a cylinder is inscribed in a right circular cone of height 2.5 and radius (at the base) equal to 7.5. what are the dimensions of such a cylinder which has maximum volume? radius
Answers
At that particular critical point, the second derivative needs to be negative in order to obtain the dimensions of the cylinder with the maximum volume. The values of the function that contain both variables are then substituted to obtain the dimensions.
A right circular cone with a height of 2.5 and a base radius of 7.5 inscribes the given cylinder.
Assume that h is the height and r is the radius of the cylinder. Using triangles that are similar, express h in terms of r as follows:
2.5/7.5 = 2.5-h/r
2.5r = 18.75 x 7.5 x 2.5 h = 2.5 x 1/3r
V= πr²h is the formula for the cylinder's volume.
As a result, only write the volume in terms of r.
V= r2h V= r2(2.5-1/3r)
V= 2.5πr² - 1/3πr³
As a result, the cylinder must have dimensions of r=5 and h=0.83.
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Related Questions
a car dealer buys a car for $500, gives it a clean new, is sold for $100. what is the percentage of loss
Answers
Answer:
Step-by-step explanation:
1. Find decrease.
If the car dealer bought the car for 100$ and only received 100$ for selling the car, he had 400$ in disadvantage!
2. Caculate Percent Loss:
400/ 500*100=
400/5=
80
There was a 80% decrease from the starting value!
Answer: 80% decrease!
Choose the correct property of addition to match the example.
3+4=7 4+3=7
Answers
The equation 3 + 4 = 7 and 4 + 3 = 7, shows the existence of Commutative Property of Addition.
What are Properties of Addition?
The properties of addition are the rules we can follow while adding numbers. Using these properties can make the calculation more straightforward and helps to solve complex problems in Math.
Solution:
Using Commutative Property of Addition the above mentioned equation can be solved.
Commutative Property of Addition - When we add two or more numbers, their sum is the same regardless of the order of the addends. We can write this property in the form of A + B = B + A.
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an experiment may have: a. only one outcome b. only two outcomes c. two or more outcomes d. several events
Answers
Using the concepts of probability, we got that an experiment may have d) several events
Event is called one or more outcomes of an experiment. Example of this is -rolling a dice, we get a possible outcomes as {1,2,3,4,5,6}.
In an experiment there can be one outcome, two outcomes, more than two outcomes or several outcomes.
An event is the collection of one or more of the outcomes of an experiment. An event that actually includes one and only one of the (final) outcomes for an experiment is called the simple event and is denoted by Ei.
Hence, an experiment may have d)several events
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Aiden is replacing the tile in a rectangular kitchen. The length of the kitchen is nine feet shorter than three times its width, w. The perimeter of the kitchen is six times the width. If tiles cost $1. 69 a square foot, what is the total cost to tile the kitchen?.
Answers
Total cost to tile the kitchen =$273.78
Let the width of kitchen = w
The length of the kitchen is nine feet shorter than three times its width, w = 3 w-9 equation-----1
The perimeter of the kitchen is six times the width = 6 w
= 2(length+width) =6 w equation----2
from equation 1 and 2
= 2(3 w-9+w) = 6 w
= 6 w-18+2 w = 6 w
2 w = 18
w = 9
Length = 3 w-9
length = 3×9-9
length = 18
Area of kitchen = length×width
= 18×9
= 162 square foot
Cost of tiles per square = $1.69
Total cost to tile the kitchen = Area of kitchen × cost of tiles per square
= 162×$1.69
=$273.78
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If the tiles cost $1.69 a square foot, the total cost to the tiles of the kitchen is $273.28.
According to the question:
Let the width be = x
Then, the length of the rectangular kitchen is L = 3x - 9
The perimeter is = 6x
It is given that the cost of the tile = $1.69 a square foot.
Then the total costs of tiles the kitchen is :
The Perimeter of the rectangle = 2(L + b)
The Perimeter of the rectangle = 2(3x - 9 + x)
The Perimeter of the rectangle = 2(4x-9)
We know that, according to the question,
the perimeter of the kitchen is six times the width = perimeter of rectangle
⇒ 6x = 8x - 18
⇒ - 2x = - 18
⇒ x = 18/2
⇒ x = 9
Thus, the width = x = 9 feet
Putting the value of x = 9
then, The length = 3x - 9 = 3(9) - 9
the length = 27 - 9
the length = 18 feet
Therefore, as we know that,
Area = Length × Width
Area = (18 × 9) feet
Area = 162 square feet.
