The correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.
The standard equation of an ellipse is (x-h)^2 / a^2 + (y-k)^2 / b^2 = 1, where (h,k) is the center of the ellipse, a is the distance from the center to the vertices, and b is the distance from the center to the covertices.
In this case, the center of the ellipse is the midpoint of the vertices and covertices, which is (7, -2). The distance from the center to the vertices is 5 (12-7) and the distance from the center to the covertices is 3 (1-(-2)).
Therefore, the standard equation of the ellipse is (x-7)^2 / 25 + (y+2)^2 / 9 = 1, which corresponds to answer choice (a).
So the correct answer is (a) (x-7)^2 / 25 + (y+2)^2 / 9 = 1.
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The height of a plant over time is shown in the table below. Using a logarithmic model, what is the best estimate for the age of the plant when it is 19 inches tall?
Moreover, we should evaluate the model's goodness of fit and take into expressions account additional elements that can influence plant development.
what is expression ?Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression. For example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
In the formula, h is the height, t is the time, and a and b are the parameters that need to be approximated.
The information in the table may be used to estimate the values of a and b. The equation is first transformed to yield:
[tex]log(b*t) = log(h/a)[/tex]
[tex]19 = 19.24 * log(53.89*t)[/tex]
t = 0.186 months, or approximately 5.58 days, or log(53.89*t) = 1 53.89*t = 10
Hence, 5.58 days is the best guess for the age of the plant at 19 inches tall. Seeing that this is a very little period of time, it is probable that the model will not be correct for values of t this low. Moreover, we should evaluate the model's goodness of fit and take into account additional elements that can influence plant development.
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the population in a particular country is growing at the rate of 1.6% per year. If 5,092,000 people lived there in 1999, how many will there be in the year 2003? Use f(x)=y 0^e^0.016t and round to the nearest ten-thousand.
The population in 2003 is 5,830,000.
The population in a particular country is growing at the rate of 1.6% per year. To calculate the population for 2003, we can use the formula f(x)=y[tex]0^e^0.016t[/tex] .
Where y0 is the population in 1999 and t is the time in years.
Plugging in the numbers we have y0 = 5092000 and t = 4 for the year 2003, the formula looks like this: f(x)=5092000e0[tex]^{016(4)[/tex].
Solving this equation, we get f(x)=5837280, which is the population in 2003. Rounding this number to the nearest ten-thousand, the population in 2003 is 5,830,000.
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Describe all the x-values at a distance of 22 or less from the number
9.
Enter your answer in interval notation.
To enter [infinity], type infinity. To enter ∪, type U.
The x-values at a distance of 22 or less from the number 9 are all the numbers in the interval [-13, 31].
The x-values at a distance of 22 or less from the number 9 can be found by solving the inequality |x-9|≤22.
Step 1: Break up the absolute value inequality into two separate inequalities:
x-9≤22 and x-9≥-22
Step 2: Solve each inequality for x:
x≤31 and x≥-13
Step 3: Combine the two inequalities using the "and" operator (∩):
-13≤x≤31
Step 4: Write the solution in interval notation:
[-13, 31]
So, the x-values at a distance of 22 or less from the number 9 are all the numbers in the interval [-13, 31].
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sharah has 35 coins in her pocket, all of which are dimes and quarters. if they are worth a total of $5.30, how many of each kind dose she have?
The number of each kind of coins Sharah have is 23 dimes and 12 quarters.
Let's use a system of equations to solve this problem. Let x be the number of dimes and y be the number of quarters that Sharah has. Then, we can write the following equations:
x + y = 35 (the total number of coins)
0.10x + 0.25y = 5.30 (the total value of the coins)
We can use the first equation to solve for one of the variables in terms of the other. Let's solve for x:
x = 35 - y
Now we can substitute this into the second equation:
0.10(35 - y) + 0.25y = 5.30
3.50 - 0.10y + 0.25y = 5.30
0.15y = 1.80
y = 12
Now we can use this value of y to solve for x:
x = 35 - 12 = 23
So Sharah has 23 dimes and 12 quarters.
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Please help me answer this
Answer: I think B & C not super sure though
Choose the correct answer from the drop-down menu. Use properties of operations to determine whether or not 3(x+2)+8 and 3x+14 are equivalent. Select... We can not determine whether the expressions are equivalent or not. The expressions are equivalent. The expressions are not equivalent.
"The expressions are equivalent." We can use the distributive property to determine whether or not the expressions are equivalent.
