The radius of cylinder = 6 meter
The height of cylinder = 11 meter
According to the question,
Surface area of the cylinder = 640.56 m²
Let the height of the cylinder = x meters
Let the radius of the cylinder = (x-5)meters
Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)
640.56 = 2 (3.14) (x-5) (x)
640.56/(6.28) = x² - 5x
x² - 5x =102
x² - 5x - 102 =0
using quadratic equation, [-b±√(b² - 4ac)]/2a.
b = -5; a=1; c=102
x =[-(-5) ±√(-5)² - 4(1)(102)]/2
= [5 ± √433]/2
x = 11 and -7
since x=-7 neglect negative value, we get x=11.
The height of the cylinder is 11 meters
The radius of the cylinder is (11 - 5) = 6 meters.
Hence, The radius of cylinder = 6 meter.
The height of cylinder = 11 meter.
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Answer:
Step-by-step explanation:
The radius of cylinder = 6 meter
The height of cylinder = 11 meter
According to the question,
Surface area of the cylinder = 640.56 m²
Let the height of the cylinder = x meters
Let the radius of the cylinder = (x-5)meters
Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)
640.56 = 2 (3.14) (x-5) (x)
640.56/(6.28) = x² - 5x
x² - 5x =102
x² - 5x - 102 =0
using quadratic equation, [-b±√(b² - 4ac)]/2a.
b = -5; a=1; c=102
x =[-(-5) ±√(-5)² - 4(1)(102)]/2
= [5 ± √433]/2
x = 11 and -7
since x=-7 neglect negative value, we get x=11.
The height of the cylinder is 11 meters
The radius of the cylinder is (11 - 5) = 6 meters.
Hence, The radius of cylinder = 6 meter.
The height of cylinder = 11 meter.
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The dashed triangle is the image of the solid triangle. The center of dilation is (6, 6).
What is the scale factor used to create the dilation?
Enter your answer as an integer or decimal in the box.
The two right triangles are graphed on a coordinate plane. The horizontal x-axis ranges from negative 10 to 10 in increments of 1. The vertical y-axis ranges from negative 10 to 10 in increments of 1. A dashed triangle has vertices at begin ordered pair 6 comma 6 end ordered pair, begin ordered pair 6 comma 9 end ordered pair, and begin ordered pair 9 comma 6 end ordered pair. A solid triangle has vertices at begin ordered pair 6 comma 6 end ordered pair, begin ordered pair 6 comma negative 9 end ordered pair, and begin ordered pair negative 9 comma 6 end ordered pair.
Answer:
The scale factor is 1/5.
Step-by-step explanation:
You can find the side length of triangles by looking at the points or it might be easier to see if you look at the graphs that I have attached. I can see that the legs of the small triangle are 3 and the legs of the large triangle are 15. What do I need to multiple 3 by to get 15? 5. That is the scale factor from the little triangle to the big triangle. If I go the other way, the scale factor is the reciprocal of 5 or 1.5
A 400 L tank is filled with pure water. A copper sulfate solution with a concentration of 20 g/L flows into the tank at a rate of 4 L/min. The thoroughly mixed solution is drained from the tank at a rate of 4 L/min. a. Write a differential equation (initial value problem) for the mass of the copper sulfate. b. Solve the differential equation
(a) Let [tex]C(t)[/tex] denote the amount (in grams) of copper (II) sulfate (CuSO₄) in the tank at time [tex]t[/tex] minutes. The tank contains only pure water at the start, so we have initial value [tex]\boxed{C(0)=0}[/tex].
CuSO₄ flows into the tank at a rate
[tex]\left(20\dfrac{\rm g}{\rm L}\right) \left(4\dfrac{\rm L}{\rm min}\right) = 80 \dfrac{\rm g}{\rm min}[/tex]
and flows out at a rate
[tex]\left(\dfrac{C(t)\,\rm g}{400\,\mathrm L + \left(4\frac{\rm L}{\rm min} - 4\frac{\rm L}{\rm min}\right) t}\right) \left(4\dfrac{\rm L}{\rm min}\right) = \dfrac{C(t)}{100} \dfrac{\rm g}{\rm min}[/tex]
and hence the net rate of change in the amount of CuSO₄ in the tank is governed by the differential equation
[tex]\boxed{\dfrac{dC}{dt} = 80 - \dfrac C{100}}[/tex]
(b) This ODE is linear with constant coefficients and separable, so we have a few choices in how we can solve it. I'll use the typical integrating factor method for solving linear ODEs.
