The area of the rectangle would be equal to the sum of the areas of these 12 squares.
The area of a rectangle is a measure of the amount of space it covers. It is calculated by multiplying the length and the width of the rectangle.
For a rectangle with sides of 3 cm and 4 cm, the area can be found by multiplying 3 by 4. The formula for finding the area of a rectangle is
=> A = l * w,
where l is the length and w is the width.
So, for the rectangle with sides 3 cm and 4 cm, the area would be
=> A = 3 * 4 = 12 square centimeters.
To visualize this, imagine a rectangle with sides of 3 cm and 4 cm. If you placed 12 squares of 1 cm each inside this rectangle, it would fill up the entire rectangle without any space left.
Complete Question:
Find the areas of the rectangles whose sides are:
(a) 3 cm and 4 cm
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Brainliest + Points! Please explain
Courtney plans to buy a new car and determines she can budget $400 monthly for six years. Her bank is offering a 7. 5% annual interest rate. What is the maximum car loan she can afford to stay within her budget?
A.
$19,873. 45
B.
$21,000. 50
C.
$23,134. 61
D.
$27,425. 75
Correct answer to the given question about Courtney's affordable car loan within her budget is option D. $27,425. 75.
To determine the maximum car loan that Courtney can afford, you need to calculate the total amount she will pay over 6 years and make sure it's less than the total amount she can afford to pay each month ($400) multiplied by the number of months (6 years x 12 months per year = 72 months).
First, calculate the total amount of interest she will pay over 6 years at 7.5% annual interest: $400 x 7.5% = $30
Next, calculate the monthly payment by dividing the annual interest amount by 12 months:$30 / 12 = $2.50
So, the monthly payment (not including the car loan amount) is $400 + $2.50 = $402.50.
Finally, you can calculate the maximum car loan amount by subtracting the monthly payment from the total amount she can afford to pay each month, and then dividing by the number of months:
$400 x 72 months = $28,800
$28,800 / $402.50 = 71.37
So, Courtney can afford a maximum car loan of $71,370.
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Suppose √x + √y = 10 and y(9) = 49. Find y'(9) by implicit differentiation.
Answer:
y'(9) = -7/3.
Step-by-step explanation:
We start by differentiating the given equation with respect to x:
d/dx(√x + √y) = d/dx(10)
1/(2√x) + (1/2)y'(x)/√y = 0
Simplifying, we get:
y'(x) = -√y/√x
To find y'(9), we plug in x = 9 and y = y(9) = 49:
y'(9) = -√49/√9 = -7/3
Therefore, y'(9) = -7/3.
Please i need a word answer fast
The 2 rectangles below are similar.
Work out the value of x.
If your answer is a decimal, give it to 1 D.P
Answer:
x = 6
Step-by-step explanation:
the opposite sides in a rectangle are congruent.
since the rectangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{5x}{18}[/tex] = [tex]\frac{10}{x}[/tex] ( cross- multiply )
5x² = 18 × 10 = 180 ( divide both sides by 5 )
x² = 36 ( take square root of both sides )
x = [tex]\sqrt{36}[/tex] = 6
Prove that x^(logy-logz)*y^(logz-logx)*z^(logx-logy) = 1
Answer:
We can start by using logarithmic properties. If a, b, and c are positive numbers, then:
loga^b = b * loga
Using this property, we can rewrite the expression as:
x^(logy - logz) * y^(logz - logx) * z^(logx - logy) = x^(logy/logx - logz/logx) * y^(logz/logy - logx/logy) * z^(logx/logz - logy/logz)
Using the change-of-base formula, we can simplify the exponents:
x^(logy/logx - logz/logx) = (logy/logx) / (logz/logx) = logy/logz
Similarly,
y^(logz/logy - logx/logy) = logz/logx
and
z^(logx/logz - logy/logz) = logx/logy
Now, we can substitute these results back into the original expression:
x^(logy - logz) * y^(logz - logx) * z^(logx - logy) = logy/logz * logz/logx * logx/logy
By the transitive property of logarithms, we have:
logy/logz * logz/logx * logx/logy = logy/logx
Finally, using the change-of-base formula again, we can simplify this result:
logy/logx = y^(1/logx) / x^(1/logx)
Since y and x are positive numbers, their exponents must also be positive. Therefore, we have:
y^(1/logx) / x^(1/logx) = 1
So,
x^(logy - logz) * y^(logz - logx) * z^(logx - logy) = 1
And we have proven that the expression is equal to 1.
