Simplify the expression. Write the answer using scientific notation.
A)2.52 × 10–3
B)2.52 × 10–2
C)2.52 × 10–1
D)4.3 × 10–2
Answers
Answer:
B.
\(2.52 \times 10 ^{ - 2} \)
Related Questions
2(2x - 4) = 3(x + 4)
Answers
Answer:
24
Step-by-step explanation:
i dont know if its correct
Determine which of the following transformations are linear transformations
A. The transformation T1
defined by T1(x1,x2,x3)=(x1,0,x3)
B. The transformation T2
defined by T2(x1,x2)=(2x1−3x2,x1+4,5x2)
.
C. The transformation T3
defined by T3(x1,x2,x3)=(x1,x2,−x3)
D. The transformation T4
defined by T4(x1,x2,x3)=(1,x2,x3)
E. The transformation T5
defined by T5(x1,x2)=(4x1−2x2,3|x2|)
.
Answers
The transformation T1 defined by T1(x1,x2,x3)=(x1,0,x3) is linear transformation among the five given questions.
A linear transformation satisfies two properties: additivity and homogeneity. That is, for any vectors u and v, and any scalars a and b:
T(u + v) = T(u) + T(v)
T(au) = aT(u)
Using these properties, we can determine which of the given transformations are linear transformations:
A. The transformation T1 defined by T1(x1,x2,x3)=(x1,0,x3)
T1(u+v) = (u1+v1, 0, u3+v3) = (u1, 0, u3) + (v1, 0, v3) = T1(u) + T1(v)
T1(au) = (au1, 0, au3) = a(u1, 0, u3) = a*T1(u)
Therefore, T1 is a linear transformation.
The transformation T2 defined by T2(x1,x2)=(2x1−3x2,x1+4,5x2)
T2(u+v) = (2(u1+v1)−3(u2+v2), u1+v1+4, 5(u2+v2))
= (2u1−3u2, u1+4, 5u2) + (2v1−3v2, v1+4, 5v2) = T2(u) + T2(v)
However, T2 does not satisfy homogeneity property. Consider a = -1 and u = (1, 1):
T2(-u) = (-2, 5, -5)
-1*T2(u) = (-2, -5, -5)
Therefore, T2 is not a linear transformation.
The transformation T3 defined by T3(x1,x2,x3)=(x1,x2,−x3)
T3(u+v) = (u1+v1, u2+v2, -(u3+v3)) = (u1, u2, -u3) + (v1, v2, -v3) = T3(u) + T3(v)
T3(au) = (au1, au2, -au3) = a*(u1, u2, -u3) = a*T3(u)
Therefore, T3 is a linear transformation.
The transformation T4 defined by T4(x1,x2,x3)=(1,x2,x3)
T4(u+v) = (1, u2+v2, u3+v3) ≠ (1, u2, u3) + (1, v2, v3) = T4(u) + T4(v)
T4(au) = (1, au2, au3) ≠ a(1, u2, u3) = a*T4(u)
Therefore, T4 is not a linear transformation.
The transformation T5 defined by T5(x1,x2)=(4x1−2x2,3|x2|)
T5(u+v) = (4(u1+v1)−2(u2+v2), 3|u2+v2|)
= (4u1−2u2, 3|u2|) + (4v1−2v2, 3|v2|) ≠ T5(u) + T5(v)
T5(au) = (4au1−2au2, 3|au2|) ≠ a*T5(u)
Therefore, T5 is not a linear transformation.
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PLEEASE help! Me please help I’m confused
Answers
The surface area of the triangular prism is S = 288 m²
Given data ,
Let the surface area of the triangular prism be represented as S
Now , the height of the triangle is h = 4 m
The base of the triangle is b = 6 m
The length of the triangle is L = 11 m
where the slant height of triangular prism a = 5 m
S = ph + ( 1/2 ) bh
The base area of the prism is B = 66 m²
On simplifying , we get
S = 144 ( 2 )
S = 288 m²
Hence , the surface area is S = 288 m²
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Suppose that there are 5 children in a gymnastics class. One day, they count the number of steps each person takes while walking on their hands until they lose balance and come down. The results are: Ashley (20), Brittany (8), Carol (22), Darla (26), and Erica (24). The mean number of steps these children took while walking on their hands is 20 steps. Identify the population and parameter.
