Answers
Answer:
radius: 14.96 in
length: 47 in
Step-by-step explanation:
The dimensions of the package with maximum volume can be found by differentiating the volume function, subject to the constraint on the dimensions.
__
volume functionThe volume of the cylindrical package is ...
V = πr²h
The constraint on the dimensions is ...
circumference + length = 141 inches
2πr +h = 141 . . . . . at maximum volume
Solving the second equation for h, we can write the volume function in terms of r alone:
h = 141 -2πr
V = πr²(141 -2πr) . . . . substitute for h
V = 141πr² -2π²r³ . . . eliminate parentheses
__
derivativeDifferentiating with respect to radius, we find the radius at maximum volume must satisfy ...
V' = 282πr -6π²r² = 0
Dividing by 6πr, we can simplify this to ...
47 -πr = 0
r = 47/π ≈ 14.96 . . . . inches (radius)
h = 141 -2πr = 47 . . . inches (length)
This is about optimization problems in mathematics.
Dimensions; Height = 48 inches; Radius = 48/π inches
We are told the combined length and girth is 144 inches.
Girth is same as perimeter which is circumference of the circular side.
Thus; Girth = 2πr
If length of cylinder is h, then we have;
2πr + h = 144
h = 144 - 2πr
Now, to find the dimensions at which the max volume can be sent;
Volume of cylinder; V = πr²h
Let us put 144 - 2πr for h to get;
V = πr²(144 - 2πr)
V = 144πr² - 2π²r³
Differentiating with respect to r gives;
dV/dr = 288πr - 6π²r²
Radius for max volume will be when dV/dr = 0
Thus; 288πr - 6π²r² = 0
Add 6π²r² to both sides to get;
288πr = 6π²r²
Rearranging gives;
288/6 = (π²r²)/πr
48 = πr
r = 48/π inches
Put 48/π for r in h = 144 - 2πr to get;
h = 144 - 2π(48/π)
h = 144 - 96
h = 48 inches
Step-by-step explanation:
Related Questions
Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the unknowns.
8 divided by the sum of 2 and a number
Answers
Answer:
8/x+2 or [tex]\frac{8}{2+x}[/tex]
Step-by-step explanation:
To answer, carefully read the question and pick up on key words like "sum." To begin, we know that "sum" means addition, therefore the sum of 2 and a number (which will be replaced by the variable x) is equivilent to 2 + x. Furthermore, we know that 8 is being divided by the sum. So, the final expression should be [tex]\frac{8}{2+x}[/tex] . Good luck!
x+3=y
what is y?
GIVING BRANLIEST
Answers
There can’t be an answer if you don’t have anything to plug in!
Answer:
There isn't a way to solve for y but I can give you this
Step-by-step explanation:
Slope=1
x-intercept is -3/1
y-intercept is 3/1
the least common multiple of 9 and 6 is 54
Answers
Answer:
18
Step-by-step explanation:
The multiples of 9 are 9,18,27,36,45,54,63,...
The multiples of 6 are 6,12,18,24,30,36,42,...
Find the area and the circumference of a circle with radius .
Use the value for , and do not round your answers. Be sure to include the correct units in your answers.
Answers
Answer: 25.12
Step-by-step explanation:
Circumference = πd or 2πr
Since the radius is given (which is 4) we will use 2πr
2× 3.14×4=
8 × 3.14 =
25.12
How do you know if a net will fold into a pyramid?
Answers
Step-by-step explanation:
A pyramid is made when 4 triangle meet on square then mate on each together .
HELPPP Pleaseeee
Last year, Dan opened an investment account with $6600. At the end of the year, the amount in the account had increased by 26.5%. How much is this increase
in dollars? How much money was in his account at the end of last year?
Answers
Answer:
1,749
8,349
Step-by-step explanation:
We can multiply 6,600 by 1.265 to get 8,349. To get the percentage all we have to do is multiply 6,600 by .265 and get 1,749.
Hope this helps
Find the area of the shaded shape. Write the area in square units
Answers
What is the value of log5 125?