Step-by-step explanation:
the 1000 students of a local high school are categorized by their attendance and gpa in the table. if a student has skipped many classes, what is the probability that their gpa is less than 2.0?
The probability that a student who has skipped many classes has a GPA less than 2.0 is 0.5.
To calculate this probability, we can use the data from the table given. If a student has skipped many classes, they are in the "Many Skips" category. From the table, we can see that there are 200 students in the "Many Skips" category and 100 of them have a GPA of less than 2.0. Therefore, the probability of a student with many skips having a GPA less than 2.0 is given by:
P(GPA < 2.0 | Many Skips) = 100/200 = 0.5
This means that if we randomly select a student who has skipped many classes, there is a 50% chance that their GPA will be less than 2.0. This calculation provides insight into the relationship between attendance and GPA, and it suggests that skipping many classes is associated with a lower GPA.
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The diagram shows a track composed with a semicircle on each end. The area of the rectangle is 14,400 square meters. What is the perimeter of the th rack? Use 3.14 for pi
Answer:
602 .6
Step-by-step explanation:
∴14,400=160b
⇒b=90m
902m=45m
2πr=2π×45≈282.6m
320m+282.6m=602.6m
Miguel’s steps in evaluating an expression are given below.
32 divided by 2 (2 cubed minus 4)
Step 1: Equals 32 divided by 2 (8 minus 4)
Step 2: Equals 32 divided by 2 (4)
Step 3: Equals 32 divided by 8
Step 4: Equals 4
What, if any, was Miguel’s mistake?
Miguel made no mistakes.
Miguel incorrectly evaluated 2³ in step 1.
Miguel incorrectly multiplied before dividing in step 3.
Miguel should have used the distributive property in step 1.
The correct statement regarding the solution of the expression is given as follows:
Miguel made no mistakes.
How to solve the expression?The expression for this problem is defined as follows:
32/[2(2³ - 4)].
The parenthesis has precedence, and inside the parenthesis, the cube has precedence, hence:
32/[2(8 - 4)] = 32/[2(4)]
Multiplying in the denominator and then dividing the numerator by the denominator, the result is given as follows:
32/[2(4)] = 32/8 = 4.
Meaning that no mistake was made.
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George has obtained a $141,000 5/130-year ARM at 5%. During the first 3 years, he has an option of paying interest only. If he were to accept this offer, what would his initial payment be?
The initial payment for the first 3 years of an interest-only loan for a $141,000 5/130-year ARM at 5% would be $7050.
An ARM, or Adjustable Rate Mortgage, is a type of mortgage loan where the interest rate can change over time. The 5/1 in the loan term "5/130-year ARM" means that the initial rate is fixed for the first 5 years and can change once every year thereafter for the remaining life of the loan (in this case, 130 years).
For an interest-only loan, the borrower pays only the interest due on the loan for a set period of time, in this case, the first 3 years. The interest payment can be calculated as:
Interest payment = Loan amount * Interest rate
The loan amount in this case is $141,000 and the interest rate is 5%, so the interest payment is:
Interest payment = $141,000 * 0.05 = $7050
So, the initial payment for the first 3 years of an interest-only loan for a $141,000 5/130-year ARM at 5% would be $7050.
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Which of the following is a pair of equivalent radical expressions?
A. 45−−√
and 315−−√
B. 75−−√
and 35–√
C. 54−−√
and 96–√
D. 180−−−√
and 320−−√
The pair of equivalent radical expression is option D. √180 and 3√20.
What are Radicals?Radicals are defined as the nth root of a number using the symbol [tex]\sqrt[n]{x}[/tex].
This is the opposite form of the exponential functions.
[tex]\sqrt[n]{x}[/tex] can be written in the exponential form as [tex]x^{1/n[/tex].
A.√45 can be written as the square root of (15 × 3).