Answers
Answer:
Population = number of children in gymnastic class = 5
Parameter = mean number of steps taken by the 5 children
Step-by-step explanation:
The population could simply be referred to as the total number or set of similar objects or subjects related to a certain study or research. In the scenario described above, the area of interest is a particular gymnastic class, therefore all individuals or children belonging to this particular gymnastic class makes up the population.
Parameter on the other hand are statistical metrics, values or calculations derived from the population figure or information. Here, the mean value of steps obtained from the step counts of the population data is called the parameter.
Population is number of children in gymnastic class = 5.
Parameter is mean number of steps taken by the 5 children.
Given that,
Suppose that there are 5 children in a gymnastics class.
One day, they count the number of steps each person takes while walking on their hands until they lose balance and come down.
The mean number of steps these children took while walking on their hands is 20 steps.
We have to Identify,
The population and parameter.
According to the question,
Parameters are descriptive measures of an entire population. However, their values are usually unknown because it is infeasible to measure an entire population. Because of this, you can take a random sample from the population to obtain parameter estimates.
The population could simply be referred to as the total number or set of similar objects or subjects related to a certain study or research.
The scenario described above, the area of interest is a particular gymnastic class, therefore all individuals or children belonging to this particular gymnastic class makes up the population.
Parameter on the other hand are statistical metrics, values or calculations derived from the population figure or information.
Here, the mean value of steps obtained from the step counts of the population data is called the parameter.
A parameter is a value that describes a characteristic of an entire population, such as the population mean.
The population mean and standard deviation are two common parameters.
Hence, Population = number of children in gymnastic class = 5.
Parameter = mean number of steps taken by the 5 children.
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Tutoring Question Help
A person is taking a 5-question multiple-choice test for which each question has three answer choices, only one of which is correct. The person decides on answers by
rolling a fair die and marking the first answer choice if the die shows 1 or 2 the second if it shows 3 or 4, and the third if it shows 5 or 6. Find the probability that the
person gets fewer than 3 correct answers.
The probability that the person gets fewer than 3 correct answers is
(Round to three decimal places as needed.)
Answers
3+
2+
1+
+
+
-3
+
-1
2
-2
1
2
3
4
-11
-2 +
-3+
-4
What is the slope of the line?
Answers
Answer:
????????????????????????
PLEASE HELP!!!
Give a real-life situation of angle measurement
Answers
Answer:
A clock forms an example of angles in real life.
Step-by-step explanation:
Stephen is combining all juice shown to make fruit punch. Does the expression (64+28+76)/6 make sense’s
Answers
Yes, the expression (64+28+76)/6 makes sense as it represents the average quantity of juice per unit when combining all the shown juices.
To determine whether the expression (64+28+76)/6 makes sense, we need to evaluate the components of the expression and consider whether the mathematical operations are valid.
The expression (64+28+76)/6 represents the sum of three numbers (64, 28, and 76), divided by 6. Let's break it down step by step:
Addition: We have three numbers being added together: 64, 28, and 76. The sum of these numbers is 168 (64 + 28 + 76 = 168).
Division: The sum of the three numbers, 168, is then divided by 6. Division is a valid mathematical operation.
Now, let's analyze whether the expression makes sense in the context of Stephen combining all the juice to make fruit punch. The numbers 64, 28, and 76 may represent quantities of juice (in some units) that Stephen is combining. However, without further information or context, we cannot determine if the expression accurately represents the combination of these juices.
If the numbers 64, 28, and 76 represent quantities of juice in the same units (such as milliliters or liters), then the expression (64+28+76)/6 would represent the average quantity of juice per unit. The result, 168/6, would be 28. This would imply that each unit (e.g., glass or serving) of the fruit punch contains an average of 28 units of juice.
In summary, mathematically, the expression (64+28+76)/6 is valid. However, without additional context regarding the units or quantities being represented, it is not possible to determine whether the expression accurately describes the process of combining the juices to make fruit punch.
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when estimating the population average using the sample mean, adding observations to a sample will always decrease the standard error of your estimate.
Answers
When estimating the population average using the sample mean, adding observations to a sample will always decrease the standard error of your estimate is random sampling variability.
In statistical analysis, estimating the population average is a common task. One way to estimate this is by using the sample mean. However, as more observations are added to the sample, the standard error of the estimate decreases. Let's explore why this is the case.
The standard error of the mean (SEM) is a measure of the amount of variability in a sample mean from one sample to another. It can be calculated using the formula:
SEM = standard deviation / square root of sample size
As we can see, the SEM is inversely proportional to the square root of the sample size. This means that as we increase the sample size by adding more observations, the denominator of the SEM formula increases, causing the SEM to decrease.
Now, let's consider how this affects our estimate of the population average. The sample mean is an unbiased estimate of the population mean. This means that on average, the sample mean will equal the population mean. However, due to random sampling variability, the sample mean can differ from the population mean.
The standard error of the mean gives us an idea of how much the sample mean can vary from one sample to another.
Therefore, adding more observations to a sample decreases the SEM, making our estimate of the population average more precise. This is because the average of a larger sample is more representative of the population average, as it is less affected by random sampling variability.
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Subtract. Express your your answer in lowest terms 21/25 - 7/25
Answers
Answer:
14/25
Step-by-step explanation:
If the denominators are the same, subtract the numerators.
21/25-7/25=14/25
14 and 25 do not have any similar factors greater than 1, so we keep it as 14/25.
After playing the "Spin to Win" game, which has a probability of 0.25 of winning on any individual spin, Nick decides
to play "Knock down the Bottles." To win, Nick has to knock down all 3 bottles. Nick determines that the probability of
winning this game is 0.8. Nick plays "Spin to Win" twice and then plays "Knock down the Bottles" twice.
What is the probability that Nick loses both times he plays "Spin to Win" and wins both times he plays "Knock down
the Bottles"?
O 0.04
O 0.0025
O 0.0225
O 0.36
Answers
Answer:
0.36
Step-by-step explanation:
Edge 2021
if you invest $550.00 and your annual interest is 4%, what will be the interest
Answers
The annual interest is $22.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
Given;
Amount invested= $550
Annual interest= 4%
SI= 550*4*1/100
=5.5*4
=22
Therefore, the simple interest will be $22.
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Find the (perpendicular) distance from the line given by the parametric equations
x(t)= -2-6t
y(t)= 1-3t
z(t)= -5+7t
to the point (-8,9,8)
Answers
Answer:
\(\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}\) Whatever this number may be
Step-by-step explanation:
The distance will be on the plane containing the point, and perpendicular to the line - which exists as long as the point doesn't sit on the line, but in that case our distance will simply be zero. Good news, since the line is given in parametric equation, the equation of the plane is easy to write by simply computing the dot product between the vector generating the line - or any multiple of it! - and the vector joining a random point x y z of the space with our given point, and setting it equal to zero. The equation of our plane is thus
\(6(x-(-8)) + 3(y-9) -7(z-8) = 0\\6(x+8)+3(y-9)-7(z-8)=0\)
We could multiply now or later, doesn't matter, so let's wait. Now, we need to know when the line passes through the plane, so let's plug the (parametric) coordinate of the line and let's see for which value of t that happens:
\(6(-2-6t+8) +3(1-3t -9) -7(-5+7t-8) =0\\6(6-6t) -3(8+3t)+7(13-7t)=0\\36-36t-24-9t+91-49t = 0\\t=103/94\)
Found this value of t, we can use it to find the coordinate of the point in common between the line and the plane:
\((-2-6\frac {103}{94};1-3\frac {103}{94}; -5+7\frac {103}{94}) = (-\frac{806}{94};-\frac{215}{94};-\frac{251}{94})\)
At this point it's simply a matter of calculating the distance between two points in 3D space, given by the usual \(\sqrt{\Delta x^2+\Delta y^2+\Delta z^2}\), whatever abomination of a number it might become:
\(\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}\)
At this point is a simple exercise in number crunching which I refuse to entertain more - but please double check all calculation above in case I didn't notice something.
