If y varies inversely as x2 and y=38 when x=18, find y if x=20.
Answers
The required value of y for the given inverse relation is 30.78
What is the inverse variation?
Inverse variation occurs when one variable varies inversely with respect to another. It represents the inverse relationship between two quantities are two quantities.
In mathematics, inverse variation refers to the relationships between variables that are expressed as y = k/x, where x and y are two variables and k is a constant value. It states that if the value of one quantity rises, the value of the other quantity falls.
Given, y varies inversely as \(x^{2}\)
That is, y∝ 1/ \(x^{2}\)
or, y = k/ \(x^{2}\)
or, \(x^{2}\)y = k
And, y=38 when x=18
Then, \(18^{2}\)*38 = k
k = 12312
Now, if x=20 then y=?
\(x^{2}\)y = 12312
or, \(20^{2}\)*y = 12312
or, 400y = 12312
or, y = 12312/400 = 30.78
Hence, the required value of y is 30.78
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Related Questions
A farmer owns a total of 9 acres of land. The land is separated into 4 2/7 equally sized sections. How many acres are in each section?
Answers
Answer:
\(2\dfrac{1}{10}\ \text{acres}\)
Step-by-step explanation:
\(9\) acres of land split into \(4\dfrac{2}{7}\).
Now
\(4\dfrac{2}{7}=4+\dfrac{2}{7}\)
One section of land will be
\(\dfrac{9}{4+\dfrac{2}{7}}\\ =\dfrac{9}{\dfrac{30}{7}}\\ =\dfrac{63}{30}\\ =\dfrac{21}{10}=2\dfrac{1}{10}\ \text{acres}\)
One section of the land is \(2\dfrac{1}{10}\ \text{acres}\).
Makesha lost 58.5 pounds in 18 weeks. Find her rate of loss in pounds per week.
Answers
Write down the next two terms into the given sequence :
-1; 1; 3 ;
Answers
Answer:
5 ;7
explantion:
-1+2=1
1+2=3
3+2=5
5+2=7
the pattern is +2
what is the operation of 24 3/4 = 18
Answers
Answer:
subtraction of 6 3/4 from 24 3/4
Step-by-step explanation:
24 3/4 - 6 3/4 = 18
The slope of the tangent to a function f(x) at point (2,7) is mt = 3. Write the equation of the tangent line at the given point.
Answers
The form of the linear equation is
\(y=mx+b\)m is the slope
b is the y-intercept
Since the slope of the tangent at point (2, 7) is 3, then
m = 3
Substitute it in the form of the equation above
\(y=3x+b\)To find b,
Substitute x by 2 and y by 7 in the equation
\(\begin{gathered} x=2,y=7 \\ 7=3(2)+b \\ 7=6+b \end{gathered}\)Subtract 6 from both sides
\(\begin{gathered} 7-6=6-6+b \\ 1=b \end{gathered}\)The equation of the tangent is
\(y=3x+1\)The answer is
The equation of the tangent at the point (2, 7) is y = 3x + 1
Use implicit differentiation to find dy/dx and d^2y/dx^2.
Answers
Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.
Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.
Given the equation x² + xy + y² = 5,
we can differentiate both sides with respect to x using the chain rule as follows:
2x + (x(dy/dx) + y) + 2y(dy/dx) = 0
Simplifying this equation yields:
(x + 2y)dy/dx = -(2x + y)
Hence, dy/dx = -(2x + y)/(x + 2y)
Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.
That is:
d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))
= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))
Simplifying this equation yields:
d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³
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Ingrid wants to buy a $20000 car in 8 years. How much money must she deposit at the end of each quarter in an account paying 5.9% compounded quarterly so that she will have enough to pay for her car?
Answers
Ingrid must deposit $402.74 at the end of each quarter for 8 years in order to have enough money to pay for her car.
What is 25 x (6 + 10)?
Answers
Answer:
400
Step-by-step explanation:
25(6+10)
25(16)
Dhebrjdjdndjdjdhajdjsjdjdkk
Answers
Answer:
write 7 then write - 420 the answer is 45
Step-by-step explanation:
Which point is a solution to the system of equations?
y = 2x + 2
Y = 3x
Answers
Answer:
(2,6)
Step-by-step explanation:
y = 2x + 2
Y = 3x
2x+2=3x
2x-3x+2=0
-x+2=0
-x=-2
x=2
y=3(2)=6
If these cylinders and prisms were broken into two separate groups, what would be an equivalent ratio to 8/2? i dont have much longer and btw it doesn't have a picture.
