Answer:
I think that the answer is c
To solve the system of equations, subtract one equation from another to eliminate a variable, then substitute back to find the values of x, y, and z. The correct solution is (x = 0, y = 1, z = 0).
To solve this system of equations, we can use various methods such as substitution, elimination, or matrices. Let's solve it using elimination:
Given the system of equations:
1. ( 4x + 3y + 6z = 3 )
2. ( 5x + 5y + 6z = 5 )
3. ( 6x + 3y + 6z = 3 )
We'll eliminate one variable at a time. Let's start by eliminating ( z ):
From equations 1 and 3, we see that (4x + 3y + 6z) and (6x + 3y + 6z) have the same coefficients for ( z ) but different constants. Subtracting equation 3 from equation 1, we get:
[ (4x + 3y + 6z) - (6x + 3y + 6z) = 3 - 3 ]
[ 4x - 6x = 3 - 3 ]
[ -2x = 0 ]
[ x = 0 ]
Now, substitute ( x = 0 ) into one of the original equations. Let's use equation 1:
[ 4(0) + 3y + 6z = 3 ]
[ 3y + 6z = 3 ]
[ 3y = 3 - 6z ]
[ y = 1 - 2z ]
Now, we have expressions for ( x ) and ( y ). Let's substitute ( x = 0 ) and ( y = 1 - 2z ) into equation 2:
[ 5(0) + 5(1 - 2z) + 6z = 5 ]
[ 5 - 10z + 6z = 5 ]
[ -4z = 0 ]
[ z = 0 ]
So, we found ( x = 0 ), ( y = 1 - 2z = 1 - 2(0) = 1 ), and ( z = 0 ).
Therefore, the solution to the system of equations is ( (x = 0, y = 1, z = 0) ), which corresponds to option c.
Kwame's team will make two triangular pyramids to decorate the entrance to the exhibit. They will be wrapped in the same metallic foil. Each base is an equilateral triangle. If the base has an area of about 3.9 square feet, how much will the team save altogether by covering only the lateral area of the two pyramids? The foil costs $0.24 per square foot. Kwame's team will save $
, altogether by covering only the lateral area of the two pyramids.
Answer:
Kwame's team will save = 7.8 [tex]\times[/tex] $0.24 = $1.87
Step-by-step explanation:
i.) Let the side of the equilateral triangle base be a
ii.) the area of the base = 3.9 square feet
iii.) the area of equilateral triangle is = [tex]\frac{\sqrt{3} }{4} a^{2}[/tex] = 3.9
iv.) Base area = 3.9 square feet
v.) The area that is not covered is the base.
vi.) The total area that is not covered = 3.9 [tex]\times[/tex] 2 since there are two pyramids
therefore the total area not covered = 7.8 square feet
vii.) therefore Kwame's team will save = 7.8 [tex]\times[/tex] $0.24 = $1.87
5. Claire is buying a new bicycle for $295. If the
sales tax is 4.75%, what will she pay in total?
Claire will pay $309.01 for the bike.
The world's population has grown at an average rate
of 1.9 percent per year since 1945. There were
approximately 4 billion people in the world in 1975.
Which of the following functions represents the
world's population P, in billions of people,
1 years since 1975 ? (1 billion = 1,000,000,000)
A) P(t) = 4(1.019)
B) P(t) = 4(1.9)
C) P(t) = 1.194 + 4
D) P(t) = 1.0197 +4
Answer:
[tex]P(t)=4(1.019)^t[/tex]
Step-by-step explanation:
we know that
The equation of a exponential growth function is equal to
[tex]P=a(1+r)^t[/tex]
where
P ---> is the world's population
t ---> is the number of years since 1945
a ---> is the initial population in 1945
r ---> is the percent rate of growth
we have
[tex]r=1.9\%=1.9/100=0.019[/tex]
substitute
[tex]P=a(1+0.019)^t[/tex]
[tex]P=a(1.019)^t[/tex]
Remember that
There were approximately 4 billion people in the world in 1975
That means
Since year 1975 the initial value a=4 billion people
substitute
[tex]P(t)=4(1.019)^t[/tex]
IS 8.8 GREATER THAN 8.01
Answer:
Yes, it is.
Step-by-step explanation:
The second 8 in 8.8 is greater than the 0 in 8.01.
