The height is 2 and radius is √2 of the largest right circular cylinder that can be put into a sphere of radius √3.
What is circular cylinder?A cylinder whose bases are circular in shape and parallel to each other is called the right circular cylinder. It is a three-dimensional shape.
Given that the radius of a sphere R = √3
Let the radius of the cylinder is r and the height of the cylinder is h.
than.
r² = R² − h²/4
and Vc = πr²h
⇒ Vc = π(R² − h²/4)h
⇒ Vc = πR²h − πh³/4
dVc/dh = πR² − 3πh²/4
(dVc/dh)R=√3 = 3π − 3πh²/4
For maximum or minimum volume,
dVc/dh = 0
⇒ 3π − 3πh²/4 = 0
⇒ 3πh²/4 = 3π
⇒ 3πh² = 3π*4
⇒ h² = 4
⇒ h=2
Also, dVc/dh changes sign from positive to negative in the neighborhood of h=2. Hence, h=2 is a maximum point.
r² = R² − h²/4
⇒ r² = (√3)² - 2²/4
⇒ r² = 3 - 1
⇒ r² = 2
⇒ r = √2
So, the height is 2 and radius is √2 of the largest right circular cylinder
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What is a point that divides a line segment into 2 equal parts called?
Answer: Midpoint
Step-by-step explanation:
what are the four conditions necessary for x to have a binomial distribution? mark all that apply.
Characteristic of binomial distribution Mean should be n *p n is the number of trials p is the successful outcome of the process
a set number of trials, such as three rolls of the dice or five flips of the coin.Each trial can either be successful or unsuccessful. Note that the example with the die seems to have six possible outcomes. We must take into account options like "get a 6" (success) or "not obtain a 6." (failure).The likelihood of success must be constant (equal for every try). P(6) = 1/6 for each roll of the die in the example.The trials are separate. The likelihood of success in future trials is unaffected by the outcome of the first.Know more about binomial at:
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Can anyone help me with the answer. Sorry if it’s hard to see , please just zoom in
Answer:
NOLO
Step-by-step explanation:
Graph the line that represents a proportional relationship between ddd and ttt with the property that an increase of 555 units in ttt corresponds to an increase of 222 units in ddd. What is the unit rate of change of ddd with respect to ttt
a) The unit rate of change of d with respect to t is equal to 1.6
b) the graph of the line in the attached figure.
Given: A proportionate relationship between d and t with the characteristic that a rise in t of 5 units causes a rise in d of 8 units.
To locate: A rise of 5 units in t causes a rise of 8 units in d, according to the line's unit rate of change with respect to t.
=> Slope = Δd/Δt = 8/5 = 1.6
the proportional relationship between d and t
=> d ∝ t
=> d = 1.6t
t d=1.6t
0 0
1 1.6
2 3.2
3 4.8
Plot the points and draw a line passing through points.
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.11 and the probability that the flight will be delayed is 0.14. The probability that it will not rain and the flight will leave on time is 0.82. What is the probability that it is raining if the flight has been delayed? Round your answer to the nearest thousandth.
The probability that the flight would be delayed when it is not raining is 12.46%.
What is probability?Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. Probability measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.
To determine what is the probability that the flight would be delayed when it is not raining, the following calculation must be performed:
Probability that it will not rain = 1 - probability that it will rain
X = 1 - 0.11
X = 0.89
Probability that the flight would be delayed when it is not raining = probability that it is not raining x probability that the flight will be delayed
X = 0.89 x 0.14
X = 0.1246
0.1246 x 100 = 12.46
Therefore, the probability that the flight would be delayed when it is not raining is 12.46%.
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How do I do this help me please
Answer: A. p + 3 = 49
B. p = 46
Step-by-step explanation:
A. represents the equation that represents the word problem. In this case, the original number of paintbrushes Kaitlyn had is represented by (p) and Claire gives her 3 more paintbrushes, the total number of paintbrushes she has is 49.
B. represents the original number of paintbrushes Kaitlyn had. To find this, we can simply solve the equation from part A for (p) by isolating it on one side of the equation.
Therefore, Kaitlyn originally had 46 paintbrushes.
Between what two consecutive integers does the square root of 12 lie
The two consecutive integers that the square root of 12 lies between are 3 and 4.
How to find the integers ?Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. This therefore means that integers can only be whole numbers and consecutive integers follow each other. For instance, 1, 2, and 3 are consecutive integers.