100 points?
Answers
The Equivalent ratio to 8/2 is 4/1, 24/6, 32/8 and 48/12.
We have,
Cylinder and prism.
Here we have to find the equivalent ratio to 8/2.
First simplifying the given ratio as
8/2
= (4 x 2)/2
= 4 /1
Now, some more ratios equivalent to 8/2.
1. 8/2 x 3/3 = 24/ 6
2. 8/2 x 4/4 = 32/8
3. 8/2 x 6/6= 48/12
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through (2,4) parrallel to y=3x+
Answers
The slope y is 3x - 10.When the line to be examined's slope is known, and the provided point also serves as the y intercept.
The slope intercept form of a line's equation can be found by using this method?When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). B stands in for the y value of the y-intercept point in the formula.
According to question:-
In the equation of a line's slope-intercept form, y = mx + b, we get y = 3x + 2, m1 = m2 gives us y = 3x +2, and m = 3 gives us the point (2 -4) where x = 2 and y = -4.
4 6 + b deducts 6 from both sides.
-10 = b, b = -10
After all, y = 3x - 10.
The complete question is,
y=3x+2 via (2,-4) parallel to
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(GIVING EXTRA POINTS AND BRAINLIEST TO WHO EVER HELPS ME!! BTW NUMBER C IS INCORECT SO THATS LEAVES ME DOWN TO A, B, AND D)
What is the missing numerator?
five over seven plus blank over six equals fifty one over forty two
A) 2
B) 3
C) 8
D) 10
(Here is a image if needed) :
Answers
Answer:
im pretty sure its b
Step-by-step explanation:
Answer:
its b
Step-by-step explanation:
For the question of total area of the cuboid is 200cm^.
I understand where we divide 150 by 4.
But why do I need to multiply by 5, when there are 6 faces.
Answers
You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.
When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.
A cuboid has six faces, but each face has a pair that is identical in size and shape.
Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.
To find the surface area of a cuboid, you can add up the areas of all its faces.
However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:
(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.
By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.
Essentially, you are considering one face from each pair and then summing their areas.
Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.
When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.
Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.
Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.
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let $l$ be the line with equation $\dbinom{10}{3} \dbinom{-2}{1}t$. let $\mathbf{v}$ be a vector from the origin to a point on $l$. find the minimum value of $\|\mathbf{v}\|$.
Answers
The minimum value of \($\|\mathbf{v}\|$\) is zero.
The minimum value of \($\|\mathbf{v}\|$\) is zero, as it is the distance between the origin and a point on the line. To solve this problem, the formula \($\|\mathbf{v}\| = \sqrt{x^2 + y^2}$\) can be used, where x and y are the coordinates of the point on the line. Since the equation of the line is \($\dbinom{10}{3} \dbinom{-2}{1}t$\), the coordinates of the point on the line can be found by substituting \($t = 0$: $x = 10 \cdot 0 - 2 \cdot 0 = 0$, and $y = 3 \cdot 0 + 1 \cdot 0 = 0$\) . Substituting these values into the formula for \($\|\mathbf{v}\|$ gives $\|\mathbf{v}\| = \sqrt{0^2 + 0^2} = 0$\). Therefore, the minimum value of \($\|\mathbf{v}\|$\) is zero.
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= Answer:
Find the y-intercept of 2x - y = -16
Answers
Lian is deciding which of two gyms to join. Each gym charges a monthly rate plus a one-time membership fee.
Lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. In her work, she substituted an expression for one variable and solved for the other. This resulted in the equation 75 = 75. What can Lian conclude?
One gym charges $75 per month.
Each gym charges $75 per month.
Both gyms charge the same monthly rate and the same membership fee.
Both gyms charge the same monthly rate, but not the same membership fee.
Answers
Solve by Graphing: Y=4x-3 and y=-x+2
Answers
2. The starting point is 2 then go up one and then go one left bc it’s negative
Find the measure of the arc or angle indicated
Answers
The unknown angle in the cyclic quadrilateral is as follows:
∠R = 86 degrees
How to find arc angle?The diagram above is cyclic quadrilateral. A cyclic quadrilateral is a four sided shape that can be inscribed into a circle.