Please help me i rlly need it
Answer:
im stuck on a similar problem right now
Answer:
8.2
Step-by-step explanation:
Use cosine law:
BC² = 7² + 9² - 2(7)(9)cos(60)
BC² = 67
BC = sqrt (67)
BC = 8.1853
BC = 8.2 (nearest tenth)
351 rounded to the nearest 10
Answer:
350 is your answer
Step-by-step explanation:
anything lower than five you wouldn't round up you'd round down so basically the 1 is pointless
Rounding 351 to the nearest 10 gives us 350, as per the rule of place value while rounding.
When rounding a number to the nearest 10, we consider the digit in the tens place. If the digit in the unit's place is 5 or greater, we round up; otherwise, we round down.
In the case of 351, the digit in the tens place is 5, and the digit in the units place is 1. Since the digit in the unit's place is less than 5, we round down. Therefore, when rounding 351 to the nearest 10, we get 350.
Rounding 351 to the nearest 10 essentially means approximating it to the nearest multiple of 10. In this case, 351 is closer to 350 than to 360, which is the next multiple of 10.
So, rounding 351 to the nearest 10 gives us 350.
To learn more about the place value;
https://brainly.com/question/27734142
#SPJ6
Solve the inequality:
4x – 2 < 10
Answer:
The solution for x is (-∞, 3).
Step-by-step explanation:
The provided inequality is: [tex]4x-2<10[/tex]
Solve for x a follows:
[tex]4x-2<10\\\\Add\ 2\ to\ both\ sides\\\\4x-2+2<10+2\\\\4x<12\\\\Divide\ both\ sides\ by\ 4\\\\\frac{4x}{4}<\frac{12}{4}\\\\x<3[/tex]
The range of the values of x is
[tex]x<3\\This\ implies\ that\ x\ belongs\ to\ the\ interval\ (-\infty, 3)[/tex]
Thus, the range of the values of x is (-∞, 3).
A bag contains 5 red marbles, 3 blue marbles, 7 yellow marbles, and 2 green marbles which ratio can be used to compare the yellow marbles to the blue marbles
Answer:
7 : 3
Step-by-step explanation:
Answer:7:3
Step-by-step explanation:
The other colors are just to throw you off,7 yellow to 3 blue is 7:3
A cup is filled with
100 milliliters of water. Every second, 2
milliliters of water are poured out of the
cup. Which function shows the amount
of water in the cup after t seconds?
Answer:
t=100-2x
Step-by-step explanation:
The amount of water in the cup after t seconds can be represented by the linear function Y = 100 - 2t. This equation is derived from the initial amount of water in the cup and the rate at which water is being poured out.
Explanation:The function that shows the amount of water in the cup after t seconds is a linear function. It can be represented as Y = 100 - 2t. In this equation, Y represents the amount of water left in the cup and t represents time in seconds.
This equation comes from the initial amount of water (100 milliliters) minus the rate of water being poured out of the cup (2 milliliters per second times the number of seconds). For example, after 3 seconds, the amount of water left would be 100 - 2*3 = 94 milliliters.
Learn more about Linear Function here:https://brainly.com/question/31353350
#SPJ3
What is the cube root of 8/125
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
Note the [tex]\sqrt[3]{8}[/tex] = 2 and [tex]\sqrt[3]{125}[/tex] = 5
Thus
[tex]\sqrt[3]{\frac{8}{125} }[/tex] = [tex]\frac{\sqrt[3]{8} }{\sqrt[3]{125} }[/tex] = [tex]\frac{2}{5}[/tex]
Answer:
2/5
Step-by-step explanation:
8 = 2^3
125 = 5^3
If there are 45 guests at the party, predict how many would choose a gift card?
Answer:
Since there is a 50-50 chance of a person at the party choosing a gift card, and since there can only be 1 of 2 outcomes, we can assume that there will either be more people choosing a gift card than not, or there will be more people not choosing a gift card than are. So, that means that there would be 23 people (more or less) choosing a gift card and 22 people (more or less) not choosing a gift card or vice-versa.
Match the measures with the correct type of measurement. a.72m b. 125mm3 c. 50cm2 Volume, Surface Area, Perimeter
a. Perimeter
b. Volume
c.Suface Area
what is the answer? plzzz
Answer:
The costs of the ski packages will be the same if you set them equal to each other. The cost will be the same after 5 hours. The cost will be $35 for both packages.
Step-by-step explanation:
5 + 5x = 20 + 2x Set the equations equal
-5 -5 Subtract 5 from both sides
5x = 15 + 2x
-2x -2x Subtract 2x from both sides
3x = 15 Divide both sides by 3
x = 5
booker owns 85 video games. He has 3 shelves to put the games on. Each shelf can hold 40 video games. How many video games does he have room for?
