A right circular cylinder with the largest volume that can fit within a sphere with a 10 cm radius will have a maximum radius of 8.165 cm and a maximum height of 11.55 cm. Additionally, the largest volume is 2417.82 cm³.
What is cylinder?A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centers of the two bases. The height of the cylinder is "h," while the radius of the cylinder is "r," measuring the distance from the axis to the outside surface.
Here,
radius=10 cm
r²+h²/4=10²
r²=10²-h²/4
volume=πr²h
=π(10²-h²/4).h
V=π(10²h-h³/4)
dV/dh=π(10²-3h²/4)
dV/dh=0
10²=3h²/4
10²*2²/3=h²
20/√3=h
h=11.55 cm
r²=10²-h²/4
=10²-(10²*2²/3)/4
r²=(100-400/12)
r²=100-33.33
r²=66.67
r=√66.67
r=8.165 cm
volume=πr²h
=3.14*8.165*8.165*11.55
volume=2417.82 cm³
The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm will be 8.165 cm radius and 11.55 cm height. Also the maximum volume is 2417.82 cm³.
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the triangle has a perimeter of 65 feet. what system of equation to use for the perimeter equals 65 feet? l= 1/3m, m, and n=l+m-15
Answer:
l = 10 feet
m = 30 feet
n = 25 feet
Total Perimeter = 65 feet
Step-by-step explanation:
The perimeter of a trianlge is the sum of its three sides, and in this case is equal to 65 feet.
65 feet = l + m + n
l + m + n = 65
We also know that:
l = (1/3)m, and
n = l+m-15
Substitute these definitions of l and n into the original equation:
l + m + n = 65
[(1/3)m] + m + [l+m-15] = 65
[(1/3)m] + m + [[(1/3)m]+m-15] = 65
Simplify:
(1/3)m + m + (1/3)m + m - 15 = 65
2m + (2/3)m = 80
(6/3)m + (2/3)m = 80
(8/3)m = 80
m = 80*(3/8)
m = (10)*(3)
m = 30 feet
Since l = (1/3)m, l = 10 feet
Since n = l+m-15, n = 10 + 30 - 15, or 25 feet
The three sides are
l: 10 feet
m: 30 feet
n: 25 feet
Total = 65 feet
Which situation can be represented by the equation 56 = 2x -10? A. Sammy's age is 10 more than twice Ted's age. Sammy is 56 years old. How old is Ted? B. Sammy's age 10 decreased by twice Ted's age. Ted is 56 years old. How old is Sammy? C. Ted's age is twice Sammy's age decreased by 10 years. Ted is 56 years old. How old is Sammy? D. Ted's age is 10 less than twice Sammy's age. Sammy is 56 years old. How old is Ted?
Answer:
I'll try here: 23
Step-by-step explanation:
X = Sam's age.
X-10 = Ted's age
X + X -10 = 56
2X -10 =56
2x = 66
X = 33 , Sam's age
33 - 10 = 23 Ted's age
Which statements are not true and true?
statement 1: the sum of two negative integers is positive
Statement 2: the product of two negative integers is positive
Statement 3: the difference of two negative integers is positive
Statement 4: the quotient of two negative integers is positive
Find the distance between point P and line ℓ.
Line ℓ contains points (0, −3 ) and (7, 4). Point P has coordinates (4, 3).
The distance between the line containing the points (0,-3) and (7,4) and the point P(4,3) is d =√2 units.
What is the distance between a line and a point?The distance between the line ax +by +c =0 and the point (x₁, y₁) is given by:
[tex]d=\frac{|ax_{1}+by_{1}+c|}{\sqrt{a^2+b^2}}[/tex]
Given that, the line passes through the points (0,-3) and (7,4).