First, let's apply the distributive property to the first expression:
3(x+2) + 8 = 3x + 6 + 8
Next, let's simplify the expression by combining like terms:
3x + 6 + 8 = 3x + 14
Now, we can see that the two expressions are equivalent because they both simplify to the same expression, 3x + 14. Therefore, we can conclude that the expressions are equivalent.
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DUE TODAY PLEASE HELP NOW!!!!!!!!!!!!!
Here is another triangle similar to DEF found in the lesson section labeled “Shrinking Triangles”.
• Label the triangle D”E”F”.
• What is the scale factor from triangle DEF to triangle D”E”F”?
• What are the coordinates of F”? Explain how you know.
• What are cos(D”), sin(D”), and tan(D”)?
The scale factοr οf dilatiοn is 1/40 and the cοοrdinates οf F" are (1440, 600)
Labelling the image οf the triangle
The image οf the label is attached
The scale factοr οf the dilatiοn
Given that
D'E' = 36 units
Then, we have
D"E" = 0.9 units
The scale factοr is calculated as
Scale factοr = D"E"/D'E'
Sο, we have
Scale factοr = 0.9/36
Evaluate
Scale factοr = 1/40
Sο, the scale factοr οf dilatiοn is 1/40
The cοοrdinates οf F"
This is calculated as
F = F'/Scale factοr
Sο, we have
F = (36, 15)/(1/40)
F = (1440, 600)
The trigοnοmetry ratiοs
The trigοnοmetry ratiοs are calculated as
sin(D") = EF/DF
cοs(D") = DE/DF
tan(D") = EF/DE
Sο, we have the fοllοwing apprοximated values
sin(D") = 15/39 = 0.36
cοs(D") = 36/39 = 0.92
tan(D") = 0.36/0.92 = 0.39
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Which system of inequalities is represented by the graph?
The following system of inequalities is represented by the graph
x+y>3
-x+y< -4
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
Consider the inequalities:
x+y>3-------(1)
-x+y< -4------(2)
Find x and y intercepts of both by considering them as equations by using equal sign in the place of inequality sign
x+y=3-------(3)
-x+y= -4------(4)
Find x and intercepts of these 2 equations:
we get x intercept when y=0 ( substitute y=0 into the respective equations and find x)
we get y intercept when x=0 ( substitute x=0 into the respective equations and find y)
x intercept of (3) is (3,0)
y intercept of (3) is (0,3)
x intercept of (3) is (4,0)
y intercept of (3) is (0,-4)
plot these points on a the plane and join them with lines
use dotted line and shade under the lines because of less than symbol
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Kendra bought a pair of $125 jeans for $93.75. What percent was taken off from the original price?
Answer:
25%
Step-by-step explanation:
p/w =x/100 for a percentage
93.75/125 = x/100
93.75×100= 9375
9375 = 125x
9375/125 =75
x=75
So she paid 75% of the original price, meaning the jeans were 25% off.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representations of the inequality –3(2x – 5) < 5(2 – x) are given as follows:
x > 5.An open circle is at 5 and a bold line starts at 5 and is pointing to the right.What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: amount greater than x -> to the right of x with an open dot at the number line. -> above the dashed horizontal line y = x on the coordinate plane.< x: amount less than x. -> to the left of x with an open dot at the number line. -> below the dashed horizontal line y = x on the coordinate plane.≥ x: amount at least x. -> to the right of x with a closed dot at the number line. -> above the solid horizontal line y = x on the coordinate plane.≤ amount at most x. -> to the left of x with a closed dot at the number line. -> above the dashed horizontal line y = x on the coordinate plane.The inequality for this problem is defined as follows:
–3(2x – 5) < 5(2 – x)
Expanding the operations, the solution is obtained as follows:
-6x + 15 < 10 - 5x
-6x + 5x < 10 - 15
-x < -5
x > 5.
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Talia deposits $350 in her savings account. The account earns 2.5% simple interest per year. What is the balance in the account after 4 years?
Answer:385
Formulate and substitute:F=350+350rt
Calculate the product or quotient:350x1+0.1
Calculate the sum or difference:350x1.1
Calculate the product or quotient:385
theres a picture of what I need help with thank you so much! Have an amazing day and will also mark brainliest <3
Answer:
5x4
Step-by-step explanation:
The dimensions of the rectangle are 20x16
The reducing factor is 0.25.
Multiple 20 * 0.25= 5
Multiple 16 * 0.25= 4
Therefore the new dimensions are 5x4.
Abbie bought 82 cases of water for her restaurant Each case had 24 bottles of water How many bottle of water did Abbie buy in all?
Answer:
1968 bottles of water
Step-by-step explanation:
24×82=1968
1968 bottles of water
Find the volume of the figure below in terms of pi.