[tex]\dfrac{dC}{dt} + \dfrac C{100} = 80[/tex]
The integrating factor is
[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{100}\right) = e^{t/100}[/tex]
Distributing [tex]\mu[/tex] on both sides gives
[tex]e^{t/100} \dfrac{dC}{dt} + \dfrac1{100} e^{t/100} C = 80 e^{t/100}[/tex]
and the left side is now the derivative of a product,
[tex]\dfrac d{dt} \left[e^{t/100} C\right] = 80 e^{t/100}[/tex]
Integrate both sides. By the fundamental theorem of calculus,
[tex]e^{t/100} C = e^{t/100}C\bigg|_{t=0} + \displaystyle \int_0^t 80 e^{u/100}\, du[/tex]
The first term on the right vanishes since [tex]C(0)=0[/tex]. Then
[tex]e^{t/100} C = 8000 \left(e^{t/100} - 1\right)[/tex]
[tex]\implies \boxed{C(t) = 8000 - 8000 e^{-t/100}}[/tex]
what is the Pythagorean theorem
Answer:
a^2+b^2=c^2
Step-by-step explanation:
leg1=a
leg2=b
hypotenuse=c
a^2+b^2=c^2
Answer:
u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D
Step-by-step explanation:
12 in.
14 in.
14 in.
Find the area of the figure above.
[?] square inches please explain how you got the answer for future questions
Answer:
168 square inches
Step-by-step explanation:
A = BH
or
Area = Base x Height
In other words multiply 12 and 14.
Elliott is standing at the top of a store escalator that leads to the ground floor below. the angle of depression from the top of the escalator to the floor is 42.51°, and the escalator is 16 feet long. how far is the top of the escalator from the ground floor? round your answer to the nearest foot.
By using what we know about right triangles, we conclude that the height is 11ft.
How far is the top of the escalator from the ground floor?We can think of this as a right triangle.
Where the length of the escalator is the hypotenuse
We know that the angle of depression is 42.51°, then the top angle of our right triangle is:
90° - 42.51° = 47.49°
Now, the height of the top of the escalator would be the adjacent cathetus to said angle, then we can use the relation:
cos(a) = (adjacent cathetus)/(hypotenuse)
Replacing what we know:
cos(47.49°) = height/16ft
cos(47.49°) *16ft = height = 10.8ft
Rounding to the nearest foot, we get:
height = 11ft
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the x and y intercept
If m ABD = 61, and m DBC = 59, then m ABC = ? PLS ASAP
Given that angle ABD and angle DBC are adjacent angle, the value of angle ABC is 120 degrees.
What is the value of angle ABC?Given the data in the question;
Angle ABD = 61°Angle DBC = 59°Angle ABC = ?Since angle ABD and angle DBC are adjacent angle, there addition will give us the value of angle ABC.
∠ABD + ∠DBC = ∠ABC
We substitute in the given values
61° + 59° = ∠ABC
∠ABC = 120°
Given that angle ABD and angle DBC are adjacent angle, the value of angle ABC is 120 degrees.
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A conical circus tent has a 20 ft central pole that supports it. the slant height of the tent is 26 ft long. explain how to find the angle the tent pole makes with the sides of the tent.
The angle the pole makes with the tent is 39.7°.
What is an angle?An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles formed by two rays are located in the plane containing the rays.Trigonometric ratio: the trigonometric ratio is used to demonstrate the relationship between the sides and angles of a right-angled triangle.
Let θ represent the angle the pole makes with the tent.
Using trigonometric ratios:
cos(θ) = 20/26θ = 39.7°Therefore, the angle the pole makes with the tent is 39.7°.
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Volume=
Help me please thanks so much asap
Answer:
600
Step-by-step explanation:
since it is a right triangle based pyramid, 2 of them will make a cube. so, it is bwh / 2.
base = 24
width = 10
height = 5
volume = 1200
volume of pyramid = 600
The expression x2y - 2xy - 24y can be factored by first factoring out a common factor of y. After the common factor is removed, the remaining factor is a\
The remaining factor of x^2y - 2xy - 24y is (x - 6)(x + 4)
How to determine the remaining factor?The expression is given as:
x^2y - 2xy - 24y
Factor out y from the expression
y(x^2 - 2x - 24)
Expand the equation
y(x^2 + 4x - 6x - 24)
Factorize
y(x - 6)(x + 4)
Hence, the remaining factor of x^2y - 2xy - 24y is (x - 6)(x + 4)
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A population of rabbits has 20 offspring per pair of rabbits. a population of cheetahs has 2 offspring per pair of cheetahs. which population will be more affected by genetic drift?
