A rectangle of perimeter 18 in. is rotated about one of its sides to generate a right circular cylinder. Find the rectangle which generates the cylinder of largest volume has area in square inches.
The volume of the cylinder from the rectangle is the size of the cylinder
The rectangle that generates the cylinder of the largest volume is 3 inches by 6 inches
How to determine the rectangleLet the dimension of the rectangle be x and y.
So, the perimeter (P) is:
[tex]P = 2 * (x + y)[/tex]
The perimeter is given as 18.
So, we have:
[tex]2 * (x + y) = 18[/tex]
Divide both sides by 2
[tex]x + y = 9[/tex]
Make y the subject
[tex]y = 9 - x[/tex]
The volume of a cylinder is:
[tex]V = \pi r^2h[/tex]
So, we have:
[tex]V = \pi x^2(9 -x)[/tex]
Expand
[tex]V = \pi(9x^2 -x^3)[/tex]
Differentiate
[tex]V' = \pi(18x -3x^2)[/tex]
Set to 0
[tex]\pi(18x -3x^2) = 0[/tex]
Divide both sides by [tex]\pi[/tex]
[tex]18x -3x^2 = 0[/tex]
Divide both sides by 3x
[tex]6 -x = 0[/tex]
Make x the subject
[tex]x = 6[/tex]
Recall that:
[tex]y = 9 - x[/tex]
So, we have:
[tex]y = 9 - 6[/tex]
[tex]y = 3[/tex]
Hence, the rectangle that generates the cylinder of the largest volume is 3 inches by 6 inches
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During the soccer season, Cathy made 27 of the 54 goals she attempted. Karla made 18 of the 45 goals she attempted. Patty made 34% of the goals she attempted. List the athletes in order of their goal-scoring percentage from least to greatest.
Answer:
Patty, Karla, Cathy
Step-by-step explanation:
The scoring percentage of goals attempted can be computed by dividing goals made by those attempted, then multiplying the result by 100%.
__
Cathy's rate is ...
27/54 × 100% = 50%
Karla's rate is ...
18/45 × 100% = 40%
Patty's rate is ...
given as 34%
__
By least to greatest scoring rate, the athletes are ...
Patty (34%), Karla (40%), Cathy (50%)
Item before tax?
3. Mrs. Noah's bill, before tax, is $50. The sales tax rate is 3%. Mrs. Noah
decides to leave a 2% tip for the gate keeper based on the pre-tax amount.
How much will the total bill be, including tax and tip?
(SHOW THE WORK PLEASE)
Answer:
$52.50
Step-by-step explanation:
Multiply $50 by 0.03 to find the tax = 1.5
Multiply $50 by 0.02 to find tip = 1
add $50 to 1.5 and 1 to get $52.50
What is the solution to 4(y–3)+19=8(2y+3)+7 ? A. −12 B. 12 C. −2 D. 2
Answer:
C. -2
Step-by-step explanation:
4(y–3)+19=8(2y+3)+7
4y-12+19=16y+24+7
4y+7=16y+31
-12y=24
12y=-24
y=-2
Answer:
4(y-3)+19=8(2y+3)+7
4y -12 +19=16y+24+7...
-12+19-24-7=16y-4y
-24=12y÷12
-2=y...
•
•. • C.-2...
5 meter by 5 meter and 1 meter by 1 meter is
Answer:
If you are asking the shape it's rectangle if you are asking 5x5 = 25 1x1 = 1
Joel is training for soccer season.
On Monday, Joel exercises for 20 minutes before school, and 25% of that time is spent playing soccer.
On Monday, Joel exercises for 60 minutes after school, and 40% of that time is spent playing soccer.
What is the total amount of time, in minutes that Joel plays soccer?