Answer:
(3 x 40) - 85
120 - 85
35 video games
Given the equation y=kx where y=1.2 and x=1.5, what is the value of k?
Answer:
The value of k is 0.8
Step-by-step explanation:
we have
[tex]y=kx[/tex]
This linear equation represent a direct variation
we have
y=1.2, x=1.5
substitute in the equation
[tex]1.2=1.5k[/tex]
solve for k
divided by 1.5 both sides
[tex]k=1.2/1.5=0.8[/tex]
The linear equation is
[tex]y=0.8x[/tex]
Suppose your friend's parents invest $15,000 in an account paying 6% compounded annually. What will the balance be after 9 years? round to nearest cent
Using the formula for compound interest, the balance of a $15,000 investment at a 6% interest rate compounded annually after 9 years is approximately $25,342.19.
Explanation:To calculate the balance of an investment of $15,000 at 6% interest compounded annually after 9 years, we can use the formula for compound interest, which is:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of times that interest is compounded per year.t is the time the money is invested for in years.In this case:
P = $15,000r = 6% or 0.06n = 1 (since it's compounded annually)t = 9 yearsPlugging these values into the formula gives us:
A = $15,000(1 + 0.06/1)^(1\*9)
A = $15,000(1 + 0.06)^9
A = $15,000(1.06)^9
A = $15,000\*1.689479
A = $25,342.19 approximately
So, after 9 years, the balance will be $25,342.19, rounding to the nearest cent.
20 pts look at pic n answer
1. [tex]\frac{x^3}{x^8}=x^{-5}[/tex]
2. [tex]\frac{6x}{2x^8} = 3x^{-7}[/tex]
3. [tex]\frac{28x^6}{21x^2} = \frac{4}{3}x^4[/tex]
Step-by-step explanation:
1. x^3/x^8
Given fraction is:
[tex]\frac{x^3}{x^8}[/tex]
When the bases are same in both numerator and denominator then the exponents can be added
i.e.
[tex]\frac{x^a}{x^b} = x^{a-b}[/tex]
So,
[tex]\frac{x^3}{x^8} = x^{3-8} = x^{-5}[/tex]
Part b:
[tex]\frac{6x}{2x^8}\\= \frac{3.2.x}{2.x^8}\\=\frac{3x}{x^8}\\=3x{1-8}\\=3x^{-7}[/tex]
Part c:
Given
[tex]\frac{28x^6}{21x^2}\\= \frac{7.4.x^6}{7.3.x^2}\\=\frac{4}{3} x^{6-2}\\=\frac{4}{3}x^4[/tex]
Keywords: Fractions, exponents
Learn more about fractions at:
brainly.com/question/5282516brainly.com/question/5424148#LearnwithBrainly
Shailyn solved 618 math problems in one week. Karla solved 549 math problems. How many more math problems did shailyn solve than Karla ?
Shailyn solved 69 more math problems than Karla by subtracting the number of problems Karla solved (549) from the number of problems Shailyn solved (618).
To find out how many more math problems Shailyn solved than Karla, we need to subtract the number of problems Karla solved from the number Shailyn solved. The calculation is as follows:
Shailyn solved = 618 math problemsKarla solved = 549 math problemsDifference = Shailyn's problems - Karla's problemsDifference = 618 - 549 = 69 math problemsTherefore, Shailyn solved 69 more math problems than Karla.
Simplify 2(6(3.5+2.1))
Answer:67.2
Step-by-step explanation:
3.5+2.1=5.6
6 times 5.6 is 33.6 then 33.6 times 2 is 67.2
The measure of one acute angle in this right triangle is 45°.
What is the measure of the other acute angle?
Answer:
45°
Step-by-step explanation:
90-45=45°
" According to the Joy Cone Company, their waffle cones have a diameter of 2 5/8 inches and a
height of 6 inches.
If you place one scoops of ice cream (in the shape of a sphere) with a diameter of 2 7/8 inches wnd let
it melt, will the cone hold all of the ice cream?
Use mathematics to explain and justify your answer.
Answer:
No, the cone will not hold all of the ice cream.
Step-by-step explanation:
Given:
" According to the Joy Cone Company, their waffle cones have a diameter of 2 5/8 inches and a height of 6 inches.
If you place one scoops of ice cream (in the shape of a sphere) with a diameter of 2 7/8 inches would let it melt.
Now, to explain mathematically will the cone hold all of the ice cream.
Taking the value of π = 3.14.
