Answer:
x= −5 /3
Step-by-step explanation:
Your challenge is to create a cylindrical can that minimizes the cost of materials but must hold 100 cubic inches. The top and bottom of the can cost $0.014 per square inch, while the sides cost only $0.007 per square inch. Show how you did it too?
Answer:
[tex]Radius = 1.997\ in[/tex] and [tex]Height = 7.987\ in[/tex]
[tex]Cost = \$1.05[/tex]
Step-by-step explanation:
Given
[tex]Volume = 100in^3[/tex]
[tex]Cost =\$0.014[/tex] -- Top and Bottom
[tex]Cost =\$0.007[/tex] --- Sides
Required
What dimension of the cylinder minimizes the cost
The volume (V) of a cylinder is:
[tex]V = \pi r^2h[/tex]
Substitute 100 for V
[tex]100 = \pi r^2h[/tex]
Make h the subject
[tex]h = \frac{100 }{\pi r^2}[/tex]
The surface area (A) of a cylinder is:
[tex]A = 2\pi r^2 + 2\pi rh[/tex]
Where
[tex]Top\ and\ bottom = 2\pi r^2[/tex]
[tex]Sides = 2\pi rh[/tex]
So, the cost of the surface area is:
[tex]C = 2\pi r^2 * 0.014+ 2\pi rh * 0.007[/tex]
[tex]C = 2\pi r(r * 0.014+ h * 0.007)[/tex]
[tex]C = 2\pi r(0.014r+ 0.007h)[/tex]
Substitute [tex]h = \frac{100 }{\pi r^2}[/tex]
[tex]C = 2\pi r(0.014r+ 0.007*\frac{100 }{\pi r^2})[/tex]
[tex]C = 2\pi r(0.014r+ \frac{0.007*100 }{\pi r^2})[/tex]
[tex]C = 2\pi r(0.014r+ \frac{0.7}{\pi r^2})[/tex]
[tex]C = 2\pi (0.014r^2+ \frac{0.7}{\pi r})[/tex]
Open bracket
[tex]C = 2\pi *0.014r^2+ 2\pi *\frac{0.7}{\pi r}[/tex]
[tex]C = 0.028\pi *r^2+ \frac{2\pi *0.7}{\pi r}[/tex]
[tex]C = 0.028\pi *r^2+ \frac{2 *0.7}{r}[/tex]
[tex]C = 0.028\pi *r^2+ \frac{1.4}{r}[/tex]
[tex]C = 0.028\pi r^2+ \frac{1.4}{r}[/tex]
To minimize, we differentiate C w.r.t r and set the result to 0
[tex]C' = 0.056\pi r - \frac{1.4}{r^2}[/tex]
Set to 0
[tex]0 = 0.056\pi r - \frac{1.4}{r^2}[/tex]
Collect Like Terms
[tex]0.056\pi r = \frac{1.4}{r^2}[/tex]
Cross Multiply
[tex]0.056\pi r *r^2= 1.4[/tex]
[tex]0.056\pi r^3= 1.4[/tex]
Make [tex]r^3[/tex] the subject
[tex]r^3= \frac{1.4}{0.056\pi }[/tex]
[tex]r^3= \frac{1.4}{0.056 * 3.14}[/tex]
[tex]r^3= \frac{1.4}{0.17584}[/tex]
[tex]r^3= 7.96178343949[/tex]
Take cube roots of both sides
[tex]r= \sqrt[3]{7.96178343949}[/tex]
[tex]r= 1.997[/tex]
Recall that:
[tex]h = \frac{100 }{\pi r^2}[/tex]
[tex]h = \frac{100 }{3.14 * 1.997^2}[/tex]
[tex]h = \frac{100 }{12.52}[/tex]
[tex]h = 7.987[/tex]
Hence, the dimensions that minimizes the cost are:
[tex]Radius = 1.997\ in[/tex] and [tex]Height = 7.987\ in[/tex]
To calculate the cost, we have:
[tex]C = 2\pi r(0.014r+ 0.007h)[/tex]
[tex]C = 2* 3.14 * 1.997 * (0.014*1.997+ 0.007*7.987)[/tex]
[tex]Cost = \$1.05[/tex]
|-3/4+1/8|- (2/3+1/6)
Answer:
-5/24
Step-by-step explanation:
-3/4 = -6/8
-6/8 + 1/8 = -5/8
|-5/8| = 5/8
2/3 = 4/6
4/6 + 1/6 = 5/6
5/8 - 5/6 = 15/24 - 20/24
15/24 + (-20/24) = -5/24
Helpp
(Show ur work please)
This is law of cosine
Answer:
13.3
Step-by-step explanation:
[tex] a^2 = b^2 + c^2 - 2bc \cos A [/tex]
[tex] a^2 = 8^2 + 18^2 - 2(8)(18) \cos 43^\circ [/tex]
[tex] a^2 = 64 + 324 - 288(0.73135) [/tex]
[tex] a^2 = 388 - 210.6299 [/tex]
[tex] a^2 = 177.370 [/tex]
[tex] a = \sqrt{177.370} [/tex]
[tex] a = 13.318 [/tex]
Answer: 13.3
Witch one is a function?