PLEASE URGENT HELP PLEASE 100 POINTS PLUS BRAILIEST AND A GOOD REVIEW PKUS 20 COMMENTS IM BEGGING YOU PLEASE HELP ME
Answer:
part A:60
Step-by-step explanation:
25% of 20 is 5 now we know 40% of 60 which is 24 add 5+24=29 .hope this is helpful
Please help I’ll give brainlyest
Answer:
80m^3
Step-by-step explanation:
Here,
For the base of pyramid which is a rectangle,
length(a) = 8m
breadth(c) = 5m
For the pyramid,
actual height (h) = 6m
Now,
The formula for the Volume of a rectangular based pyramid is,
1/3 * Area of base rectangle * height
= 1/3 * (a*c) * 6 [ Because area of rectangle is product of its two sides, length and breadth]
= 2 * 8 * 5
80m^3
Identify the congruent corresponding parts.
Which segments are perpendicular to
CD.
Answer:
GF where G is at (6,5) and F is at (10,2)
Step-by-step Explanation:
Perpendicular lines always have the negative reciprocal as the other line as their slope. This is such that (1/3) × (-3/1) = -1, so -3/1 is the negative reciprocal to 1/3.
This means we are looking for a line with the slope -3/4, and we can find the slopes by using the formula (y2 - y1)/(x2 - x1).
For the first option, LM, we get (9 - 3)/(-10 - 2) = 6/-12 = -1/2, so it is not this.
For the second option, GF, we get (2 - 5)/(10 - 6) = -3/4, which is the slope we were looking for. This means that the second option is our answer.
I hope this helps!
The difference between 2.4 and a number is 1.61, as shown below. What number should go in the box to complete the subtraction problem?
Answer:
4.37
Step-by-step explanation:
23.8+ 4.37= 28.17
10
13 + 18 - (
46)
1318-146)
30-(4.6)
120-
Color this answer orange,
I need help
Hey there!
13 + 18 - (4 * 6)
= 31 - 4 * 6
= 31 - 24
= 7
Thus, the answer MIGHT be: 7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
please help worth a lot
Answer:
(-2, -3)
Step-by-step explanation:
when its relected its just flipping over the horizontal axis (x-axis) so in turn that is the answer! :) hope this helped you
At the school store, notebooks cost $3 You buy x notebooks and 4 packs of markers.
Answer:
3x + 4y
Step-by-step explanation:
You need to explain more. If you are asking for an equation, x represents the cost of each notebook and y represents the cost of each pack of markers. Also, you did not mention how much each pack of of marker costed, so I used y to substitute that amount. If you do know how much a pack of markers costs, multiply that number by 4 and your new equation will be 3x + (whatever the product is).
Solve for x.
[tex] \: \: \: [/tex]
[tex] \: \: \: \: \: [/tex]
Step-by-step explanation:
In the figure,
145° and 3x - 5 are vertically opposite angles which are equal, so
=> 3x - 5 = 145°
=> 3x = 145 + 5
=> 3x = 150°
=> x = 150°/3
=> x = 50°
Hope it helps you!!Answer:
x = 50
explanation:
vertically opposite angles are of equal measure.
solve:
3x - 5 = 145
3x = 145 + 5
3x = 150
x = 50
Suzanne drove 3,000 miles in 75 hours. At
this rate, how long will it take her to drive
4,000 miles?
Answer: I believe that, at that specific rate, it will take Suzanne 100 hours to drive 4,000 miles.
Contessa is solving an absolute value inequality. She writes the compound inequality as her first step. Which inequality is Contessa solving?
The compound inequality that Contessa is solving is |8 - 3q| ≤ 7
What is an inequality?
An inequality is an expression that shows the non equal comparison between two or more numbers and variables.
