The volume of the solid obtained by rotating about the x-axis the region enclosed by the curves is 32π/5 cubic units.
In this problem, we are asked to find the volume of a solid obtained by rotating a region enclosed by curves about the x-axis. We will use integration to calculate the volume.
First, let's sketch the region and the solid we need to find the volume of.
The region is enclosed by the curves
=> y = 16 /(x² + 16), y = 0, x = 0, and x = 4.
When we rotate this region about the x-axis, we get a solid with a hole in the center, shaped like a donut.
To find the volume of this solid, we can use the method of cylindrical shells.
We start by taking a thin strip of the region, parallel to the y-axis, and of width dy. This strip has height y, and we rotate it about the x-axis to get a cylindrical shell of thickness dy and radius x.
The volume of this cylindrical shell is given by the formula V = 2πxy dy, where x is the distance from the y-axis to the edge of the shell.
To express x in terms of y, we can solve for x in the equation
y = 16 /(x² + 16).
y(x² + 16) = 16
x² = 16/y - 16
x = √(16/y - 16)
Now we can substitute x into the formula for V to get:
V = 2πx(16/(x² + 16)) dy
[tex]= 2\pi(16/y - 16)^{1/2}(16/y) dy \\\\= 32\pi(y - y^{3/2}) dy[/tex]
To find the total volume, we integrate this expression from y = 0 to y = 1 (since the maximum value of y is 16/16 = 1):
[tex]\int_0^1 32\pi(y - y{(3/2)}) dy = 32\pi/5[/tex]
Therefore, the volume of the solid obtained by rotating the region about the x-axis is 32π/5 cubic units.
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Aubrey broke a cell sample into 15 batches, each way 1.3×10 to the -7th grams. How much did the original sample weigh? Use scientific notation to express your answer.
Answer:
Step-by-step explanation:
1.3 * 10 ^-7
is 0.00000013
0.00000013 times 15 is
0.00000195.
0.00000195 in scientific notation is
1.95*10^-6
Rectangle A: 2 * 3 Rectangle B: 8 * 12 Rectangle C: 5 * 7 Rectangle D: 10 * 12 Which pair of rectangles is similar?
Answer: your mom
Step-by-step explanation:
Let S be the universal set, where: S = { 1 , 2 , 3 , ... , 18 , 19 , 20 } Let sets A and B be subsets of S , where: Set A = { 1 , 2 , 4 , 10 , 12 , 14 , 16 } Set B = { 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 } Find the following: The number of elements in the set ( A ∪ B ): n ( A ∪ B ) = The number of elements in the set ( A ∩ B ): n ( A ∩ B ) is
The values for the sets are -
A∪B = { 1 , 2 , 4 , 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 } and n(A∪B) = 14.
A∩B = { 10 , 12 , 14 , 16 } and n(A∩B) = 4
What is sets?
A set is a precisely defined collection or aggregate of all feasible objects with predetermined qualities that are specified in accordance with a precisely defined rule. Elements of sets are the items used to compare sets.
The set S is - S = { 1 , 2 , 3 , ... , 18 , 19 , 20 }
The set A is - A = { 1 , 2 , 4 , 10 , 12 , 14 , 16 }
The set B is - B = { 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 }
A∪B is the set of elements of S that are part of A or B, or both.
A∪B = { 1 , 2 , 4 , 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 }
Count the number of elements present in set A∪B.
Therefore, n(A∪B) value is 14.
A∩B is the set of elements of S that are common to A and B.
A∩B = { 10 , 12 , 14 , 16 }
Count the number of elements present in set A∩B.
Therefore, n(A∩B) value is 4.
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A town has a population of 4.11 x 10^4 and shrinks at a rate of 9.6% every year. Which equation represents the town's population after 4 years?
Answer:
Step-by-step explanation:
The equation that represents the town's population after 4 years can be found using the formula:
P = P0 * (1 - r)^t
Where P is the population after t years, P0 is the initial population (4.11 x 10^4), r is the annual shrink rate as a decimal (9.6% as 0.096), and t is the number of years (4).
P = 4.11 x 10^4 * (1 - 0.096)^4
P = 4.11 x 10^4 * 0.6994^4
P = 4.11 x 10^4 * 0.4139
P = 1.70 x 10^4
So the town's population after 4 years is 1.70 x 10^4.