√45 = √(15 × 3) ≠ 3√15
B. √75 cannot be written as 3√5, since, if we have to take 3 outside, inside he root there must be 3² = 9. But 75 is not a multiple of 9.
C. √54 = √(9 × 6) = 3√6 ≠ 9√6
D. √180 = √(9 × 20) = √9 × √20 = 3√20
Hence the correct option is D.
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The clear question is given below.
Which of the following is a pair of equivalent radical expressions?
A. √45 and 3√15
B. √ 75 and 3√5
C. √54 and 9√6
D. √180 and 3√20
Lincoln drives 15 miles in 12 minutes. If he drove one hour in total at the same rate, how far did he go?
Before you try that problem, answer the question below.
How many minutes did Lincoln drive in total?
Answer: Lincoln drove 15 miles in 12 minutes, so he drove a total of 60 minutes because 60/12 = 5.
Thus, Lincoln drove a total of 15 * 5 = 75 miles.
Step-by-step explanation:
2 more than 5 times a number is 13 less than 8 times a number. Write the equation and solve.
Answer:
x=5
Step-by-step explanation:
5x+2=8x-13
add the 13
5x+15=8x
subtract the 5x
15=3x
divide by 3
x=5
Use the figure below to answer the following questions. Be sure to
symbols where necessary.
15. Obtuse
6.
7.
Classify 21.
Classify 22.
Classify ZABC.
8.
Name 22.
Find the value of 'x' in each of the following.
A
98°
B
BE bisects /DBC.
C
The classifications are done as follows
6. < 2 : acute angle
7. < ABC : angle on a straight line
8. < 2 = 41 degrees
9. x = 45
How to find xIn the figure, BE bisects < DBC hence < 2 = < 3 = y
98 + < 2 + < 3 = 180
y + y = 180 - 98
2y = 82
y = 41
In the figure, < WXY = 88 where the adjacent angles are
< WXZ = 4x - 3 and < ZXY = 2x + 1
4x - 3 + 2x + 1 = 88
4x + 2x = 88 + 3 - 1
2x = 90
x = 45
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Find the value of P and please do your best and double check your answers, thanks!!!
The value of P in this triangle is equal to 14.
What is the basic proportionality theorem?In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.
By applying the basic proportionality theorem to the given triangle, we have the following:
24/p = 12/(21 - p)
By cross-multiplying, we have the following:
12p = 24(21 - p)
12p = 504 - 24p
36p = 504
p = 504/36
p = 14.
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Now answer the following ques Write 1930.54 in standard form. A. B. C. D. 1.93054 × 10² 1.93054 x 10² 1.93054 x 10-2 1.93054 × 10³
1930.54 can be written in standard form as 1.93054 × 10³. Option D is correct.
What is a standard form?A number can be written in standard form to make it simpler to read. It is frequently used for extremely high or extremely low figures. Mathematics and other science fields employ the use of standard form, which is similar to scientific notation.
When a decimal number is multiplied by a power of 10, it is said to be expressed in standard form.
Similar to scientific notation, standard form represents a number as a decimal number times a power of 10. (i.e a*10^b)
From the given information:
1930.54 can be written in standard form as 1.93054 × 10³
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x is an angle in the second quadrant with 3sinx-4cosx=5 1) write sinx in terms of cosx 2) show that cosx=-4/5 then deduce the exact value of sinx
The value of sin(x) in terms of cos(x) is √1 - cos²(x). The value of sin(x) is 3/5.
Since x is an angle in the second quadrant, sin(x) is positive and cos(x) is negative.
To write sin(x) in terms of cos(x), we can use the identity sin²(x) + cos²(x) = 1 and solve for sin(x):
sin²(x) + cos²(x) = 1
sin²(x) = 1 - cos²(x)
sin(x) = ± √(1 - cos²(x))
Since sin(x) is positive in the second quadrant, we have:
sin(x) = √(1 - cos²(x))
To show that cos(x) = -4/5, we can use the given equation:
3sin(x) - 4cos(x) = 5
We can rearrange this equation to get cos(x) on one side:
4cos(x) = 3sin(x) - 5
cos(x) = (3sin(x) - 5) / 4
Now we can substitute the expression for sin(x) that we found earlier:
cos(x) = (3√(1 - cos²(x)) - 5) / 4
Multiplying both sides by 4 and simplifying, we get:
4cos²(x) + 3cos(x) - 4 = 0
This is a quadratic equation in cos(x). We can solve it using the quadratic formula:
cos(x) = [-3 ± √(3² - 4(4)(-4))] / (2(4))
cos(x) = (-3 ± 7) / 8
cos(x) = 1/2 or cos(x) = -4/5
Since x is in the second quadrant, we have cos(x) < 0, so cos(x) = -4/5.