This shows a list of points where the x coordinate does not repeat. This means that any given x input leads to exactly one y output.
Something like choice A has x = 6 repeated; showing that x = 6 leads to both y = 11 and y = -9 at the same time. So this is why choice A is not a function. Choice B has x = 1 repeat, so it's not a function either. Choice C has x = 19 repeated, so it's not a function.
As a visual tool, you can use the vertical line test to check each set of points. If you are able to draw a single vertical line through more than one point on the graph, then it is not a function.
Answer: A
Step-by-step explanation: I hope I help you if it was wrong I'm sorry
An online shopping club has 10,000 members when it charges $7 per month for membership. For each $1 monthly
increase in membership fee, the club loses approximately 400 of its existing members. Write and simplify a function
R to represent the monthly revenue received by the club when x represents the price increase.
Answer:
The function that can be used in the online shopping club about its monthly revenue is:
[tex]R = -400x^{2} +7200x+70000[/tex]
Step-by-step explanation:
First, we're gonna take into account the different values we have in the exercise:
10,000 members$7 per month for membershipLoses of 400 members by each $1 monthly increaseHow the variable [tex]x[/tex] represents the price increase, we can do the formula below:
[tex](10000 - 400x) * (7+x)[/tex]In this formula, we represent in the first part that by each 1 in the variable [tex]x[/tex], the total of members will be reduced in 400, in the second part, we mention that at the same time, the membership fee will be increased in the same value of [tex]x[/tex]. Now we must simplify this function:
[tex](10000 - 400x) * (7+x)[/tex]We operate the values:
[tex]70000+10000x-2800x-400x^{2}[/tex]Solve we can:
[tex]70000+7200x-400x^{2}[/tex]And organize:
[tex]-400x^{2} +7200x+70000[/tex]At the end, how [tex]R[/tex] represents the monthly revenue received by the club, we use that variable for our formula:
[tex]R=-400x^{2} +7200x+70000[/tex]HELP!!! LOTS OF POINTS
A bakery did a survey among 100 customers to find their food preference . The customers were asked about their preferences for cupcakes or brownies. Out of the total 72 people who liked cupcakes, 37 also liked brownies. There were 59 people who liked brownies.
Part A. Summarize the data by writing the values that the letters A to I in the table below represents
PART B. What percentage of the survey respondents did not like cupcakes or brownies ?
PART C . Do the survey results reveal a greater dislike for brownies or cupcakes? Justify your answer
(I added a picture down below)
Answer:
Answer:
put 37, 22,59,35,6,41,72,28,100 in chart < That is for the ppl who cant click on the brainly site but it still shows alitttle
For the ppl who can click on brainly:
Part A:
Like Cupcakes
Do Not Like Cupcakes
Total
Like Brownies
37
22
59
Do Not Like Brownies
35
6
41
Total
72
28
100
Part b: 6
Part c: You really have to figure out how to word this 37- 72=35 35-41=6
hope it helps
The diagram shows a piece of cheese in the shape of the triangular prism.Work out the area of the cling film needed to cover the cheese
Answer:
488.4 cm²
Step-by-step explanation:
Area of cling film needed = surface area of the triangular prism = 2(B.A) + P×H
Where,
B.A = triangular base area = ½*base*height
height = 10.5 cm
base = √(13.7² - 10.5²) = √77.44 = 8.8 cm
B.A = ½*8.8*10.5 = 46.2 cm²
P = perimeter of the triangular base = 10.5 + 13.7 + 8.8 = 33
H = height of prism = 12 cm
Surface area of triangular prism = 2(46.2) + 33*12
= 92.4 + 396
= 488.4 cm²
Find a formula for the area of the figure in terms of s.
Answer:
D. is √3/2 s^2
The area of the given triangle is (√3/6) s² so option (C) will be correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.
Area of right angle triangle ;
A = (1/2) × Base × Hight
Tan 30° = height/s
1/√3 = height/s
height = s/√3
Now,
A = (1/2) × s × s/√3
A = 1/(2√3) × s²
Multiply √3 on numerator and denominator
A = √3/6 × s²
Hence "The area of the given triangle is (√3/6) s²".