The equation of the line is given by:
[tex]y -(-3)=\frac{4-(-3)}{7-0}(x-0)\\\\y+3=x\\\\x-y-3=0[/tex]
Now, the distance between the line x - y - 3 = 0 and point (4,3) is:
[tex]d=\frac{|1\times4+(-1)\times3+(-3)|}{\sqrt{1^2 +(-1)^2}}\\\\d=\frac{2}{\sqrt{2}}\\\\d=\sqrt{2}[/tex]
Hence, the distance between the line containing the points (0,-3) and (7,4) and the point P(4,3) is d =√2 units.
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A line passes through point (-5,-1) and has a slope of -3.
Write an equation in Ax+By=C form for this line.
Use integers for A,B, and C.
Answer:
y+3x=-16
Step-by-step explanation:
y=mx+c
y=-3x+c
-3x is the gradient
-5 is the x value and -1 is the y value
-1=-3x-5+c
-1=15+c
-16=c
y=-3x-16
y+3x=-16
Edward did the following work to solve a system shown below. What does his answer mean?
Answer:
see explanation
Step-by-step explanation:
After solving a system of equations.
the solution is
36 = 32 ← not possible
the fact that we have 36 = 32, an impossible equation, means that the system has no solution.
5% of what number is 9?
Answer:
180
Explanation:
5% of x = 9
9 × 100 = 900
900 ÷ 5 = 180
So,
5% of 180 = 9
5Answer:
45
Step-by-step explanation:
9x0.5=4.5
In the order of operations, the absolute value sign is considered to be at which level?
Answer:
Note that with embedded parentheses (parentheses within parenthesis), you always perform operations inside out; do the math on the inside before the outside. Note that if you have an absolute value | | sign which means take the positive value only of a number inside.
Answer: Absolute Value is the first level.
Step-by-step explanation:
2 |-10|
2 * 10
20
round 163 to the nearest 10? round it to the nearest ten it would be 160 i think because 163 is close to 160 so it has to 160
Answer:
163 rounded to the nearest ten = 160.
Step-by-step explanation:
yes since 163 is not 165 or greater its 160 but if it the number was greater than 165 than it would be 170. in this case its not so the answer would be 160.
Marisa buys a car for $20,000. The car depreciates at a rate of 12% per
year. Which equation shows the value of Marisa's car over a period of x
years?
[tex]A = 20,000 (1-0.12)^x[/tex] this equation shows the value of Marisa's car over a period of x years. Using the concept of depreciation we get this -
What is depreciation?Depreciation is an accounting technique for spreading out the expense of a tangible item over the course of its useful life. Depreciation is a measure of how much an asset has been utilized for. It enables businesses to purchase assets over a predetermined length of time and generate income from those assets.
Given that,
Marisa buys a car for $20,000 = P
depreciates at a rate of 12% per year = r
and t is the for the time period.
As we know,
[tex]A = P (1-r)^t[/tex]
Where, A is the value of object after x period of time.
The value of Terrence's car after x years is:
[tex]A = 20,000 (1-0.12)^x[/tex]
Hence, the value of Marisa's car after x years is: [tex]A = 20,000 (1-0.12)^x[/tex]
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Answer:f(x)=20,000(.12)^x
Step-by-step explanation:
took test
A motorcycle covers 315 km distance with 7 liters of petrol.
i)how many kilometres does it cover with 12 liters of petrol in the same mileage?
ii)how much petrol is needed to cover 270 km in the same mileage?
Step-by-step explanation:
225 km travels in =25 ltr
1 km travel = 225 25
540 km will require = 22525 ×540=60 L
Was this answer helpful?
Answer:
1) 540 km
2) 6 liters of petrol
Step-by-step explanation:
To answer the two questions, it is easiest to fist find the relationship between kilometers (km) and liters of petrol. Since 7 liters (L) results in 315 km, we can find the km/liter petrol conversion factor (converts liters of petrol to km):
(315 km)/(7 liters) = 45 km/L
1) 12 liters times the conversion factor will tell us how many km the motorcycle will travel"
(12 liters)*(45 km/liter) = 540 km [Note that the liters unit cancles, leaving only km]
2) To find the liters of petrol to travel 270 km, we can use the same conversion factor, but now we need to divide to get the units we want, which is km:
(270 km)/(45 km/l) = 6 liters [Note that km cancels and l moves to the top, leaving liters as the only unit.
what common side do △ADE and △BED share?