Now,
Cost of a Tile = $1.69 per sq. ft.
Thus,
Total Cost of tile = $1.69 × 162
Total Cost of tile = $273.28
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Given s(x) = 2x - 3 and t(x) = 5x + 4. Find the formula and domain for v(x) = and w(x) =.
Answers
With the exception of x=4/5, the domain of s(x) over t(x) is all real numbers. Except when x=-3/2, all real numbers fall within the domain of w(x).
Given,
The value of the independent variable, often x, for which the supplied function is specified is the domain of a function.
When the value of the denominator falls to zero, a function that is composed of the fraction of two polynomials is not defined.
The numerator of t(x) should not be zero since the domain of s(x) over t(x) will be all real integers except the numerator of zero.
t(x) = 0
5x + 4 = 0
5x = -4
x = -4/5
With the exception of x=-4/5, all real numbers fall into the domain of s(x) over t(x).
Similar to w(x), s(x) should not be zero because the domain of w(x) will be all real numbers except for the one that makes the denominator equal to zero.
s(x) = 0
2x - 3 = 0
2x = 3
x = 3/2
With the exception of x=-3/2, all real numbers fall within the domain of w(x).
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consider the continuous random variable x, which has a uniform distribution over the interval from 30 to 38. the probability that x will take on a value between 34 and 35 is . a. 0.125 b. 0 c. 1 d. 0.875
Answers
Probability that a continuous random variable (x) will take on a value between 34 and 35 is 1/8
Uniform distribution is a type of probability distribution which consists constant probability.
It is also known as Rectangular distribution and
denoted by U( x,y ) .
let X be a continuous random variable then
X ~ U( x,y) where x is maximum value and y is minimum value .
Probability density function of uniform distribution is f(X) = 1/(b-a) , where
b---> maximum value , a---> minimum value
we have provided the interval of uniform distribution as 30 to 38 i.e b = 38 , a = 30
then , f( X) = 1/ (38-30) = 1/8
Probability that X will take on value between c and d is
P ( c ≤X≤ d ) =( d -c )/ (b-a )
Probability that X will take on a value between 34 and 35 is
P ( 34≤X≤35) = ( 35-34)/ 8 = 1/8
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Mrs. Nicholas baked two batches of cookies. The first batch consisted of 120 gingerbread cookies and the second batch consisted of 150 shortbread cookies. Mrs. Nicholas saved the same fraction of cookies from each batch. If Mrs. Nicholas saved 20 more shortbread cookies than gingerbread cookies, what fraction of the cookies did she save?
I know the answer, but I don't know how to solve.
Answers
2/3 of cookies were she saved.
What is Fraction?A fraction represents a part of a whole.
The first batch consisted of 120 gingerbread cookies
Second batch consisted of 150 shortbread cookies.
And, the same fractions of cookies from each batch were saved.
Let x parts of each of cookies were saved.
Then The number of the saved gingerbread cookies = 120 x
While, The number of the saved shortbread cookies = 150 x
150x-120x=20
30x=20
x=20/30
x=2/3
Hence 2/3 of cookies were she saved.
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Jan enters a 20-foot by 30-foot rectangular room.The long sides face north and south.Jan enters exact center of the south side and walks 10 feet north.Then she walks 8 feet east.How far is she from the east side of the room.(Please explain it in 5th grade terms)(I lied about me being in high school)
Answers
The parallel must be the 20 side
20/2 = 10 = center
So from south , Jan walks 10 forward and turns 8 foot east
Since she started in the middle already only 10 foot counts
So 10-8 = 2 foot away from east side
Hope that made sense!
I have a diagram explaining it too
You can use indirect measurement to estimate the height of a flag pole. First measure your distance from the base of the flagpole and the distance from the ground to a point on the flag pole that you are looking at. Maintaining the same angle of sight, move back until the top of the flag pole is in your line of sight. Explain why AABC and ADBE are similar. a. b. What is the height of the flagpole? E 7.5 ft Bi AT 4.5 ft 51-22 ft- D T 4.5 ft
Answers
The height of the flagpole is 17.7 ft after applying the concept of the similarity of triangles.