A. 36pi
B: 288pi
C: 144pi
D: 864pi
Work Shown:
[tex]V = \text{Volume of a sphere}\\\\V = \frac{4}{3}\pi*r^3\\\\V = \frac{4}{3}\pi*6^3\\\\V = \frac{4}{3}\pi*216\\\\V = \frac{4}{3}*216\pi\\\\V = 288\pi\\\\[/tex]
Find the LCM of:
x² - 3x + 2, x² + x + 2
Answer:
The two polynomials cannot be factored using integer coefficients. Therefore, we need to use the quadratic formula to find their roots:
For x² - 3x + 2 = 0:
a = 1, b = -3, c = 2
x = (-(-3) ± √((-3)² - 4(1)(2))) / (2(1)) = (3 ± √1) / 2
x = 1 or x = 2
For x² + x + 2 = 0:
a = 1, b = 1, c = 2
x = (-1 ± √(1² - 4(1)(2))) / (2(1)) = (-1 ± √(-7)) / 2
x = (-1 ± i√7) / 2
Therefore, the LCM of x² - 3x + 2 and x² + x + 2 is:
(x - 1)(x - 2)(x - (-1/2 + i√7/2))(x - (-1/2 - i√7/2))
Use the Intermediate Value Theorem to show thatf has a zero
between a and b .
f(x)=2x 3 +6x 2
-3 a -2
There is a zero for f(x) between a and b.
How to calculateUsing the Intermediate Value Theorem, we can show that the function f(x)=2x3+6x2-3a-2 has a zero between a and b.
The Intermediate Value Theorem states that if a continuous function f(x) takes on different values at two points a and b, then there must exist at least one value c in between a and b such that f(c) = 0. Since f(x) is a continuous function, it takes on different values at a and b.
Thus, by the Intermediate Value Theorem, there must exist at least one value c in between a and b such that f(c) = 0, meaning that there is a zero for f(x) between a and b.
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given f(x)=x^3-27x+5 answer the following:
Is the function increasing or decreasing at x=2?
List the interval (a,b) where the f(x) is increasing.
At what x-value does f(x) have a relative maximum?
(a) The function is decreasing at x=2.
(b) The interval where f(x) is increasing is (-3, 3).
(c) The function, f(x) has a relative maximum at x=-3.
Is the function increasing or decreasing at x=2?
To determine whether the function is increasing or decreasing at x=2, we need to find the derivative of f(x) and evaluate it at x=2.
f(x) = x³ - 27x + 5
f'(x) = 3x² - 27
At x=2, f'(2) = 3(2)² - 27 = -15, which is negative.
Therefore, the function is decreasing at x=2.
To find the interval where f(x) is increasing, we need to find the values of x where f'(x) > 0.
f'(x) = 3x² - 27
3x² - 27 > 0
3(x² - 9) > 0
(x - 3)(x + 3) > 0
The critical points are x=-3 and x=3.
We can test each of the intervals created by these critical points to see where f(x) is increasing or decreasing.
When x < -3, f'(x) < 0, so f(x) is decreasing.
When -3 < x < 3, f'(x) > 0, so f(x) is increasing.
When x > 3, f'(x) > 0, so f(x) is increasing.
Therefore, the interval where f(x) is increasing is (-3, 3).
To find the relative maximum of f(x), we need to find the critical points where f'(x) = 0.
3x² - 27 = 0
x² - 9 = 0
(x - 3)(x + 3) = 0
The critical points are x=-3 and x=3.
To determine which of these critical points corresponds to a relative maximum, we need to use the second derivative test.
f''(x) = 6x
At x=-3, f''(-3) = -18, which is negative.
Therefore, f(x) has a relative maximum at x=-3.
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Please I news help please send me the full explanation please
List three additional combos of length width and height that have a volume of 24 and please include the surface area too
The solution is then:
l = 6cm
w = 2cm
h = 2cm
What is the total surface area of cuboid?The surface area of a cuboid is the total area of all of the faces of a cuboid. If, the length (l), width (w), and height (h) of the cuboid
then, use the formula: surface area (SA)=2lw+2lh+2hw.
here, we have,
We know that the formula for the volume of a box is:
V = l*w*h
Where:
l = length
w = width
h = height
The formula of the surface area of a box is:
SA = 2(lw+lh+wh)
Based on the given we know the following:
24 = l*w*h
and
56 = 2(lw+lh+wh)
If we factor out the given volume, you can come up with 3 numbers that will satisfy the surface area formula:
24 = 6*2*2
Let:
l = 6cm
w =2cm
h =2cm
Now let's try this on the surface area formula:
56 = 2(6*2+6*2+2*2)
so, 56 = 56
The answer is then:
l = 6cm
w = 2cm
h = 2cm
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For g(x)=2x/3, find g(3) and g(12)
In response to the supplied query, we may state that Therefore, equation g(12) = 8.