Answer:
Let P(t) be the population of the town after t years. We know that P(0) = 4.11 x 10^4. Then, the rate of change of the population is given by -0.096P(t), so we can write the differential equation:
dP/dt = -0.096P(t)
To find the population after 4 years, we need to solve this differential equation with the initial condition P(0) = 4.11 x 10^4. We can do this by separating variables and integrating both sides:
∫(dP/P) = -0.096 ∫dt
ln|P(t)| = -0.096t + C
where C is a constant of integration that can be found using the initial condition. Solving for P(t), we get:
P(t) = Ce^(-0.096t)
where C = e^(ln|P(0)|) = e^(ln|4.11 x 10^4|) = 4.11 x 10^4
Substituting in t = 4, we get:
P(4) = 4.11 x 10^4 e^(-0.096 × 4) = 4.11 x 10^4 e^(-0.384)
So, the equation representing the town's population after 4 years is:
P(t) = 4.11 x 10^4 e^(-0.096t)
PLEASE HELP!!! VERY URGENT
A person walks due south from point A for 500 yards and then due west for 300 yards, arriving at point B. Answer the following questions using complete sentences. 2 points for each correct answer and 2 points for each correct explanation.
i. What is the person's displacement from the starting point? How did you calculate this? Be sure to round to the nearest hundredth.
ii. From point B, in what direction would the person have to look in order to be looking back at point A (the starting point)? Give your answer as a true bearing calculated to the nearest hundredth of a degree. Explain how you got this answer.
iii. A friend is standing at point A looking at point B. In what direction would that friend be looking? Give your answer as a true bearing calculated to the nearest hundredth of a degree. Explain how you got this answer.
The answers are mentioned below.
What do you mean by Displacement?In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.
i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500^2 + 300^2) = 583.1 yards (rounded to the nearest hundredth).
ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the direction in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using trigonometry, where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500. Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 360 - 31.39 = 328.61 degrees (rounded to the nearest hundredth).
iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 90 + 59.04 = 149.04 degrees (rounded to the nearest hundredth).
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i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500² + 300²) = 583.1 yards
What do you mean by Displacement?In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.
i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle.
Therefore, the displacement can be calculated as the
√(500² + 300²)
= 583.1 yards (rounded to the nearest hundredth).
ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the ²in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using ², where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500.
Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be
360 - 31.39
= 328.61 degrees (rounded to the nearest hundredth).
iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees.
However, the true bearing is measured from the north and therefore, the true bearing would be
90 + 59.04
= 149.04 degrees (rounded to the nearest hundredth).
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The number of candies sold can be determined by the equation: T = 0.3c,
where T is number of candies and c is the number of children. Find the
constant of proportionality.
The constant of proportionality in the equation is 0.3.
What is constant of proportionality?Firstly, there is proportional relationship.
Two values x and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.
The constant k is called constant of proportionality.
WE are given that number of candies sold can be determined by the equation: T = 0.3c, where T is number of candies and c is the number of children.
0.3 = constant of proportionality
0.3 = p / n
which is the ratio of p to n
The constant of proportionality is the ratio between the two quantities that are directly proportional.
Therefore,
0.3 is the constant of proportionality in the equation.
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put these decimals lease to greatest 2.16,2.1682,2.2,2.016?
Answer:
2.016, 2.16, 2.1682, 2.2
How to put anything from least to greatest?
The decimals that you have put are the following:
2.16
2.1682
2.2
2.016
How to do it:
If you look at the decimals the last one, 2.016 does not have a 1 or a 2 instead it has a 0 so that would be a our first decimal in the least to greatest form.
We can also include the third one 2.2 is the only one that has a 2 so now we know that 2.2 will go last.
Lets compare the first and second ones which are 2.16 and 2.1682 and I think we obviously know that the answer is 2.1682 because it is greater then 2.16.
So now here are the decimals from least to greatest:
2.016, 2.16, 2.1682, 2.2
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se the log tables in your book to find the following logarithms. You should use a calculator ONLY TO MULTIPLY and ONLY in parts c,d, andg. a.log(2^100)=b.log(100^2)=c.log(3.0862.062)=d.log(55^−3.1)=e.log(51)=f.log(1/51)=g.log(1/81^2)=
The logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.
