What would be equation would be perpendicular to p(1,3), y = 2x - 1?
Find the dimensions of a right circular cylindrical can with both a top and a bottom that holds 5832 cubic cm and is constructed with the least amount of material possible.
The dimensions of a right circular cylindrical can that holds 5832 cubic cm and uses the least amount of material are a radius of approximately 10.614 cm and a height of approximately 16.526 cm.
Explanation:The question asks for the dimensions of a right circular cylindrical can that holds 5832 cubic cm of liquid and is designed to use the least amount of material. This scenario fits into the realm of mathematical optimization. Here, we’re being asked to identify dimensions that minimize the surface area of the cylinder while holding a fixed volume. This kind of problem is typically addressed using calculus.
The volume V of a cylinder is given by the formula V = πr²h where r is the cylinder radius and h is the cylinder height. The surface area A of a cylinder closed at both ends is given by A = 2πrh + 2πr².
From the volume equation, we can express h in terms of V and r, h = V/πr². Substituting this into the surface area equation yields: A = 2πr(V/πr²) + 2πr² = 2V/r + 2πr².
To find the radius that minimizes the surface area, we would set the derivative of the surface area with respect to r equal to zero and solve for r. After these calculations, we find that r = (V/(2π))^(1/3). For V = 5832 cubic cm, this yields r ≈ 10.614 cm.
Substitute r ≈ 10.614 cm back into the equation h = V/πr² to find h ≈ 16.526 cm. So, the dimensions of the can that minimizes the material used are radius 10.614 cm and height 16.526 cm.
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To find the dimensions of the cylindrical can that holds a specific volume and is made from the least material, utilize the volume and surface area formulas for a cylinder. Using calculus, find the radius that minimizes the surface area, then find the corresponding height.
Explanation:This problem is a classic calculus optimization problem. The volume of the cylindrical can is given by the formula V = πr²h, where r is the radius and h is the height of the cylinder. To minimize the amount of material used in constructing the can, we need to minimize the surface area, given by the formula [tex]A = 2\pi rh + 2\pi r^2[/tex] (which includes both top and bottom of the can).
From the volume formula, we can express h as h = V/πr² = 5832/πr². Substituting this value into the surface area equation, we get A = [tex]2\pi r(5832/\pi r^2) + 2\pi r^2 = 11664/r + 2\pi r^2.[/tex] Differentiating this equation with respect to r and setting the derivative equal to zero, will provide the radius that minimizes the material used. The height can be obtained by substituting this radius value back into the equation h = 5832/πr².
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The sum of two numbers is 50 . the smaller number is 12 less than the larger number. what are the numbers?
The two numbers are 31 and 19, where 31 is the larger number and 19 is the smaller number which is 12 less than the larger number.
The sum of two numbers is given to be 50, and the question states that the smaller number is 12 less than the larger number. To find these numbers, let's denote the larger number as x and the smaller number as x - 12. According to the problem, the sum of these two numbers is 50, so we can write the equation:
x + (x - 12) = 50
Simplifying the equation gives us:
2x - 12 = 50
Adding 12 to both sides gives us:
2x = 62
Dividing both sides by 2 gives us:
x = 31
Now that we know the larger number is 31, we can find the smaller number by subtracting 12:
x - 12 = 31 - 12
x - 12 = 19
Therefore, the two numbers are 31 and 19.
wilson jarred 45 liters of jam after 5 days. how much jam did wilson jar if he spent 7 days making jam? solve using unit rates.
Today a car is valued at $42000. The value is expected to decrease at a rate of 8% each year. What is the value of the car expected to be 6 years from now?
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For what values of x and y must each figure be a parallelogram?
The required values are x = 60 and y = 30 for the given parallelogram.
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal. A parallelogram is a square and a rhombus is a square.
The parallelogram is represented in the given figure
A parallelogram has two pairs of adjacent sides that are congruent.