In 2011, the maximum amount that you could have contributed to your RRSP (Registered Retirement Savings Plan) was
the lesser of $22,450 or 18% of your earned income from the previous year. How much income do you need to claim a
$22,450 contribution in 2011?
Answers
Using proportions, it is found that you need an income of $124,722.22 to claim a $22,450 contribution in 2011.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
To claim a $22,450 contribution in 2011, this amount has to be 18% of your income, hence:
0.18x = 22450
x = 22450/0.18
x = $124,722.22.
You need an income of $124,722.22 to claim a $22,450 contribution in 2011.
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A bank advertises that they will pay 1.5% simple annual interest on new savings accounts. Lorenzo puts $400 in a new account. If he does not deposit or withdraw any money, how much will he have altogether after one year?
Answers
Answer:
$406
Step-by-step explanation:
The formula for simple interest is I=prtI=prt where II is the amount of interest earned, pp is the initial deposit, rr is the annual interest rate, and tt is the number of years.
It is given that he deposits p=$400p=$400, the bank pays r=1.5%= 0.015r=1.5%=0.015 in annual interest, and t=1t=1 year. The amount of interest he will earn is then I=prt=400(0.015)(1)=$6I=prt=400(0.015)(1)=$6.
His total balance after one year will then be p+i=$400+$6=$406p+i=$400+$6=
$406
.
On the first day of travel, a driver was going at a speed of 40 mph. The next day, he increased the speed to 60 mph. If he drove 2 more hours on the first day and traveled 20 more miles, find the total distance traveled in the two days.
Answers
The Total mileage is "400" and the further solution can be defined as follows:
Let t become the time he spent commuting on the first day of his vacation.
It is then calculated as \(t + 2\).
\(\to 40\times(t+2) = 60(t) + 20 \\\\\to 40t+80 = 60t + 20 \\\\\to 80-20 = 60t + 40t \\\\\to 60 = 20t \\\\\to t=\frac{60}{20} \\\\\to t=\frac{6}{2} \\\\\to t= 3\\\\\)
It traveled \(40\times (3 + 2) + 20 = 40\times 5 + 20 = 200+20=220\) miles on its first day of operation.
The car traveled \(180\ miles\) on the second day, which was \(60 \ miles \times 3\).
So,
Total mileage= first day traveled + second day traveled \(= 220+ 180= 400 \miles\)
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A baker is baking a giant cookie in the shape of a equilateral triangle what is the area of the cookie if the base is 17 inches and the height is 10 inches
Answers
To find the length of one of the sides, we can use the Pythagorean theorem. Since this is an equilateral triangle, all sides are equal in length. Let's call the length of one side "x". We know that the height (which is also one of the sides) is 10 inches, so we can set up a right triangle with one leg being x/2 (half of one side) and the other leg being 10 inches. The hypotenuse (the other side of the equilateral triangle) is x.
Using the Pythagorean theorem:
(x/2)^2 + 10^2 = x^2
x^2/4 + 100 = x^2
100 = 3x^2/4
400/3 = x^2
x = sqrt(400/3)
Now that we know the length of one side, we can plug it into the formula for area:
A = (sqrt(3)/4) x (sqrt(400/3))^2
A = (sqrt(3)/4) x (400/3)
A = 100sqrt(3)/3
Therefore, the area of the giant cookie in the shape of an equilateral triangle with a base of 17 inches and a height of 10 inches is approximately 57.74 square inches.
Answer:
85 square inches.
Step-by-step explanation:
The area of a triangle can be found by the formula \(1/2bh\), assuming b is the base and h is the height.
If b is 17 inches and h is 10 inches:
\(1/2(17)(10)\)
\(1/2(170)\)
\(A = 85\)
Therefore, the area is 85 square inches.
brainliest to correct quickly
Answers
Goodluck!!
Solve y=3x-4 and y=2/5x+ 9
using systems of linear eqautions
Answers
Answer:
(5 , 11)
Step-by-step explanation:
\(Equation\ 1\\\\\y=3x-4\\\\Equation\ 2\\\\\y=\frac{2}{5}x+9\)
There are three ways to solve the systems of linear equations
1) Elimination method - where we add/subtract the equations to eliminate the variable
2) Substitution method - where we substitute one variable in the form of another variable
3) Graphing method - where we sketch the graphs of both the equations and if they intersect that point would be the solution and if they don't there is no solution
We use the second method the Substitution method which is the easiest in my opinion.