Answer:
ED
Step-by-step explanation:
They both have side ED in their triangles!
In a fish tank, 4/9 of the fish have a red stripe on them. If 12 of the fish have red stripes, how many total fish are in the tank?
Answer: If 4/9 of the fish have a red stripe, we can determine the total number of fish in the tank by dividing the number of fish with red stripes by the fraction of fish with red stripes. This gives us 12 / (4/9) = 12 * (9/4) = 27 fish. So, there are 27 fish in the tank.
[tex] \frac{4}{9} x = 12[/tex]
[tex]x = 12 \times \frac{9}{4} [/tex]
[tex]12 \times 9 = 108[/tex]
[tex]4 \times 1 = 4[/tex]
[tex]x = \frac{108}{4} [/tex]
[tex]x = 27[/tex]
There are 27 fish in the tank. Hope this helps.
3x+8 = x-6
x=?
pls help
Answer:
x = -7Step-by-step explanation:
3x+8 = x-6
x=?
3x + 8 = x - 6
2x = -14
x = -7
---------------------------
check
3 × (-7) + 8 = -7 - 6
-21 + 8 = -13
-13 = -13
the answer is good
A virus reproduces by tripling every half hour. If a single virus gets into your system and continues at this rate, how much of it will be in your system after a 24-hour period. (hint: there would be two instances of tripling after the first hour)
In 24-hour period there will be 94143178827 virus in system.
What is geometric Sequence?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given:
A virus reproduces by tripling every half hour.
In start the virus is 1.
After half an hour, virus= 3
After one hour= 9 virus
After 1 1/2 hour= 27
We get a geometric Sequence
1, 3, 9, 27, 81, ....
Using
[tex]a_n = a_1 (r)^{n-1[/tex]
[tex]a_{24} = 1 ( 3/1)^ {23[/tex]
[tex]a_{24[/tex] = 94143178827
Hence, In 24-hour period there will be 94143178827 virus in system.
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Andy goes shopping with his friend Silvio, an exchange student from Brazil. Silvio wants to know what everything costs in
Brazilian reals. He knows 1 American dollar is equivalent to 2 Brazilian reals. Let x represent American dollars and y represent Brazilian reals. This situation is graphed below. Which equation represents this situation?
A) y=-2x
B) y=4x
C) y-2x
D) y=1/2x
Answer:
Step-by-step explanation:
answer is b
Barbara wants to restore her '66 Mustang in 4 years. She puts $200 into an account every month that pays 1.05% interest, compounded monthly. How much interest did she gain in 4 years?
Using the formula of compound interest, the amount accumulated over 4 years is $15,849.46
Compound InterestCompound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period. In Mathematics, compound interest is usually denoted by C.I.
The formula is often given as;
C.I = P(1 + r/n)^nt
C.I = Compound InterestP = principal r = raten = number of times compoundedt = timeSubstituting the values into the formula
C.I = 200(1 + 0.0105/12)^12*4
However, over the period of 4 years, the Principal becomes
Principal = 200 * 4 * 12 = 9600
Rate = 1.05 * 12 = 12.6
C.I = 9600(1 + 12.6/12)^12 * 4
C.I = $15,849.46
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Khadia raie bee and ell honey. He give a dicount to hi neighbor. The table how price of ,n of buying honey that ha a regular price of r dollar
The equation for the relationship between the regular price (r) and the neighbor's price (n) will be r - n = 250.
What are equations?A mathematical expression with an equals sign is referred to as an equation.
Algebra is widely used in equations.
When performing calculations but unsure of the precise number, algebra is used.
Linear equations: Any equation that can be expressed as ax + by + c = 0, where a, b, and c are all real numbers and a and b are not equal to zero.