To find the two consecutive integers that the square root of 12 lies between, find the square root of 12 :
= √ 12
= 3.46
This means that the lower integer would be 3 and the consecutive integer following would be 4.
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Ages Numbers of students 15-18 2 19-22 7 23-26 5 27-30 5 31-34 6 35-38 3 Based on the frequency distribution above, find the relative frequency for the class with lower class limit 27 Relative Frequency =%Give your answer as a percent, rounded to one decimal place
Relative frequency for the class with lower class limit 27 is 20.0%.
To find the relative frequency for the class with lower class limit 27, we must first find the total frequency of the data set. The total frequency is 28 (2+7+5+5+6+3=28). Since the class with lower class limit 27 has a frequency of 5, we can calculate the relative frequency of this class by dividing the frequency of the class by the total frequency.
Formula:
Relative Frequency = (Number of Students in the Class)/(Total Number of Students in the Group) x 100
Relative Frequency = (5)/(28) x 100
Relative Frequency = 0.1786 x 100
Relative Frequency = 17.86%
Rounded to one decimal place, Relative Frequency = 20.0%.
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Becky has 14 pints of pudding. How many cups of pudding does she have?
Answer:
28 cups
Step-by-step explanation:
[tex]\frac{2}{1}[/tex] = [tex]\frac{x}{14}[/tex]
1 x 14 = 14, so 2 x 14 = 28
I messed up on the last one by like 2 more then I put can someone explain how to do this
Answer:
m∠TQR = 80°------------------------------------
If you add a parallel line through the point Q, then angle TQR will be divided by two angles.
One of them is congruent to ∠STQ and another one is congruent to ∠PRQ as alternate interior angles.
Therefore:
m∠TQR = m∠STQ + m∠PRQ m∠TQR = 45° + 35° m∠TQR = 80°f(n)=n+3
g(n)=2n-4
Find (fog)(-3)
Answer:
-7
Step-by-step explanation:
(fog)(-3) = f(g(-3)) = f (2(- 3) - 4) = f(-10) = -10 + 3 = -7
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Given the following point on the unit circle, find the angle, to the nearest tenth of a
degree (if necessary), of the terminal side through that point, 0° ≤ 0 < 360°.
P=
√15
5
√10
5
Answer:
60°
Step-by-step explanation:
To find the angle of the terminal side through a point P on the unit circle, we can use the coordinates of the point. The angle is given by the inverse tangent (atan) of the y-coordinate divided by the x-coordinate.
The point P is given as (√15/5, √10/5)
Using the arctan function we have:
theta = arctan(√10/5/√15/5) = arctan(√2/√3)=atan(√2/√3) = pi/3
The angle theta is in radians, to convert it to degree we multiply it by 180/pi
Theta = (pi/3) * (180/pi) = 60. Therefore, the angle of the terminal side through the point P is 60°.
Two APs have same common difference. If the first term is -1 and that of the other is -8. then the difference between their 4th term is?
Answer:
7
Step-by-step explanation:
Let the common difference of the two APs be" D"
Let 1st term of 1st AP be A₁ i.e = -1
And the first term of the second AP b₁ i.e = -8
We know that the nth term of an AP is;
an = a+(n-1)d
4th term of first AP,
a₁ + (4-1)d = − 1 + 3d. --Eqn. 1
And 4th term of the second AP,
b₁ + (4-1) d=-8+ 3d -- Eqn 2
Now, the difference between their 4th terms is i.e.
= (- 1+ 3d ) - (-8 + 3d )
= -1 + 3d + 8 - 3d = 7
So, the answer is 7.
suppose you are offered one slice from a round pizza, that is, a sector of a circle, and the slice must have a perimeter of 32 inches. what diameter pizza will produce the largest slice?
On solving the provided question, we can say that D, diameter pizza will produce the largest slice is 16
what is diameter?Any straight line segment with an endpoint on the circle and that travels through its center is considered a circle's diameter in geometry. The longest chord of a circle is another way to describe it.
Let r be the radius and be the angle of a circle.
According with the graph, the area of the sector is given by
A = 1/2r^2∅
The arc length of a circle with radius r and angle∅ is r∅
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches.
Thus the perimeter has length
2r + r∅ = 32 in
r∅ = 32 - 2r
∅ = 32- 2r / r
Now,
A = 1/2r^2[32- 2r / r]
A = 16r - r^2
A' = 16 - 2r 16 -2r = 0
r = 8
A" = -2
so, D, diameter pizza will produce the largest slice is 16
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if the radius of a circle is 12 ft what is the area in terms of π
Step-by-step explanation:
The area of a circle is radius²· π
12x12=144
So the answer is 144π.
