Answer:
a = 158.3 units²
Step-by-step explanation:
a = (∅/360) * πr²
using 11 ft as the radius
a = (150/360) * 3.14 * 11²
a = 158.3 units²
A cone-shaped paper drinking cup is to be made to hold 24 cm3 of water. Find the height and radius of the cup that will use the smallest amount of paper. (Round your answers to two decimal places.)
Answer:
I. Radius, r = 2.90 cm
II. Height, h = 4.10 cm
Step-by-step explanation:
Given the following data;
Volume of cone = 24 cm³
To find the height and radius of the cup that will use the smallest amount of paper;
Mathematically, the volume of a cone is given by the formula;
[tex] V = \frac{1}{3} \pi r^{2}h[/tex] ......equation 1
Where;
V is the volume of the cone.
r is the radius of the base of the cone.
h is the height of the cone.
Substituting into the formula, we have;
[tex] 36 = \frac{1}{3} \pi r^{2}h[/tex]
Multiplying both sides by 3, we have;
[tex] 108 = \pi r^{2}h[/tex]
Making radius, r the subject of formula, we have;
[tex] r^{2} = \frac {108}{ \pi h} [/tex]
Taking the square root of both sides, we have;
[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]
Mathematically, the lateral surface area of a cone is given by the formula;
[tex] LSA = \pi rl [/tex] ......equation 2
Where;
r is the radius of a cone
l is the slant height of a cone.
To find the slant height, we would apply the Pythagorean' theorem;
[tex] l = \sqrt {r^{2} + h^{2}} [/tex]
Substituting r into the above equation, we have;
[tex] l = \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]
Substituting the values of r and l into eqn 2, we have;
[tex] LSA = \pi * \sqrt { \frac {108}{ \pi h}} * \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]
Simplifying further, we have;
[tex] LSA = \sqrt {108} * \sqrt { \frac {\pi h^{3} + 108}{\pi h}} [/tex]
[tex] LSA = \sqrt {108} * \sqrt { \frac {108}{ h^{2}} + \pi h}} [/tex]
Next, to find the value of h, we differentiate the above mathematical equation with respect to h;
[tex] \frac {dS}{dh} = \sqrt {108} * (\pi - \frac {216}{h^{3}}) * (\pi h + \frac {108}{h^{2}}) [/tex]
Limiting [tex] \frac {dS}{dh} [/tex] w.r.t 0;
[tex] \frac {dS}{dh} = 0 [/tex]
[tex] (\pi - \frac {216}{h^{3}}) = 0 [/tex]
Rearranging the equation, we have;
[tex] \pi = \frac {216}{h^{3}} [/tex]
We know that π = 3.142
[tex] 3.142 = \frac {216}{h^{3}} [/tex]
Cross-multiplying, we have;
[tex] 3.142h^{3} = 216 [/tex]
[tex] h^{3} = \frac {216}{3.142} [/tex]
[tex] h^{3} = 68.75 [/tex]
Taking the cube root of both sides, we have;
Height, h = 4.10 cm
Lastly, we find the value of r;
[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]
[tex] r = \sqrt { \frac {108}{3.142 * 4.10}} [/tex]
[tex] r = \sqrt { \frac {108}{12.88}} [/tex]
[tex] r = \sqrt {8.39} [/tex]
Radius, r = 2.90 cm
The height and radius of the cup that will use the smallest amount of paper is;
Radius = 2.52 cm
Radius = 2.52 cmHeight = 3.58 cm
Let us first state some relevant formulas;
Volume of a cone is;
V = ⅓πr²h
Surface area of a cone is;
S = πrL
Where L is Slant height and has a formula;
L = √(h² + r²)
We are told that the cone is to hold 24 cm³. Thus; V = 24 cm³
24 = ⅓πr²h
πr²h = 72
r = √(72/πh)
Putting √(72/πh) for r in the Slant height equation gives;
L = √(h² + (72/πh))
Thus;
S = π × √(72/πh) × √(h² + (72/πh))
Differentiating with respect to h gives;
dS/dh = √72 × (π - 144/h³) × 1/√(πh + 72/h²)
At dS/dh = 0,we will have;
(π - 144/h³) = 0
Thus;
h³ = 144/π
h = 3.58 cm
Thus, from r = √(72/πh);
r = √(72/(π × 3.58))
r = 2.52 cm
Read more at; https://brainly.com/question/4405937
What is the equation of the line that is perpendicular to the line y= 3/5x+10 and passes through the point (15,5)?
Answer:
Step-by-step explanation:
This is really super super simple as long as you know the rules for finding a perpedicular slope from a given line. The perpendicular slope of a line is the opposite reciprocal of the given slope. Our given slope is 3/5, therefore, the perpendicular slope is -5/3. There's only one line with that exact slope, so the choice is the last one. (BTW, check the coordinate you gave. It should be
(15, -5), not (15, 5)!)