In light of the posed query.
Khalid keeps bees and sells honey from them.
Additionally, n stands for the neighbor's honey price in dollars and r stands for the ordinary honey price in dollars.
We can determine the discount from the provided information.
7 - 4.50 = 2.50
8 - 5.50 = 2.50
10 - 7.50 = 2.50
12 - 9.50 = 2.50
Khalid gives his neighbor $2.50.
The equation for the link between the regular price r and the neighbor's price n will therefore be: r - n = 250
Therefore, the equation for the relationship between the regular price (r) and the neighbor's price (n) will be r - n = 250.
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Complete question:
Khalid raises bees and sells the honey. He gives a discount to his neighbors. The table shows the neighbors' price, n, of buying honey that has a regular price of r dollars. Write an equation that represents the relationship. I put two pictures below to help. :)
Answer: r - n = 2.5
Step-by-step explanation: Took Quiz
64/8 I’m the simplest form
Answer:
8
Step-by-step explanation:
The first step would be to determine if both the numerator and the denominator have a highest common factor. If they do, then the number can be simplified into a smaller fraction. Here, the denominator can be fully divided out by 64 to make the whole number 8
Answer the statistical measures and create a box and whiskers plot for the following set of data.
1, 3, 3, 5, 6, 6, 6, 7, 7, 10, 10, 11, 14
1,3,3,5,6,6,6,7,7,10,10,11,14
For the box and whiskers plot for the following set of data the value of Min is 3, Q1 is 6, Med is 12, Q3 is 14.5 and Max is 17.
What is box and whiskers plot?Box and whiskers plot is the way of representation of data which gives the graphical image of the data set to understand better. In this the data is represented with the help of quartile.
The minimum and the maximum values in the box plot is plotted at the end points.
The following set of data which i s given in the problem.
3, 4, 5, 6, 6, 7, 7, 12, 13, 14, 14, 15, 15, 16, 17
Min: 3
The minimum value in the given data is 3. Thus, the min is 3.
Q1:6
First quartile appears at 6. Thus, the value of Q1 is 6.
Med:12
The middle value of the given data is 12 which appears at the center of all the values. Thus the med is 12.
Q3:14.5
Second quartile appears at 14.5. Thus, the value of second quartile Q2 is 6.
Max: 17
The minimum value in the given data is 17 as shown in the image attached below. Thus, the min is 17.
Hence, for the box and whiskers plot for the following set of data the value of Min is 3, Q1 is 6, Med is 12, Q3 is 14.5 and Max is 17.
The complete question is : Answer the statistical measures and create a box and whiskers plot for the following set of data. You may optionally click and drag the numbers into numerical order.
3, 4, 5, 6, 6, 7, 7, 12, 13, 14, 14, 15, 15, 16, 17
3,4,5,6,6,7,7,12,13,14,14,15,15,16,17
Min:
Q1:
Med:
Q3:
Max:
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what is the product of 73 and 4.4 x 10^6 expressed in scientific notation
Answer:
321.2 * 10^6
Step-by-step explanation:
First at all:
4.4 x 10^6 = 4.400.000
Then 73 * (4,4 x 10^6) = 73* 4.400.000
(73)*(4.400.000) = 321.200.000
In scientific notation:
321.2 * 10^6
Skylar bought 30 movie ticket for a total of $200. Adult ticket cot 58 each, child ticket cot $3. 50 cach, and enior ticket cot $6 each. He bought twice the number of adult ticket than the number of child and enior ticket combined. How many of each type of ticket did Skylar buy?
He spent $200 on 0 tickets for children, 10 tickets for adults, and 20 tickets for seniors.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
Total number of tickets brought=30
Total amount paid=$200
Cost of kid ticket=$3.5
Cost of adult ticket=$8
Cost of senior ticket=$6
Let x, y, z be the number of tickets brought for kid, adult, senior.
x+y+z=30
3.5x+8y+6z=200
2y=x+z
x+y+z=30
3y=30
y=10
x+z=20
z=20-x
3.5x+80+6(20-x)=200
3.5x+80+120-6x=200
2.5x=0
x=0
z=20
He bought 0 tickets for kid, 10 tickets for adult and 20 tickets for senior with an amount of $200.