Finally, we can use the expression for sin(x) that we found earlier to get:
sin(x) = √(1 - cos²(x))
sin(x) = √(1 - (-4/5)²)
sin(x) = √(1 - 16/25)
sin(x) = √9/25
sin(x) = 3/5
Therefore, the exact value of sin(x) is 3/5.
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2. A man gets 1.8 million loan to buy a house, he paid interest at the rate of 9% per annum. In the first year, he paid the interest on the loan, he also paid back 140,000 of the money he borrowed. (1) how much did he pay in the first year altogether, (2) if he paid this money by monthly installment, how much did he pay per month.
(1) The amount of interest he paid in the first year altogether is 302,000.
(2) The monthly installment is 25,166.67 per month
How did we get the values?(1) The amount of interest he paid in the first year is 1.8 million x 9% = 162,000.
So, in the first year, he paid a total of 162,000 + 140,000 = 302,000.
(2) To calculate the monthly installment, we first need to find out the total amount he paid in a year and then divide it by 12:
302,000 ÷ 12 = 25,166.67
So, he paid 25,166.67 per month.
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Answer:
$296,318.52$24,693.21Step-by-step explanation:
You want to know the total paid during the first year of a $1.8M loan at 9% if the balance is reduced by $140,000 after 12 monthly payments. You also want to know the amount of the monthly payment.
Future valueThe remaining balance of an amortized loan is given by the formula ...
FV = PV(1 +r)^n - <future value of payments>
where r is the monthly interest rate, and n is the number of months.
Using the given loan values, we have ...
1,800,000 -140,000 = 1,800,000(1 +0.09/12)^12 -<payment value>
(2) Payment amountSolving for the future value of the payments, we find ...
<payment value> = 1,800,000(1.093806898) -1,660,000 = 308,852.42
This is the future value of the payments made, so some further calculation is required to find the amount of the payment.
<payment future value> = P((1+r)^n -1)/r = P(1.0075^12 -1)/0.0075
P = <payment future value>/12.5075864
P = 308,852.42/12.5075864 = 24693.21
The amount of the monthly payment was $24,693.21.
(1) Total paid12 monthly payments were made in the first year, so the total paid was ...
12 × $24,693.21 = $296,318.52 . . . . total paid in the first year
__
Additional comment
The attachment confirms these numbers. It is the output of an online remaining balance calculator. The difference of $0.04 between the bottom two numbers is a consequence of rounding. The given payment actually reduces the balance by $140,000.04.
Which of the following are units of volume choose all the correct answers
G2 cm3 m2 kg3 cubic metre
Units of volume are cm³ and cubic meter.
What is volume?Volume is the measure of the capacity that an object holds.
A unit of volume is a unit of measurement for measuring volume or capacity, the extent of an object or space in three dimensions.
For example, if a cup can hold 100 ml of water up to the brim, its volume is said to be 100 ml.
Given units of measurement,
G² - It is not unit of volume
cm³- It is unit of volume
m² - It is not unit of volume
kg³ - It is not unit of volume
cubic meter = meter³ - It is unit of volume
Hence, cm³ and cubic-meter are units of volume.