For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3
a. log(2^100) = 100 log(2) ≈ 30.103
b. log(100^2) = 2 log(100) = 2 log(10^2) = 2 × 2 = 4
c. log(3.0862.062) = log(3.086) + log(2.062) ≈ 0.488 + 0.316 = 0.804
(Note: The multiplication of 3.086 and 2.062 can be done using a calculator.)
d. log(55^(-3.1)) = -3.1 log(55) ≈ -3.1 × 1.740 = -5.394
e. log(5/1) = log(5) - log(1) ≈ 0.699 - 0 = 0.699
f. log(1/5) = log(1) - log(5) ≈ 0 - 0.699 = -0.699
g. log(1/81^2) = log(1) - 2 log(81) = -2 log(9^2) = -2 × 2 log(9) ≈ -2 × 0.954 = -1.908
(Note: We can use the property that log(a^b) = b log(a) to simplify the expression.)
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Which of the symbols correctly relates the two numbers below? Check all that
apply.
A. =
B. >
C. Z
☐ D. <
E. >
OF. s
364? 225
The symbols which correctly relate the numbers 364 and 225 are '>' and '≠'.
The solution has been obtained by using concept of relational symbols.
What are relational symbols?
Relational symbols are used in mathematics to represent mathematical relations, which combine with one or more other mathematical objects to construct complete mathematical statements. These are the relational symbols for equality and comparison in arithmetic and common mathematics.
We are given 2 numbers as 364 and 225.
It is clearly visible that both the numbers are not same so, the symbol '≠' depicts the relationship between the two numbers.
Also, we know that the number 364 is greater than 225. So the another symbol depicting relation between the numbers is '>'.
Hence, the symbols which correctly relate the numbers 364 and 225 are '>' and '≠'.
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Question: Which of the symbols correctly relates the two numbers below? Check all that apply.
364? 225
A. =
B. >
C. ≥
D. <
E. ≤
F. ≠
Help!!!!
I am very lost!
The height of the plane to the nearest metres is 1023 metres. Therefore, the answer is A.
How to find the height of the plane?A pilot flying over the gulf of Mexico sees an island at an angle of depression of 12 degrees. At this time the horizontal distance from the plane to the island is 4812 metres .
Therefore, the height of the plane can be found as follows:
The situation forms a right angle triangle.
Using trigonometric ratios,
tan 12 = opposite / adjacent
tan 12° = x / 4812
cross multiply
x = 4812 tan 12°
x = 4812 × 0.21255656167
Therefore,
x = 1022.82217476
x = 1023 metres.
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what are some three statements Symons why any of the objects does not belong with the others.
Here are three statements explaining why each of the objects doesn't belong with the others:
The StatementsSphere:
A sphere is a three-dimensional object with a curved surface, while the other objects listed have flat or angled surfaces.A sphere has an equal diameter at every point, making it a true round object, while the other objects have varying shapes and angles.The volume of a sphere can be calculated using the formula 4/3 * π * r^3, which is different from the formulas used to calculate the volume of the other objects listed.Cylinder:
A cylinder has two flat circular bases, while the other objects listed do not have flat circular bases.A cylinder has a curved lateral surface, while the other objects listed have flat or angled lateral surfaces.The volume of a cylinder can be calculated using the formula π * r^2 * h, which is different from the formulas used to calculate the volume of the other objects listed.Pyramid:
A pyramid has a flat base and triangular sides that meet at a single point, while the other objects listed have different shaped bases and sides.A pyramid has no curved surfaces, while the other objects listed have curved surfaces.The volume of a pyramid can be calculated using the formula (B * h) / 3, where B is the area of the base and h is the height, which is different from the formulas used to calculate the volume of the other objects listed.Cube:
A cube has square faces and equal lengths on all sides, while the other objects listed do not have square faces and/or do not have equal lengths on all sides.A cube has right angles between all faces, while the other objects listed do not have right angles between all faces.The volume of a cube can be calculated using the formula s^3, where s is the length of a side, which is different from the formulas used to calculate the volume of the other objects listed.Read more about squares here:
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16. Higher Order Thinking The box plots show the average daily high temperatures
of two cities from January to December. Which city should you live in if you want
a greater variability in temperature? Explain.
The city that you should live in if you want a greater variability in temperature is city Y.
Which city should you live in?In order to determine the city that has the greater variability in temperature, the interquartile range has to be determined. The interquartile range is used to measure the variation in a dataset.
The interquartile range is the difference between the third quartile and the first quartile.
interquartile range = third quartile - first quartile
Interquartile range for City X = 50 - 30 = 20
Interquartile range for City Y = 50 - 25 = 25
The interquartile range for city Y is greater than that of city X. This means that city Y has a greater variation in temperature.
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si en una division el dividendo es 872 el cociente es 62 y el residuo es 4 cual es el divisor
The divisor in the situation given is 14.