What is equation?Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.
To find g(3), we substitute x=3 into the function g(x):
g(3) = 2(3)/3
g(3) = 6/3
g(3) = 2
Therefore, g(3) = 2.
To find g(12), we substitute x=12 into the function g(x):
g(12) = 2(12)/3
g(12) = 24/3
g(12) = 8
Therefore, g(12) = 8.
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O is the center of the regular octagon below. Find its perimeter. Round to the nearest tenth if necessary.
The perimeter of the regular octagon with an apothem of 5 units will be 33.14 units.
What is the perimeter of the regular polygon?All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.
P = (Side length) x n
The Apothem of a regular octagon is 5 units. Then the side length of the regular octagon is given as,
tan (360° / (2 × 8)) = (n/2) ÷ 5
tan 22.5° = n / 10
n = 4.142
Then the perimeter is given as,
P = 8 x 4.142
P = 33.14 units
The perimeter of the regular octagon with an apothem of 5 units will be 33.14 units.
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-15y-4
45
27
38%
十
15
24
Find X and
Find Y
Answer:
42
Step-by-step explanation:
you asding it all up
Watch help video What are the roots of the equation x^(2)-12x+61=0 in simplest a+bi form?
The roots of the equation x^(2)-12x+61=0 in simplest a+bi form are 6 + 5i and 6 - 5i.
The roots of the equation x^(2)-12x+61=0 in simplest a+bi form can be found using the quadratic formula.
The quadratic formula is x = (-b ± √(b^(2)-4ac))/(2a), where a, b, and c are the coefficients of the equation. In this case, a = 1, b = -12, and c = 61.
Plugging in the values into the quadratic formula, we get:
x = (-(-12) ± √((-12)^(2)-4(1)(61)))/(2(1))
Simplifying the equation, we get:
x = (12 ± √(144-244))/2
x = (12 ± √(-100))/2
Since the square root of a negative number is a complex number, we can write the equation as:
x = (12 ± 10i)/2
Simplifying further, we get:
x = 6 ± 5i
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A company makes a single serving cereal box that contains a volume of 1. 2 ounces of cereal. They plan to make an extra large box for school cafeterias. The extra large box will be dilation of the single serving box using a scale factor of 4. How many ounces of cereal will the extra large box contain?
If the extra large box have a dilation scale factor of 4, then the extra large box contain 76.8ounces.
If the extra large box is a dilation of the single serving box with a scale factor of 4, then
The ratio of the volumes of the extra large box to the single serving box will be 4³,
We know that, Volume is a three-dimensional measurement and is affected by the cube of the scale factor.
So, the volume of the extra large box will be;
⇒ 4³ × 1.2 ounces = 4×4×4×1.2 ounces = 76.8 ounces,
Therefore, the extra large box will contain 76.8 ounces of cereal.
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1 Select the correct answer. What is the simplified form of this expression? (-3x² + 4x) + (2x²-x-11)
a. -x2 + 5x − 11
b. -x² + 3x - 11
c. -x² + 3x + 1
d. -x2 + 5x + 11
Blynomials: Mastery Test
The value of the given expression is - x² + 3x - 11 and option b is the correct answer.
What is binomial expression?Binomial is the name for an algebraic expression with only two terms. It is a polynomial with two terms. It is sometimes referred to as the sum or difference of two or more monomials. It is a polynomial's most basic form. Therefore, A binomial is a two-term algebraic statement that includes a constant, exponents, a variable, and a coefficient.
The given expression is:
(-3x² + 4x) + (2x²-x-11)
-3x² + 4x + 2x² - x - 11
Subtract the like terms:
- x² + 3x - 11
Hence, the value of the given expression is - x² + 3x - 11 and option b is the correct answer.
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Question 4 Solve the inequality and write your answer in interval notation 16+12x<19x+12
The solution to the inequality 16 + 12x < 19x + 12 is all the values of x between the interval notation (4/7, ∞).
To solve the inequality 16 + 12x < 19x + 12, we need to isolate the variable x on one side of the inequality. We can do this by subtracting 12x from both sides and subtracting 12 from both sides:
16 + 12x - 12x - 12 < 19x + 12 - 12x - 12
4 < 7x
Solving for x, we can divide both sides by 7:
4/7 < x or x > 4/7
In interval notation, this would be (4/7, ∞). Therefore, the solution to the inequality is (4/7, ∞) in interval notation.
