The formula for volume of cylinder is:
V = π r^2 h
since volume is 100 cubic inches, so:
100 = π r^2 h
Rewriting in terms of h:
h = 100 / π r^2
The least amount of metal means least amount of surface area needed. The surface area of cylinder is:
A = 2 π r h + 2 π r^2
insert the value of h in terms of r:
A = 2 π r (100 / π r^2) + 2 π r^2
A = 200 r-1 + 2 π r^2
Take the 1st derivate and set to 0, dA/dr = 0:
dA/dr = - 200 r-2 + 4 π r
0 = - 200 r-2 + 4 π r
200 / r^2 = 4 π r
r^3 = 50 / π
r = 2.52 inches
So height h is:
h = 100 / π r^2
h = 100 / π (2.52)^2
h = 5.01 inches
Answers:
r = 2.52 inches
h = 5.01 inches
How can I work out this: (6x-1)(4x+6)
How do I find the value of b
Emelina wrote the equation of a line in point-slope form as shown below.
(y+4)=3(x+2)
What is Emelina’s equation in slope-intercept form?
y = 3x + 2
y = 3x +10
y = 3x – 4
y = 3x – 10
Answer: [tex]y=3x+2[/tex]
Step-by-step explanation:
Given: Emelina wrote the equation of a line in point-slope form as shown below.
[tex](y+4)=3(x+2)[/tex]
To write the equation in intercept form, first we multiply 3 inside the bracket values in the right side , we get
[tex]y+4=3x+6[/tex]
Now, subtract 4 from both sides , we get
[tex]y=3x+2[/tex]
Hence, Emelina’s equation in slope-intercept form : [tex]y=3x+2[/tex]
Answer: A. y = 3x + 2
Step-by-step explanation:Because it matches up the most to the problem. Its A. Have a great day and stay safe <3
Jack invests $500 at a certain annual interest rate, and he invests another $2000 at an annual rate that is one-half percent higher. if he receives a total of $85 interest in 1 year, at what rate is the $500 invested?
Final answer:
The $500 was invested at an annual interest rate of 3%.
Explanation:
Let's assume the interest rate for the $500 investment is x %. Therefore, the interest rate for the $2000 investment would be (x + 0.5) %, since it is one-half percent higher.
The total interest received is $85. So, we can set up the equation:
$500(x/100) + $2000((x + 0.5)/100) = $85
Simplifying and solving the equation, we get:
5x + 20(x + 0.5) = 85
5x + 20x + 10 = 85
25x = 75
x = 3
The $500 was invested at an annual interest rate of 3%.
Leon drew Triangle ABC and Triangle DEF so that Angle A is congruent to Angle D, Andgle B is Congruent to Angle E, AB = 4, and DE = 8. Are Triangle ABC and Triangle DEF similar? If so, identify the similarity postulate or theorem that applies.
Answer:
The correct option is D
Step-by-step explanation:
Given triangle ABC and triangle DEF so that ∠A≅∠D, ∠B≅∠E, AB = 4, and DE = 8. we have to tell the similarity theorem or postulate that applies to prove above triangles congruent.
In ΔABC and ΔDEF
∠A=∠D (Given)
∠B=∠E (given)
Two angles are congruent
Hence, by AA similarity postulate which states that if the two corresponding angles of two triangles are congruent they are similar i.e ΔABC~ΔDEF
Hence, The correct option is D
Greg is 5 feet three inches tall and weighs 260 pounds. greg is ________.
Eight times the reciprocal of a number equals 4 times the reciprocal of 8. find the number
How do you factor trinomials with a common monomial factor?
Help!!!!!!!!!!!!!!!!!!!!!!!!!
If angles are supplementary, then one of the angles is an obtuse angle
a. True
b. False
A man has 20 coins in his pocket, all of which are dimes and quarters. if the total value of his change is 425 cents, how many dimes and how many quarters does he have? your answer is
Write an equation of the line passing through each of the following pairs of points.
a) (−10, 4), (2, −5)
b) (5, 7), (−6, −3)
The required equation of the line passing through the coordinates (−10, 4), (2, −5) is 4y+3x = -14
The required equation of the line passing through the coordinates (5, 7), (−6, −3) is 11y-10x = -27
The formula for finding the equation of a line is expressed as:
[tex]y-y_0=m(x-x_0)\\[/tex]
Given the coordinates (−10, 4), (2, −5)
Get the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-5-4}{2-(-10)} \\m=\frac{-9}{12}\\m=\frac{-3}{4}[/tex]
Get the required equation
[tex]y-4=-3/4(x+10)\\4(y-4)=3(x+10)\\4y-16=-3x-30\\4y + 3x = -30+16\\4y+3x = -14\\[/tex]
b) For the equation of the line with the coordinates (5,7) and (-6, -3)
Get the slope
m = -3-7/-6-5
m = -10/-11
m = 10/11
The required equation will be:
y - 7 = 10/11(x-5)
11(y-7) = 10(x-5)\
11y - 77 = 10x - 50
11y - 10x = -50 + 77
11y - 10x = -27
Hence the required equation of the line passing through the coordinates (5, 7), (−6, −3) is 11y-10x = -27
Learn more here: https://brainly.com/question/17003809
james conducted an eperent with 4 possible outcomes he determine that the eperimental probability
Solve the equation for t.
3t + 2 = 5(t – 2) – 2t + 8
Question 4 options:
Infinitely many solutions
x = 2
x = 3
No solution
If a square has side length s, then the perimeter is less than the area.
s = 3
s = 5
s = 7
s = 9
A landscaper builds a square garden behind a house.if the outside border of the garden consist of 36 feet of bricks then what is the area of the garden in square feet?