Answers
The log base value is three.
Which distribution has the greatest spread?
A. Mean: 13.7 & Standard Deviation: 3.1
B. Mean: 423.6 & Standard Deviation: 1.3
C. Mean: 38.4 & Standard Deviation: 7.2
D. Mean: 231.4 & Standard Deviation: 5.5
Answers
Answer:
C. Distribution 3
Step-by-step explanation:
The more spread out a data distribution is, the greater its standard deviation.
solve only number 6
Answers
To find the tangent line of the graph:
⇒ must find:
point at which the tangent line touches the graphslope of the tangent lineLet's find the point at which the tangent line touches the graph:
At x = -1,
[tex]y = ((-1)^3+2)^5=(-1+2)^5=1^5=1[/tex]
Point: (-1,1)
Let's find the slope of the tangent line
⇒ get the derivation of function than plug (-1) in the x-position to get
the exact slope
[tex]\frac{d}{dx}(x^3+2)^5=5(x^3+2)^4*\frac{d}{dx}(x^3+2)=5(x^3+2)^4*3x^2\\ \\ 5((-1)^3)+2)^4*3(-1)^2=5(-1+2)^4*3*1=5*(1)^4*3=5*1*3=15[/tex]
Slope of tangent line: 15
Now put all the calculated value into the point-slope form:
[tex](y-y_{0})=m(x-x_{0} )[/tex]
[tex](x_{0} ,y_{0} )[/tex] --> point on the tangent linem --> tangent slope's valueSo:
[tex](y-1)=15(x+1)\\y - 1= 15x + 15\\y = 15x + 15 + 1\\y = 15x + 16[/tex]
Thus the tangent line's equation is y = 15x + 16
Answer: y = 15x + 16
Hope that helps!
Oil leaks from a tank. At hour t = 0 there are 360 gallons of oil in the tank. Each hour after that, 3% of the oil leaks out.
(a) What percent of the original 360 gallons has leaked out after 8 hours?
%
(b) if Q(t) = Q0e^kt the quantity of oil remaining after t hours, find the value of k.
k=
(c) What does k tell you about the leaking oil? Select all that apply if more than one statement is true
A. It tells what percent of oil remains after each hour.
B. It is the amount that the oil that leaks out each second.
C. Because it is less than one, we know the amount of oil in the tank is decreasing,
D. It tells by what percent of oil decays each hour.
E. Because it is negative, we know the amount of oil in the tank is decreasing.
F. It gives the continuous hourly rate at which oil is leaking.
G. None of the above
Answers
The table shows the weights (in pounds) and the prescribed dosages (in milligrams) of medicine for six patients.
Weight (lb), x Dosage (mg), y
94 72
119 90
135 103
150 115
185 140
202 156
a. Find an equation of the line of best fit. Round the slope and the y -intercept to the nearest tenth, if necessary.
y=
Question 2
Identify the correlation coefficient. Round your answer to the nearest thousandths.
Question 3
Interpret the correlation coefficient.
0 / 10000 Word Limit
Question 4
b. Interpret the slope of the line of best fit.
Question 5
c. A patient who weighs 140 pounds is prescribed 135 milligrams of medicine. How does this affect the line of best fit? Explain.
Answers
(A) Using calculator, the equation of the line of best fit is y=0.77x-1.1y=0.77x−1.1 and correlation coefficient is 0.9990.999
The relationship is strongly positive as correlation coefficient is very close to +1.
Step 2
(B) The slope of best fit gives the change in dosage for a unit (lb) increase in weight of patient. We find that the dosage increases by about 0.77 mg for a unit increase in weight of patient.
Step 3
(C) Adding observation (140, 135)(140,135) to the data set. the regression line changes to y=6.12+0.75xy=6.12+0.75x. It increases the intercept but decreases slope.
But the correlation falls to 0.9340.934, weakening the relationship. This happens as the observation is an outlier.
Result
a. y=0.77x-1.1y=0.77x−1.1, strong positive relationship
b. represents change in dosage for a unit increase in weight
c. regression line changes to y=6.12+0.75xy=6.12+0.75x.