What is the similarity law for triangles?It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
It is given that:
You can use indirect measurement to estimate the height of a flag pole.
Given:
AC || DE
The common angle: Angle B = Angle B
Angle BAC = Angle BDE
Triangle ABC = Triangle DBE (By AA rule)
BC/BE = BA/BD
(7.5 - 4.5)/BE = 5/22
BE = 13.2
The height of the flag pole
h = BE + 4.5 = 13.2 + 4.5 = 17.7 ft
Thus, the height of the flagpole is 17.7 ft after applying the concept of the similarity of triangles.
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Solve the system of linear equations by graphing.
- 6x - y = -8
1/2Y = 4-3x
Answers
Answer:
[tex]x=\frac{-8+y}{6}[/tex]
Step-by-step explanation:
Let us evaluate this problem.
First, add Y to both sides
[tex]-6x-y+y=-8+y[/tex]
Always remember to simplify.
[tex]-6x=-8+y[/tex]
Divide both sides by -6
[tex]\frac{-6x}{6} =\frac{8}{-6} +\frac{y}{-6}[/tex]
Simplify one more time.
[tex]x=\frac{-8+y}{6}[/tex]
Your final answer is:
[tex]x=\frac{-8+y}{6}[/tex]
Need help asap. Simplify the expression 4/x-3/x show work
Answers
Answer:
1/x
Step-by-step explanation:
2
2 points
If I || m, find the value of x and y.
(7x + 12)
(12x - 28)
(9y-77)"
m
Answers
If I || m, find the value of x and y.
Given (7x + 12)
(12x - 28)
(9y-77)
What does the term " l || m " represents?
This term indicates that the line 'l' is parallel to the line 'm'.
It can be seen that, ∠(7x + 12) and ∠(12x - 28) from alternate interior angles as line 'l' and 'm' are parallel. These angles will be equal to each other. Therefore, we can write -
7x + 12 = 12x - 28
12x - 7x = 12 + 28
5x = 40
x = 8
Now, ∠(12x - 28) and ∠(9y - 77) form a straight angle. Therefore, we can write -
(12x - 28) + (9y - 77) = 180
(12 x 8 - 28) + (9y - 77) = 180
68 + 9y - 77 = 180
9y = 180 + 9
9y = 189
y = 21
Hence the answer is, the values of [x] and [y] will be 8 and 21 respectively.
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What is the domain of the exponential function y = 8^x+2?
Answers
hola buenas tardes como está el día de hoy ? yo estoy bien gracias por preguntar, espera...hablas español verdad...?
Answer: All real numbers
Step-by-step explanation: It is pretty simple. Just see if the x can be undefined. In this case x works with every number. So, it's all real numbers
Two angles of a quadrilateral measure 260° and 15º. The other two angles are in a ratio of 7:10. What are the measures of those two angles?
Answers
The measures of those two angles are 35° and 50°.
How to calculate the angle?It's important to note that the sum of angles on a quadrilateral is 360°. In this case, two angles of a quadrilateral measure 260° and 15º.
The remaining angles will be:
= 360° - (260° + 15°)
= 85°
Since the other two angles are in a ratio of 7:10, the measure will be:
= 7 / (7 + 10) × 85°
= 7/15 × 85°
= 35°
Also, 10/17 × 85°
= 50°
The angles are 35° and 50°.
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Four friend go out to eat and their meal cot $86. 50. The ale tax i 6. 75% and they hould tip the waiter 20%. How much do they have to pay?Round to the nearet cent
Answers
Four friends go out to eat and their meal cost $86. 50. The sales tax 6. 75% and they should tip the waiter 20%.each person must pay $27.7 for their meal
Four friends go out to eat and $86.50 for their meals.
The sales tax is 6.75%, and the waiter is tipped 20%.
M = 86.5 * 10675 / 10000 = 92.34
92.34$, and the total amount of money that four friends will give, including waiter tip, is
T=92.35 * 120 / 100 = 110.80
and each person must give
110.8/4= $27.7
each person must pay $27.7
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Find the inverse of the function y=2x+8
Answers
The inverse function of the given is [tex]y^-1[/tex]= [tex]\frac{x}{2}[/tex]-4 .
What is inverse function?