Cheetahs population will be more affected by genetic drift
What is genetic drift?Genetic drift is the change in a population's frequency of an existing gene variant brought on by chance. Gene variations may totally vanish due to genetic drift, hence reducing genetic variation. Additionally, it may lead to the considerably greater frequency and even fixation of previously rare alleles.
What causes genetic drift?Random drift is a result of recurrently small populations, drastic population reductions known as "bottlenecks," and founder events in which a new population is created from a small number of individuals.
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10. There are 355 students at Median Middle School. If there 8% of the students were absent on Tuesday, how many students were absent? How many were present?
To solve this question, we simply need to divide the total amount of students by 8% to find out how many students were absent and how many were present.
However, we can't simply multiply it by 8%, so we need to turn that into a decimal.
8% - 0.08
Multiply:
355 x 0.08
= 28.4
Round:
28 kids were absent
Subtract:
355 - 28
= 327
This means that 28 kids were absent, and 327 kids were present.
.
Let’s assume the following statements are true: Historically, 75% of the five-star football recruits in the nation go to universities in the three most competitive athletic conferences. Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to. If this pattern holds true for this year’s recruiting class, answer the following:
a. Based on these numbers, what is the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship?
b. What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences? Explain.
c. Explain whether these are independent or dependent events. Are they Inclusive or exclusive? Explain.
The probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship is 69.75%.
What is the computation for the above solution?
Note that this is simple probability.
Hence probability of the 75% football starts selected randomly where the chance is 93% =
75% x 93%
= 69.75%
What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences?The chance that 25% of the five-star recruit will not select a university form one of the three best conferences is explained as follows:
Because only 75% stand the chance of being selected into the three ivy leagues, this means that 25% stand no chance.
Recall that the total population is 100%.
Are these are independent or dependent events. Are they Inclusive or exclusive?From the statement of problem given, it is clear that the events are mutually exclusive. Recall "Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to.
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The average of 15,19,23,41,and Z is 20. What is the value of x
The value of x from the given data is 2
Calculating the average of numbersMean is the ratio of sum of numbers to the total samples. Given the following data
15,19,23,41, and Z
The mean is calculated as
Mean = 15+19+23+41+z/5
Since the mean the of the data is given as 20. Substitute
20 = 15+19+23+41+z/5
Cross multiply
20*5 = 15+19+23+41+z
100 = 15+19+23+41+z
100 = 98 + z
z = 100- 98
z = 2
Hence the value of x from the given data is 2
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Seema had 150 marbles.rani had 20 marbles more than seema.alok had 50 marbles lass than rani how many marbles did rani have
Answer:
120
Step-by-step explanation:
seema 150 marbles
rani 20 more marbles
alok 50 less marble
150+20=170_rani
170-50=120_alok
What is the perimeter of kite OBDE?
12 units
22 units
38 units
58 units
By definition of perimeter, direct observation and Pythagorean theorem, the perimeter of kite OBDE is 38 units. (Correct choice: C)
How to determine the perimeter of a kite OBDE
In geometry, the perimeter is the sum of the lengths of the sides of a figure. Herein we must determine the perimeter of a quadrilateral, the kite OBDE, that is, the sum of the lengths of its four sides:, which can be found both by direct observation or by the use of the Pythagorean theorem.
Please notice that the quadrilateral has an axis of symmetry passing through the points O and D, which implies that OB = OE and BD = DE. The length of sides BD and DE is 6 units and the length of the sides OB and DE are:
OB = DE = 0.5 · √(24² + 10²)
OB = DE = 13
Lastly, the perimeter of kite OBDE is p = 2 · 6 + 2 · 13 = 38 units.
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Answer: C. 38 units
Step-by-step explanation: TRUST ME!!! Answer is correct on Edge!!! :)
Just did it and got it correct!