(A) The line of best fit's equation is y=0.77x-1.1y=0.77x1.1, and the correlation coefficient is 0.9990.999. The correlation coefficient is near +1, indicating that the link is positive.
What is the equation?The definition of an equation in algebra is a mathematical statement demonstrating the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Step 2
(B) The change in dosage for a unit (lb) increase in patient weight is indicated by the best-fit slope. We discover that for every unit increase in patient weight, the dosage rises by around 0.77 mg.
Step 3
(C) Including observation (140, 135) in the data set. y=6.12+0.75xy=6.12+0.75x is the new value of the regression line. Although the slope is reduced, the intercept is increased.
However, the link is weakened when the correlation drops to 0.9340.934. This occurs because the observation is an anomaly.
Result
a. Strong positive association, y=0.77x-1.1y=0.77x1.1
B. indicates a dose modification for a unit weight increase
C. y=6.12+0.75xy=6.12+0.75x is the new value of the regression line.
Therefore, y=0.77x-1.1y=0.77x1.1 is the equation for the line of best fit, and the correlation coefficient is 0.9990.999.
Learn more about the equation here:
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I need help with this please.
Answers
Answer:
1782 cm²
Step-by-step explanation:
the required surface area =1782
units= cm²
DE joins the midpoints of AB and AC. Find the value of x
and y.
Answers
Answer:
x = 6
y = 4
Step-by-step explanation:
2(4x + 1) = 11x - 16
8x + 2 = 11x - 16
8x + 2 + 16 = 11x - 16 + 16
8x + 18 = 11x
8x + 18 - 8x = 11x - 8x
18 = 3x
6 = x
5y + 4 = 8(y - 1)
5y + 4 = 8y - 8
5y + 4 + 8 = 8y - 8 + 8
5y + 12 = 8y
5y + 12 - 5y = 8y - 5y
12 = 3y
4 = y
Three companies offer swim lessons by the hour. Their information is shown in the tables below.
Which company has a signup fee of $11 and a cost per hour of $6
Answers
The answer is B because 6*2 = 12 + 11 = 23 !
Solve using the elimination method -4x-2y=-18
Answers
Step-by-step explanation:
-4x – 2y= -18
Add 2y to both sides
-4x- 2y+ 2y = -18 + 2y
Simplify
-4x = -18 + 2y
Divide both sides by -4
-4x/-4= -18/-4+ 2y/-4
simplify
x= - -9+y/2
"Place a number in each box so that each equation is true and each equation has at least one negative number."
Answers
Answer:
x=1, y=-1
Step-by-step explanation:
Given the equation:
where x and y are the blank boxes.
We want to find
A positive value of x
A negative value of y
That makes the equation true.
If x=1, y=-1
This can be confirmed using addition law of indices()
In general, any pair of a number and its negative value will satisfy the equality.
Step-by-step explanation:
A bucket of water was 1/2 full, but it still had 3 and 3/5 gallons of water in it. How much water would be in one fully filled bucket?
Answers
Question:
A bucket of water was 1/2 full, but it still had 3 and 3/5 gallons of water in it. How much water would be in one fully filled bucket?
Answer:
7 1/5
Step-by-step explanation:
The bucket was halfway full. It still had 3 3/5 gallons in it. So all you'd have to do is multiply 3 3/5 by 2. Here is the actual work for proof:
3 3/5 × 2 =
18/5 × 2 =
18 × 2
5 × 1 =
36/5 = 7 1/5.
When randomly choosing two coins from a cup of coins that contains a penny, nickel, a dime, and a quarter, what is the probability of choosing a penny and a nickel?
Answers
tan(x)+cot(x)= sec(x)*csc(x)
show me all of the steps, labeled. I would really appreciate it!
Answers
hence proved
hope it helps...!!!
4) Louise stops at the gift store to buy a souvenir of the Statue of Liberty. THe original
height of the statue is 151 ft. If a scale factor of 1in = 20 ft is used to design the
souvenir, what is the height of the replica?
