volume of a cylinder is 1540 cm³ and the difference of its height and radius is 3 cm, then find the total surface area of the cylinder.
Answers
Answer:
Let's assume the height of the cylinder to be 'h' and its radius to be 'r'. We can use the given information to form two equations.
First, we know that the volume of the cylinder is 1540 cm³:
V = πr²h = 1540
Second, we know that the difference between the height and the radius is 3 cm:
h - r = 3
Using the second equation, we can solve for 'h' in terms of 'r':
h = r + 3
Substituting this into the first equation, we get:
πr²(r + 3) = 1540
Expanding the left side of the equation and simplifying, we get:
πr³ + 3πr² - 1540 = 0
We can solve for 'r' using the cubic formula, but it's easier to notice that 'r' must be close to 10. We can try different values of 'r' until we get an answer close to 1540. If we try 'r' = 10, we get:
π(10)²(10+3) = 3300π
So, the radius is approximately 10 cm and the height is approximately 13 cm.
To find the total surface area of the cylinder, we need to find the area of the top and bottom circles and the area of the curved surface. The area of each circle is πr², so the total area of the circles is:
2πr² = 200π cm²
The area of the curved surface is the circumference of the circle times the height of the cylinder, or 2πrh. Substituting the values of 'r' and 'h' that we found earlier, we get:
2π(10)(13) = 260π cm²
Therefore, the total surface area of the cylinder is:
200π + 260π = 460π ≈ 1442.4 cm²
So, the total surface area of the cylinder is approximately 1442.4 cm².
Related Questions
PLEASEEE HELPPPPP :(((
Solve for x.
5(x−2 2/5)=−5.2
Enter your answer as a decimal in the box.
Answers
A 32-foot tall ladder rests against a
vertical wall. If the top of the
ladder reaches a point 18 feet up
the wall, what angle does the
bottom of the ladder make with
the ground?
Answers
The angled form from the bottom of the ladder with the ground is 30°.
Here we have to find the angle formed from the bottom of the ladder make with the ground.
Data given:
The ladder rests on the wall and is of length 32 feet which is the hypotenuse.
The wall is of length 18 feet which is perpendicular.
Let Ф be the angle formed from the bottom of the ladder made with the ground
As we know that:
sinФ = perpendicular/ hypotenuse
= 18/ 32
= 1/2
sinФ = sin 30°
Ф = 30°
Therefore the angle is 30°.
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Find a value for x and a value for y so that 2x+3y=24 and 5x-2y=22
Answers
The values of x and y are 6 and 4, respectively. So, x = 6 and y = 4.
Given equations:
2x + 3y = 24, and
5x - 2y = 22
To find the values of x and y,
we have to solve the equations by using the elimination method.
Here's how:
Step 1:
Multiply equation (1) by 2 and equation (2) by 3.
4x + 6y = 48 (Equation 1 multiplied by 2)
15x - 6y = 66 (Equation 2 multiplied by 3)
Step 2: Add both equations to eliminate y,
4x + 6y = 48
15x - 6y = 66 ___________________________
19x = 114
Step 3: Divide both sides by 19.
x = 6
Step 4: Substitute the value of x in any of the given equations.
2x + 3y = 24
Putting the value of x, we get:
2 (6) + 3y = 24
Simplifying, we get:
12 + 3y = 24
Step 5: Solve for y,
3y = 24 - 12
y = 4
Thus, the values of x and y are 6 and 4, respectively. So, x = 6 and y = 4.
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A gardener planted a newly sprouted oak tree that was just 3.5 inches tall. The sapling grew 12 inches each year.
Write an equation that shows how the sapling's height in inches, y, depends on the number of years since it was planted, x.
Answers
Answer:
y = 12x + 3.5--------------------------------------
Initial height is the y-intercept of the line.
Yearly growth rate is the slope.
So we have:
m = 12, b = 3.5.The equation of the line with these constants is:
y = mx + by = 12x + 3.5Random question, BUT is God real?
Answers
Answer:
Yes of course God is real.
Step-by-step explanation:
One way god is to prove that God is real is to simply look at the world in which we live. The beauty, complexity and organization of the material world around us point toward a master Designer.