Answer:
37.71428571425567788
A large church has a niche in one wall. On the floor plan it appears as a semicircular indentation of radius 2.60 m. A worshiper stands on the center line of the niche, 1.70 m out from its deepest point, and whispers a prayer. Where is the sound concentrated after reflection from the back wall of the niche
40m is the sound concentrated after reflection from the back wall of the niche.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
with radius 2.60m , the cylindrical wall is a highly efficient mirror for sound , with focal length
f = R/2 = 2.60/2 = 1.30
in a vertical plane the sound disperses as usual butthat radiated in a horizontal plane is concentrated in a soundimage at a distance q from the back of niche ,
so 1/p+1/q = 1/f
so 1/1.70 +1/q = 1/1.3
1/q = 1/1.3 - 1/1.70
q = 40m
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A regular tetrahedron is a pyramid with four faces, each of which is an equilateral triangle. Let $ABCD$ be a regular tetrahedron and let $P$ be the unique point equidistant from points $A,B,C,D$. Extend $\overrightarrow{AP}$ to hit face $BCD$ at point $Q$. What is the ratio $PQ/AQ$
On solving the provided question, we can say that the unique point equidistant from points in tetrahedron are PQ/AQ = 3/8
what is tetrahedron?A polyhedron with four triangular faces, six straight edges, and four vertex corners is known as a tetrahedron in geometry, also known as a triangle pyramid. The only regular convex polyhedron with fewer than five faces is the tetrahedron, which is also the simplest of them all. Tetrahedra make up the pyramid at the bottom of the triangle. It is a tetrahedron if it has four faces that are triangular in shape. Regular tetrahedrons are those that have isosceles triangles for their faces and equilateral triangles for their bases. with four sides, a polyhedron
here,
the unique point equidistant from points
PQ/AQ = 3/8
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Okay so like yeah can u help me
Answer:
1.2
Step-by-step explanation:
[tex]\frac{v}{5}[/tex] = [tex]\frac{3}{13}[/tex] Cross multiply and solve for v
13v = 15 Divide both sides by 13
[tex]\frac{13v}{13}[/tex] = [tex]\frac{15}{13}[/tex]
v = 1.2 rounded to the nearest tenth
Why this works
[tex]\frac{v}{5}[/tex] = [tex]\frac{3}{13}[/tex] we can clear the fraction by multiplying both sides of the equal sign by (5·13)
[tex]\frac{(5x13)}{1}[/tex] · [tex]\frac{v}{5}[/tex] = [tex]\frac{(5x13)}{1}[/tex] ·[tex]\frac{3}{13}[/tex] On the left of the equal sign the 5's cancel out and the on the right of the equal sign the 13's cancel out.
13v = 5(3)
13v = 15
The value of a ring ($1000) increases exponentially so that it has a value of $3,000 after 5 years. Find the rate.
Answer: [tex]\sqrt[5]{3}-1[/tex]
Step-by-step explanation:
Let the annual rate of increase be [tex]r[/tex].
[tex]3000=1000(1+r)^5\\\\3=(1+r)^5\\\\\sqrt[5]{3}=1+r\\\\r=\sqrt[5]{3}-1[/tex]
june has 27 coins, made up of quarters and dimes. in total, the coins are worth $4.20. how many quarters and how many dimes does she have?
June has 27 coins, made up of quarters and dimes. in total, the coins are worth $4.20. Therefore, there are 10 quarters and 17 dimes she have.
Dime Coin:
A cent is a dime in US parlance, one tenth of the US dollar, and is officially called a "one cent". The name was first authorized by the Money Act of 1792.
The 10-cent coin is the smallest in diameter and the thinnest US coin in circulation, measuring 17.91 mm (0.705 inches) and 1.35 mm (0.053 inches) in diameter thickness. The obverse of the current cent features a profile of President Franklin D. Roosevelt, while the reverse depicts, from left to right, an olive branch, a torch, and an oak branch.
Quarter Coin:
The quarter (short for quarter dollar) is a United States coin denominated in 25 cents (quarter dollar). The obverse of the coin depicts George Washington in profile, and since 1998 the design of the reverse has changed frequently. In continuous production from 1796 to 1831. 955 inches (24.26 mm), 0.069 inches (1.75 mm) thick. The current version consists of two layers of cupronickel (75% copper, 25% nickel) plated on a pure copper core. The overall composition of the coin is 8.33% nickel and 91.67% copper, as the cupronickel layer accounts for 1/3 of the total weight. Its weight is 0.1823 troy ounces or 0.2000 regular Dupo ounces (5,670 grams).