For more about triangles,
https://brainly.com/question/2773823
#SPJ2
What is the solution to the equation? a+5 2/3=9
Answer:
a = 3.333... (3 repeating) or 3 1/3
Step-by-step explanation:
Solve for a by simplifying both sides of the equation, then isolating the variable.
HELPPPPPPPP ASAP HELPPPPP PLSSSSSSSSSS
Two students on roller skates stand face-toface, then push each other away. Which student will always have the fastest speed
Answer:
The student with lower weight will move faster than the one with higher weight.
Step-by-step explanation:
The students are on roller skates and it is assumed that their wheels are identical. They are on a frictionless flat horizontal ground. According to Newton's Law F=ma
Mass of student 1 is 97 kg
Mass of student 2 is 61 kg
The force magnitude is assumed to be equal and acceleration is same. The student with higher weight will have lesser force exerted than the student with lighter weight.
Find mZVUT if IZAUT = 88
and mZVUA = 55°.
T
U
V
9514 1404 393
Answer:
143°
Step-by-step explanation:
Angle VUT is the sum of the angles into which it is divided.
∠VUT = ∠VUA +∠AUT
∠VUT = 55° +88°
∠VUT = 143°
40% of 115 is what number
Answer:
46
Step-by-step explanation:
first multiply 115 by .40 then you got your answer
Answer:
46
Step-by-step explanation:
First, we will convert the text, 40% of 115 is what number, into a math equation, 40% * 115 = x. To get rid of the % sign (who like those?) we will multiply both sides by 10. 4 * 115 = 10x. Simplifing, we get 460 = x. So, x = 46
Which number line diagram represents the solution to the inequality?
A
B
C
D
Answer:
C
Step-by-step explanation:
5. If rectangle ABCD is similar to rectangle MNOP, which of the following must be true? Explain how you know.
a)
b)
BC.NO
CD OP
2C - ZO
ZB ZM
c)
Answer:b and c
Step-by-step explanation:
solve the inequality -1/3h_<7
Answer:
The solution to the given inequality
[tex]h\geq \frac{-1}{21}[/tex]
Step-by-step explanation:
Given inequality
[tex]\frac{-1}{3h} \leq 7[/tex]
⇒ -1≤ 7× 3h
⇒ -1 ≤ 21 h
⇒ 21 h ≥ -1
⇒ [tex]h\geq \frac{-1}{21}[/tex]
George buys pizza. He eats 3/8 of pizza for lunch and 1/4 of the pizza for dinner
Answer:
Step-by-step explanation:
To find the amount he ate we just add the fractions:
3/8 +1/2 = 7/8 or 0.875
HOPE THIS HELPS!
HAVE A GR8 DAY ;-)
what is the 28% of 349 multiplied by 7
Answer:
Step-by-step explanation:
E X P L A N A T I O NAnswer:
The answer is 684.04
Step-by-step explanation:
ASAP need help with system of equations... I'm too small brain to do it.
Answer:
(x=0, y=11)
(x=2, y=9)
Step-by-step explanation:
first equation substitution for x first.
y=11-x
plug into 2nd equation
(x+2)^2+(11-x-7)^2=20
this should lead you into a quadratics equation.
you get x=0, x=2.
do the same for y value this time, subbing in the x value
(11-y+2)^2+(y-7)^2=20
this also leads into a quad equation
solve and you get y=11, and y=9
b) Simplify (4ab^2)^3
Answer:
[tex]64a^{3} b^{6}[/tex]
Step-by-step explanation:
[tex](4ab^2)^3[/tex]
=> [tex]4^{3} a^{3} b^{6}[/tex]
=> [tex](4 \times 4 \times 4) a^{3} b^{6}[/tex]
=> [tex]64a^{3} b^{6}[/tex]
A distribution of measurements is relatively mound-shaped with a mean of 40 and a standard deviation of 15. Use this information to find the proportion of measurements in the given interval. between 25 and 55
Answer:
The proportion of measurements between 25 and 55
P( 25 ≤ X≤ 55) = 0.6826
Step-by-step explanation:
Step(i):-
Given that the mean of the Population = 40
Given that standard deviation of the Population = 15
Let 'x' be the random variable in normal distribution
Let 'X' = 25
[tex]Z = \frac{x-mean}{S.D} = \frac{25-40}{15} = -1[/tex]
Let 'X' = 55
[tex]Z = \frac{x-mean}{S.D} = \frac{55-40}{15} = 1[/tex]
Step(ii):-
The probability that between 25 and 55
P( 25 ≤ X≤ 55) = P( -1≤z≤1)
= A(1) - A(-1)
= A(1) + A(1)
= 2 × A(1)
= 2× 0.3413
= 0.6826
The proportion of measurements between 25 and 55
P( 25 ≤ X≤ 55) = 0.6826
Final answer:-
The proportion of measurements between 25 and 55
P( 25 ≤ X≤ 55) = 0.6826
The solution to -3x + 5x - 7 = -11 is _____.