The domain of the original function becomes the range of the inverse function, and the range of the given function becomes the domain of the inverse function. The inverse function is denoted by the notation f-1 in relation to the original function f. Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function. Only when f is both a one-one and an onto function does it have an inverse, indicated by the symbol f-1. Keep in mind that f-1 is NOT f's inverse. The domain value of x is given by combining the function f and the reciprocal function f-1.
Here the given function is,
=> y = 2x+8
Now interchange x and y then
=> x=2y+8
Now simplify the expression with respect to y then,
=> x-8=2y
=> y = [tex]\frac{x}{2}[/tex]-4
=>[tex]y^-1[/tex]= [tex]\frac{x}{2}[/tex]-4
Hence inverse function is [tex]y^-1[/tex]= [tex]\frac{x}{2}[/tex]-4 .
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A company claims that the mean weight per apple they ship is 120 grams with a standard deviation of 12 grams. Data generated from a sample of 49 apples randomly selected from a shipment indicated a mean weight of 122. 5 grams per apple. Calculate and interpret a 95% confidence interval for the mean weight per apple.
Answers
The 95% confidence interval for the average apple weight is (119.14, 125.86).
Given info,
The average weight per apple, according to one manufacturer, is 120 grams, with a standard deviation of 12 grams. The average weight per apple, according to data produced from a sample of 49 apples drawn at random from a shipment, was 122. 5 grams.
Let,
n = 49
x = 122.5
σ = 12
To calculate and interpret a 95% confidence interval for the mean weight per apple;
∴ A 95% confidence interval is given by,
(x ± 1.96*σ/√n)
(122.5 ± 1.96*12/√49)
(119.14, 125.86)
Hence, a 95% confidence interval for the mean weight per apple is (119.14, 125.86).
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11. Tia drives 127 miles a week. Mac drives 23 times as many miles as Tia a week. How many miles does Mac drive a week?
Answers
Answer:
He drives 2921 a week.
Step-by-step explanation:
If Tia drives 127 miles in a week, and Mac drives 23 times as many miles as Tia, then we multiply. 127x23=2921.
Hope this helped :)
What did I do wrong?
Answers
Step-by-step explanation:
I gone through your work and I don't see anything wrong.
Try reaching out to your teacher.
Answer:
You answered every question correctly. All ten of them. The program you are using has some issues. lol
Step-by-step explanation:
[tex]\sf x+ (-9) =-18[/tex]
what's the value x ?
Answers
Answer:
x = -9
Step-by-step explanation:
Below:-
Answer:
x = -9
Step-by-step explanation:
Given equation,
→ x + (-9) = -18
Now the value of x will be,
→ x + (-9) = -18
→ x - 9 = -18
→ x = -18 + 9
→ [ x = -9 ]
Hence, the value of x is -9.
Simplify 1 over 6x + 3 over 4 ( 1 over 2x - 4)
Answers
The after simplification of the expression 1 over 6x + 3 over 4 ( 1 over 2x - 4), we get (26 - 144)/48x.
We need to simplify 1 over 6x + 3 over 4 ( 1 over 2x - 4)
1/6x + 3/4 (1/2x - 4)
1/6x +3/4 ((1 - 8x)/2x)
1/6x + (3 - 24x)/8x
(8 + 6(3 - 24x))/(6x8) x
(8 + 18 - 144x)/48x
(26 - 144)/48x
Therefore, the after simplification of the expression 1 over 6x + 3 over 4 ( 1 over 2x - 4), we get (26 - 144)/48x.
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A board 65 inches long is sawed into two pieces. One of the pieces in 7 inches shorter than twice the length of the other piece. Find the length of the two pieces.
Answers
Answer:
24 and 41 inches.
Step-by-step explanation:
Let the lengths of the two pieces be a and b.
The total length of the two-piece should be the length of the original board.
Therefore:
a + b = 65
One piece, say b, is 7 inches shorter than twice the length of the other, a.
Therefore, we can write the following equation:
b = 2a - 7
The “2a” represents the twice, and the “-7” represents the 7 shorter inches.
We now have a system of equations:
a + b = 65
b = 2a - 7
We can solve using substitution. Substitute the second equation with the first. Hence:
a + (2a - 7) = 65
Combine like terms:
3a - 7 = 65
Add 7 to both sides:
3a = 72
Divide both sides by 3:
a = 24
So, the shorter piece is 24 inches.