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Based on the results in the table, about how
many times should Jaylon and Paula expect the
pointer to land on 4 out of a total of 130 spins
Jaylon and Paula should expect the pointer to land on 4 around 30 and 43 times respectively.
What is the experimental probability?A probability calculated by a series of tests is known as experimental probability.
The given table is as follows:
1 2 3 4
Jaylon: 6 8 9 7
Paula: 8 5 7 10
To determine the experimental probability of the pointer landing on 4 for Jaylon, we add up the number of times the pointer landed on 4 for Jaylon and divide by the total number of spins:
Experimental probability for Jaylon = (number of times the pointer landed on 4 for Jaylon) / (total number of spins)
= 7 / 30
Similarly,
Experimental probability for Paula:
= 10 / 30
Expected number of times the pointer will land on 4 = (experimental probability) x (total number of spins)
For Jaylon: (7 / 30) × 130 = 30.33
For Paula: (10 / 30) × 130 = 43.33
Therefore, Jaylon and Paula should expect the pointer to land on 4 around 30 and 43 times respectively.
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The missing table has been attached below.
Help solve this question
The measure of angle FLI is 56=
What is sum of angle in triangle?The sum of angles of a triangle equals the straight angle. A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides. It was unknown for a long time whether other geometries exist, for which this sum is different.
Therefore the sum of angle in a triangle is 180
Since FIL is right angle , then angle FLI =
180-(90+34)
= 180- 124
= 56°
therefore the measure of angle FLI is 56°
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What are the solutions of the equation 0=x^2-9x+8
The solutions of the equation 0=x^2-9x+8 are x = 8 and x = 1
How to determine the solutions of the equationFrom the question, we have the following parameters that can be used in our computation:
0=x^2-9x+8
Rewrite as
x^2 - 9x + 8 = 0
Expand the equation
So, we have the following representation
x^2 - 8x - x + 8 = 0
When the equation is factorized, we have
(x - 8)(x - 1) = 0
This gives
x - 8 = 0 and x - 1 = 0
Evaluate
x = 8 and x = 1
Hence, the solutions are x = 8 and x = 1
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The volume of a cylinder is 12,566.4 cm cubed. The height of the cylinder is 8 cm.
a) Find the radius of the cylinder to the nearest tenth of a centimeter.
b) Find the area of the base of the cylinder to the nearest tenth of a centimeter.
c) Find the lateral area to the nearest tenth of a centimeter.
d) Find the surface area of the cylinder.
As a result of the cylinder's volume being 12,566.4 centimetres³ and its height being 8 cm, the surface area of the cylinder is approximately 942.5 cm².
what is volume ?
Volume in mathematics refers to how much room a three-dimensional object takes up. It is a way to quantify how much enclosed room there is overall in a solid figure. Depending on the shape of the item, a number of formulas can be used to calculate its volume. A rectangular prism's volume, for instance, can be calculated by multiplying its length, breadth, and height, whereas a cylinder's volume can be calculated by dividing its base area by its height. The system being used will determine the unit of measurement for volume, but typical units include cubic metres (m³) and cubic centimetres (cm³).
given
a) V = πr²h, where V is the volume, r is the radius, and h is the height, is the expression for a cylinder's volume. By rearranging the calculation, we can find r:
V/(h) = √12,566.4/(*8)) Equals r ≈ 10 centimetres (rounded to the closest tenth of a cm) (rounded to the nearest tenth of a cm)
Consequently, the cylinder's radius is roughly 10 centimetres.
b) The equation A = r² determines the area of a cylinder's base. Using the r number we just discovered, we have:
A = π(10)² ≈ 314.2 cm² (rounded to the closest tenth of a cm) (rounded to the nearest tenth of a cm)
Consequently, the cylinder's base has a surface area of about 314.2 cm².
c) The equation L = 2πrh, where r is the radius and h is the height, determines the lateral area of a cylinder. With the numbers from the problem substituted, we obtain:
L = 2π(10)(8) ≈ 502.7 cm² (rounded to the closest tenth of a cm) (rounded to the nearest tenth of a cm)
Consequently, the cylinder's side area is roughly 502.7 cm².
d) The equation S = 2πr² + 2πrh gives the surface area of a cylindrical. Using the r and h numbers we discovered earlier, we have:
S = 2π(10)² + 2π(10)(8) ≈ 942.5 cm² (rounded to the nearest tenth of a centimetre) (rounded to the nearest tenth of a cm)
As a result of the cylinder's volume being 12,566.4 centimetres³ and its height being 8 cm, the surface area of the cylinder is approximately 942.5 cm².
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