We can consider that:
Let d = the number of dimes
Let q = the number of quarters
Now,
d + q = 27 -------------------------- (1)
⇒ d = 27 - q
⇒ 0.10d + 0.25q = 4.20 -------------------------- (2)
Multiply both sides of this equation by 100 to get rid of the decimal points.
10d + 25q = 420
⇒ 10(27- q) + 25q = 420
⇒ 270 - 10q + 25q = 420
⇒ 15q = 150
⇒ q = 10
Now, Putting the value of q = 10 in equation (1) :
d + 10 = 27
⇒ d = 27 - 10
⇒ d = 17
Therefore, there are 10 quarters and 17 dimes she have.
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it takes 3 people 12 hours to paint a room. How long would it take 1 person to paint the same room?
Answer:
36 hours
Step-by-step explanation:
3 x 12 = 36
Answer:
36 hours
Step-by-step explanation:
if it took 3 people to paint a room in 12 hours, we have,
3 people = 12 hours
divide by 3. multiply by 3
1 person = 36 hours.
If A(2, 3) and B(-4, -6), find AB. Round to the nearest tenth.
Write the slope-intercept form of the equation of each line.
7) y - 9 =2/3 (x + 6)
8) y + 4 = 8(x - 2)
Answer:
7) y = [tex]\frac{2}{3}[/tex]x + 13
8) y = 8x - 20
Step-by-step explanation:
Question 7
y - 9 = [tex]\frac{2}{3}[/tex](x + 6)
Step 1: Distribute [tex]\frac{2}{3}[/tex] to (x + 6); y - 9 = [tex]\frac{2}{3}[/tex]x + 4
Step 2: Add 9 to both sides; y = [tex]\frac{2}{3}[/tex]x + 13
Question 8
y + 4 = 8(x - 2)
Step 1: Distribute 8 to (x - 2); y + 4 = 8x - 16
Step 2: Subtract 4 from both sides; y = 8x - 20
3x + 3y = 3
\y=-1/x+2
y=-2
y = 0
y = 3
y = 1
Answer: [tex]y=3[/tex]
Step-by-step explanation:
The intersection point of the graphs is the solution. So, you need to find the [tex]y[/tex]-coordinate of the intersection point.
the radius of a sphere is decreasing at a constant rate of 6 feet per second. at the instant when the volume of the sphere is 163163 cubic feet, what is the rate of change of the volume? the volume of a sphere can be found with the equation v
865.96 is the rate of change of the volume. This can be solved using the concept of rate of change of the volume.
What is volume of sphere?The volume of a sphere is the maximum volume of air that may be contained within it. Volume of sphere = 4/3 πr³ is the formula for computing the volume of a sphere of radius "r."
As we know,
volume (V) = 4/3 πr³
Given that,
volume of the sphere is 163 cubic feet
the radius of a sphere is decreasing at a constant rate of 6 feet per second (dr/dt) = 6
So, 163 = 4/3 × 22/7 r³
or, r³ = (3423/88)
or, r = [tex][\frac{3423}{88}]^{1/3}[/tex]
again, dv/dt = 4/3 × π × 3 r² × dr/dt
or, dv/dt = 4 × π × r² × dr/dt
or, dv/dt = 4 × 22/7 ×[tex][\frac{3423}{88}]^{2/3}[/tex] × 6
or, dv/dt = 75.43 × [tex][\frac{3423}{88}]^{2/3}[/tex]
or, dv/dt = 865.96
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PLS HELP DUE TOMORROW!! PLSS
The shaded region corresponding to all values of x and y that satisfy these requirements is shown the graph
How do we make graph of a function?Suppose the considered function whose graph is to be made is
f(x)
The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values
f(x)
are plotted on the vertical axis.
They are together plotted on the point
(x,y) = (x, f(x))
This is why we usually write the functions as:
y = f(x)
Therefore, the graph is given with shaded region
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Nikhil and Mae work at the same company. Nikhil has been at the company 4 times as long as Mae. Nikhil's time at the company is 8 more than 2 times Mae's time. The following system of equations models the scenario:
x = 4y
x = 8 + 2y
How many years has each person been employed by the company?
Nikhil has been with the company for 16 years, while Mae has been there for 4 years.