As per the given figure, we have
x + 5x - 180 = 180
6x = 360
x = 360/6
Apply the division operation, and we get
x = 60
2y + 4y = 180
Apply the addition operation, and we get
6y = 180
y = 180/6
y = 30
Thus, the required values are x = 60 and y = 30
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what is the estimate 5% of 59
belinda has twice as many nickels as dimes. how many of each does she have if they total
A) 80 cents
B) $1.20
Show all work using an equation
Find the value of x. Then find the measure of each labeled angle
Answer:
x=107
[tex]x-34=107-34=73[/tex]
Step-by-step explanation:
Sum of angles in a quadrilateral is 360 degree
right angle is 90 degree
[tex]90 +90+x+x-34= 360[/tex]
[tex]180+x+x-34=360[/tex]
subtract 180 from both sides
[tex]x+x-34=180[/tex]
[tex]2x-34=180[/tex]
add 34 on both sides
[tex]2x=214[/tex]
divide by 2 on both sides
x=107
[tex]x-34=107-34=73[/tex]
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. Which property justifies this statement?
If x = −2, then 5x = −10.
A. Symmetric Property of Equality
B. Multiplication Property of Equality
C. Subtraction Property of Equality
D. Transitive Property of Equality
2. Drag a statement or reason to each box to complete the proof.
If 3(x−4)=x+4, then x=8.
Statement: Reason:
1. 3(x−4)=x+4 ----> Given
2. 3x−12=x+4 ----> ________
3. 3x−12+12=x+4+12 ----> ________
4. 3x=x+16 ----> Simplifying
5. 3x−x=x+16−x ----> ________
6. 2x=16 ----> Simplifying
7. 2x2=162 ----> ________
8. x=8 ----> Simplifying
A. Subtraction Property of Equality
B. Distributive Property
C. Addition Property of Equality
D. Division Property of Equality
This is irrelevant, but was THAT many exclamation points necessary?
Anyway, these aren't that hard, you gotta just use your brain a bit. These problems use a bit of simple common sense if you put 2-and-2 together and look into it. Look for signs and just use your head, it's hard to explain but just try. ^^
Two classrooms are sharing seven packages of unit cubes if the packages are split evenly how many packages with each classroom receive
I need answers to all of these. Please help!! I suck at math..
1) (-4) + (-9) =
2) 5 + (-12) =
3) -6 + 5 =
4) -7 + 7 =
5) Which symbol correctly completes the statement?
-7 + 2 ___ 3 + (-9)
<
>
=
6) Which symbol correctly completes the statement?
4 + (-8) ___ 6 + (-8) + (-6)
<
>
=
7) Your checking account balance is $50. You spend $11 and then deposit $27.
What is your current balance?
$12
$44
$66
$88
8) You currently have a balance of $34 in your checking account. You then write a check for $76 dollars to pay for groceries. Finally, you deposit a check for $30.
What is your new balance?
-$72
-$12
$12
$72
((worth THIRTY points and THE BRAINLIEST answer!!))
How many 5 pound bags of apples can be made from 400 apples each weighing 1/4 pound?
Answer:
You can make 20 - 5 pound bags
Step-by-step explanation:
You first find the number of total pounds that the 400 applying ratios :
400 apples * ¼ pound / 1 apple = 100 pounds by simplifying units
Then we find the number of bags as:
100 pounds* (1 bag/5 pounds ) = 20 bags by simplifying units
So the final answer is 20 bags for this problems by using ratios
Select the correct product.
(2x + 9)(x + 1)
2x^2 + 11x + 9
3x^2 + 11x + 9
2x^2 - 7x + 9
2x^2 + 11x + 10
PLEASE HELP ME WITH THIS! WILL MARK BRILLIANT!!! ✨✨
Answer:
b. linear; y +2 = -5/4(x +9)
Step-by-step explanation:
From the first line of the table to the second, we have ...
slope = (change in y)/(change in x) = (-7-(-2))/(-5-(-9)) = -5/4
Only one equation shows a slope of -5/4: the second one.