Prepare a grid with magic number 30. You can choose any set of numbers in sequence but the numbers should not be repeated.
The grid of numbers with a row and column sum of 30 is
3 15 12
17 11 2
10 4 16
How to prepare the grid?The grid in the question has a row sum and column sum of 15
The question implies that we create a similar grid with a row sum and column sum of 30
Represent the grid as follows:
a b c
d e f
g h j
So, we have the following sum of rows
a + b + c = 30
d + e + f = 30
g + h + j = 30
And, we have the following sum of rows
a + d + g = 30
b + e + h = 30
c + f + j = 30
Using trial by error, we have:
3 + 15+ 12 = 30
17 + 11 + 2 = 30
10 + 4 + 16 = 30
When the columns are added, we have
3 + 17 + 10 = 30
15 + 11 + 4 = 30
12 + 2 + 16 = 30
Hence, the grid of numbers is
3 15 12
17 11 2
10 4 16
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necesito la respuesta, urgente
The value of the function f(x) = ( 8x² - 2x + 4 ) / 2 when x = -3/5 is 101/25.
Hence, f(-3/5) = 101/25.
What is the value of the function at f(-3/5) ?Given the function; f(x) = ( 8x² - 2x + 4 ) / 2
To determine the value of the function when x = -3/5, we simply replace the variable x with -3/5 in the function.
f(x) = ( 8x² - 2x + 4 ) / 2
f(-3/5) = ( 8(-3/5)² - 2(-3/5) + 4 ) / 2
Divide each term by 2
f(-3/5) = 4(-3/5)² - (-3/5) + 2
f(-3/5) = 4(9/25) - (-3/5) + 2
f(-3/5) = 36/25 +3/5 + 2
f(-3/5) = ( 36 + 3×5 + 2×25 ) / 25
f(-3/5) = ( 36 + 15 + 50 ) / 25
f(-3/5) = 101/25
The value of the function f(x) = ( 8x² - 2x + 4 ) / 2 when x = -3/5 is 101/25.
Hence, f(-3/5) = 101/25.
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If the top ten nations were randomly selected to march, one after another, into the stadium at the closing ceremonies, in how many ways could the nations have marched in?
Step-by-step explanation:
1. Entrance of Head of State and IOC President
2. Playing of the national anthem
3. The parade of the athletes
4. The symbolic release of doves
5. Olympic Laurel Award
6. Official Speeches
7. Opening of the Games
8. Raising the Olympic flag and playing the Olympic Anthem
9. Athletes, judges and coaches’ oath
10. Lighting of the Olympic flame
11. The artistic programme
you purchased 18.000 milliliters of juice. Juice costs $2 per liter. The cashier
ays you owe $12,000 for the juice, but you know that is not correct. Look at
the cashier's work and figure out how much you should pay. Explain what
he cashier did wrong.
18,000 + 3 = 6,000 liters
6,000 liters x $2 = $12,000
Answer:
cashier needed to divide by 1000, not 3.
Step-by-step explanation:
there are 1000ml in one liter. in order to find the amount of liters, youd have to divide the milliliters by 1000. its only after then that you can multiply by $2. answer would be $36
An industrial machine produces widgets, but it has a 0.07 defective rate. what is the probability that the machine produces fewer than 5 defective widgets in a production run of 100 items?
The probability that the machine produces fewer than 5 defective widgets in a production run of 100 items is 0.10
What is the probability?A probability refers to the ratio of favorable events to the n number of total events.
Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.
Given data
An industrial machine produces 5 widgets.
It has a 0.07 defective rate.
Defective rate fewer than 5
Total Probability = P of 4 defective + P for 3 defective + P for 2 defective + P for 1 defective.
Total Probability = 4/100 + 3/99 + 2/98 + 1/97
Total Probability ≈ 0.10
Therefore, the required probability for fewer than 5 defective rate is 0.10
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does anyone know how to do this? pls help
Answer:
-3
Step-by-step explanation:
If you reflect over the y-axis and then move 2 units to the left(x-2), then ABCD will be 3 units above EHGF. Since you need to move it down 3 units to map ABCD onto EHGF, you will need to do y-3, which is the same as y+-3
Which function has exactly one zero?
Answer:
Step-by-step explanation:
Answer:
i think no 3 hasexactly one 0
Use the recursive formula to find the first five terms in the arithmetic sequence.