The sum of angles in a cyclic quadrilateral is 360 degrees. The opposite angles in a cyclic quadrilateral is supplementary.
Hence, let's find the unknown angle.
∠R = 1 / 2 (92 + 80)
∠R = 1 / 2 (172)
∠R = 86 degrees
Therefore, the unknown angle is 86 degrees.
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0.2(7 + 2t) = 0.4t + 1.4
Answers
Answer:
all real numbers
Step-by-step explanation:
When you factor in the .2 on the left side you are left with 1.4 + .4t which is equal to the other side. And so, no matter what value for t you plug in, they will always be equal to eachother.
HELP ASP 20 POINTS PLSp
Answers
Answer:
Step-by-step explanation:
$499.99 - 15% will give your answers
Answer:
424.99
Step-by-step explanation:
the correct answer.
Which inequality represents the values of that ensure triangle ABC exists?
A
2x+4
B
O D.
18
OA.
<< 1
OB. -< < ¹
O c. 1 < x < 5
6x
2 < < 6
Answers
The Inequality which ensure triangle exists is A. 7/4 < x < 11/2
What is the inequalityInequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."
Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal.
Theorem used In ΔABC,
AB + BC >AC
AC+ BC >AB
AC + AB > BC
According to the question,
In triangle ABC.
AC = 18units
BC = 6x units,
AB = 2x + 4 units
Substitute the value in the inequality to ensure triangle exists we get 7/4 < x < 11/2. The correct option is A.
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I need help with a math question. Ilinked it below
Answers
EXPLANATION:
We are given a dot plot as shown which indicates the ages of members of an intermediate swim class.
The dot plot indicates a cluster to the right for the values;
\(11yrs-14yrs\)This indicates that a reasonable amount of the members are within that age range.
For this reason, it is not likely that Mira will be able to convince her mother.
This is because Mira's age (13 years old) is within the area where the data are clustered.
Therefore;
ANSWER:
(1) The data are clustered between 11 and 14 years old
(2) It is not likely that she will be able to convince her mother
(3) Mira's age is within the area where the data are clustered.
Solve -2a -5 > 3 Which graph shows the solutions?
Answers
Answer: a< -4 D
Step-by-step explanation:
Evaluate x + y when x = -3/8 and y = 7/12.
Answers
Answer:
Solutions: x=1.
Step-by-step explanation:
Choose all the expressions that are equal to 4.19 + 6.53.
A. 4.2 + 6.5
B. 16.75 – 6.03
C. 1.72 + 9
D. 15 – 4.38
E. 6.53 + 4.19
Answers
Answer:
16.75-6.03
1.72+9
6.53+4.19
Step-by-step explanation:
4.19 + 6.53 = 10.72
The expressions that is equal to 10.72 can be calculated as follows
4.2 +6.5 = 10.7
16.75-6.03 = 10.72
1.72 + 9= 10.72
15-4.38= 10.62
6.53 + 4.19= 10.72
Hence the expressions which is equal to 10.72 are
16.75-6.03 , 1.72+9 , 6.53+4.19
if 6 pipes fill a tank in 120 minutes, then 5 pipes can fill it in how many minutes
Answers
Answer:
It'll take 144 minutes for 5 pipes.
Step-by-step explanation:
\({ \sf{6 \: pipes = 120 \: mins}} \\ { \sf{5 \: pipes = ( \frac{6}{5} \times 120) \: mins}} \\ \\ = { \sf{144 \: mins}}\)
but practically, it seems to be abnormal. if 6 pipes take 120 mins, 5 pipes must takes a time greater than 120 mins cause amount of water flowing to the tank is decreasing.
But there is a possibility that pressure of water was increased for the case of five pipes, that's why it takes a time less than 120 mins. (t < 120)
Answer:
144 minutes
Step-by-step explanation:
here we use inverse proportion because the more pipes there are the less time is needed
the formula for inverse proportion is y = k/x
first we need to find k which is the constant
if y is the number of minutes and x is the number of pipes we can substitute these into the formula like so: 120 = k/6
to find k rearrange the formula to get k = 6 * 120 = 720
now that we have k we can substitute 720 (k) and 5 (x) into y = k/x
y = 720 / 5
y = 144
(y is the number of minutes in this case so the answer is 144 minutes)
Consider the age distribution in the United States in the year 2075 (as projected by the Census Bureau). Construct a cumulative frequency plot and describe what information the plot communicates about the distribution of ages in the future.
