Answers
If a circle with a radius 3x is inscribed in a square, then the difference between the area of the square and the area of the circle is [tex]9x^{2} (4-\pi )[/tex]
Given,
The radius of the circle = 3x
The area of the circle = [tex]\pi r^{2}[/tex]
Where r is the radius of the circle
Substitute the values in the equation
Area of the circle = [tex]\pi (3x)^{2}[/tex]
=[tex]9x^{2} \pi[/tex]
We know when a circle is inscribed in a square the diameter of the circle is equal to the side of the square
Diameter of the circle = 2× radius
=2×3x
=6x
The area of the square = [tex]a^{2}[/tex]
Where a is the side of the square
Area of the square = [tex](6x)^{2}[/tex]
=[tex]36x^{2}[/tex]
The difference between the area of the square and the area of the circle= Area of the square - Area of the circle
[tex]=36x^{2} -9x^{2} \pi \\=9x^{2} (4-\pi )[/tex]
Hence, if a circle with a radius 3x is inscribed in a square, then the difference between the area of the square and the area of the circle is [tex]9x^{2} (4-\pi )[/tex]
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Related Questions
Is the given point interior,exterior, or on the circle (x+2^)2+(y-3^)2=81? Q(3,0)
Answers
Six times a number w is at least -24
solve for the inequality
Answers
Answer:
w is -4
Step-by-step explanation:
W is -4 because a positive number times a negative number is always a negative that is why the answer is a negative and 6 times 4 is 24 but for the 24 to be a negative the 4 has to be a negative 4.
A carpenter has a wooden dowel that is 72 cm long. She wants to cut it into two pieces so that one piece is 7 times as long as the other. What is the length of the longer piece?
Answers
Answer: 39.5 cm long
Step-by-step explanation: The equation can also be written s 72=2x+7, (x= length of short piece) (x+7+length of long piece.):
72=2x+7
72-7=2x
65=2x
x=32.5
Then to find out the long piece:
x+7
32.5+7=39.5
construct potential hypotheses or research questions to relate the variables in each of the following examples. also, write a brief statement explaining why you believe there is a relationship between the variables as specified in your hypotheses.
Answers
Construct potential hypotheses or research questions to relate the variables in each of the following examples -
Political party and support of the affordable care act -
Given this, there can be a relationship between the ideological group and the support of the moderate consideration act.that various ideological groups may support various types of government disability conspiracies and might have various goals.A few gatherings might focus on a list of topics or problems and might provide serious thought at some random time.which might facilitate the implementation of the Affordable Care Act, while others would be gradually forgiving toward such arrangements.The implementation and success of the Affordable Care Act may depend on the rise of certain ideological movements.and their ability to express what they think about the Act's purpose.
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an object moves along a parabolic path defined by the equation in such a way that the y-value is decreasing at a constant rate of 2 units per second. at what rate is the x-coordinate changing when x
Answers
So the change of rate of x is -1/3 .
The Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Given that object is decreasing at constant rate of 2 units per second so we have [tex]y = 2x^2 + 1[/tex]
[tex]\frac{dy}{dt} = 4x \frac{dx}{dt}[/tex]
given dy/dt = -2
when x = 3/2
-2 = 4(3/2) dx/dt
-2 = 6 dx/dt
dx/dt = -2/6
= -1/3
Hence the change of rate of x is -1/3 .
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Trey bakes 70 cupcakes for the school Bake Sale. Worried they might run out, he bakes some extra and now has 112 cupcakes.
What is the Percent Change in the number of cupcakes?
Answers
The Percent Change in the number of cupcakes is 60%
How to determine the Percent Change in the number of cupcakes?The given parameters are:
Initial number of cupcakes = 70
Final number of cupcakes = 112
The Percent Change in the number of cupcakes:
Percent = (Final number of cupcakes - Initial number of cupcakes)/Initial number of cupcakes * 100%
This gives
Percent = (112 - 70)/70 * 100%
Evaluate the quotient
So, we have
Percent = 0.6 * 100%
Evaluate the product
So, we have
Percent = 60%
Hence, the Percent Change in the number of cupcakes is 60%
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in simple linear regression the estimated slope from the regression of y on x is the same as the estimated slope in the regression of x on y.
Answers
In the given statement is:
In simple linear regression the estimated slope from the regression of y on x is the same as the estimated slope in the regression of x on y.
If Y depends on X then the regression line is Y on X.
Y is dependent variable and X is independent variable. If X depends on Y, then regression line is X on Y and X is dependent variable and Y is independent variable. The regression equation Y on X is Y = a + bx, is used to estimate value of Y when X is known.
What is Simple linear regression?
Simple linear regression is a regression model that estimates the relationship between one independent variable and one dependent variable using a straight line. Both variables should be quantitative.
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Brianna picks tomatoes on a local farm. she receives 11 cents per crate. last week, her total piecework earnings was 500 dollars. express the number of crates she picked algebraically.
Answers
Answer:
4,545.45 crates
Step-by-step explanation:
.11x = 500
Divide both sides by .11
x = 4,545.45
The number of crates she picked algebraically is 4545.
Let us consider the variable "c" to represent the number of crates Brianna picked.
We know that she receives 11 cents per crate.