So, to get the volume of waffle cone we put formula:
Height (h) = 6 inches.
Diameter = [tex]2\frac{5}{8}=\frac{21}{8}\ inches.[/tex]
Thus radius (r) = Diameter ÷ 2 = [tex]\frac{\frac{21}{8}}{2} =\frac{21}{16} \ inches.[/tex]
[tex]Volume=\pi r^2\frac{h}{3}[/tex]
[tex]Volume=3.14\times \frac{21}{16} \times \frac{21}{16} \times \frac{6}{3}[/tex]
[tex]Volume=3.14\times 1.31\times 1.31\times 2[/tex]
[tex]Volume=10.78\ inches^3.[/tex]
The volume of waffle cone = 10.78 inches³.
Now, to get the volume of scoop which is in the shape of sphere we put formula:
Diameter = [tex]2\frac{7}{8} =\frac{23}{8} \ inches.[/tex]
Thus radius (r) = Diameter ÷ 2 [tex]=\frac{\frac{23}{8}}{2} =\frac{23}{16} \ inches.[/tex]
[tex]Volume = \frac{4}{3} \pi r^3[/tex]
[tex]Volume = \frac{4}{3} \times 3.14\times \frac{23}{16} \times \frac{23}{16} \times \frac{23}{16}[/tex]
[tex]Volume=1.33\times 3.14\times 1.44\times 1.44\times 1.44[/tex]
[tex]Volume=12.47\ inches^3.[/tex]
The volume of one scoop of ice cream = 12.47 inches³.
So, as the volume of scoop of ice cream is more than the volume of cone.
Thus, if placing one scoop of ice cream in the cone and let it melt, the cone will not hold all of the ice cream.
Therefore, no the cone will not hold all of the ice cream.
The ice cream scoop will not fit into the cone due to volume differences.
The ice cream scoop will not fit into the cone. To determine this mathematically, we need to compare the volume of the cone to the volume of the ice cream scoop.
The volume of the cone can be calculated using the formula for the volume of a cone: V = 1/3 × π × r² × h.
Similarly, the volume of the sphere (ice cream scoop) can be calculated using the formula for the volume of a sphere: V = 4/3 × π × r³.
By plugging in the given measurements, we can determine that the volume of the ice cream scoop will be greater than the volume of the cone, indicating that the ice cream scoop will not fit into the cone.
The mean and the standard deviation of a normal
population are called
. The mean
and the standard deviation of a random sample
from a population are called
95%
DONE
Answer:
(B) Parameters
(A) Statistics
Step-by-step explanation:
edg 2020
The mean and the standard deviation of a normal population are called parameters, and of a random sample from a population are called statistic
Normally distributed data In a normal distribution, data is symmetrically distributed with no skewNormally distributed data is the distribution of probability which is symmetric about the mean.Normal distributions are symmetric, unimodal, and asymptotic, and the mean, median, and mode are all equalHow to solve this problem?The steps are as follow:
The mean of the data is the average value of the given data. The standard deviation of the data is the half of the difference of the highest value and mean of the data set.Those numbers who summarize information about sample are called statistic.The numbers which summarize information about population are called parameters.The numbers which summarize information about the sample are called statistic.Therefore, the mean and the standard deviation of a normal population are called parameters, and of a random sample from a population are called statistic
Learn more about Normally distributed data here:
https://brainly.com/question/1407349
#SPJ2
her 6. Karen buys a sweatshirt for $30. The sales
suld be tax in her state is 7%. What is the total
amount Karen will pay for the sweatshirt,
including sales tax?
The total amount that Karen will be for the sweatshirt including tax will be $32.10.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Karen buys a sweatshirt for $30. The sales sold be tax in her state is 7%.
The total amount that Karen will be for the sweatshirt including tax will be calculated as,
Total cost = $30 x (1 + 7%)
Total cost = $30 x (1 + 0.07)
Total cost = $30 x (1.07)
Total cost = $32.10
The total amount that Karen will be for the sweatshirt including tax will be $32.10.
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ2
What is the equation for the line of reflection? On a coordinate plane, triangle A B C has points (6, 3.7), (5.4, 2), (1, 3). Triangle A prime B prime C prime has points (3.7, 6), (2, 5.4), (3, 1). x = 3 y = 3 y = x x = 6
Answer:
The answer is y = x
The equation for the line of reflection can be found by using the midpoint formula and the slope formula. The equation for the line of reflection for the given points (6, 3.7) and (3.7, 6) is y = -x + 9.7.