Then, we can use our second equation again:
b = 2a - 7
Since we now know a substitute 24 for a and evaluate. Hence:
b = 2(24) - 7
= 48 - 7
= 41
Therefore, the length of the other two pieces is 24 and 41 inches.
5.1 contracts for two construction jobs are randomly assigned to one or more of three firms, a, b, and c. let y1 denote the number of contracts assigned to firm a and y2 the number of contracts assigned to firm b. recall that each firm can receive 0, 1, or 2 contracts. a find the joint wackerly, dennis; mendenhall, william; sheaffer, richard l.. mathematical statistics with applications (p. 232). cengage textbook. kindle edition.
Answers
The solutions are;
The joint probability of y1 and y2 is [tex]\left[\begin{array}{ccc}0\\1\\2\end{array}\right][/tex][tex]\left[\begin{array}{ccc}1/9&2/9&1/9\\2/9&2/9&0\\1/9&0&0\end{array}\right][/tex] and F(1,0) = 1/3.
Given data;
Let y1 signify the number of contracts awarded to firm a and y2 the number of contracts assigned to firm b. Recall that each firm can receive 0, 1, or 2 contracts. Contracts for two construction tasks are randomly assigned to one or more of three firms, a, b, and c.
To find,
(a) The joint probability function for y₁ and y₂
Let y₁ denote the number of contracts assigned to firm A,
y₂ the number of contracts assigned to firm B
y₁
[tex]\left[\begin{array}{ccc}0&1&2\\\\\end{array}\right][/tex]
y₂
[tex]\left[\begin{array}{ccc}0\\1\\2\end{array}\right][/tex][tex]\left[\begin{array}{ccc}1/9&2/9&1/9\\2/9&2/9&0\\1/9&0&0\end{array}\right][/tex]
(b) Find F(1,0)
F(1,0) = p(y₁ ≤ 1, y₂ ≤ 0)
= p(0,0) + p(1,0)
= 1/9 + 2/9
= 1/3.
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I really need help for interpreting the remainder. Here is the question.
The student in class of 24, share 48 apple slices end 36 orange slices equally among them. How many pieces of fruit did each student get.
Whoever is going to be answering this question, please give me a valid answer and show your work
Answers
Answer:
so that means they would each get 2 and a half of apple and orange slices
Step-by-step explanation:
48 ÷ 24 =2
36 ÷ 24 =1.5
=2 1.5
Simplify:
[tex]\frac{4-i\sqrt{2}}{4+i\sqrt{2}}[/tex]
Answers
(7-4i)√2/7 is the simplified form of (4-i√2)/(4+i√2)
What is complex number?a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit
The given expression is
(4-i√2)/(4+i√2)
Now we have to rationalize the above expression
((4-i√2)/(4+i√2))×((4-i√2)/(4-i√2))
(4-i√2)(4-i√2)/(4+i√2)(4-i√2)
16-4i√2-4i√2-2/16-2
16-8i√2-2/14
14-8i√2/14
2(7-4i√2)/2(7)
(7-4i)√2/7
Hence (7-4i)√2/7 is the simplified form of (4-i√2)/(4+i√2)
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Steven's birthday party will cost $168 if he invites 14 guests. If there are 59 guests, how much will Steven's birthday party cost? Solve using unit rates.
Answers
explanation:
we want to find out how much it is a person first so
168/14= $12
so it’s $12 per person
now we want to find how much it will be for 59 guests
so 12x59= $708
hope this helps <3 have an amazing night :)
Question
Forty-five people are going on a road trip. Each car seats 5 people.
How many cars are needed for 45 people?
Answers
9 cars are needed
1. Write this math statement as an algebraic expression:
The sum of one half of an unknown value and three times itself.
Answers
Answer:
Step-by-step explanation:
n = some unknown natural number
n/2 = half of that natural number
n-1 = number right before the unknown natural number
2*(n-1) = twice the number before the natural number n
it would be great if someone could help me with these please?
Answers
Answer:
Find the angle measurement like a 90 degree angle or something for both of them and then find the solution following it. If you need further help post the question with the name where these questions are posted!
PLEASE GIVE BRAINLIEST THANK YOU!!!
what is 3/36 times 60
Answers
Answer:
5
Step-by-step explanation:
Answer: The answer to that would be 5.
Step-by-step explanation:
Hope this helps!