Use the net to find the surface area of the regular pyramid.
Answer:
D
Step-by-step explanation:
Base perimeter = side x 5 = 8 x 5 = 40 cm
LA = (base perimeter x slant height)/2 = (40 x 9)/2 = 180 cm^2
SA = base area + lateral area = 110.1 + 180 = 290.1 cm^2
what is the ratio of 20cm to 1m
9514 1404 393
Answer:
1 to 5
Step-by-step explanation:
20 cm to 1 m = 20 cm to 100 cm = 20 to 100 = 1 to 5
What is the value of h(2)?
0 -2
0 -11
ОО
O 3
Need help fast!!!
Use two equations in two variables to solve the problem.
A merchant wants to mix peanuts and cashews, as shown in the illustration, to get 42 pounds of mixed nuts that will be sold at $6 per pound. How many pounds of each should the merchant use?
Answer:
Step-by-step explanation:
Tom has a steel box that has a capacity of 5 gallons. What is the maximum amount of fluid, in quarts, that this box can hold?
A. 10 qt.
B. 15 qt.
C. 18 qt.
D. 20 qt.
Answer:
d. 20 qt.
Step-by-step explanation:
4 quarts to a gallon so 4x5= 20
HOW COULD MAKE 7 TO BECOME EVEN NO. WITHOUT FOUR FUNDAMENTAL PRINCIPLE
LIKE :
PLUS
MINUS
SOBRACTION
DIVISION
Answer:
2,4,6,8,10,12,14,16,18,20
Answer:
How do you make the number 7 an even number without addition, subtraction or multiplication?
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22 Answers

Yogesh Rana, B.Sc. Mathematics, University of Delhi (2016)
Answered 4 years ago
You can remove alphabet S from SEVEN.
You can change the convention. Whole mathematics works like that. After all it is just a name, ie, call the numbers divisible by 2 odd and not divisible by 2 even. Everything will still work fine. You got to rename some theorems also.
Introduce and derive a new number system from the current number system, name the symbol 6 as seven and the symbol 7 as Six. Just rename the symbols.
Introducing a new number system and interchange position of 7 with an even number.
If we remove one number before 7 ( 1 - 6 ) with its name, we have again a new number system with base 9 and technically no. 7 is still no. 7 with value = 6.
These are some genuine ways rather than dividing.
ANSWERS OF DIVISION ARE TECHNICALLY WRONG AND RIDICULOUS BECAUSE DIVISION BY ‘x’ is MULTIPLICATION BY ‘1/x’ .
Match each system of equations to the inverse of its coefficient matrix, A^-1and the matrix of its solution, X.
Answer: Hello the system of equations and other data required are missing attached below are the missing data
answer :
attached below
Step-by-step explanation:
1st system of equations ( top left ) = Image number 8
system of equation ( Image 10 ) = Image 4
system of equation ( Image 9 ) = Image 6
system of equations ( Image 7 ) = Image 2
attached below is a pictorial representation of the solution
Find the value of x to the nearest tenth. 2 4 x 8
192 because if you put 24 into 8 groups there are 192
If each 2 cm on the scale drawing below equals 9 feet, what is the actual area of the shape in square units?
Answer: 18 cm
Step-by-step explanation: 9 feet x 2
Small circular disks are being cut from thin sheets of steel. The steel weighs 1.6 grams per square centimeter. The disks need to have a diameter of 5 centimeters.
(A) find the area of the disk to the nearest hundredth of a square centimeter. Show the steps in your calculation.
Answer:
[tex]A = 19.63cm^2[/tex]
Step-by-step explanation:
Given
[tex]d =5cm[/tex]
[tex]Weight = 1.6g/cm^2[/tex]
Required
The area (A) of the disk
This is calculated as:
[tex]A = \frac{\pi * d^2}{4}[/tex]
So, we have:
[tex]A = \frac{3.14 * 5^2}{4}[/tex]
[tex]A = \frac{3.14 * 25}{4}[/tex]
[tex]A = \frac{78.5}{4}[/tex]
[tex]A = 19.625[/tex]
[tex]A = 19.63cm^2[/tex] --- approximated
(120+2x)+(70+2x)=15,000
not angles, area. also foiling
Answer:
x =3702.5
Step-by-step explanation:
Given data
(120+2x)+(70+2x)=15,000
Let us open the bracket
120+2x+70+2x=15,000
Collect like terms
120+70+2x+2x=15,000
190+4x=15000
4x=15000-190
4x= 14810
Divide both sides by 4
x=14810/4
x= 3702.5
Hence the value of x =3702.5
Use the given values to complete each table.