Jaidee and Beth each improved their yards by planting rose bushes and ivy. They bought their supplies from the same store. Jaidee spent $140 on 2 rose bushes and 12 pots of ivy. Beth spent $120 on 6 rose bushes and 6 pots of ivy. What is the cost of one rose bush and the cost of one pot of ivy?
Answers
The cost of one rose bush is $10 and the cost of one pot of ivy is $10.
Let's assume the cost of one rose bush is represented by "R" and the cost of one pot of ivy is represented by "I".
According to the given information:
Jaidee spent $140 on 2 rose bushes and 12 pots of ivy:
2R + 12I = 140 ...(1)
Beth spent $120 on 6 rose bushes and 6 pots of ivy:
6R + 6I = 120 ...(2)
We now have a system of two equations with two variables. To solve this system, we can use either substitution or elimination method. Let's use the elimination method.
Multiply equation (1) by 3 and equation (2) by 2 to make the coefficients of "R" in both equations equal:
6R + 36I = 420 ...(3)
12R + 12I = 240 ...(4)
Now, subtract equation (4) from equation (3):
(6R + 36I) - (12R + 12I) = 420 - 240
-6R + 24I = 180 ...(5)
Now we have a new equation (5) that relates "R" and "I".
Let's solve equations (5) and (2) together:
-6R + 24I = 180 ...(5)
6R + 6I = 120 ...(2)
Add equation (5) and equation (2):
(6R - 6R) + (24I + 6I) = 180 + 120
30I = 300
Divide both sides of the equation by 30:
I = 10
Now substitute the value of "I" into equation (2) to find the value of "R":
6R + 6(10) = 120
6R + 60 = 120
6R = 120 - 60
6R = 60
Divide both sides of the equation by 6:
R = 10
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Suppose a student picks 3 points at random from A, B, C, and D shown below. Find the probability that these randomly chosen points are collinear.
B
The probability that 3 randomly selected points from A, B, C, and D are collinear is
(Type an integer or a simplified fraction.)
Answers
The probability that 3 randomly selected points from A, B, C, and D are collinear is; 3/4
How to Identify Collinear Points?
Collinear points are the points that lie on the same straight line or in a single line. If two or more than two points lie on a line close to or far from each other, then they are said to be collinear.
Now, from the given image, there are 4 points but only three of them namely A, B and C are collinear. Thus, the 4 possible points picked could be; ABC, ABD, ACD, BCD
Thus, there are only three that can be collinear and so the probability is; 3/4
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Find the value of X.
Answers
Answer:
x=28
Step-by-step explanation:
90-33=57
2x+1=57
2x=56
x=28
I don’t like to beg but I guess I’m in need..
Answers
Answer:
-4 < n ≤ 5
Step-by-step explanation:
Since the left inequality is an open circle and going to the right, the sign will be >
Since the right inequality sign is a closed circle and is going left, the sign would be ≤
The open circle ends at -4 so, n > -4
The closed circle ends at 5 so, n ≤ 5
You combine them and it looks like this:
-4 < n ≤ 5
A local company employs a varying number of employees each year, based on its needs. The labor costs for the company include a fixed cost of $32,782.00 each year, and $31,009.00 for each person employed for the year. For the next year, the company projects that labor costs will total $3,133,682.00. How many people does the company intend to employ next year?
Answers
Let's start by using the formula for the total labor cost:
Total labor cost = Fixed cost + (Number of employees x Cost per employee)
We know that the fixed cost is $32,782.00, and the cost per employee is $31,009.00. Let's represent the number of employees with the variable "x". So we have:
$3,133,682.00 = $32,782.00 + (x * $31,009.00)
Simplifying the equation:
$3,133,682.00 - $32,782.00 = x * $31,009.00
$3,100,900.00 = x * $31,009.00
x = $3,100,900.00 / $31,009.00
x ≈ 100
Therefore, the company intends to employ approximately 100 people next year.
Helpppppppppp plssssss
Answers
Given the ______ of the z-distribution, the p-value for a two-tailed test is twice that of the p-value for a one-tailed test.
Answers
Answer:
the answer is symmetry.