__
We know the relation is linear because the same slope can be computed from any pair of lines of the table. In particular, from one row to the next, x changes by the constant value +4 and y changes by the constant value -5.
What can be used as a reason in a two-column proof?
Select each correct answer.
a true premise
a conjecture
a definition
a theorem
Answer :- A definition and a theorem can be used as a reason in a two-column proof.
Explanation:-
A two column proof is assembled into statement and reason columns, where each statement should have verified reason. The reason in a two column proof are usually given information, vocabulary definitions, postulates and previously proved theorems.
Therefore, from the given options a definition and a theorem can be used as a reason in a two-column proof.
A definition and a theorem can be used as a reason in a two-column proof.
Further explanation:
Given:
The options are as follows,
(a). A true premise
(b). A conjecture
(c). A definition
(d). A theorem
Explanation:
True premise is an assumption about something is true. It is not proved.
Conjecture is a statement that has not been proved.
Definition is a statement which tells us the meaning of the word.
Theorem is a statement that has been proved.
A definition and a theorem can be used as a reason in a two-column proof.
Conjecture and true premise cannot be used as a reason in a two-column proof as they are not proved.
Option (a) is not correct as a true premise cannot be used as reason in two-column proof.
Option (b) is not correct as a conjecture cannot be used as reason in two-column proof.
Option (c) is correct can be used as a reason in a two-column proof.
Option (d) is correct can be used as a reason in a two-column proof.
Learn more:
1. Learn more about inverse of the function https://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Simple interest
Keywords: two-column proof, a true premise, a conjecture, a definition, a theorem, correct answer, reason.
The lengths of the base and legs of an isosceles triangle are in the ratio of 3;2 the perimeter of triangles is 105 find the length of the base
Find the median of the data: 206, 194, 198, 172, 190
Determine the vertex point, domain, and range of the following function
y = -|x| + 2
Are 2/4 and 20/36 proportional?
And y?
What is the slope of the line segment XY?
2
1/2
-1/2
-2
the line has points (-1,3) and (1,-1)
slope = change in y over change in x
change in y = 3- -1 = 3+1 =4
change in x = -1 - 1 = -2
slope = 4/-2 = - 4/2 = -2
16x=1.6 what is x? please help
Which equation represents a line which is parallel to the line y=4x-8y=4x−8?
find m<p the diagram is not to scale
What is the value of the function at x=−2?
y=−4
y = 0
y = 2
y = 3
Answer:
Option D.
Step-by-step explanation:
If the graph of a function f(x) passes through the point (a,b), then the value of the function f(x) is b at x=a.
[tex]f(a)=b[/tex]
[tex]y=b[/tex]
The graph of a function is given.
We need to find the value of function at x=-2.
From the given graph it is clear that the graph is passes through the point (-2,3).
It means the value of function is 3 at x=-2.
[tex]y=3[/tex]
Therefore, the correct option is D.
Two–thirds of the children in the fourth–grade class are girls. if there are 18 girls, what is the total number of children in the class?
Mike and Kate plan to save money for their wedding over a 20 month period. They will need to save $8,000 to help pay for the wedding. They set aside the same amount each month. After a year they saved $4,000. Mike and Kate know they must adjust their plan in order to meet their goal, so they came up with the following options: Option A: Stay with saving the same amount they've been saving each month but postpone the wedding 2 months. Option B: Increase the amount of money they save each month by $80 from what they've been saving. Which of the following is a true statement? a. Only option A will allow them to meet their goal. b. Only option B will allow them to meet their goal. c. Both options A and B will allow them to meet their goal. d. Neither option A nor option B will allow them to meet their goal.
If there is 20 students and 20 chairs how many way for a student to sit
Answer:
40. Just add 20+20 and you will get your answer.
There 20 colored pencils in a box:4 red, 5 green, 10blue , and 1 black. You pick a pencil without looking. What is the sum of the probability of picking a red pencil and the probability of picking a black pencil