Answer:
x = -2
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Diego scored nine points less than Andre in the basketball team Noah scored twice as many points as Diego if Noah scored 10 points how many ponts did Andre score
Answer:
1..........................
Answer:
Andre scored 14 points.
Step-by-step explanation:
set up expressions with the info given:
Diego's points: a –9
Andre's points: 2d. and
n = 2d
Noah's points = 10
Use the expressions to set up equations to solve.
To find a, Andre's points, we can work backwards.
Substitute the 10 from the last expression for n in the equation n=2d, and solve for d:
10 = 2d. Divide both sides by 2
5 = d
Substitute the value of d, Diego's points, to make an equation using the first expression:
5 = a –9 Add 9 to both sides.
5 + 9 = a a = 14
Andre scored 14 points
(+12) + (-13) =
Cuánto es y porque, operación completa.
Answer:
-1
Step-by-step explanation:
12 + -13 = -1
A number cube is rolled three times. An outcome is represented by a string of the sort OEE (meaning an odd number on the first roll, an even number on the
second roll, and an even number on the third roll). The 8 outcomes are listed in the table below. Note that each outcome has the same probability,
For each of the three events in the table, check the outcomes) that are contained in the event. Then, in the last column, enter the probability of the event
Answer:
Event A: Exactly 1 odd number: EOE, EEO, OEE 3/8 Probability
Event B: More even numbers than odd numbers: EOE, EEO, OEE,EEE 1/2 Probability
Event C: Alternating even number and odd number (with either coming first): EOE, OEO 1/4 Probability
Step-by-step explanation:
The probability of the given events is:
[tex]\frac{1}{4}[/tex][tex]\frac{1}{4}[/tex][tex]\frac{3}{8}[/tex]According to the question,
Number of outcomes = 8
Event A:
Having the alternative even and odd numbers.
→ [tex](EOE, OEO) = \frac{2}{8}[/tex]
[tex]= \frac{1}{4}[/tex]
Event B:
No even number and last two rolls.
→ [tex](EOO,OOO) = \frac{2}{8}[/tex]
[tex]= \frac{1}{4}[/tex]
Event C:
Exactly on odd number:
→ [tex](EOE,OEE,EEO) = \frac{3}{8}[/tex]
Thus the above approach is correct.
Learn more about probability here:
https://brainly.com/question/11234923
please answer i know the picture is a little blurry but please i will give you brainliest!!
Answer: the 1st one.
Step-by-step explanation: becuase today I was helping out a freind with this. So it the first one
The difference between two numbers is 2.5 . The product of those two numbers is 21. Provide the 2 equations needed to solve the application separated by a comma and NO SPACES.
Answer:
x-y=2.5,xy=21
Step-by-step explanation:
This question can be solved by a system of equations.
I am going to say that:
One of the numbers is x.
The other number is y.
The difference between two numbers is 2.5
This means that x - y = 2.5
The product of those two numbers is 21.
This means that xy = 21.
So the two equations are: x-y=2.5,xy=21
Find the equation of the linear function represented by the table below in slope-
intercept form.
Answer:
[tex]y = x +2[/tex]
Step-by-step explanation:
Given
The attached table
Required
Determine the equation
First, calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (-3,-1)[/tex]
[tex](x_2,y_2) = (1,3)[/tex]
So, we have:
[tex]m = \frac{3 - (-1)}{1 - (-3)}[/tex]
[tex]m = \frac{3 +1}{1 +3}[/tex]
[tex]m = \frac{4}{4}[/tex]
[tex]m =1[/tex]
The equation in slope intercept form is calculated using
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = 1(x - (-3)) -1[/tex]
[tex]y = 1(x +3) -1[/tex]
[tex]y = x +3 -1[/tex]
[tex]y = x +2[/tex]
mary ann spent $26.85 total on two new toys. She had a coupon for 1.00 off her total purchase and spend 1.75 on sales tax. Each toy cost the same amount how much did each toy cost?
Answer: $13.80
Step-by-step explanation:
Mary ann spent $26.85 total on two new toys but had a coupon for $1.00 off her total purchase. Therefore, we subtract $1.00 from $26.85. This will be:
= $26.85 - $1.00
= $25.85
Shw then spend $1.75 on sales tax. Total coat will now be:
= $25.85 + $1.75
= $27.60
Since each toy coat same amount, therefore each toy will cost:
= $27.60 / 2
= $13.80
Integrate [tex]e^{4x}\sqrt{1+e^{2x} } dx[/tex] please show work so i can learn
Answer:
the picture is attachedand sorry I can't explain you much about it