What is division algorithm?We can write the division algorithm as -
dividend = (divisor × quotient) + remainder
Given is that in a division the dividend is 872 the quotient is 62 and the remainder is 4
We can write -
dividend = (divisor × quotient) + remainder
872 = (d x 62) + 4
62d = 868
d = 868/62
d = 14
Therefore, the divisor in the situation given is 14.
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{Question in english -
if in a division the dividend is 872 the quotient is 62 and the remainder is 4 what is the divisor}
PLS HELPPPPP!!!!!!!!! DUE TODAY!!!!!! 100 points and brainliest if correct!!!! pls answer all of them!
Answer and solve the proportions then the percent equation.
what is the percent equation for the following:
6.5% of $400 is
what number?
12.5% of $100 is
what number?
130 is what percent
of 650?
$5.40 is what
percent of $4.50?
$8.40 is what
percent of $28?
56% of what
number is $21.84?
$495 is 55% of
what number?
144 is what percent
of 240?
Answer:The first question requires the calculation of the 6.5% of $400, which is equal to $26.
The second question requires the calculation of 12.5% of $100, which is equal to $12.50.
For the third question, 130 is 20% of 650.
For the fourth question, $5.40 is 120% of $4.50.
For the fifth question, $8.40 is 30% of $28.
For the sixth question, 56% of 39 is $21.84
For the seventh question, $495 is 55% of $900.
For the last question, 144 is 60% of 240.
Step-by-step explanation:
Answer:
Step-by-step explanation:
26
12.5
20%
120%
30%
12.23
900
60%
Problem 10
1. The hexagon represents 1 whole.
Draw a pattern-block diagram that represents the equation 4.
Draw your diagram on paper, take a picture, and upload it using the image upload icon
If you do not have the ability to upload an image of your work, type "Diagram is on paper."
Porfavor lo necesito para el martes o si no voy a reprobar
According to the information, the graph would be as shown in the attached image (4 * 1/3 = 1 1/3)
How to graph the equation?According to the information we must take into account that a complete hexagon represents an integer. So one third of the hexagon would be the rhomboid. So, to graph this equation, we must replace the values with the corresponding figures.
In this case we must multiply the rhomboid by four, the rhomboid represents 1 of 3 elements that make up a hexagon. Therefore, if we have 4 rhomboids, we would have a hexagon and a rhomboid.
Note: This question is incomplete. Here is the complete information:
Image attached
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Justin jogged for four days in a row. On the second day, he jogged 75% of the distance he jogged the first day. On the third day, he jogged 1.5 miles, more than the distance he jogged the first day. If Justin jogged a total distance of 9.25 miles, how many miles did he jogged on the fourth day?
On solving the prοvided question, we can say that 4.75 miles were ran on day four.
What is equation?A mathematical equation is a formula that jοins two statements and uses the equal symbol (=) tο indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is known as an equatiοn in algebra.
Fοr instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences οn either side of a letter is described by a mathematical formula. Often, there is only οne variable, which alsο serves as the symbol. for instance, 2x – 4 = 2.
On day one, Justin ran two miles.
He ran two miles on the second day, or 75% of it. Divide by 100 and multiply by 75 to get the percentage of two miles that is 75%.
On the secοnd day, I ran 1.5 miles, or 2 / 100, or 0.02 x 75. (I've run 3.5 miles so far)
He ran 1.5 miles further on the third day than the previous one:
1.5 + 1.5 = 3 (6.5 miles jogged sο far) (6.5 miles jogged so far)
The total number of miles run was 9.25, thus tο find the solution, we must subtract 6.5 from 9.25.
4.75 miles were ran οn day four, or 9.25 minus 6.5.
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Find an angle α that is coterminal with an angle measuring 550∘, where 0∘≤α<360∘.
Answer:
190°
Step-by-step explanation:
Subtract 360° (this is one complete rotation)
"coterminal" is the exact same angle, but 360° bigger (or smaller)
550° - 360°
= 190°
Using logarithmic properties, what is the solution to log4(y - 9) + log43 = log481? Show all necessary steps.
