Answer:
[tex]r=1.05\ \text{ft}[/tex]
[tex]h=2.12\ \text{ft}[/tex]
[tex]20.91\ \text{ft}^3[/tex]
Step-by-step explanation:
r = Radius
h = Height
Volume of cylinder = [tex]7.35\ \text{ft}^3[/tex]
[tex]V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}[/tex]
Surface area is given by
[tex]A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}[/tex]
Differentiating with respect to radius we get
[tex]\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}[/tex]
Equating with zero we get
[tex]0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05[/tex]
[tex]\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0[/tex]
So, the value of the function is minimum at [tex]r=1.05[/tex]
[tex]h=\dfrac{7.35}{\pi r^2}=\dfrac{7.35}{\pi 1.05^2}\\\Rightarrow h=2.12[/tex]
So, the radius and height which would minimize the surface area is 1.05 feet and 2.12 feet respectively.
Surface area
[tex]A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi \times 1.05^2+2\pi 1.05\times 2.12\\\Rightarrow A=20.91\ \text{ft}^3[/tex]
The minimum surface area is [tex]20.91\ \text{ft}^3[/tex].
Does the rule y = 6x7 represent an exponential function?
yes
no
No , the rule y = 6x ^7 does not represent an exponential function.
The exponential function is a mathematical function of the form f(x) = a^x. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0. The exponential function is defined by the formula f(x) = a^x. where the input variable x is displayed as an exponent. An exponential curve depends on the exponential function and the value of x.
We have given y =6 x^7.
Here the variable is base & the exponent is an integer.
But an exponential function has a constant as its base and a variable as its exponent .
So, it does not represent an exponential function .
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Solve the given equation for x.
2x-B = 10
Answer:
x=5+b/2
Step-by-step explanation:
move all terms that dont contain x to the right, and solve
Answer:
2 times 6-2+10
Step-by-step explanation:
A device produces random 64-bit integers at a rate of one billion per second. After how many years of running is it unavoidable that the device produces an output for the second time? Round to the nearest number of years.
Answer:
3171 × 10^(44) years
Step-by-step explanation:
For each bit, since we are looking how many years of running it is unavoidable that the device produces an output for the second time, the possible integers are from 0 to 9. This is 10 possible integers for each bit.
Thus, total number of possible 64 bit integers = 10^(64) integers
Now, we are told that the device produces random integers at a rate of one billion per second (10^(9) billion per second)
Let's calculate how many it can produce in a year.
1 year = 365 × 24 × 60 × 60 seconds = 31,536,000 seconds
Thus, per year it will produce;
(10^(9) billion per second) × 31,536,000 seconds = 3.1536 × 10^(16)
Thus;
Number of years of running is it unavoidable that the device produces an output for the second time is;
(10^(64))/(3.1536 × 10^(16)) = 3171 × 10^(44) years
what is the awnser to y=3/2x-1
Answer:
On a coordinate graph, make a point at (0, -1)
Move the point up 3 units and right 2 units, and make another point. Continue across the plane and draw the line connecting the dots.
Answer:
Step-by-step explanation:
Given two objects represented by the tuples (22, 1, 42, 10) and (20, 0, 36, 8):(a)Compute the Euclidean distance between the two objects. (b) Compute the Manhattan distance between the two objects.
Answer:
(a) 6.708
(b) 11
Step-by-step explanation:
Tuples ( 22, 1, 42, 10) and (20, 0, 36, 8)
Euclidian distance formula
[tex]D = \sqrt{(q1 -p1)^2 + (q2-p1)^2 + (q3 - p3)^2 + (q4 -p4)^2}[/tex]
D = [tex]\sqrt{(22-20)^2 + (1-0)^2 + (42 -36)^2 + (10 -8)^2 }[/tex]
= [tex]\sqrt{(2)^2 + (1)^2 + (6)^2 + (2)^2}[/tex]
= [tex]\sqrt{4 + 1 + 36 + 4 }[/tex]
= [tex]\sqrt{45}[/tex]
D = 6.708
Therefore the Euclidean distance between the tuples is 6.708
Manhattan Distance formula
D = |q1-p1| + |q2 -p2| + |q3 -p3| + |q4-p4|
= |22-20| + | 1-0| + | 42 -36| + | 10-8|
= |2| + |1| + |6| + |2|
D = 11
Therefore the Manhattan distance is equal to 11
Pls graph and answer!