Nikhil has been with the company for 24 years, while Mae has been there for 6 years.
Nikhil has been with the company for 20 years, while Mae has been there for 5 years.
Nikhil has been with the company for 12 years, while Mae has been there for 3 years.
Answer:
1) Nikhil 16 years & Mae 4 years
Step-by-step explanation:
x = 4y {equation 1}
Hence, x - 4y = 0 { equation 2}
x = 8 + 2y {equation 3}
Then, x - 2y = 8 { equation 4}
{equation 4-2}
x -x -2y - ( - 4y) = 8 -0
-2y +4y = 8
2y = 8
2 2
y = 4
By substituting { equation 1}
x = 4y
x = 4 × 4
= 16//
(Deleted Answer)
A 7x1 board is completely covered by mx1 tiles without overlap; each tile may cover any number of consecutive squares, and each tile lies completely on the board. Each tile is either red, blue, or green. Let N be the number of tilings of the 7x1 board in which all three colors are used at least once. For example, a 1x1 red tile followed by a 2x1 green tile, a 1x1 green tile, a 2x1 blue tile, and a 1x1 green tile is a valid tiling. Note that if the 2x1 blue tile is replaced by two 1x1 blue tiles, this results in a different tiling. Find the remainder when N is divided by 1000.
The remainder when N is divided by 1000 is 106.
What is the Principle of Inclusion-Exclusion?The Principle of Inclusion-Exclusion, often known as PIE, offers a method/formula for organizing information about the size of each set, the number of elements in the union of a given set of sets, and the size of all potential set intersections.
From the question,
First, we think about all the possible divisions of the 7×1 board. Since we require at least one tile of each color, we exclude the cases of just one or two pieces.
Three pieces = 5+1+1 , 4+2+1 , 4+1+2 etc (6C2) = 15 ways
Four pieces = 6C3 = 20
Five pieces = 6C4 = 15
Six pieces = 6C5 = 6
Seven pieces =6C6 = 1
Now, we apply the Principle of Inclusion-Exclusion to consider how many ways to color them:
Three pieces : 3³ - 3 × 2³ + 3 = 6
Four pieces: 3⁴ - 3 × 2⁴ + 3 = 36
Five pieces : 3⁵ - 3 × 2⁵ + 3 = 150
Six pieces : 3⁶ - 3 × 2⁶ + 3 = 540
Seven pieces : 3⁷ - 3 × 2⁷ + 3 = 1806
Adding them together, we get
15×6 + 20×36 + 15×150 + 6×540 + 1×1806 = 8106
Hence, the remainder when it is divided by 1000 is 106.
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Answer:
106
Step-by-step explanation:
Solve for X, Leave in simplest radical form.
Hope it helps.
If you have any query, feel free to ask.
Paul usually makes the 100 km journey to visit his family. The trip involves three separate stages:
a) A stage of 20 km that is travelled on small roads at a constant speed of 30 km/h.
b) A stage of 50 km that is travelled on the highway at a constant speed of 100 km/h.
c) A stage of 30 km that is travelled on standard roads at a constant speed of 40 km/h.
The length of the section of roadworks was 121 km.
What is the concept of time and distance?
Time is directly proportional to distance. It means that speed remains constant, if we have two vehicles moving two distances for two different time duration then the time is directly proportional to the distance. Speed is directly proportional to distance.
1) Total time = 1 hr 55 minutes
2) Distance = 121 km
To calculate Matthew's journey we have to use the formula of :
Time = distance /speed
Are doing the calculations for each Stage, like this:
Stage A, we know that:
Distance: 20 km
speed: 30 km/h
Time = 20/30
T = 2/3h
Time = 40 minutes
Stage B, we know that:
Distance: 50 km
speed: 100 km/h
Time = 50/100
T = 0.5 h
Time = 30 minutes
Stage C, we know that:
Distance: 30 km
speed: 40 km/h
Time = 30/40
T = 3/4 h
Time = 45 minutes
1) So using all the values calculated above, let's calculate the total value of the trip that will take place by:
Total = (40 + 30 + 45)minutes
Total = 115 minutes
Total = 1 hour 55 minutes
2) For the second part of this question we want to calculate the total distance of travel hours so:
Speed: 60 km/h
Time: 6 minutes + x
x =1 hr 55 minute + 6 minutes 2 hr 1 minute
Time = 2.01666667
Distance = speed * time
Distance = 60 * 2.01666667
Distance = 121 km
hence, the length of the section of roadworks was 121 km.
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