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please help! precalculus (concavity and graphing)
pls helpp me i dont understan
Answer:
Given functionf(x) = -1 - 7/2 x*3
Plugging X = 2f(2) = -1 -7/2 (2)*3
f(2) = -1 -7/2 (8)
f(2) = -1 -56/2
f(2) = -1 -28
f(2) = -29please hurry i dont have long
Answer:
141°
Step-by-step explanation:
In order to find the missing angle, we must first find the total sum of all the interior angles. To find this we use the following equation:
(n – 2) × 180°
Where n is equal to the number of sides
There are 7 sides therefore:
(7 – 2) × 180°
5 × 180°
900°
The sum of the total angles in the heptagon is 900°
We then must subtract all of the known angles
900 - 148 = 752
752 - 90 = 662
662 - 142 = 520
520 - 130 = 390
390 - 129 = 261
261 - 120 = 141
The missing angle is 141°
At Cal’s Computer Warehouse, Cal wants to know the probability that a customer who comes into his store will buy a computer or a printer. He collected the following data during a recent week: 327 customers visited the store, 196 purchased computers, 72 purchased printers, and 87 made no purchase
The percentage of No purchase is 26%, the computer is 59.9% and the printer is 22%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that he collected the following data during a recent week: 327 customers visited the store, 196 purchased computers, 72 purchased printers, and 87 made no purchase.
The percentage of No purchase is:-
P = 87 / 327
P = 26%
The percentage of computer purchases:-
P = 196 / 327
P = 59.9%
The percentage of printer purchases is:-
P = 72 / 327
P = 22%
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HELP PLEASE!!!!
(-8,7) and (-2,-3)
Answer:
Slope is -5/3
Step-by-step explanation:
Let [tex](x_1,y_1)\rightarrow(-8,7)[/tex] and [tex](x_2,y_2)\rightarrow(-2,-3)[/tex]:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-3-7}{-2-(-8)}\\ \\m=\frac{-10}{-2+8}\\\\m=-\frac{10}{6}\\ \\m=-\frac{5}{3}[/tex]
how many ways can a person toss a coin 12 times so that the number of heads is between 7 and 11 inclusive?
The number of ways can a person toss a coin 12 times so that the number of heads is between 7 and 11 inclusive is 1585.
Combinations:Combinations are methods for choosing elements from collections of objects. Unlike permutations, selection order is unimportant. The number of combinations can be counted in simpler situations.
The formula for combinations is given by
ⁿCₓ = n! /n!(n - x)!
Here we have
Number of tosses = 12 times
The number of heads is between 7 and 11 inclusive
Number of ways of getting 7 heads and 5 tails
= 12! / (7!5!) = 792
Number of ways of getting 8 heads and 4 tails
= 12!/(8!4!) = 495
Number of ways of getting 9 heads and 3 tails
= 12!/(9!3!) = 220
Number of ways of getting 10 heads and 2 tails
= 12!/ (10!2!) = 66
Number of ways of getting 11 heads and 1 tail
= 12! / (11!1!) = 12
Total number of ways = 792 + 495 + 220 + 66 + 12
= 1585
Therefore,
The number of ways can a person toss a coin 12 times so that the number of heads is between 7 and 11 inclusive is 1585.
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for a game of chance, there is a 20% chance of winning $60, a 20% chance of winning $100, a 30% chance of breaking even. what is the overall expected outcome for this game?
The overall expected outcome for this game is $32.
Therefore the answer is $32.
The expected outcome for a game of chance can be calculated by multiplying the payoffs for each outcome by the probability of each outcome, and then summing these products.
For this game, the expected outcome would be calculated as follows:
Expected outcome
= (0.20 * $60) + (0.20 * $100) + (0.30 * $0)
= $12 + $20 + $0
= $32
So the overall expected outcome for this game is $32. This means that, on average, if you were to play this game many times, you could expect to win $32 each time. It's worth noting that expected outcome is just an average and does not guarantee a win, as the outcomes of each game are uncertain.
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Let f be the function defined by
f(x) = 3^x. If three subintervals of equal
length are used, what is the value of the left Riemann sum approximation for
3.5
2
3 dx? Round to the nearest
thousandth if necessary.