PLEASE HELP.
Find the value of the polynomial when x=1 and y=-2
Answer:
the answer is : ................
5
which statement is true?
Answer:
The y-intercept of function a is greater than the y intercept of function b
Step-by-step explanation:
function a:
y = 4x + 2
function b:
y = 2x + 1
To evaluate whether or not the intake of a vitamin or mineral is adequate, comparisons are made between the intake distribution and the requirement distribution. Here is some information about the distribution of vitamin C intake, in milligrams per day, for women aged 19 to 30 years:
Percentile (mg/d)
Mean 1st 5th 19th 25th 50th 75th 90th 95th 99th
84.2 31 43 47 60 79 103 126 141 180
Use the 5th, the 50th, and the 95th percentiles of this distribution to estimate the mean (±0.01) and standard deviation (±0.01) of this distribution assuming that the distribution is Normal.
μ = _________
σ = _________
Answer:
[tex]Mean=79[/tex]
[tex]\sigma=30.3951.[/tex]
Step-by-step explanation:
From the question we are told that:
[tex]Age Bracket :19-20[/tex]
[tex]5th\ percentile = 42[/tex]
[tex]50th\ percentile = 79[/tex]
[tex]95th\ percentile = 142.[/tex]
Generally the mean Median and mode of the 50th percentile is are all equal
[tex]Mean=Median=Mode[/tex]
Therefore
[tex]Mean=79[/tex]
Generally for Normal distribution
[tex]5th\ percentile\ = mean - 1.645*\sigma[/tex]
[tex]95th\ percentile\ = mean + 1.645*\sigma[/tex]
Therefore
[tex](95th\ percentile\ - 5th\ percentile) = 2*(1.645*SD).[/tex]
[tex]\sigma=(95th\ percentile\ - 5th\ percentile)/3.29[/tex]
[tex]\sigma=\frac{142-42}{3.29}[/tex]
[tex]\sigma=30.3951.[/tex]
Find the missing length indicated
Answer:
D) 20
Step-by-step explanation:
Answer:
D) 20
Step-by-step explanation:
they are asking for the longest length of the triangle. as you can see, 20 is just over 15, and from the diagram, the missing length is just over 15 so we can apply our knowledge to come to the answer of 20.
Use your graph to find estimates of the solutions to the equation x^2-x-6=-2
9514 1404 393
Answer:
x ≈ -1.5 or 2.6
Step-by-step explanation:
It appears as though your graph crosses the line y = -2 at approximately x = -1.5 and also at x = 2.6.
These are estimates of the solutions to the equation.
x ≈ {-1.5, 2.6}
Answer:
-2 and 3
Step-by-step explanation:
From the graph, the solution is the points where the curve cuts the x axis. From the graph, you can see that the equation cuts the x axis at two points that is at x=-2 and 3.
Hence the solutions to the equation is -2 and 3
Giải các phương trình sau
√3x-√3=√3
Answer:
2
Step-by-step explanation:
√3x=√3+√3=2√3⇒x=2
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = 2}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \sqrt{3} x - \sqrt{3} = \sqrt{3} [/tex]
➺ [tex] \: \sqrt{3} x = \sqrt{3} + \sqrt{3} [/tex]
➺ [tex] \: \sqrt{3} x = 2 \sqrt{3} [/tex]
➺ [tex] \: x = \frac{2 \sqrt{3} }{ \sqrt{3} } [/tex]
➺ [tex] \: x = 2[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35☂}}}}⋆[/tex]
A website posts evaluations on airlines. It posts the most positive and the most negative comments for each airline. Discuss the usefulness of this feedback for a reader wanting to know about the airline.
choose the correct statement below. SELECT ALL THAT APPLY:
A. The reader can accurately assess the airline based on the posted evaluations.
B. the reader cannot accurately assess the airline because the evaluations are not necessarily representative of all evaluations.
C. the reader cannot accurately assess the airline because the method of choosing the sample is unclear.
D. the reader cannot accurately assess the airline without reading all the evaluations.
Answer:
B. the reader cannot accurately assess the airline because the evaluations are not necessarily representative of all evaluations.D. the reader cannot accurately assess the airline without reading all the evaluations.Step-by-step explanation:
Using the most positive and the most negative comments to evaluate the airlines will not be an accurate measure of the airline because these are not a good enough sample. The opinions of those who fall in-between the most positive and negative should also be included as they could have some vital details as well.
Also, in order to be completely accurate, all the comments of the airline should have been posted because this would represent the entire population of comments and so would give the best assessment.