Answer:
y = 36
Step-by-step explanation:
Given logarithmic equation:
[tex]\log_4(y-9)+\log_43=\log_481[/tex]
[tex]\textsf{Apply the \textbf{log product law}}: \quad \log_ax + \log_ay=\log_axy[/tex]
[tex]\implies \log_4\left(3(y-9)\right)=\log_481[/tex]
[tex]\textsf{Apply the \textbf{log equality law}}: \quad \textsf{If $\log_ax=\log_ay$ then $x=y$}[/tex]
[tex]\implies 3(y-9)=81[/tex]
Divide both sides of the equation by 3:
[tex]\implies \dfrac{3(y-9)}{3}=\dfrac{81}{3}[/tex]
[tex]\implies y-9=27[/tex]
Add 9 to both sides of the equation:
[tex]\implies y-9+9=27+9[/tex]
[tex]\implies y=36[/tex]
Therefore, the solution to the given logarithmic equation is y = 36.
Please helppppp me with the question
Answer: 30 in
Step-by-step explanation:
To figure out perimeter, you have to add up all of the sides.
The sides of the triangle are 7, 10, and 13 in.
7+10+13=30
The answer is 30 inches.
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F(x)=|x| is transformed to g(x)=|x|+4 what transformation happens from f(x) to g(x)
Step-by-step explanation:
The transformation from the function f(x) = |x| to the function g(x) = |x| + 4 can be thought of as a vertical shift upward by 4 units. The shape of the absolute value function remains unchanged, but the entire graph is shifted upward along the y-axis by 4 units. This can be visualized by observing that for any value of x, g(x) = f(x) + 4.
So, the transformation of f(x) to g(x) is a vertical shift upward by 4 units
NEED HELP!!!!!!!!!!!
Answer:
[tex]4x^{2} y^{3}[/tex]
Step-by-step explanation:
[tex]\frac{36x^{4}y^{5}}{(3xy)^{2}}[/tex]
In the denominator, all the terms in the brackets or parenthesis will be squared:
= [tex]\frac{36x^{4}y^{5}}{9x^{2} y^{2}}[/tex]
Law of indices is applied:
[tex]\frac{a^{n}}{a^{m}}[/tex]= [tex]a^{n - m}[/tex]
= [tex]4x^{4 - 2} y^{5 - 2}[/tex]
= [tex]4x^{2} y^{3}[/tex]
∴Option B
factorise 1331x³y-11y³x pls i really need it!! thank you :) !!
Answer:
11xy(121x²-y²)
Step-by-step explanation:
When factorizing, you should always look for what each term has in common.
First, let's look at the coefficients (numbers) in each term: 1331 and 11. Both are divisible by 11, so let's factorize out 11:
1331x³y-11y³x
11(121x³y-y³x)
Looking at the terms in the bracket, we see they both have 'x's in common (121x³y has three x's multiplied in and y³x has one). Let's factorize out this x:
11(121x³y-y³x)
11x(121x²y-y³)
We can also see both terms in the brackets have 'y's in common (121x²y has one y and y³ has three multiplied in). Let's factorize out this y:
11x(121x²y-y³)
11xy(121x²-y²)
Since there is nothing in common left between the terms, we can say the expression is fully factorized!
Mrs. Becker is walking down the hallway and suddenly spots the world's largest ladybug. If her eyes are 6 feet off the ground and the bug is 100 feet away, what angle is she looking down at?
Answer:
Step-by-step explanation:
To find the angle that Mrs. Becker is looking down at, we can use the tangent function. We know the height of her eyes (6 feet) and the distance from her eyes to the ladybug (100 feet), so we can use the formula:
tan(angle) = height/distance
First, we'll solve for the angle:
angle = tan^-1(height/distance)
angle = tan^-1(6/100)
Using a calculator, we can find that the angle is approximately 0.0349 radians, or approximately 2 degrees.
So, Mrs. Becker is looking down at an angle of approximately 2 degrees.
Solve for x.
3/4x + 3 = 27
Answer:
x = 32
Step-by-step explanation:
First we would move the x's to the left and the numbers to the right. When doing so they switch from being positive to negative or from negative to positive.
3/4x = 27-3
Now we would try to simplify it as much as we can. Here I would make 3/4 a decimal and subtract 37-3
0.75x = 24
Now we can divide 24 by 0.75 to find x
x = 32
x = 32.
Step-by-step explanation:1. Write the expression.[tex]\frac{3}{4} x+3=27[/tex]
2. Subtract "3" from both sides of the equation.[tex]\frac{3}{4} x+3-3=27-3\\ \\\frac{3}{4} x+3-3=27-3\\ \\\frac{3}{4} x=24[/tex]
3. Divide by " [tex]\frac{3}{4}[/tex] " ob both sides of the equation.[tex]\frac{\frac{3}{4} x}{\frac{3}{4}} =\frac{24}{\frac{3}{4}}\\ \\x=24*\frac{4}{3}\\ \\x=\frac{24*4}{3} \\ \\x=\frac{96}{3} \\\\x=32[/tex]
4. Verify the answer.If "32" is our correct answer, then substituting it by variable "x" on the original equation should make the equation return the same number on both sides of the equal (=) symbol. Let's test it!