Given the inequality:
-7 ≤ 8 - 3q ≤ 7
8 - 3q ≤ 7 and; 8 - 3q ≥ -7
8 - 3q ≤ 7 and; -(8 - 3q) ≤ 7
|8 - 3q| ≤ 7
The compound inequality that Contessa is solving is |8 - 3q| ≤ 7
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Answer
IT's C
Step-by-step explanation:
Can i have help with i cant figure this out
Answer:
The circumference of a circle with radius 48 is 301.6(*)
Step-by-step explanation:
Formulas:
d = 96C = 302C = 2·π·r C = π·d C = √4·π·A π = 3.1415A = area of the circleC = circumference or perimeterr = radius, d = diameterStep-by-step Solution:
Circumference of a cicle in terms of radius:Circumference = 2·π·r = 2·3.14·48 = 301.58(*)In terms of diameter:Circumference = π·d = 3.14·96 = 301.44(*)In terms of area:Circumference C = √4·π·A = √4·π·7238 = 301.58(*)(*) 301.6 cm exactly or limited to de precision of this calculator (13 decimal places).
Note: for simplicity, the operations above were rounded to 2 decimal places and π was rounded to 3.14.
A circumference of 301.6 centimeters is equal to:
0.003016 kilometers (km)3.016 meters (m)3016 millimeters (mm)0.00187406 miles (mi)3.29834 yards (yd)9.89501 feet (ft)118.74 inches (in)Answer:
301.6
Step-by-step explanation:
circumference = πD
Diameter = r x 2
diameter = 48 x 2 = 96
96 x π = 301.592895
301.6 to 1dp
If you need further help, let me know!
- profparis
if the sides of a triangle QRS are QR=10X-6, RS=6X-15,QS=X+24, find a range of possible values for X?
The range of the possible values for X will be;
⇒ X < 5
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The sides of a triangle QRS are;
⇒ QR=10X - 6,
⇒ RS = 6X - 15,
⇒ QS = X + 24,
Now,
We know that;
The sum of two sides of a triangle is always greater than the third side.
So, We can formulate;
⇒ 10X - 6 < (6X - 15) + (X + 24)
⇒ 10X - 6 < 7X + 9
⇒ 10X - 7X < 9 + 6
⇒ 3X < 15
⇒ X < 5
Thus, The range of the possible values for X will be;
⇒ X < 5
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. Linda is a customer service representative. She must answer at least 15% of the customer e-mails her company receives each day. Today, there were 40 e-mails awaiting response. How many e-mails must she answer?
Answer:
6 Emails
Step-by-step explanation:
If you take 15% of 40, or 0.15*40, you will get 6
So if she must respond to 15 percent of the total emails, you can use this equation to figure out how many emails she must respond to.
The bike store marks up the wholesale cost of all of the bikes they sell by 30%.
Andre wants to buy a bike that has a price tag of $125. What was the wholesale cost of this bike?
The wholesale price was $
( 10 / 13 ) * 125 = original price
( 10 / 13 ) * 125 = 96.15
A boat is heading towards a lighthouse, whose beacon-light is 132 feet above the
water. The boat's crew measures the angle of elevation to the beacon, 5º. What is the
ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to
the nearest tenth of a foot if necessary.
Applying the tangent ratio, the horizontal distance, rounded to the nearest tenth, is: 1,508.8 ft.
What is the Tangent Ratio?Tangent ratio, TOA, is expressed as, tan ∅ = opposite/adjacent.
The situation has been sketched in the diagram atatched below, where:
∅ = 5°Height of beacon = 132 ft (hypotenuse)The ship's horizontal distance from the light house = BC = ? (opposite)Apply the tangent ratio:
tan 5 = 132/BC
BC = 132/tan 5
BC = 1,508.8 ft.
Therefore, applying the tangent ratio, the horizontal distance, rounded to the nearest tenth, is: 1,508.8 ft.
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write as many mathematical expressions or equations as you can about the image include a fraction, a decimal number, or a percentage in each.
Fundraiser
our Goal
250,000
Answer:
110/250
Step-by-step explanation:
If the fraction goal is 250 then put the 250 as the denomanator and the 110 as the top common denomanator.
Percentage of funds raised is 44 % , Fraction of funds raised is (11/25) and Fraction of funds raised in decimal form is 0.44.