HELP QUICK I NEED ANSWER
Answer:
The answer is 23
Step-by-step explanation:
Answer:
the answer of the question is 23
Paul signs up for a new cell phone plan. He is offered a discount for the first five months. After this period, his rate increases by $8.50 per month. His total cost at the end of the year is $245.50. Paul wrote the following equation to represent his plan. 5x + 7(x + 8.50) = 245.50
Answer:
The first 5 months Paul paid $ 15.50, and in the next 7 months he paid $ 24.
Step-by-step explanation:
Since Paul signs up for a new cell phone plan, and he is offered a discount for the first five months, and after this period, his rate increases by $ 8.50 per month, and his total cost at the end of the year is $ 245.50, and Paul wrote the following equation to represent his plan: 5x + 7 (x + 8.50) = 245.50; To determine the value of X, the following calculation must be performed:
5X + 7 x (X + 8.50) = 245.50
5X + 7X + 59.50 = 245.50
12X + 59.50 = 245.50
12X = 245.50 - 59.50
12X = 186
X = 186/12
X = 15.50
Therefore, the first 5 months Paul paid $ 15.50, and in the next 7 months he paid $ 24.
Solve the inequality 0>_3x-2x
Answer:
x<0
Step-by-step explanation:
See image below:)
The height ofthe saddle ofa horse above the base ofa carousel can be modeled 4t by the equation f-rr) : 12 sin ^ r 42, where I represents seconds after the ride started. I How much time does to take for the horse to complete one cycle of motion and return to its starting height. What is the maximum height and the minimum height ofthe horse's saddle above the base ofthe carousel
Answer:
(a) The time to complete 1 cycle and return is 16/3
(b) The minimum height is 30 inches and the maximum is 54 inches
Step-by-step explanation:
Given
[tex]f(t)=12\sin(\frac{3\pi}{8}t) + 42[/tex]
Solving (a): Time to complete 1 cycle and return
This implies that we calculate the period.
This is calculated using:
[tex]T = \frac{2\pi}{w}[/tex]
Where:
[tex]w = \frac{3\pi}{8}[/tex]
So, we have:
[tex]T = \frac{2\pi}{3\pi/8}[/tex]
Rewrite as:
[tex]T = \frac{8*2\pi}{3\pi}[/tex]
[tex]T = \frac{16}{3}[/tex]
Solving (b): The maximum and the minimum height
To do this, we have:
[tex]-1 \le \sin(\theta) \le 1[/tex]
Which means:
[tex]-1 \le \sin(\frac{3\pi}{8}) \le 1[/tex]
So, the maximum and the minimum of [tex]\sin(\frac{3\pi}{8})[/tex] are:
[tex]\sin(\frac{3\pi}{8}) = -1[/tex] --- minimum
[tex]\sin(\frac{3\pi}{8}) = 1[/tex] --- maximum
Given that:
[tex]f(t)=12\sin(\frac{3\pi}{8}t) + 42[/tex]
So, the minimum height is:
[tex]h_{min} = 12 * -1 + 42 = 30[/tex]
The maximum is:
[tex]h_{max} = 12 * 1 + 42 = 54[/tex]
1 ÷ 7
pls help me
hi)
Answer:
7 lol
Step-by-step explanation:
self explanatory-
but you divide 1 by 7 you get 7
What’s the standard form for 1,000,000+80,000+30+3
Answer:
1080033
Step-by-step explanation:
=========================================
Explanation:
1,000,000 = 1 million
80,000 = 80 thousand
Adding those two would get us
1,000,000+80,000 = 1,080,000
Then we change those last two zeros at the end of "1,080,000" to 33 instead to get the final answer 1,080,033. This is done because we're adding 30+3 = 33 at the end.
----------------------
Extra info:
The number 1,080,033 is slightly over 1.08 million1,080,033 = 1 million, 80 thousand, 331,080,033 = one million, eighty thousand, thirty-threeThe use of commas between the words is optional. It's to give a sense of the pacing or pauses when reading out the number.What is the slope of the line through (-5, -10) and (-1, 5)
Answer:
Slope = 15/4
Step-by-step explanation:
Use the slope formula and you'll get the same answer.
Hope this helps:)
If x = -2, y = 3 and t = 2 then (x/y)t =
Answer:
-4/3
Step-by-step explanation:
2(-2/3)
= -4/3
Answer:
[tex]( \frac{x}{y} ) \times t \\ \frac{ - 2}{3} \times 2 \\ = \frac{ - 4}{3} [/tex]
Why are unit fractions important?
Answer:
Unit fractions play an important role in modular arithmetic, as they may be used to reduce modular division to the calculation of greatest common divisors. Specifically, suppose that we wish to perform divisions by a value x, modulo y. In order for division by x to be well defined modulo y, x and y must be relatively prime.
Step-by-step explanation: