Step-by-step explanation:
So you have 5/8 and you want the equivalent fraction to have a denominator of 40. You put 5/8=X/40 and find for x.
First, multiply both sides by 40
5/8*40=x
Express 5/8 * 40 as a single fraction.
5*40/8=x
Multiply 5 40 to get 200.
200/8=x
Divide 200 by 8 to get 25.
25=x
Swap sides so that all variable terms are on the left-hand side.
x=25
Witch rate is equivalent to 15 milesper hours
Answer: 60 miles per 4 gallons. If that's the question.
Step-by-step explanation:
can someone help i will give brainlest:)
A. Width = 16.5 ft B.Width = 55.25 ft
Height = 9.3 ft Height = 91 ft
Area = 153.45 ft² Area = 5027.75 ft²
The formula for Area of rectangle:The area of the rectangle is a place covered by a rectangle in a 2D plane
The formula for Area of the rectangle is given by
Area = Length × WidthHere we have
1 in = 3 feet and 1 cm = 6.5 ft
Calculation for rectangle A :
In rectangle A
Width = 5.5 in
=> Width in feet = 5.5 × 3 feet = 16.5 ft
Height = 3.1 in
=> Height in feet = 3.1 × 3 feet = 9.3 ft
By the given formula
Area = 16.5 ft × 9.3 ft = 153.45 ft²
Calculation for rectangle B :
In rectangle B
Width = 8.5 cm
=> Width in feet = 8.5 × 6.5 feet = 55.25 ft
Height = 14 cm
=> Height in feet = 14 × 6.5 feet = 91 feet
By the given formula
Area = 55.25 ft × 91 ft = 5027.75 ft²
Therefore,
A. Width = 16.5 ft B. Width = 55.25 ft
Height = 9.3 ft Height = 91 ft
Area = 153.45 ft² Area = 5027.75 ft²
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answer question below
The equations that represent a linear function are :
y = 2x - 94x + y = 7y = 1 / 2 xHow to know a linear function?A linear function is a function that represents a straight line on the coordinate plane. The degree of a linear equation must be 0 or 1 for each of its variables.
A linear function has the following form. y = mx + b.
A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
Therefore, linear function can be represented in slope intercept form as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore, the linear function of the equations are as follows;
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Can you help me with this
2. Natalie is selling candles to raise money for her softball team. The team has two different options for selling the candles. The first option is to sell a package of 5 candles for $18. The second option is to sell individual candles for $4 each.
(a) The team wants to earn $1404. How many candles do the members need to sell if they sell candles only in packages? How many candles do they need to sell if they sell only single candles? Explain your answer using an equation for each situation.
(b) Describe at least one advantage of selling the candles in packages. Describe at least one disadvantage of selling the candles in packages
a) The amounts that the team needs to sell is given as follows:
Packages: 390 candles.Single candles: 351 candles.b) The advantage and disadvantage is given as follows:
Advantage: Better opportunity cost when a person needs one candle, the person will have to purchase the entire package.Disadvantage: Lower revenue per candle.How to obtain the amounts?The amounts needed are found applying the proportion, considering the costs and the number of candles.
A package of 5 candles for $18, hence the number of candles needed to earn $1404, in packages, is given as follows:
5 candles - $18
n candles - $1404
Applying cross multiplication, we have that:
18n = 5 x 1404
n = 5 x 1404/18
n = 390 candles.
With a single candle, the number of candles is calculated as follows:
1404/4 = 351 candles.
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What is the fourth root of 625
The required answer is the fourth root of 625 is 5. In summary, the fourth root of 625 is 5.
To find the fourth root of 625, we need to determine the number that, when raised to the power of 4, equals 625. Here's the step-by-step process:
Step 1: Start with the number 625.
Step 2: Take the fourth root of 625.
Since we're looking for the fourth root, we need to find a number that, when raised to the power of 4, equals 625.
Step 3: Determine the number that, when raised to the power of 4, equals 625.
To find this number, we can use the concept of exponentiation. Let's denote the unknown number as "x". Mathematically, we have [tex]x^4 = 625[/tex]..
Step 4: Solve the equation [tex]x^4 = 625[/tex].
To solve this equation, we need to find the value of x. Taking the fourth root of both sides of the equation, we have [tex]\sqrt[4]{(x^4)} =\sqrt[4] {625}.[/tex]
The fourth root of 625 is (625)^(1/4).
Step 5: Simplify the expression.
We can simplify [tex]\sqrt[4]{ 625}[/tex] as follows:
[tex]\sqrt[4]{ 625} = \sqrt[4]{ 5^4}= 5^{4/4} = 5^1 = 5.[/tex]
Therefore, the fourth root of 625 is 5. In summary, the fourth root of 625 is 5.
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the absolute value of -7-3
negative 7 minus three
Max found a car he wants to buy that costs $16,000. He can
afford to pay $250 a month for the car. His bank offers him a car
loan of 7.3%. How will the length of his loan be for this payment
amount?
Answer: To calculate the length of a loan, you need to know the total cost of the loan, the monthly payment amount, and the interest rate. In this case, the total cost of the car is $16,000, the monthly payment amount is $250, and the interest rate is 7.3%.
First, you need to calculate the total interest that will be paid on the loan. This can be done by multiplying the total cost of the loan by the interest rate, and then dividing by 100 to convert the result to a percentage. In this case, the total interest paid would be $16,000 * 7.3 / 100 = $1,168.
Next, you need to subtract the total interest from the total cost of the loan to find the total amount of the loan that will be used to pay for the car. In this case, the total amount of the loan used to pay for the car would be $16,000 - $1,168 = $14,832.
Finally, you can use this total amount and the monthly payment amount to calculate the length of the loan by dividing the total amount by the monthly payment amount. In this case, the length of the loan would be $14,832 / $250 = 59.32 months, or just over four years. The answer is 59.32 months.
Step-by-step explanation:
Find out the missing frequency in the following incomplete distribution
CI F
0-10 3
10-20 ?
20-30 20
30-40 12
40-50 ?
The Value of median and mode are 27 and 26 respectively.
8 and 7 are missing frequency in the incomplete distribution.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Class Interval frequency Cumulative frequency
0 - 10 3 3
10 - 20 a 3+a
20 - 30 20 23+a
30 - 40 12 35+a
40 - 50 b 35+a+b
Mode = 26 hence lies in 20 - 30
f of modal class = 20
Mode = 20 + 10( 20 - a) / (20 - a + 20 - 12)
26 = 20 + 10 (20 - a) / (28 - a)
60(28 - a) = 10 ( 20 - a)
168 -6a = 200 - 10a
4a = 32
a = 8
Class Interval frequency Cumulative frequency
0 - 10 3 3
10 - 20 8 11
20 - 30 20 31
30 - 40 12 43
40 - 50 b 43+b
Median = 27
27 = 20 + 10 ( (43 + b)/2 - 11)/ 20
7 = ( (21 + b)/ 4
28 = (21 + b)
b = 7
Hence, the missing frequencies are 8 and 7.
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A train travels at 80 miles per hour. An equation can be written that compares the time (t) with the distance (d). What is the domain and range?
1. The domain is distance (d) and the range is time (t).
2. The domain is time (t) and the range is distance (d).
3. The domain is time (t) and the range is 80.
4. The domain is 80 and the range is time (t).
The required answer is the domain is time (t) and the range is a distance (d) i.e. Option 2.
What are domain and range?
The value range that can be plugged into a function is known as its domain. In a function like f, this set represents the x values f(x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
From the given question, and the above definition of domain and range,
the time (t) acts as an x-values or input value and the distance (d) acts as a y-value or output value
Hence, the domain is time (t) and the range is a distance (d) i.e. Option 2.
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(7x6)÷2[{45÷3(7×2-15+6)}+4)
Answer:
21/79
Step-by-step explanation:
(7x6)÷2[{45÷3(7×2-15+6)}+4)
(7*6)/2[{15(7*2-15+6)}+4)
(42)/2[{15(14-15+6)}+4)
(42)/2[{15(5))}+4)
(42)/2[{75}+4)
(42)/2[75 + 4]
(42)/2 * 79
42/2 * 79
21/79
A biologist is studying a plant blight. At the start of their research, the blight covers a circular area with a radius of 5 kilometers. When they re-examine the blight two years later, the area has grown to a circular area with a radius of5.2kilometers. How rapidly did the radius change over the interval? _____Year/km
Step-by-step explanation:
Area of circle 1= pie r²
=3.14 x 5²
=3.14x 25
= 78.5km²
Area of circle 2=3.14 x 5.2²
= 3.14 x 27.04
= 84.9km²
change in area= 84.9-78.5
=6.4
radius²= 6.4/ 3.14
r²=2.03
r =√2.03
r=1.42
Jeremy has 3/4 pound of fish food if fish food is used to feed 24 fish how much food is there for each fish
Answer:
There is 1/32 pound food for each fish
Step-by-step explanation:
24 fish = 3/4 pound food
1 fish = (3/4)/24 pound food = 1/32 pound food
(Problem solved by using unitary method)
two different two-digit whole numbers are selected at random. what is the probability that their product is less than 200. express your answer as a common fraction. (hints: (l) there are 90 different two-digit numbers, (2) the pair {10, 11} produces the smallest product and the pair {11, 18} produces the largest product less than 200).
The probability that the product of the two two-digit numbers is less than 200 is given as follows:
43/8010.
How to calculate the probability?A probability is calculated as the division of the number of desired outcomes in the context of the experiment by the number of total outcomes.
There are 90 different two-digit numbers, hence the number of total outcomes for the product is of:
90 x 89 = 8010.
(the numbers have to be different)
The desired outcomes which result in a product of less than 200 are of given as follows:
10 multiplied by 9 numbers, from 11 to 19.11 multiplied by 10, 12, 13, 14, 15, 16, 17, 18. (8 numbers).12 multiplied by 10, 11, 13, 14, 15, 16. (6 numbers).13 multiplied by 10, 11, 12, 14, 15 (5 numbers).14 multiplied by 10, 11, 12, 13. (4 numbers).15 multiplied by 10, 11, 12, 13. (4 numbers).16 multiplied by 10, 11, 12. (3 numbers).17 multiplied by 10, 11. (2 numbers).18 multiplied by 10, 11. (2 numbers).Hence the number of desired outcomes is given as follows:
9 + 8 + 6 + 5 + 4 + 4 + 3 + 2 + 2 = 43.
Meaning that the probability is of:
43/8010.
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Please hurry I have been stuck on this question for a while
One week, Heather opens a bank account with $125. Each week, starting the second week, she deposits $25 into her account.
What is the explicit rule for amount of money Heather has in her account after n weeks?
Enter the simplified answer in the box.
Answer:
125+25n
Step-by-step explanation:
We are given that
Heather opens a bank account with=$125
Each week she deposited money into her account=$25
We have to find the explicit rule for the amount of money that has Heather after n weeks.
Heather has money after 1 week=125+25=$150
Heather has money after 2 week=125+2(25)=$175
Heather has money after 3 weeks=125+3(25)=$200
Heather has money after n weeks=125+25(n)
Hence, the explicit rule for the amount of money that has Heather after n weeks is given by
125+25n
Solve using Substitution Method
x=4-8y
3x +24y = 12
Observing the provided equation, We can't solve these equations using substitution method or any other methods because these lines are parallel and never intersect each other.
What do you mean by equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
What is a substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.
x=4-8y
3x+24=12
Taking first equation and rearranging it we get,
x+8y=4
multiply this with 3, we get 3x+24y=12 which are identical in nature. Which shows these two lines are parallel in nature. We can't solve them because parallel lines never intersect.
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Observing the provided equation, We can't solve these equations using substitution method or any other methods because these lines are parallel and never intersect each other.
What do you mean by equations?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
What is a substitution method?
The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.
x=4-8y
3x+24=12
Taking first equation and rearranging it we get,
x+8y=4
multiply this with 3, we get 3x+24y=12 which are identical in nature. Which shows these two lines are parallel in nature. We can't solve them because parallel lines never intersect.
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let w represent the number of attempted experiments to get one experiment that is not successful. the random variable w has a geometric distribution with mean 4 and standard deviation 3.5. which of the following is the best interpretation of the standard deviation? responses a single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments. a single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments. a single value randomly selecte
The best interpretation of the standard deviation on this problem is given as follows:
A single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments.
How to interpret the standard deviation?The standard deviation of a data-set is calculated as the square root of the sum of the differences squared between each observation of the data-set and the mean, divided by the number of observations in the data-set.
The interpretation of this calculation is that the standard deviation represents by how much each value of the distribution is expected to vary from the mean, on average.
This means that the correct statement is given as follows:
A single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments.
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Given: ABCD is a parallelogram with AE = 9x−5, AC = 14x + 34. Find AC
The value of AC according to given equation of Parallelogram is 188 units.
What is parallelogram?
In elementary geometry, a parallelogram may be a quadrilateral with 2 pairs of parallel sides. the alternative or facing sides of a quadrangle square {measure} of equal length
Main body:
according to question:
AE = 9X-5
AC = 14X+34
as E is midpoint of AC so , we can say
2AE = AC
2(9x-5)= 14x+34
18x-10= 14x+34
4x = 44
x = 11
Now we need to find AC = 14x+34
= 14*11+34
= 188 units
Hence the value of AC according to given equation of Parallelogram is 188 units.
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A video store manager observed that the number of DVDs sold seem to vary inversely as the price per DVD. If the store sells 710 DVDs per week when the price per DVD is $18.90, how many does he expect to sell if he lowers the price to $11.40.
If the price is reduced to $11.40 the number of DVDs sold will be 1177.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a video store manager observed that the number of DVDs sold seems to vary inversely to the price per DVD. If the store sells 710 DVDs per week when the price per DVD is $18.90.
The number of DVDs sold for $11.40 will be calculated by forming the inverse equation for the number of DVDs.
N = K / P
Here, N is the number and P is the price and K is the inverse constant.
The value of K will be,
K = N x P
K = 18.90 x 710
K = 13419
The number of DVDs for $11.40 will be,
N = K / P
N = 13419 / 11.40
N = 1177
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I need. Help with this question
Derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.
What is differentiation?
In arithmetic, the derivative of a function of a true variable measures the sensitivity modification of the perform price with relation to a change in its argument. Derivatives are a elementary tool of calculus.
Main body:
by using product rule;
Let = u = x² + 4x + 6
⇒ du/dx = 2x + 4 .
Now y = u⁵
⇒ dy/dx = 5u⁴ .
dy/dx = dy/dx * du/dx = 5u⁴ * (2x + 4)
= 5 * (x² + 4x + 6)⁴ * (2x + 4)
= 5(2x + 4) * (x² + 4x + 6)⁴
hence , derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.
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-3/2 passes through (-4, 3)
what is the y intercept and equation
(in slope intercept form)
consider having two jars with numbers 1,23. find the probability of drawing two numbers from both the jars whose product is even
The probability of drawing two numbers from both jars whose product is even = 5/9.
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
Total number of outcomes =9
Favorable cases = (1,2), (2,1), (3,2), (2,3), (2,2)
The probability of drawing two numbers from both the jars whose product is even = 5/9
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i need the answers please
(7) Slope of line AB = -6/5 and Slope of the line CD = -6/5 and line AB and line CD are parallel in nature.
(8)Slope of line AB = 3/4 and the Slope of line CD = 1 and line AB and line CD is neither parallel nor perpendicular.
(9) We have drawn the graph passing through the point P and parallel to line AB.
(10)We have drawn the graph passing through the point P and perpendicular to line AB.
What is the property of slopes of parallel lines and perpendicular lines?
If two lines are given and they are parallel to each other then the slopes are equal and for perpendicular lines, the product of their slopes is equal to -1.
(7) The line AB is passing through the points (-1, 5/2) and (3/2, -1/2).
Slope = y2 - y2/x2 - x1
= (-1/2 - 5/2)/(3/2-(-1))
= -6/5
As line AB and line CD are parallel in nature so the slope of line CD is also -6/5.
(8) The line AB is passing through the points (1/2, 1) and (5/2, 5/2).
Slope = y2 - y2/x2 - x1
= (5/2 - 1)/(5/2-1/2)
=3/2/2
= 3/4
Line CD is passing through points (1, 1) and (2, 3).
Slope = y2 - y2/x2 - x1
= (3 - 1)/(2-1)
=2/2
= 1
As the product of their slopes is not equal to -1.
So lines are neither parallel nor perpendicular.
(9) Slope of AB can be computed as (-2, 1) and (-5, 5)
Slope = 5 - 1/-5 + 2
= 4/-3.
The slope of line passing through the point P = -4/3 as we have to draw the parallel line.
Point P = (-1, 3)
Equation of the line :
y - 3 = -4/3(x + 1)
3y +9 = -4x - 4
3y = -4x - 13
Now we can draw the line
(10) Slope of line AB = -4/3
So the slope of the line passing through point P should be 3/4 in order to be perpendicular to line AB.
Equation of the line passing through point P:
y - 3 = 3/4(x - (-1))
y - 3 = 3/4(x+1)
Hence,
(7) Slope of line AB = -6/5 and Slope of the line CD = -6/5 and line AB and line CD are parallel in nature.
(8)Slope of line AB = 3/4 and the Slope of line CD = 1 and line AB and line CD is neither parallel nor perpendicular.
(9) We have drawn the graph passing through the point P and parallel to line AB.
(10)We have drawn the graph passing through the point P and perpendicular to line AB.
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You win an online auction for a toy. Your winning bid of $30 is 60% of your maximum bid. How much more were you willing to pay for the toy than you actually paid?
Answer:
I was willing to pay $20 more for the toy than I actually paid.
Step-by-step explanation:
Let us take the maximum bid be y
So,
(y × 60) ÷ 100 = 30
60y/100 = 30
60y/100 × 100 = 30 × 100
60y = 3000
60y/60 = 3000/60
y = 50
60% of $50 is $30
So,
50 - 30 = 20
Thus, I was willing to pay $20 more for the toy than I actually paid.
Cylinders A and B are similar solids. The base of cylinder A has a circumference of 47 units. The base of cylinder B
has an area of 97 units.
The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?
+/a N/mm/~ alt
The factor that produces the corresponding dimensions of cylinder B is: 3/2.
What are Similar Solids?Similar solids have the same shape but different sizes, and which means the ratio of their corresponding linear measurements are the same.
How to Find the Scale Factor of Similar Solids?To find the scale factor of similar solids, you can use the formula:
scale factor = (size of the similar solid) / (size of the original solid)
For example, if you have two similar solids, one with a volume of 64 cubic units and the other with a volume of 16 cubic units, the scale factor would be:
scale factor = (16 cubic units) / (64 cubic units) = 1/4
This means that the smaller solid is 1/4 the size of the larger solid.
Given the following:
Circumference of the base of cylinder A = 4π units [the radius = 2 units]
Area of the base of cylinder B = 9π units² [the radius = 3 units]
Scale factor = radius of the base of cylinder B / radius of the base of cylinder A
Scale factor = 3/2
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Complete Question:
Cylinders A and B are similar solids. The base of cylinder A has a circumference of 4π units. The base of cylinder B has an area of 9π units. The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?
Which statement correctly demonstrates using limits to determine a vertical asymptote of g (x) = StartFraction 2 (x + 4) squared Over x squared minus 16 EndFraction
There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = negative infinity
There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = infinity
There is a vertical asymptote at x = –4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = negative infinity
There is a vertical asymptote at x = –4 because Limit of g (x) as x approaches 4 minus = negative infinity and limit of g (x) as x approaches 4 plus = infinity
The correct option that describes the vertical asymptote is; B: There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = infinity
How to find the vertical asymptote of a function?A vertical asymptote of a graph is defined as a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.
A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;
In a graph, these vertical asymptotes are given by dashed vertical lines.
An example is a value of x for which the denominator of the function is 0, and the function approaches infinity for these values of x.
We are given the function;
g(x) = 2(x + 4)²/(x² - 16)
Simplifying the denominator gives;
(x² - 16) = (x + 4)(x - 4)
Thus, our function is;
g(x) = 2(x + 4)²/[(x + 4)(x - 4)]
(x + 4 ) will cancel out to give;
g(x) = 2(x + 4)/(x - 4)
Vertical asymptote:
Point in which the denominator is 0, so:
(x - 4) = 0
x = 4
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If line BG and CF are parallel,then the supplement of BIE = the supplement of GMD. Is this statement correct? Explain your answers
The supplement of BIE equals the supplement of GMD is a false assertion if lines BG and CF are parallel.
Describe the supplement angle.Angles with a supplementary sum are those whose sum is 180 degrees. For instance, the total of angle 130° and angle 50° is 180°, hence they are supplementary angles.
Lines BG and CF are parallel, as shown in the figure.
If BIE = X, then its supplement of BIE will be 180 - X;
similarly, if GMD = Y, then its supplement of GMD will be 180 - Y.
Since BG and CF are parallel, the supplements of BIE and GMD are interior angles on the same side ( as shown in figure)
and for parallel line the interior angle on the same side is 180
so 180 - X and 180 -Y there sum should be 180
They cannot be equal
line BG and CF are parallel, then the supplement of BIE = the supplement of GMD are not equal.
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A lamina occupies the region inside circle x2 +y2 = 2y but outside circle x2 +y2 = 1. Find the center of mass if the density atany point is inversely proportional to its distance from theorigin.
the answer is {0, [3√3/2(3√3-π)]}
Ф {0, [3√3/2(3√3-π)]}
The poster above has good diagrams ; so , I will just go through the calculations .
The region of integration is with in the circle x ^2+y^2=2y but outside the circle x^2+y^2=1.
I would convert to polar . With polar , we have x^2+y^2=r^2 ,x=rcosФ and y=rsinФ
We thus have the first circle becomes x^2+y^2=2y ⇒r^2=2rsinФ Divide through by r, and you get r=2sinФ(1).
This is the upper circle in the previous posters diagrams .
The other equation of a circle becomes :
x^2 + y^2 = 1 ⇒ r^2 = 1 ⇒ r = 1 (2)
These two curves intersect at :
r= 2sinФ =1 ⇒ sinФ=1/2 ⇒Ф= [tex]\alpha[/tex]/6 or 5[tex]\pi[/tex]/6
From the previous poster's diagrams , we can see that there is as much mass on either side of the positive. y axis or
Ф=[tex]\pi[/tex]/2 axis in polar ; so , the X coordinate of the center of mass is zero
X=0 We can also see from his diagrams that the mass and moment of mass is symmetrical about the Ф=[tex]\pi[/tex]/2
we only need to integrate from Ф=[tex]\pi[/tex]/6 to Ф=[tex]\pi[/tex]/2 ( the answers from to are the same and double )
The differential of area in polar coordinates is
d A=rdrdФ They say the area mass density is inversely proportional to the distance from the origin .
This can be written as : p=k/r. We can thus say the differential of mass is
d M=PDA=
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The area of a rectangle is 35 m², and the length of the rectangle is 3 m more than double the width. What is the dimensions of the rectangle?
The dimensions of the rectangle with area 35 m² is
length = 7.6 m and width = 4.6 m
How of find the dimension of the rectangleThe dimension of the rectangle is calculated using the formula for area of rectangle
= length x width
where
length = 3 + w width = warea of rectangle
35 = (w + 3) * w
35 = w² + 3w
w² + 3w - 35 = 0
solving for w gives
w = 4.6 OR -7.6
using the positive value, the w = 4.6 m, l = 4.6 + 3 = 7.6 m
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l
a professor at a certain school polled 12 colleagues about the number of meetings they attended in the last five years (x) and the number of papers they submitted to peer reviewed journals (y) during the same period. the summary data are as follows: n
The number of meetings they attended in the last five years (x) and the number of papers they submitted to peer reviewed journals (y) during the same period is [tex]-8.6+3.15[/tex].
What is formula for slope and intercept is?
[tex]$$\begin{aligned}& b=\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& a=\bar{y}-b \bar{x} \\& \hat{y}=a+b x\end{aligned}$$[/tex]
The slope is
[tex]$$\begin{aligned}b & =\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& =\frac{12 \times 318-(12 \times 4)(12 \times 4)}{12 \times 232-(12 \times 4)^2} \\& =3.15\end{aligned}$$[/tex]
The intercept is
[tex]$$\begin{aligned}a & =\bar{y}-b \bar{x} \\& =4-3.13 \times 4 \\& =-8.6\end{aligned}$$[/tex]
The regression equation is
[tex]$$\begin{aligned}\hat{y} & =a+b x \\& =-8.6+3.15 x\end{aligned}$$[/tex]
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Use the vertex and intercepts to sketch the graph of each quadratic function give the equation of the parabola axis of symmetry use the graph to determine the function domain and range f(x)=(x-1)^2+2
The vertex of the parabola is (1,2) when the function is f(x) = (x-1)²+2 when the equation for the parabola's axis of symmetry.
Given that,
Give the equation for the parabola's axis of symmetry by sketching the graph of each quadratic function using its vertex and intercepts.
We have to determine the function domain and range using the graph is f(x) = (x-1)²+2
We know that,
Its vertex A quadratic function's form is provided by
f(x) = a(x-h)²+k
So, (h,k) is the vertex of the parabola
Take
f(x) = (x-1)²+2
(1,2) is the vertex of the parabola.
Therefore, The vertex of the parabola is (1,2) when the function is f(x) = (x-1)²+2 when the equation for the parabola's axis of symmetry.
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