What is Percentage?To find the % of a number, divide it by its value, then multiply the result by 100. Percentage is a relative value that denotes one tenth of any quantity. As one percent (symbolised as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified.
As per the given data:
In the diagram given, we can find the total amount of funds to be raised and the amount of fund which is raised currently.
Total amount to be raised = $250,000
Amount already raised = $110,000
Percentage of funds raised = (110,000/250,000) × 100 = 44 %
Fraction of funds raised = (110,000/250,000) = (11/25)
Fraction of funds raised in decimal form = 0.44
Hence, Percentage of funds raised is 44 % , Fraction of funds raised is (11/25) and Fraction of funds raised in decimal form is 0.44
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(The question is incomplete, the complete question is given below.)
A triangle has side lengths of 54, 72 & 90. Is it a right triangle? Explain.
No, there always has to be an odd number for it to work out to be a right triangle.
No, it is obtuse.
No, it is acute.
Yes, the Pythagorean Theorem works out to be equal.
Yes, because 52 + 72 > 90.
Answer: C: Yes, the Pythagorean Theorem works out to be equal.
Step-by-step explanation:
to test if a triangle is right angled or not, just use the Pythagorean Theorem:
a²+b²=c², where a and b are the two shorter sides of the triangle, and c is the longest side.
plugging this in:
54²+72² ?= 90²
2916 + 5184 ?= 8100
8100 = 8100
Yes! Its correct, so we know that this triangle is a right triangle. the justification is C: Yes, the Pythagorean Theorem works out to be equal.
If x = 9 units, y = 6 units, and h = 5 units, then what is the area of the parallelogram shown above?
Answer:
D. 45 unit
Step-by-step explanation:
parallelogram:
A = b . hA = 9 units × 5 unitsA = 45 unitsthe area of the parallelogram is 45 units(D.)
There is R240000 in your company bank account at the beginning of the month.Two-fifths of this money is immediately used to pay for various operating expenses.The remaining money is to be used to cover daily expenses over a period of twenty working days .if 13/20ths of this remaining money is used within the first 10 working days of the month,how much is left per day for the remaining 10 working days?
Answer:
$50400
Step-by-step explanation:
2/5 of 240000 is 96000.
So the remaining money is 240,000-96000, which is 144000.
If 13/20 is used in the first ten days, that leaves 7/20 to be used in the next 10 days.
7/20 of 144000 is 50400.
There's the answer!
Find the product of -8y^2(2y^2+7y-5) PLEASE HELP
Which of the following functions has an initial value of 3/2 and a rate of change of -2/3?
Answer:
B. because 3/2 is equal to 1.5 or 1 and a half and because of the negative on -2/3 it is a downward facing slope that has the ratio of down 2 over 3 for the slope.
Step-by-step explanation:
help !!!!!!!!!!!!!!!!!!
Answer:
Second Option
Step-by-step explanation:
The ratio of a 30-60-90 triangle is
a: a times root of 3: 2a.
Since the side opposite of 60 degree angle
[tex] \frac{3 \sqrt{3} }{2} [/tex]
The smallest angle is divided that of root 3.
[tex] \frac{3 \sqrt{3} }{2} \times \frac{1}{ \sqrt{3} } = \frac{3}{2} [/tex]
That side is b. Side A is twice of Side B. Which is
3.
Answer:
I do believe the answer is the second one
Pls help I need it pls
Answer:
Formula for area of triangle:
A = bh x 1/2
1) height is 8, and base is 8, so:
8(8) x 1/2 = 32 yd
2) height is 5, base is 6, so:
6(5) x 1/2 = 15 ft
3) height is 8, base is 10, so:
10(8) x 1/2 = 40 in
Explain why knowledge of statistics is important.
Answer:
Statistical knowledge helps you use the proper methods to collect the data, employ the correct analyses, and effectively present the results. Statistics is a crucial process behind how we make discoveries in science, make decisions based on data, and make predictions.