Answer:
3, 1, - 1, - 3, - 5
Step-by-step explanation:
using the recursive formula and f(1) = 3 , then
f(2) = f(1) - 2 = 3 - 2 = 1
f(3) = f(2) - 2 = 1 - 2 = - 1
f(4) = f(3) - 2 = - 1 - 2 = - 3
f(5) = f(4) - 2 = - 3 - 2 = - 5
first 5 terms are 3, 1, - 1, - 3, - 5
The mean if four numbers is 25 if three numbers are 36, 12 and 24 what is the fiurth number
correct answer is 28.
If the mean of four numbers is 25 and three numbers are 36, 12 and 24 then fourth number is 28.
Find fourth number?given terms are:
first number =36
second number=12
third number=24
fourth number=?
let us assume the fourth number be x.
what is mean?we know the formula to find mean is:
Mean=addition of given terms / total number of terms
According to given statement, we put the values in above equation and we get,
25=(36+12+24+x) / 4
By rearranging, we get
36+12+24+x=100
72+x=100
x=100-72
x=28
so, the fourth number is 28.
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What is the slope of a line perpendicular to the line whose equation is 3x + y = -9.
Fully simplify your answer.
Considering the definition of perpendicular line, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is [tex]\frac{1}{3}[/tex].
Linear equationA linear equation o line can be expressed in the form y = mx + b.
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles.
Two nonvertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other. In other words, if you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseIn this case, the line is 3x+y=-9. Expressed in the form y = mx + b, you get: y= -9 - 3x or, what is the same, y= -3x -9
If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of -3. So:
(-3)× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-3)
slope perpendicular line= [tex]\frac{1}{3}[/tex]
Finally, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is [tex]\frac{1}{3}[/tex].
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Given the function defined in the table below, find the average rate of change,
in simplest form, of the function over the interval 12 ≤ ≤ 36.
0
12
36
48
60
37
34
31
28
25
22
The average rate of change of [tex]f(x)[/tex] on [tex]12\le x\le36[/tex] is the difference quotient
[tex]\dfrac{f(36) - f(12)}{36 - 12} = \dfrac{28 - 34}{24} = \boxed{-\dfrac14}[/tex]
Which describes the combined variation shown in the equation F = kxy/z?
1) F varies directly with x, and inversely with y
and z.
2)F varies directly with z, and inversely with x
and y.
3)F varies directly with y, and inversely with x and z.
4) F varies directly with x and y, and inversely
with z.
Answer:
option 4
Step-by-step explanation:
F = [tex]\frac{kxy}{z}[/tex]
k is the constant of variation
• if the variables are on the numerator they vary directly
• if the variables are on the denominator they vary inversely
In this case F varies directly with x and y ( variables on numerator ) and inversely with z ( variable on denominator )
What value of z* should be used to construct an 88% confidence interval of a population mean?
Z = 1.555 should be used
If we seek an 88% confidence interval, that means we only want a 12% chance that our interval does not contain the true value.
Assuming a two-sided test, that means we want a 6% chance attributed to each tail of the Z-distribution.
the zα/2 value of z0.06.
This z value at α/2=0.06 is the coordinate of the Z-curve that has 6% of the distribution's area to its right, and thus 94% of the area to its left. We find this z-value by reverse-lookup in a z-table.
What is Z-distribution?The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.
Any normal distribution can be standardized by converting its values into z-scores. Z-scores tell you how many standard deviations from the mean each value lies.
Why is z-score used?The standard score (more commonly referred to as a z-score) is a very useful statistic because it
(a) allows us to calculate the probability of a score occurring within our normal distribution and
(b) enables us to compare two scores that are from different normal distributions.
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if x : y = 0.75 : 0.90 and y : z = 1/3 : 1/4
(A) simplify the ratio x : y and y : z
(B) find x : y : z
Step-by-step explanation:
x:y=0.75:0.90
Here,
Dividing by the value of y=0.90,
x:y=0.75/0.90:0.90/0.90
=5/6:1
Similarly,
y:z=1/3:1/4
Dividing by 1/3,we get,
y:z=1:3/4
Now,
X:y:z=5/6:1:3/4
Multiplying by both value of y,0.90×1/3=3/10
x:y:z=5/6×3/10:1×3/10:3/4×3/10
By solving this,
x:y:z=1/4:3/10:9/40