Answer:
Closed bracket “ ] “
at -5 facing the left then fill in the graph from -5 to -10
It’s facing left because -5 is greater than -x-4
Answer:
x ≥ 1
Step-by-step explanation:
Move all terms not containing x to the right side of the inequality.
−x ≤ −1
Divide each term in −x ≤ −1 by −1 and simplify.
x ≥ 1
Hope this helps! :)
1. Shlomo Benartzi begins his talk by outlining three things that we as a people are not
doing well. What are these three things? Do you agree or disagree with his evaluation of
these things?
According to Shlomo Benartzi's talk, the three things we humans do badly are risk taking, insurance and money management.
The biblical king who is most well-known for his wisdom is Solomon. When Solomon offered a sacrifice to God, God later asked him in a dream what he wanted from Him. Solomon prayed for wisdom in order to lead and govern his people more effectively.
The processes of setting up a budget, saving money, making investments, and spending are all examples of money management. To help you overcome the barriers to wealth, money management gives you a 360-degree view of your financial situation while putting important financial disciplines into practice. You have much more control over your financial future when you have a clear purpose for your money and sound money management principles behind it. Budgeting, investing, spending, and other types of capital usage oversight are all included in the definition of money management.
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Mayfield Water Company manufactures two types of bottled water: regular and flavored. The company produces at least twice as many bottles of regular water as bottles of flavored water. The company can produce, at most, 1,500 bottles of water per week. Which of these combinations would be reasonable for the company to produce in one week’s time?
A. 750 flavored and 750 regular
B. 500 flavored and 1,000 regular
C. 750 flavored and 1,000 regular
D. 1,000 flavored and 2,000 regular
Answer:
the answer is A
Step-by-step explanation: it's a because if u add 750 + 750 it will give you 1,500
giving brainliest if correct!
There are 8 sprinters in the Olympic 100-meter finals. The gold medal goes to first place, silver to second, and bronze to third. In how many ways can the medals be awarded?
Answer:
I think it is 336 ways the medals can be given out.
Step-by-step explanation:
Use the original price and the markup to find the retail price.
Original price: $60; Markup: 20%
Answer:
$72 would be the retail price
Step-by-step explanation:
Suppose a one-year subscription to a magazine costs $12.99 and a three-year subscription costs $25.98. The cost and length of a subscription are related. Write a slope-intercept equation to model the cost of a subscription for any period of time.
Answer:
[tex]y = 6.495x + 6.495[/tex]
Step-by-step explanation:
Represent years with x and cost with y.
So, we have:
[tex](x_1,y_1)=(1,12.99)[/tex]
[tex](x_2,y_2)=(3,25.98)[/tex]
Required
Determine the slope intercept equation
First, we calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{25.98 - 12.99}{3 - 1}[/tex]
[tex]m = \frac{12.99}{2}[/tex]
[tex]m = 6.495[/tex]
The equation is then calculated as:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = 6.495[/tex]
[tex](x_1,y_1)=(1,12.99)[/tex]
[tex]y - 12.99 = 6.495(x - 1)[/tex]
[tex]y - 12.99 = 6.495x - 6.495[/tex]
Make y the subject
[tex]y = 6.495x - 6.495 + 12.99[/tex]
[tex]y = 6.495x + 6.495[/tex]
f(x)=2x+3 find the
x-int:
y-int:
Asymptote:
End behavior:
Also put in a table f(x)=2x+3
Could y’all PLEASE HELP
Answer:
should be complementary angles
the question: a computer manufacturer built a new facility for assembling computers. there were construction and new equipment cost. the company paid for these cost and made combined profits of $80 million after four years as shown in the graft.
answers:
a: f(x)=60x-160
b:f(x)=-60x+160
c:f(x)=-80x +4
d: f(x)= 80x -4
Answer:
The equation that closely represents the graph is [tex]\mathbf{y=60x-160}[/tex]
Option A is correct.