Explanation:The equation for the line of reflection can be found by using the midpoint formula and the slope formula. The midpoint of each corresponding pair of points can be calculated to find the coordinates of the image points. Then, the slope of the original line and the slope of the reflected line can be calculated. Using the midpoint and slope, the equation of the line of reflection can be determined.
For example, to find the equation for the line of reflection for points (6, 3.7) and (3.7, 6), we can calculate the midpoint: ( (6 + 3.7) / 2, (3.7 + 6) / 2 ) = (4.85, 4.85).
Next, we can calculate the slope of the original line using the points (6, 3.7) and (5.4, 2) using the slope formula: (2 - 3.7) / (5.4 - 6) = -1.7 / -0.6 = 2.83.
Finally, we can calculate the slope of the reflected line using the points (4.85, 4.85) and (3.7, 6) using the slope formula: (6 - 4.85) / (3.7 - 4.85) = 1.15 / -1.15 = -1.
So, the equation for the line of reflection is y = -x + b. To find b, we can use the point (4.85, 4.85). Substituting the values into the equation, we get 4.85 = -(4.85) + b, which simplifies to b = 9.7.
Therefore, the equation for the line of reflection is y = -x + 9.7.
parallel to x = 3 and passes through (6, 1)
Answer:
x = 6
Step-by-step explanation:
x = 3 is the equation of a vertical line parallel to the y- axis.
The equation of a parallel line will therefore be a vertical line.
The equation of a vertical line is
x = c
where c is the value of the x- coordinates the line passes through.
The line passes through (6, 1) with x- coordinate 6, thus
x = 6 ← equation of parallel line
Final answer:
The equation of the line that is parallel to x = 3 and passes through (6, 1) is x = 6.
Explanation:
The question relates to finding the equation of a line that is parallel to another line, specifically the line x = 3, and that also passes through a given point, namely (6, 1). Since the line x = 3 is a vertical line, any line parallel to it will also be vertical and have an equation of the form x = k, where 'k' is a constant.
In this case, the line we are looking for must go through the point (6, 1), which means it will have the same x-coordinate as this point. Therefore, the equation of the line is simply x = 6.
h(x) = x^2 - 1
Over which interval does h have a negative average rate of change?
The function h(x) = x^2 - 1 has a negative average rate of change over the interval from x = -∞ to x = 0, which is where the parabola is decreasing toward its vertex at the origin.
Explanation:The student asked over which interval the function h(x) = x^2 - 1 has a negative average rate of change. The average rate of change is negative when the function is decreasing. In the case of h(x) = x^2 - 1, which is a parabola opening upwards, the function decreases as x moves from the left to the right towards the vertex. Therefore, the interval in which the function has a negative average rate of change is from x = -∞ to x = 0, because this is where the function values are falling. To find the average rate of change between two points x1 and x2, we can use the formula: (h(x2) - h(x1)) / (x2 - x1). If x1 is to the left of the y-axis (x1 < 0) and x2 is the y-axis (x2 = 0), we will get a negative result since h(x2) < h(x1) in that interval, showing a negative average rate of change.
The function h(x) = x^2 - 1 has a negative average rate of change over the interval − 3 ≤ x ≤ 1. This interval includes the vertex of the parabola at x = 0, where the function is decreasing, resulting in a negative rate of change.
The function h(x) = x2 - 1 has different average rates of change depending on the interval we are considering. To find an interval where the average rate of change is negative, we need to look at intervals where the function is decreasing. The function h(x) will be decreasing on any interval that includes the value x = 0 since this is where the vertex of the parabola represented by h(x) is located, and it is a parabola opening upwards.
Analyze intervals around x = 0 to find where the function decreases. Looking at Choice C (−3 ≤ x ≤ 1), we can calculate the average rate of change as:
[(h(1) - h(-3)) / (1 - (-3))] = [(12 - 1) - ((-3)2 - 1)] / (4) = [0 - (9 - 1)] / 4 = -8 / 4 = -2Since the average rate of change is negative (-2), Option C is the interval over which h(x) has a negative average rate of change.
the complete Question is given below:
h(x)=x 2 −1h, left parenthesis, x, right parenthesis, equals, x, squared, minus, 1 Over which interval does h hh have a negative average rate of change? Choose 1 answer: Choose 1 answer: (Choice A) A − 3 ≤ x ≤ 5 −3≤x≤5minus, 3, is less than or equal to, x, is less than or equal to, 5 (Choice B) B 1 ≤ x ≤ 4 1≤x≤41, is less than or equal to, x, is less than or equal to, 4 (Choice C) C − 3 ≤ x ≤ 1 −3≤x≤1minus, 3, is less than or equal to, x, is less than or equal to, 1 (Choice D) D − 1 ≤ x ≤ 5 −1≤x≤5minus, 1, is less than or equal to, x, is less than or equal to, 5 Show Calculator
How does knowing x=52 help you find the value of your?