Answers
Answer:
The cumulative frequency plot is also attached below.
Step-by-step explanation:
The data provided is as follows:
Age Group Frequency
0 - 9 34.9
10 - 19 35.7
20 - 29 36.8
30 - 39 38.1
40 - 49 37.8
50 - 59 37.8
60 - 69 34.5
70 - 79 27.2
80 - 89 18.8
90 - 99 7.7
100 - 109 1.7
Consider the Excel output attached.
The cumulative frequency are computed in the Excel sheet.
The cumulative frequency plot is also attached below.
From the cumulative frequency plot it can be seen that in the future most people will belong to a higher age group rather then the lower ones.
ASAPPPP PLSSS HELP!!!! WILLL GIVE YOU THE BRANLIEST ANSWERRRR
Answers
Answer:
\((r^{2*3/3^1^* ^ 3)\)
Step-by-step explanation:
Given
\((r^2/3)^3\)
Required
Determine the equivalent expression
\((r^2/3)^3\)
Apply the following law of indices:
\((a^n)^m = a^m^n\)
\((r^2/3)^3\)
\((r^2/3^1)^3\)
So, the expression becomes:
\((r^{2*3/3^1^* ^ 3)\)
Option D answers the question.
Swornima is an unmarried nurse in a
hospital. Her monthly basic salary is Rs
48,000. She has to pay 1% social
security tax on her income up to Rs
5,00,000 and 10% income tax on Rs
5,00,001 to Rs 7,00.000. She gets 1
months' salary as the Dashain
allowance. She deposits 10% of her
basic salary in Citizen Investment Trust
(CIT) and gets 10% rebate on her
income tax. Answer the following
questions. (i) What is her annual
income? How much tax is rebated to
her? (iii) How much annual income tax
should she pay?
Answers
To calculate Swornima's annual income and the amount of tax she should pay, let's break down the information provided:
Monthly basic salary: Rs 48,000
Social security tax rate: 1%
Income tax rate on income up to Rs 5,00,000: 0% (no tax)
Income tax rate on income from Rs 5,00,001 to Rs 7,00,000: 10%
Dashain allowance: 1 month's salary
Deposit in Citizen Investment Trust (CIT): 10%
Rebate on income tax: 10%
(i) Annual Income:
Swornima's monthly basic salary is Rs 48,000, so her annual basic salary would be:
Annual Basic Salary = Monthly Basic Salary x 12
= Rs 48,000 x 12
= Rs 5,76,000
Additionally, she receives 1 month's salary as the Dashain allowance, which we can add to her annual income:
Annual Income = Annual Basic Salary + Dashain Allowance
= Rs 5,76,000 + Rs 48,000
= Rs 6,24,000
Swornima's annual income is Rs 6,24,000.
(ii) Tax Rebate:
Swornima receives a 10% rebate on her income tax. To calculate the rebate, we need to determine her income tax first.
(iii) Annual Income Tax:
First, let's calculate the income tax for the range of income from Rs 5,00,001 to Rs 7,00,000. The tax rate for this range is 10%.
Taxable Income in this range = Rs 6,24,000 - Rs 5,00,000
= Rs 1,24,000
Income Tax in this range = Taxable Income x Tax Rate
= Rs 1,24,000 x 0.1
= Rs 12,400
Now, let's calculate the total annual income tax:
Total Annual Income Tax = Income Tax in the range Rs 5,00,001 to Rs 7,00,000
= Rs 12,400
Next, we calculate the rebate on income tax:
Tax Rebate = Total Annual Income Tax x Rebate Rate
= Rs 12,400 x 0.1
= Rs 1,240
Swornima's annual income tax is Rs 12,400, and she receives a tax rebate of Rs 1,240.
To summarize:
(i) Swornima's annual income is Rs 6,24,000.
(ii) Swornima's tax rebate is Rs 1,240.
(iii) Swornima should pay an annual income tax of R