Step-by-step explanation:
We need to find equation that represents the graph.
We can write equation in slope-intercept form: [tex]y=mx+b[/tex] where m is slope and b is y-intercept.
For finding the equation we need to find slope and y-intercept
Finding slope
The slope can be found using formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we can find [tex]x_1=0, y_1=-160, x_2=1, y_2=-100[/tex]
Putting values and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-100-(-160)}{1-0} \\Slope=\frac{-100+160}{1}\\Slope=-100+160\\Slope=60[/tex]
We get Slope = 60
Finding y-intercept
Using point (0,-160) and slope m = 60, we can find y-intercept
[tex]y=mx+b\\-160=60(0)+b\\b+0=-160\\b=-160[/tex]
Writing the equation
So, the equation for given graph having slope m = 60 and y-intercept b =-160 is:
[tex]y=mx+b\\y=60(x)+(-160)\\y=60x-160[/tex]
So, The equation that closely represents the graph is [tex]\mathbf{y=60x-160}[/tex]
Option A is correct.
According to the Rational Root Theorem, which number is a potential root of f(x) = 938 + 946 – 12x + 7?
Answer:
938
Step-by-step explanation:
So if you are taking a quiz it's C.
4y-7-(y-7) find answer
Answer:
3y
Step-by-step explanation:
4y-7-1(y-7)
4y-7-y+7
4y-y
3y
A scuba diver descends from the surface at a rate of 40 feet per minute.
What is the position of the scuba diver relative to the surface after diving for 4
minutes?
-44 ft
10 ft
-160 ft
36 ft
Is y=3x+5 a relation or not ?
the equation you have given is linear because x directly influences y
2 tablets, 3x per day for 10 days
Answer:
60
Step-by-step explanation:
Simple
First you multiply 2 x 3 =6
Then you multiply 6 x 10 =60
That mean 60 is the answer you are looking for
Hope This Helps :)
5x – 24 > 26
what is the solution to the inequality?
Answer:
x > 10
Step-by-step explanation:
5x - 24 > 26
Add 24 on both sides.
5x -24 + 24 > 26 + 24
5x > 50
Divide by 5 on both sides.
x > 50 ÷ 5
Find x.
x > 10
Solve the following equation. Express your answer as an integer, simplified fraction, or decimal rounded to two decimal places.
A rectangular-shaped parking lot is to have a perimeter of 546 yards. If the width must be 61 yards because of a building code, what will the length need to be?
The length of the parking lot will be 212 yards
Perimeter of rectangleFrom the question, we are to determine what the length of the parking lot needs to be
From the given information, we have that
"A rectangular-shaped parking lot is to have a perimeter of 546 yards"
and
"the width must be 61 yards"
From the formula for perimeter of a rectangle,
P = 2(l +w)
Where P is the perimeter
l is the length
and w is the width
From the given information,
P = 546 yards
w = 61 yards
Putting the parameters into the equation,
546 = 2(l + 61)
546 = 2l + 122
2l = 546 - 122
2l = 424
l = 424/2
l = 212 yards
Hence, the length of the parking lot will be 212 yards
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A shop sells 3 different types of tea
200 g of Kenyan tea costs £2.10
300 g of Columbian tea costs £3.45
150 g of Indian tea costs £1.70
a) Work out the cost of 100g of each type of tea
b) Which type of tea is the cheapest?