While catching fireflies, you and a friend decide to have a competition. after mm minutes, you have (3m+13)(3m+13) fireflies and your friend has (4m+6)(4m+6) fireflies.
a. how many fireflies are caught each minute during the competition?
To find for the number of fireflies caught in a minute, we simply look at the equation. The equation is linear and takes the form y = slope * x + b
where slope is also equivalent to the fireflies caught each minute.
So the equation of you and your friend is: (where y is the total fireflies caught)
you:
y = 3 m + 13
your friend:
y = 4 m + 6
So the fireflies caught each minute is:
you: 3
your friend: 4
So a total of 7 fireflies each minute combined
Quick Question. After dividing 30 by 2, do I multiply 15 by 3 or add 3 it to? (for question d) And thanks!
Answer:
6
Step-by-step explanation:
Frank’s bookshelf is 1 1/2 meters high. Each row in the bookshelf is 3/16 meters high. How many rows are there in Frank’s bookshelf?
will give brainliest to a reasonable answer :P
a)3
b)6
c)8
d)12
Answer:
8 rows
Step-by-step explanation:
WILL GIVE BRAINLIEST-The number of pollinated flowers as a function of time in days can be represented by the function.
f(x)=(3)x/2
What is the average increase in the number of flowers pollinated per day between days 4 and 10?
Enter your answer in the box.
Final answer:
The average increase in the number of flowers pollinated per day between days 4 and 10 is calculated by finding the values of the function on days 4 and 10, subtracting these values, and dividing by the number of days between 4 and 10. The result is an average increase of 39 flowers per day.
Explanation:
Calculating the Average Increase in Pollinated Flowers
To find the average increase in the number of flowers pollinated per day, we need to evaluate the function f(x) = (3)x/2 at days 4 and 10 and then find the difference between these two values. First, let's calculate the number of flowers pollinated on day 4.
f(4) = (3)4/2 = (3)2 = 9
Now, let's calculate the number of flowers pollinated on day 10.
f(10) = (3)10/2 = (3)5 = 243
The difference between these two values is:
243 - 9 = 234
Lastly, to find the average increase per day between days 4 and 10, we will divide this difference by the number of days between 4 and 10, which is 6 days (10 - 4 = 6).
Average increase per day = 234 / 6 = 39
Therefore, the average increase in the number of flowers pollinated per day between days 4 and 10 is 39 flowers.
An electronics store makes a profit of $25 for every portable DVD player sold and $55 for every DVD recorder sold. The manager’s target is to make at least $225 a day on sales of the portable DVD players and DVD recorders. Write an inequality that represents the number of both kinds of DVD players that can be sold to reach or beat the sales target. Let p represent the number of portable DVD players and r represent the number of DVD recorders.
An inequality that represents the number of both kinds of DVD players that can be sold to reach or beat the sales target is [tex]25p+55r\geq225[/tex].
To determine the inequality that represents the number of portable DVD players (p) and DVD recorders (r) that need to be sold to achieve the target profit of at least $225 per day, we can use the information provided about the profits from selling each item.
The store makes a profit of $25 for every portable DVD player sold and $55 for every DVD recorder sold. This can be represented by the following inequality:
[tex]25p+55r\geq225[/tex]
Here, p represents the number of portable DVD players sold.
Here, r represents the number of DVD recorders sold.
This inequality ensures that the total profit from selling portable DVD players and DVD recorders meets or exceeds the manager’s target of $225 per day.
If the ratio of raisins to bran flakes in a box of raisin bran flakes cereal is 3:27, how many raisins are there in a box that contains 3,000 raisins and bran flakes
Answer:
320?
Step-by-step explanation:
sorry if its wrong edg 2020
Hal, Zelda, Maya, and Jason each recorded the height and age of five classmates. They used the data to create the tables below.
(Image)
In which student’s data can height be considered a function of age?
Answer:
Step-by-step explanation:
Hal's because there is one age for every height .
Answer:
The answer is A
Step-by-step explanation:
I got it right on edge 2021
What is the equation of a line that is parallel to −x+3y=6 and passes through the point (3, 5) ? Enter your answer in the box.
Now that you have selected the correct unit above, what is the value of x?
In how many ways can you order 3 red balls and 2 white balls taken from a bin of 5 blue, 7 red, 3 yellow, and 8 white? (balls with the same color are indistinguishable) (233,2)
Answer:
It is 8 since I got it right.
Which is equivalent to log2n=4 ?
Answer:
Option (B): Logn=4Log2
Step-by-step explanation:
Math.
Worth 99 points and brainliest if correct.
Option C is your answer
I believe that the question is asking which one is false (as all the other are true).
Angles 2 and 3 are not congruent, because they are next to each other (not vertical angles). Rather, they are supplementary angles, meaning they would add up to 180° in measurement.
hope this helps
What is the repeating decimal 0.242424.... as a fraction in simplest form?
A repeating decimal is a decimal that has reoccurring numbers in a particular sequence.
The fraction in the simplest form is 8/33
The decimal is given as:
[tex]Decimal = 0.242424....[/tex]
The repeating numbers in the decimal are 2 and 4.
So, we express the number as follows (as a fraction)
[tex]Fraction = \frac{24}{100}[/tex]
Subtract 1 from the denominator
[tex]Fraction = \frac{24}{100 -1}[/tex]
[tex]Fraction = \frac{24}{99}[/tex]
Reduce the fraction by dividing the numerator and the denominator by 3
[tex]Fraction = \frac{24/3}{99/3}[/tex]
Simplify
[tex]Fraction = \frac{8}{33}[/tex]
Hence, the fraction is 8/33
Read more about repeating decimals at:
https://brainly.com/question/12453251
what is the solution of the following system?
3x+3y=10
-9x-9y=-30
Please give me a step by step!