Here we got two equations so lets just substitute equation 1 with equation 2 meaning insert equation 1 into equation 2 like here:
\(3x-4=\frac{2}{5}x+9\)
as you can see here we eliminated the variable y by substituting y in terms of x.
Now we just solve the equation algebraically
\(3x-4=\frac{2}{5}x+9\\3x-\frac{2}{5}x=9+4\\\frac{15x-2x}{5} =13\\\\\frac{13x}{5}=13\\\\13x=65\\x=65/13\\x=5\\\)
The value of x is 5 now to find the value of y we insert the value of x in any two equations lets insert the value of x into equation 1
\(y=3x-4\\y=3(5)-4\\y=15-4\\y=11\)
so the solution of the system of linear equations is (5 , 11)
On a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 40. Find the z-score of a person who scored 300 on the exam.
Answers
A z-score of 0 indicates that the person's score is equal to the mean, so they are right at the Average Performance level.the z-score of a person who scored 300 on the exam is 0.
The z-score of a person who scored 300 on the exam, we can use the formula:
z = (x - μ) / σ
where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.
In this case, the person scored 300 on the exam, which is equal to the mean (μ). Therefore, we can substitute these values into the formula:
z = (300 - 300) / 40
Simplifying the equation, we have:
z = 0 / 40
Since any number divided by zero is undefined, we can conclude that the z-score of a person who scored 300 on the exam is 0.
The z-score measures the number of standard deviations a data point is away from the mean. In this case, a z-score of 0 indicates that the person's score is equal to the mean, so they are right at the average performance level.
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SOMEONE PLEASE HELP
The number of chips of different colors in Gail's bag is shown below
-2 blue chips
-4 pink chips
-8 white chips
Gail takes out a chip from the bag randomly without looking, She replaces the chip and then takes out another chip from the bag. What is the probability that Gail takes out a white chip in both draws?
Answers
Answer:
8 over 15 multiplied by 7 over 14 is equal to 56 over 210
8 over 15 plus 7 over 14 is equal to 217 over 210
8 over 15 plus 8 over 15 is equal to 16 over 15
8 over 15 multiplied by 8 over 15 is equal to 64 over 225
She's taking it out and then she replaces it
and so that means the denominator would stay 15 both times
and since it's a white chip in both draws, it would be 8/15 * 8/15
What is the slope of the line passing through the points (- 2, 1 ) and ( 6, - 1)? *
A 2
B - 4
C - ¼
D ½
Answers
Answer:
C. - ¼
Step-by-step explanation:
1) if A(-2;1) and B(6;-1), then the required slope can be calculated according to the formula:
\(s =\frac{Y_A-Y_B}{X_A-X_B};\)
2) after the substitution the slope is:
\(s= \frac{1+1}{-2-6}=-\frac{1}{4}.\)
3) answer: C. - ¼
Can the sides of a triangle have lengths 2, 5, and 9?
Help?
Answers
Answer:
no
Step-by-step explanation:
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The table shows the amount it costs to rock climb in indoor rock climbing facility based on the number of hours. What is the rule to find the amount charged rock climb for x hours?
Answers
Answer:
5,45
Step-by-step explanation:
There is a mother-daughter tea that will be attended by 20 mother-daughter pairs, including the hosts. The rules of conduct are very strict; the host mother-daughter will greet everyone, all the guest mothers will greet everyone, and all the guest daughters will greet all the mothers only. How many greetings will there be?
Answers
In total, the number of greetings will be 1159.
Why do you use the term "numbers"?Mathematical symbols used to represent quantities or values include numbers. They are employed in the measurement, comparison, addition, subtraction, multiplication, and division processes in mathematics. According to their qualities and properties, numbers can be categorized into a variety of groups, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. There are specific properties and guidelines for mathematical operations for each group of numbers. Mathematics depends on numbers, which are also utilized in many other disciplines, including science, engineering, economics, and statistics.