Which of the following is true about the curve x^2 - xy + y^2 = 3 at the point (2,1)?
all of these are different answers, only one can be right.
a: dy/dx exists at (2,1) but there is no tangent line at that point
b; dy/dx exists at (2,1) , and the tangent line at that point is horizontal
c; dy/dx exists at (2,1), and the tangent line at that point is neither horizontal nor vertical
d: dy/dx does no exists at (2,1) and the tangent line at that point is vertical.
Answers
The correct answer is option C. At the point (2,1) on the curve x² - xy + y²= 3, the derivative dy/dx exists, and the tangent line at that point is neither horizontal nor vertical.
To determine the correct option, we need to analyze the properties of the curve x² - xy + y² = 3 at the point (2,1). First, let's find the derivative dy/dx. Taking the derivative of the given equation implicitly with respect to x, we get:
2x - y - x(dy/dx) + 2y(dy/dx) = 0
Rearranging the terms, we have:
dy/dx = (2x - y) / (x - 2y)
Now, substituting the values x = 2 and y = 1 into the expression for dy/dx, we can determine its value at the point (2,1):
dy/dx = (2(2) - 1) / (2 - 2(1)) = 3 / 0
Since the denominator is zero, dy/dx is undefined at (2,1). Therefore, option D, stating that dy/dx does not exist at (2,1) and the tangent line at that point is vertical, is incorrect.
However, we can still determine the nature of the tangent line at (2,1). Although the derivative is undefined, it is still possible for the tangent line to exist and have a defined slope. In this case, the tangent line would be neither horizontal nor vertical. Therefore, option C, which states that dy/dx exists at (2,1) and the tangent line at that point is neither horizontal nor vertical, is the correct answer.
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Ms. Rivera created two dot plots to compare the results of her recent science quiz for 1st period students compared to 7th period students. The dot plots are displayed to the right. Use this information to answer the questions below.
Answers
The dot plots is an illustration of charts and graphs
The average score of period 7 is greater than the average score of period 1
How to determine the period with the higher average?From the dot plots in the complete question, we have the following frequency tables
Period 1 Period 7
Score Students Score Students
55 1 65 1
70 1 75 3
75 6 80 5
80 6 85 6
85 2 90 3
90 3 95 2
95 1
The average is calculated using:
\(\bar x = \frac{\sum fx}{\sum f}\)
For period 1, we have:
\(\bar x_1 = \frac{55 * 1 + 70 * 1 + 75 * 6 + 80 * 6 + 85 * 2 + 90 * 3 + 95 * 1}{1 + 1 + 6 + 6 + 2 + 3 + 1}\)
Evaluate the sum
\(\bar x_1 = \frac{1590}{20}\)
Evaluate the quotient
\(\bar x_1 = 79.5\)
For period 7, we have:
\(\bar x_7 = \frac{65 * 1 + 75 * 3 + 80 * 5 + 85 * 6 + 90 * 3 + 95 * 2}{1 + 3 + 5 + 6 + 3 + 2}\)
Evaluate the sum
\(\bar x_7 = \frac{1660}{20}\)
Evaluate the quotient
\(\bar x_7 = 83\)
By comparison, 83 is greater than 79.5
Hence, the average score of period 7 is greater than the average score of period 1
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1a. Explain why chess is not a static game of complete information?
Answers
Chess is not a static game of complete information for several reasons. Firstly, the game is dynamic, meaning that the position of the pieces on the board changes constantly throughout the game.
Unlike in games like Tic Tac Toe or Connect Four, the state of the game at any given point is not fixed, and there are a vast number of possible outcomes. This means that players cannot simply memorize the best moves and outcomes for every situation, as they would in a game of complete information.
Secondly, chess is a game of imperfect information, as both players do not know what moves their opponent will make. Even with a complete understanding of the game's rules, players cannot predict with certainty the moves of their opponent, and must instead make strategic decisions based on their best assessment of their opponent's likely choices.
Finally, chess is a game of hidden information, as players do not know what their opponent is thinking or planning. A player may be able to predict their opponent's next move, but cannot know for sure what their long-term strategy is, making it difficult to make optimal decisions.
Overall, chess is a highly dynamic and complex game that is not static or complete in terms of information. Players must make strategic decisions based on incomplete and uncertain information, making it a challenging and rewarding game for those who play it.
Chess is a strategic board game played between two players, with each player starting with 16 pieces on a 64-square board. The game has been around for centuries and is considered one of the most popular and complex games in the world.