Answer:
The cheapest is the Kenyan tea which costs £1.05 for each 100g.
Step-by-step explanation:
A)
200 g of Kenyan tea costs £2.10
1. Calculate the rate of each gram, by dividing 2.10/200
0.0105 x 100 = £1.05 for each 100g
300 g of Columbian tea costs £3.45
1. Calculate the rate of each gram, by dividing 3.45/300
0.0115 x 100 = £1.15 for each 100g
1. Calculate the rate of each gram, by dividing 1.70/150
150 g of Indian tea costs £1.70
0.01133333333 x 100 = £1.133333333 for each 100g
B) The cheapest is the Kenyan tea which costs £1.05 for each 100g.
Sophie answered 84% of the questions on her science test correctly. If she answered 21 questions correctly, how many questions were on the test?
Answer:25
Step-by-step explanation:
Martine wants to open an after-school tutoring service for students in 6th through 9th grade. How can a thorough knowledge of customers' expectations improve the probability of her success?
Answer:
it would help her know how to prepare her teaching to match the students learning and expectations
Step-by-step explanation:
This idea of opening this tutoring service for students in these grades would prove a success if if martine has adequate knowledge of her students/customers. That is the learners requirements, their expectations, their experiences, and their strengths and weaknesses in particular subject areas.
Knowledge of these expectations would help to set Martine on the path of tutoring success and this would attract more students. So for her to have a strong tutoring business she has to know the approaches to use to make students strong academically, and how to match learning ability with her teaching.
Determine whether each sum or product is even or odd.
10,481 + 4,569
Answer:
even
Step-by-step explanation:
11050 it's even because it ends in a zero
Graph the image of this triangle after a dilation with a scale factor of 1/2 centered at (−5, 1).
Use the Polygon tool to graph the dilated triangle.
Answer:
Please see picture below.
Step-by-step explanation:
Convert 0.45 to a percent. Remember to add the percent sign.
0.45%
4.5%
45%
50%
Answer:
45%
Step-by-step explanation:
Two dice are rolled; find the probability for total: a) 1, b) 4 or 6; c) <13
Answer:
0 ; 2/9 ; 1
Step-by-step explanation:
In a roll of two dice ;
The sample space = (Number of faces on die)^number of dice rolled = 6^2 = 36
The total possible outcome = sample space = 36
The probability of an event (A) :
P(A) = number of required outcome / number of total possible outcomes
find the probability for total: a) 1,
P(total of 1)
Number of 1 total = 0
Hence, P(total of 1) = 0
b) 4 or 6;
Number of 4 total = 3
Number of 6 total = 5
3 /36 + 5 / 36 = 8/36 = 2/9
c) <13
P(total < 13)
Number of total < 13 = 36
36 / 36 = 1
A card is selected at random from an ordinary deck of 52 cards. What is the probability that it is either an ace or a spade
Answer: 4/13
Step-by-step explanation:
Number of cards in a deck = 52
Number of spades = 13
Number of aces = 4
Number of ace of spade = 1
Probability of either a spade or an ace :
P(spade or ace) = P(spade U ace)
P(spade U ace) = p(spade) + p(ace) - p(spade n ace)
Probability = required outcome / Total possible outcomes
P(spade) = 13 / 52
P(ace) = 4 / 52
P(spade n ace) = 1 / 52
P(spade U ace) = p(spade) + p(ace) - p(spade n ace)
= 13/52 + 4/52 - 1/52
= 16 / 52 = 4 /13
The graph of the function f(x) = (x – 4)(x + 1) is shown below.
On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1.75, negative 6.2), and goes through (4, 0).
Which statement about the function is true?
The function is increasing for all real values of x where
x < 0.
The function is increasing for all real values of x where
x < –1 and where x > 4.
The function is decreasing for all real values of x where
–1 < x < 4.
The function is decreasing for all real values of x where
x < 1.5.
the funcn is decreasing for all real values of x where x<1.5