The number of greetings exchanged between the host and the other mothers and daughters must be counted first. Since there is only one host, the number of mother-daughter pairs is 20 - 1 = 19. There are thus a total of 38 greetings, 19 between the host and the other moms, and 19 between the host and the other daughters.
The number of pleasantries exchanged between the guest mums and everyone else must next be tallied. The host, the other mothers, and the daughters must all be greeted, making a total of 20 - 1 = 19 guest mothers. Thus, each host mother must extend 1 + 19 + 20 = 40 greetings. There will be 760 greetings exchanged between the guest mothers and everyone, or 19 x 40.
The number of pleasantries exchanged between the mothers and the invited girls must also be tallied. Moreover, there are 20 guest girls, so 19 of them must welcome the mothers. As a result, there will be 361 pleasantries exchanged between the mothers and the guest daughters.
In total, the number of greetings will be 38 + 760 + 361 = 1159.
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The zero of F -1(x) in F(x) = x + 3 is
-3
0
3
Answers
Answer:
The only zero of \(F^{-1}(x)\) is \(3\).
Step-by-step explanation:
The function \(F^{-1}\) is the inverse of function \(F\).
For a given \(x\) and a given \(y\), \(F^{-1}(y) = x\) if and only if \(F(x) = y\).
Let \(y\) be a zero of \(F^{-1}(y)\). That is, \(F^{-1}(y) = 0\).
By the reasoning above, since \(x = 0\) and this particular \(y\) satisfy \(F^{-1}(y) = x\), it must be true that \(F(x) = y\) for the same \(x = 0\!\) and \(y\!\).
Since \(x = 0\) and \(F(x) = x + 3\), \(F(0) = 3\). Therefore, \(y = F(0) = 3\) since \(y = F(x)\).
Thus, the zero of \(F^{-1}(y)\) would be \(y = 3\).
If it rains 40% of the days in April, how many days will it rain? (HOW DID YOU GET YOUR ANSWER. PLEASE SHOW WORK!! ONLY ANSWER IF YOU SHOW ON HOW YOU GOT YOUR ANSWER!!!)
A. 12
B. 1/169
C. 11 1/8
D. 60%
E. 0.5
F. 2/112
G. 25%
H. 0.25
I. 25
Answers
Step-by-step explanation:
40% of 30 dsys =12 by dividing
9514 1404 393
Answer:
A. 12
Step-by-step explanation:
"Of" means "times" when you're talking about percentages. 40% of 30 means 40% times 30:
40% × 30 = 40/100 × 30 = 1200/100 = 12
40% of 30 days is 12 days
_____
In general "%" and "/100" are interchangeable. They mean the same thing.
Which sequence of transformations was applied to the parent tangent function to create the function m(x) = 2tan(3x+4)
Answers
The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.
To determine the sequence of transformations, let's break down the given function:
1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.
2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.
3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.
4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.
5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.
In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.
Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.
After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)
This example helps illustrate the effect of the transformations on the graph of the function.
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A goalie saves 14 and goals scored against 6 what percent of shots did goalie save
Answers
How much space will a cylindrical water tank occupy if its height is 100 cm and its diameter is 30
find the volume
Answers
Answer:
volume of a cylindrical water tank = 70,650cm³
Step-by-step explanation:
volume of cylinder, V = πr²h
where π = 3.14
h = 100cm
r = ?
given is diameter = 30cm
r = d/2 = 30/2 = 15cm
substituting the values in the formula,
V = 3.14 * 15² * 100
= 3.14 * 225 * 100
= 70,650cm³
Answer:
How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm
Volume: 706,500 cm³
Step-by-step explanation:
How much space it would take up:
To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.
The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.
To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.
A = π(15 cm)²
A = π(225 cm²)
A ≈ 706.86 cm²
So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.
The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.
Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.
Volume:
To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
First, we need to find the radius by dividing the diameter by 2:
Radius = 30 cm / 2 = 15 cm
Now we can calculate the volume:
V = π(15 cm)²(100 cm)
V = 3.14 * 225 cm² * 100 cm
V = 706,500 cm³
Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.