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Line segment Z E is the angle bisector of AngleYEX and the perpendicular bisector of Line segment G F. Line segment G X is the angle bisector of AngleYGZ and the perpendicular bisector of Line segment E F. Line segment F Y is the angle bisector of AngleZFX and the perpendicular bisector of Line segment E G. Point A is the intersection of Line segment E Z, Line segment G X, and Line segment F Y.
Triangle G E F has angles with different measures. Point A is at the center. Lines are drawn from the points of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A X, A Z, and A Y.
Which must be true?
Point A is the center of the circle that passes through points E, F, and G but is not the center of the circle that passes through points X, Y, and Z.
Point A is the center of the circle that passes through points X, Y, and Z but is not the center of the circle that passes through points E, F, and G.
Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
Point A is not necessarily the center of the circle that passes through points E, F, and G or the center of the circle that passes through points X, Y, and Z
Answers
The correct option that depicts the centroid of the triangle is; C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
How to interpret the segments formed from Triangle Centroid?The center of inscribed circle into the triangle is the point where the angle bisectors of the triangle meet.
The center of the circumscribed circle over the triangle is the point where the perpendicular bisectors of the sides meet.
Line segments ZE, FY and GX are both angle bisectors and perpendicular bisectors of the sides. Thus, the point of intersection of line segments ZE, FY and GX is the center of inscribed circle into the triangle and the center of the circumscribed circle over the triangle.
Inscribed circle passes through the points X, Y and Z. Circumscribed circle passes through the points E, F and G. So, point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
Thus, the correct option is option C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
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Help? Please I’m desperate
Answers
Answer:
its called a calculator division and multiplication
Step-by-step explanation:
For whole number n, n3 will be odd if n is odd and even if n is even
Answers
So we want to prove that if n is not odd, then n^3 is not odd, i.e. if n is even, then n^3 is even.
If n is even, then it can be written as n = 2p, where p is some integer. n^3 = (2p)^3 = 2(4p^3), which is even. So if n is even, then n^3 is even.
A sales tax of P9,000 is added to a purchase of P120,000 worth of
jewelry. What is the rate of sales tax?
Answers
Answer:
Find the rate of sales tax
R= 9000/120000
=0.075
=7.5%
So, the rate is 7.5%
look at the image and answer please .
Answers
Answer:
(-2, 0)
Step-by-step explanation:
y=5/2x-5/6
find the slope and simplify
Answers
Answer:
5/2
Step-by-step explanation:
The slope of this equation is 5/2
Step by step explanation:
The slope of the line passing through the points (7, 5) and (21, 15) is
.
Another line with a slope that is one-third that of the slope you just calculated passes through the origin and the point
(21, 5)
.
Answers
Step-by-step explanation:
a) The slope formula is given by
m = (y2 - y1)/(x2 - x1)
Let P1(7, 5) and P2(21, 15)
m = (15 - 5)/(21 -7)
= 10/14
= 5/7
b) Let's see if the slope is only a third of the one found in part (a) or m = 5/21. Let P1(0, 0) and P2(21, 5).
m = (5 -0)/(21 - 0)
= 5/21
Indeed, the slope is only a third of part (a), as we predicted.
Answer:
the answers are 7/5 and (21,5)
Step-by-step explanation:
sorry this is late by 2 months
help me with geomtry please
Answers
Answer:
AM=8
Step-by-step explanation:
the length of BQ is the same as the length of PA, if BQ is 18 then, if PM is 10 then MA is 8 knowing that 18 is the whole length.
18-10=8
what is the area, in square units, of a triangle that has sides of $4,3$ and $3$ units? express your answer in simplest radical form.
Answers
Therefore, the area of the triangle is 2√5 square units, expressed in simplest radical form.
To find the area of a triangle, we can use Heron's formula, which states that the area (A) of a triangle with side lengths a, b, and c is given by:
A = √(s(s - a)(s - b)(s - c))
where s is the semi-perimeter of the triangle, calculated as:
s = (a + b + c) / 2
Given the side lengths of the triangle as 4, 3, and 3 units, we can calculate the semi-perimeter:
s = (4 + 3 + 3) / 2
= 5
Now, substituting the values into Heron's formula, we have:
A = √(5(5 - 4)(5 - 3)(5 - 3))
= √(5 * 1 * 2 * 2)
= √(20)
= 2√5
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The continuous random variable V has a probability density function given by: 6 f(v) = for 3 ≤ ≤7,0 otherwise. 24 What is the expected value of V? Number
Answers
The expected value of the continuous random variable V is 5. The expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.
