \div 8[/tex]
Note :- We have put the bracket because they have asked the quotient. To form a quotient you need 2 numbers - a divisor & a dividend. Hence, 2 numbers -> (p - 17) & 8.
So, Option D [tex]\boxed{\underline{\bf \: (p-17)÷8}}[/tex] is the correct answer.
________
Hope it helps.
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