Answer:2
Step-by-step explanation:
At a convention of science teachers, various attendees are asked to name their favorite subject in high school.
a.
teachers at the convention
c.
favorite subject
b.
teachers surveyed
d.
cannot be determined
The amount of fuel used by jumbo jets to take off is normally distributed with a mean of 4000 gallons and a standard deviation of 125 gallons. What is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons?
Answer:
0.6554 is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 4000 gallons
Standard Deviation, σ = 125 gallons
Sample size, n = 40
We are given that the distribution of amount of fuel is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
Central limit theorem:
As the sample size increases, the distribution of sample mean has a similar popular distribution shape.
P(sample of 40 jumbo jets will be less than 3950 gallons)
P(x < 3950)
[tex]P( x < 3950) = P( z < \displaystyle\frac{3950 - 4000}{125}) = P(z < -0.4)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 3950) = 0.6554 = 65.54\%[/tex]
0.6554 is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons.
The probability that the number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons is 0.66.
it is given that
Mean μ= 4000 gallons
Standard deviation σ = 125 gallons
Number of trials x = 3950 gallons
What is the formula for a z-score?Z-score = (x-μ)/σ
Z-score = (3950-4000)/125
Z-score = -0.4
So probbaility P(x<3950) = P(z<-0.4)
From the standard normal table,
P(x<3950) = 0.66
Therefore, the probability that the number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons is 0.66.
To get more about normal distribution visit:
https://brainly.com/question/4079902
The surface area of a cylinder is given by the formula SA = 2r2 + 2rh. A cylinder has a radius of 10 cm and a surface area of 1,220 cm2. What is the height
Final answer:
To find the height of a cylinder with a known radius and surface area, subtract the area of the bases from the total surface area to get the lateral surface area, and then solve for the height. Using the surface area formula SA = 2πr² + 2πrh, the height is computed to be approximately 9.4 cm.
Explanation:
To calculate the height of a cylinder when you know its surface area and radius, you use the surface area formula for a cylinder, SA = 2πr² + 2πrh, where SA is the surface area, r is the radius, and h is the height of the cylinder. Given that the surface area (SA) is 1,220 cm² and the radius (r) is 10 cm, the formula can be rearranged to solve for h (height). The first step is to calculate the area of the circular bases, which is 2πr², then subtract this value from the total surface area to get the lateral surface area (2πrh), and finally divide by (2πr) to solve for h.
First, calculate the area of the circular bases:
Area of one base = πr² = 3.14159 × 10² cm² = 314.159 cm²
Total area of both bases = 2 × 314.159 cm² = 628.318 cm²
Subtract this from the total surface area to find the lateral surface area:
Lateral surface area = SA - area of bases = 1,220 cm² - 628.318 cm² = 591.682 cm²
Finally, solve for the height:
2πrh = 591.682 cm²
h = 591.682 cm² / (2 × 3.14159 × 10 cm)
h ≈ 9.4 cm
Thus, the height of the cylinder is approximately 9.4 cm.
The height is approximately 9.42 cm.
To find the height of a cylinder when given the radius and the surface area, use the formula for the surface area of a cylinder: [tex]SA = 2\pi r^2+2\pi rh[/tex]. Here, we know the surface area (SA) is 1220 [tex]cm^2[/tex], and the radius (r) is 10 cm.
First, let's write down the formula with the given values:
[tex]1220 = 2\pi (10)^2 + 2\pi (10)h[/tex]
We can simplify the equation step by step:
Calculate [tex]2\pi (10)^2: 2\pi (10)^2=2\pi (100)=200\pi[/tex]Substitute this into the equation: [tex]1220 = 200\pi + 20\pi h[/tex]To isolate 20πh, subtract 200π from both sides: [tex]1220-200\pi =20\pi h[/tex]Approximate the value of [tex]\pi[/tex] (3.142): [tex]200\pi \approx 628.4[/tex]Subtract this value: 1220 - 628.4 [tex]\approx[/tex] 591.6Now, isolate h by dividing both sides by [tex]20\pi : h = \frac{591.6}{20*3.142}\approx9.42[/tex]Therefore, the height of the cylinder is approximately 9.42 cm.