To calculate the expected value of a continuous random variable V with a given probability density function (PDF), we integrate the product of V and the PDF over its entire range.
The PDF of V is defined as:
f(v) = 6/24 = 0.25 for 3 ≤ v ≤ 7, and 0 otherwise.
The expected value of V, denoted as E(V), can be calculated as:
E(V) = ∫v * f(v) dv
To find the expected value, we integrate v * f(v) over the range where the PDF is non-zero, which is 3 to 7.
E(V) = ∫v * (0.25) dv, with the limits of integration from 3 to 7.
E(V) = (0.25) * ∫v dv, with the limits of integration from 3 to 7.
E(V) = (0.25) * [(v^2) / 2] evaluated from 3 to 7.
E(V) = (0.25) * [(7^2 / 2) - (3^2 / 2)].
E(V) = (0.25) * [(49 / 2) - (9 / 2)].
E(V) = (0.25) * (40 / 2).
E(V) = (0.25) * 20.
E(V) = 5.
Therefore, the expected value of the continuous random variable V is 5.
The expected value represents the average value or mean of the random variable V. It is the weighted average of all possible values of V, with each value weighted by its corresponding probability. In this case, the expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.
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8. 1219 kg of Swiss cheese is
packaged in 3 kg bags. Will there be
any cheese left over? How do you
know?
Answers
Answer:
1.divide the total kg of swiss cheese by kg per bag.
2.if the answer comes out in decimals or fraction then there is leftover cheese, if not then there won't be any cheese left.
3.1219/3=406.33333
This means there is only enough cheese for 406 bags and a bit of left over.
Eva is working two summer jobs, making $16 per hour tutoring and $8 per hour clearing tables. Last week Eva worked 3 times as many hours clearing tables as she worked hours tutoring hours and earned a total of $80. Graphically solve a system of equations in order to determine the number of hours Eva worked tutoring last week, x,x, and the number of hours Eva worked clearing tables last week, yy.
Answers
Answer:
48 and 32 6 hours clearing tables and 2 hours tutoring
Step-by-step explanation:
we can rewrite this as a fraction. we will use 1/10s because 80 can be divided by 8 which is in the problem. we then have to find out what two numbers add up to 8 but one is 3 times the other. 6 and 2 fit into this problem so we plug it into the equation and we write it as this 6x+4x=80 where x is 8. we get 48 and 32.
Write a variable expression for each phrase
1. M more than nineteen
2. 8 less than z
3. N divided by 3
4. 3 divided by n
5. The sum of 5 and a
6. Thirty-two times g
No links
Answers
Answer:
1.M+19
2. Z-8
3. N/3
4. 3/N
5. 5+a=x
6. 32g
suppose that for some hypothesis test on the mean of a normally distributed population, standard deviation known, the p-value is computed as 0.11. if a level of significance of 0.05 is used, is rejecting the null hypothesis in favor of the alternative the correct decision?
Answers
If the p-value for a hypothesis test is greater than the chosen level of significance, then the null hypothesis cannot be rejected.
In this case, the p-value is 0.11 and the level of significance is 0.05. Since the p-value is greater than the level of significance, we cannot reject the null hypothesis.
Therefore, we do not have sufficient evidence to conclude that the population mean is different from the hypothesized value. In other words, we do not have enough evidence to support the alternative hypothesis.
Thus, rejecting the null hypothesis in favor of the alternative hypothesis is not the correct decision in this case.
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When point A(-4,2) ir rotated 90 degrees
counterclockwise, where is the image of
A?
(-2,-4)
(-4,-2)
Answers
Answer:
(-2, -4)
Step-by-step explanation:
Given the coordinate (x, y), if rotated 90degrees, counterclockwise, the resulting coordinate will be (-y, x)
For the coordinate (-4, 2)
When rotated 0 degrees counterclockwise, the resulting coordinate will be at (-2, -4)
Note that the coordinates were switched and the x negated