The left Riemann sum approximation is 14.892
How to determine the left Riemann sum approximationFrom the question, we have the following parameters that can be used in our computation:
f(x) = 3^x
The left Riemann sum can be expressed as:
[tex]R_n = h \sum_{i=1}^{n} \frac{4}{a + ih}[/tex]
Such that:
h = (b - a)/n
In this case, a = 2, b = 3.5, n = 3, and f(x) = 3^x
So, the left Riemann sum approximation is:
Approximation = (3.5-2)/3 * (f(2 + 1/3 * (3.5-2)) + f(2 + 2/3 * (3.5-2)) + f(2 + 3/3 * (3.5-2)))
Approximation = 0.5/3 * (3^(2 + 1/3 * (3.5-2)) + 3^(2 + 2/3 * (3.5-2)) + 3^(2 + 3/3 * (3.5-2)))
Approximation = 14.892
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The average sale price of new one family houses in the United States for a recent year was $238,100. Find the range of values in which at least 88. 89% of the fake prices will lie if the standard deviation is $53,500
The range of values in which at least 88.89% of the fake prices will lie if the standard deviation is $53,500 will be $84,600 and $391,600.
What does standard deviation mean in plain English?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.
Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
The lower boundary of the range is calculated by subtracting two standard deviations from the average sale price
$238,100 - $53,500 = $84,600
The upper boundary of the range is calculated by adding two standard deviations to the average sale price
$238,100 + $53,500 = $391,600
Therefore, the range of values in which at least 88.89% of the fake prices will lie is between $84,600 and $391,600.
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After a procedure has been completed, what questions can be asked to help evaluate the results? Check all that
apply.
When should this procedure be performed again?
Were the steps completed in order?
What could be done differently in the future?
Was the expected outcome reached?
-Who else has completed this procedure?
The answers to questions 2, 3, and 4 can be used to assess the effectiveness of a technique after a procedure is finished.
What questions can be asked to help evaluate the results?Were the steps completed in order?
This is a crucial question to ask since it reveals the steps in the process and their chronological order, allowing the processes to be adjusted as necessary in the future.
What could be done differently in the future?
It is crucial since it can identify existing problems as well as those that can develop in the future, and it will aid in resolving them.
Was the expected outcome reached?
The most crucial question to ask is what result you want the process to produce; if not, you'll need to adjust the phases and the process.
Evaluation: Evaluation is the methodical conclusion of any topic, problem, or subject using predetermined standards or criteria. To judge their worth or value, the step and the methods are analyzed and assessed.
Therefore, the answers to questions 2, 3, and 4 can be used to assess the effectiveness of a technique after a procedure is finished.
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A cylinder with a height of 11.2 cm and radius of 4.9 cm is shown. Use the image to answer the question. Find the lateral surface area of the cylinder. Use 3.14 for π and round to the nearest whole number.
The lateral surface area of the cylinder would be 157.78π.
What is lateral surface area of a cylinder? How will you derive the volume of a cylinder?The lateral surface area of a cylinder with radius 'r' and height 'h' is given by →LSA = 2πr(h + r) .... Eq { 1 }
Consider a very thin cross - section of a cylinder whose thickness is [dh] {differential or very small value}. The volume of this cross section would be -dV = πr² dh
For complete cylinder -
∫dV = πr² ∫dh
V - 0 = πr² [h - 0]
V = πr²h .... Eq { 2 }
Given is a cylinder with a height of 11.2 cm and radius of 4.9 cm.
We can write the lateral surface area of a cylinder as -
LSA = 2πr(h + r)
LSA = 2π x 4.9 x (11.2 + 4.9)
LSA = 2π x 78.89
LSA = 157.78π
Therefore, the lateral surface area of the cylinder would be 157.78π.
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At Rental Company A, a rental car costs $55.50 and every
kilometer costs $14.40. At Rental Company B, a rental car
costs $91.50 and every kilometer costs $10.80.
At how many kilometers will they cost the same, and how
much will it cost?
kilometers
dollars
Answer:
1/ At 10km, they will cost the same.
2/ It costs $199.50
Step-by-step explanation:
We know
Rental Company A, a rental car costs $55.50, and every kilometer costs $14.40.
Let Y represent the total cost, and x is the number of kilometers. We have the equation
y = 14.40x + 55.50
Rental Company B, a rental car costs $91.50, and every kilometer costs $10.80.
y = 10.80x + 91.50
How many kilometers will they cost the same?
14.40x + 55.50 = 10.80x + 91.50
3.6x = 36
x = 10 km
How much will it cost?
y = 14.40(10) + 55.50
y = 144 + 55.50
y = $199.50