[tex]\frac{3}{4} (32)+3=27\\ \\\frac{3*32}{4}+3=27\\ \\\frac{96}{4}+3=27\\ \\24+3=27\\ \\27=27[/tex]
That's correct!
5. Conclude.x = 32.
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The median monthly rent in 1990 was $447 and $658 in 2002. What was the percent increase in the median monthly rent prices from 1990 to 2002? Round to the nearest tenth of a percent.
Answer:
Step-by-step explanation:
Step 1: Define each variable
Let's define some variables to make the calculations easier:
t1 = the median monthly rent in 1990, which is $447
t2 = the median monthly rent in 2002, which is $658
Δ = the change in median monthly rent, which is t2 - t1
Step 2: Calculate the change in median monthly rent
Δ = t2 - t1 = $658 - $447 = $211
This means that the median monthly rent increased by $211 from 1990 to 2002.
Step 3: Divide the change by the original amount
To find the percentage increase, we need to divide the change by the original amount and multiply by 100:
Δ / t1 * 100 = ($211 / $447) * 100 = 47.2%
This means that the median monthly rent increased by 47.2% from 1990 to 2002.
Step 4: Round to the nearest tenth of a percent
The final answer is 47.2%, rounded to the nearest tenth of a percent.
The percent increase in the median monthly rent prices from 1990 to 2002 was 47.2%.
Solve the system by substitution.
y = 5x
y = 4x + 9
Answer:
x=9
Step-by-step explanation:
Since y=5x, you plug it into the other equation's y and it'd look like this 5x=4x+9. Then you subtract 4x on both sides and that would leave you with an x=9.
Complete the sentence below.
325 is a hundred times bigger than
Answer:3.25
Step-by-step explanation:
Divide 325/100=3.25
Problem #1
A motorist travelling at 90 km/h applied the brakes until the car stopped. If the stopping distance was 12 m, what was the acceleration? (-26 m/s2)
The acceleration was -26.04 m/s².
What are Equations of Motion?Equations of motion are a set of equations which describes the basic motion concepts like velocity, position, time and acceleration.
There are mainly three equations of motion.
v = u + at
s = ut + [tex]\frac{1}{2}[/tex] at²
v² = u² + 2as
v is the final velocity, u is the initial velocity, a is the acceleration, t is the time and s is the displacement.
Given,
Initial velocity of the motorist, u = 90 km/h = 90 × (5/18) m/s = 25 m/s
Final velocity of the motorist, v = 0 m/s (since the bike stopped)
Stopping distance, s = 12 m
Using the third equation of motion,
v² = u² + 2as
0² = 25² + (2a × 12)
24a = -625
a = -625 / 24 = -26.04 ≈ -26 m/s²
Hence the acceleration of the motorist was -26 m/s².
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(SAT Prep) Find the value of x.
X
Answer: 70˚
Step-by-step explanation:
Goal: find the other angles in the triangle and subtract them from 180 to find x:
180 - 105 = 75˚
the other angle is 35˚, (alternate interior angles).
.: x = 180 - 75 - 35 = 70˚
Write an equation in slope intercept form for the line that passes through the two given points.(-3,4) (3,2)
Answer:
y = -1/3 x + 3
Step-by-step explanation:
To find the equation of the line that passes through the two points (-3,4) and (3,2) in slope-intercept form, we'll first find the slope of the line using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the two given points.
Plugging in the given points, we get:
m = (2 - 4) / (3 - (-3)) = -2 / 6 = -1/3
Next, we'll use the point-slope form of a line to find the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) is one of the given points, and m is the slope of the line.
We'll use the first given point, (-3,4), so we have:
y - 4 = -1/3 (x - (-3))
Expanding the right side of the equation, we get:
y - 4 = -1/3 x + 1
Finally, we'll rearrange the equation to get it in slope-intercept form, which is:
y = -1/3 x + b
where b is the y-intercept. To find b, we'll plug in one of the given points and solve for b:
y = -1/3 x + b
4 = -1/3 * (-3) + b
4 = 1 + b
b = 4 - 1
b = 3
So the equation of the line in slope-intercept form is:
y = -1/3 x + 3