Pls I need help ASAP
Answers
To find the height of Replica,
we'll divide the original height by the given scale factor ⇢151/20 inches⇢7.55 inchesDialted scale factor=1in=20ft
So height of replica
151/207.557.6inHELPPP PLS IM GIVING 60 POINTSSSSS IT'S EASYYYYYY 6TH GRADE MATHH
Answers
The surface area of rectangular prism B is 856 square centimeters
Prism B’s surface area is 4 times greater then prism A’s surface area
Find the value of x. Round to the nearest degree.
Answers
Answer:
x = 39°Step-by-step explanation:
The opposing side and the hypotenuse for the angle are given.
Remember, when the opposing side and the hypotenuse are given, take the cos ratio.
cosx = 7/9x = cos⁻¹ (7/9)x = 38.9424413°x = 39°The equation y - 1 =-7(x-3) is written in point-slope form. What is the y-intercept of the line?
O -4
O-2
O 20
O 22
Answers
Next time I’d recommend also including x coordinates, it’s just easier if you have them
A line has a slope of min Which ordered pairs could be
points on a parallel line? Select two options.
D (-8, 8) and (2, 2)
0 (-5, -1) and (0, 2)
(-3, 6) and (6, -9)
D (-2,1) and (3, -2)
D (0, 2) and (5, 5)
Answers
Answer:
-2,1 and 3,-2 also -5,-1 and 0,2
Step-by-step explanation:
A random survey found that 6
prefer blueberry candies from
of the 27 people surveyed prefer blueberry candies. Based on those results, about how many people
a population of 108 people?
A. 24
B. 18
C. 30
D. 12
Answers
Answer:
A
Step-by-step explanation:
108/24 finds you the ratio from people surveyed to population
gets you 1:4
so for the 6 who prefer candies you sub it it
6:(4*6)
6:24
so its 24 = A :)
help please I realy nead help
Answers
Answer:
B) 77.5 square feet
Step-by-step explanation:
cut shape into rectangle and triangle
area of rectangle = x*y
area of rectangle = 5*13
area of rectangle = 65
area of triangle = (z-x)*(y-w)/2
area of triangle = 5*3/2
area of triangle = 7.5
Total area = 65 + 7.5
Total area = 77.5, B)
Answer:
77.5
Step-by-step explanation:
Cut the figure into a triangle and a rectangle
XxY=65
Z-x=5
Y-W=5
5x5=25
25/2=13.5
65+35.5=77.5
solve for the value of k
pls help me asap
Answers
Answer:
k=13
Step-by-step explanation:
We know that
straight angle is equal to 180⁰
(4k-7)⁰+90⁰+(3k+6)⁰=180⁰
4k-7+3k+6=90
7k=91
k=13
I hope it helped you
Explain how you would create and use a spinner to simulate the probability of an event with the following probabilities:
Percent chance: 20% green, ¼ blue, ⅖ yellow, and 15% orange
Answers
To simulate the probability in a spinner divide the spinner into colors depending on the probability each color represents.
What does the word "probability" mean?This word refers to the likelihood for an event to occur. Moreover, it is often expressed either as a fraction, a percentage, or a number.
How to create a spinner to simulate probability?In this case, each of the colors represents a probability:
Green 20%Blue 1/4 or 25%Yellow 2/5 oe 40%Orange 15%Due to this, the best is to divide the spinner by colors and considering the percentanges of each color. For example 40% of the spinner should be red, while 15% should be orange.
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Find the value of x.
Explain your answer.
Answers
Answer:
Step-by-step explanation:
The hypotenuse is 16 and the adjacent angle is x.
So using SohCahToh
O is opposite, H is the hypotenuse, and A is adjacent.
Soh: sin(theta)= O/H
Cah: cos(theta)= A/H
Toh: tan(theta)= O/A
Any side length that is next to degree 60° is adjacent so x is adjecent.
Using Cah.
cos(theta)= A/H
cos(60°)= x/16
x=16*cos(60°)
x=16*1/2
x=8