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For the cards shown below what is the probability of choosing yellow card and then a 1 if the first card is replaced before the second card is drawn?
The study of probability is a field of mathematics that focuses on determining the possibility that an event will occur.
Describe probability..?"Finding the likelihood of the occurrence of an event" is the focus of the mathematical discipline known as probability.Formula of the probability of an event A is: [tex]P(A) = \frac{n(A)}{n(S)}[/tex]where [tex]n(A)[/tex] is the number of favorable outcomes[tex]n(S)[/tex] is the total number of events in the sample space.Given: a deck of cards with 2 red cards and 3 yellow cardsTotal cards = 5First we find the probability of choosing red cards.The probability of choosing one red card is 2/5.To learn more about probability refer to:
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Similar Triangles Sorting Activity 1 (be sure each pair of triangle is in the right column)
Similar Triangles
*sorting mat*
Similar Triangles
NOT Similar Triangles
The triangle pair that is similar from the given pair is "Triangle Pair 2" .
In the question ,
four triangle pairs are given ,
we have to select the triangle pair that is similar ,
In triangle Pair 2 ,
In triangle BAD and triangle BCD ,
angle A = angle C ....given ,
side BD = side BD ......because common side
side AD = side BC ....because opposite side of parallelogram are equal.
So , the triangle BAD is congruent to triangle BCD ,
So , the triangle pair 2 is congruent .
Therefore , the correct option is (b) Triangle Pair 2 .
The given question is incomplete , the complete question is
Similar Triangles Sorting Activity , Which triangle pair shows similar triangles ?
(a) Triangle Pair 1
(b) Triangle Pair 2
(c) Triangle Pair 3
(d) Triangle Pair 4
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Your parents are saving up for a fun vacation at Disney. They have figured out it will
cost them a total of $3,400. If they already have $1,500 and plan on saving for the next
6 months, how much will they need to save each month to have at least enough money for
the trip? Write and solve an inequalit. Interpret your solution in sentence form.
A total of $316.67 has to be saved per month for the vacation at Disney.
What is equation modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.
Given is that your parents are saving up for a fun vacation at Disney. They have figured out it will cost them a total of $3,400. They have already saved $1,500 and plan on saving for the next 6 months,
Assume that they will have to save $x every month. So we can write the inequality as -
6x ≥ (3400 - 1500)
6x ≥ 1900
x ≥ (1900/6)
x ≥ 316.67
Therefore, your parents will have to save a total of $316.67 per month for the vacation.
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A C Which are the solutions of x² + 81 = 0 ? B x = +40i D X = +80i X = +9i X = +9 A
Solution for the equation x² + 81 = 0 is x = ± 9i.
What is an equation ?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation is,
x² + 81 = 0
To find the solution of the given equation,
Simplify the equation,
x² = -81
x = √-81
x = ±9√-1
Since, i = √-1
x = ± 9i
The solution for the given equation is x = ± 9i.
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Express the radical using the imaginary unit, ¿.
Express your answer in simplified form.
√-18 = ±
Answer: √-18 = 3√2 i
Because i is √-1 so think like √18 x √-1 which means √18 i so answer is 3√2 i
At a coffee shop, the first 100 customers' orders were as follows. Small Medium Large Hot un 48 22 Cold 8 12 5 What is the probability that a customer ordered a medium given that he or she ordered a hot drink? Rounded to the nearest percent, [? ]% Enter
solve for C
7(c-12)=-21
Answer: c=9
Step-by-step explanation:
Write the coordinate rule for a dilation by a scale factor of 4 centered at the point (5,
-8).
Answer: use a graf
Step-by-step explanation:
find the negative numbers and positive number