1 crate = $0.11 (11 cents)
Her total earnings from picking "c" crates can be expressed as:
Earnings = 0.11c
Now, we know her total piecework earnings for last week were $500. So, we can set up an equation:
Total Earnings = $500
0.11c = $500
To find the number of crates Brianna picked, we need to solve for "c":
c = $500 / 0.11
c = 4545.45...
c = 4545 crates
So, algebraically, Brianna picked approximately 4545 crates last week.
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at a gathering of50 people, there are 30 people who all know each other and 20 people who know no one. people who know each other hug, and people who do not know each other shake hands. how many handshakes occur within the group?
Answers
Total 790 number of handshakes occur within the group.
According to the given question.
Total number of people = 50
Number of people who know each other = 30
Number of people who know no one = 20
Since, 20 people doesn't knw each any one, so they will shake hands.
So, the total number of hand shakes by these 20 people
= 20(20 -1)/2
= 10(19)
= 190
Also, we have to consider that other 30 people will also shake hands with these 20 people.
So, the total number of hanshakes by these 30 and 20 people = 30 × 20 = 600
Therefore, the total number of handshakes occur within the group
= 600 + 190
= 790
Hence, total 790 number of handshakes occur within the group.
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What is the scale factor from polygon JKLM to polygon ABCD?
Answers
Answer:
for part c
JM=36
AD=12
36=3
JKLM is 3x bigger than polygon ABCD
Find the 11th term of the arithmetic seqence 2x+ 9, 7x+11 ,12x +13,...
Answers
Answer:
52x + 29.
Step-by-step explanation:
d = 7x + 11 - (2x + 9)
= 5x + 2.
11th term
= 2x + 9 + (11-1)(5x + 2)
= 2x + 9 + 50x + 20
= 52x + 29.
A line intersects the points
(3, 2) and (5, 12).
m = 5
Write an equation in point-slope form
using the point (3, 2).
y - [?] = [](x-[ ])
Answers
The point slope of the the line using the point (3,2) and slope 5 is (y-2)=5(x-3).
Given that A line intersects the points (3, 2) and (5, 12) and asked to write an equation of line passing through (3,2) and having slope as 5.
Point slope form:
The point-slope form of a stright line is y-y1=m(x-x1)
Here (x1,y1) is the fixed point with which the line passes and m is the slope of the line
Here, (x1,y1) is given as (3,2) and m(slope)=5
The equation straight line in point-slope form is (y-2)=5(x-3).
Therefore,The point-slope form of the the line using the point (3,2) and slope 5 is (y-2)=5(x-3).
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Pleaseee help me I need this done rn.
Area of a right triangle ABC is 120 sq feet. If AABC goes through a dilation transformation with a scale
factor of 1.5, then what will be the area of the transformed triangle (in sq feet)?
Answers
Answer:
270
Step-by-step explanation:
The area is the same as the original area multiplied by the square of the scale factor.
A, B & C form the vertices of a triangle.
∠
CAB = 90°,
∠
ABC = 61° and AB = 9.2.
Calculate the length of AC rounded to 3 SF.
Answers
Answer:
AC = 16.6
Step-by-step explanation:
Use sine rule
9.2 / sin(180-90-61) = AC/ sin(61)
There is a gas station exactly halfway between Stan and Drew’s houses. The map coordinates for Stan’s house are 5 miles East and 2 miles north. The map coordinates for Drew’s house are 3 miles East and 4 miles north. Find the map coordinates for the gas station
Answers
Answer:
4 miles east and 3 miles north (4, 3)
\frac{3}{8} times \frac{1}{9} in simplest form help me
Answers
Answer: 3/72 is your answer.
Marco owed his father $210 and began paying him back $20 at the end of each week, beginning November 1. Joni owed her father $180 and began paying back $10 at the end of each week, beginning on the same day. What Marco owed his father in dollars at the end of n weeks can be represented by f(n) = 210 − 20n. What Joni owed her father in dollars at the end of n weeks can be represented by g(n) = 180 − 10n.
Find the value of n for which f(n) = g(n). What does that value mean in this situation?
After _____ weeks, Jonie and Marco each owed their fathers the same amount
Answers
In the given situation n gives us the number of weeks. after 3 weeks, Jonie and Marco each owed their fathers the same amount.
What are mean?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
We have been given that Marco owed his father in dollars at the end of n weeks can be represented by f(n) = 210 − 20n. and Joni owed her father in dollars at the end of n weeks can be represented by g(n) = 180 − 10n.
Also we get f(n) = g(n)
210 − 20n = 180 − 10n
Now n gives us the number of weeks thus solve for n
210 − 20n = 180 − 10n
210 - 180 = -10n + 20n
30 = 10n
n = 3
Now check your solution;
f(n) = 210 − 20n = 210 - 60 = 250
g(n) = 180 − 10n = 180 - 30 = 150
So our answer checks out after 3 weeks, Jonie and Marco each owed their fathers the same amount.
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What is the area of a rectangle with a length of 9 feet and a width of 7 grade
Answers
9 x 7 = 63 feet
Answer:
63
Step-by-step explanation:
area=length×width so 9×7=63
i need help on this problem pls
Answers
Step-by-step explanation:
2 3 4 6...................
- Lyle needs 200 g of chocolate that is 86% cocoa
for a cake recipe. He has one kind of chocolate
that is 99% cocoa and another kind that is 70%
cocoa. How much of each kind of chocolate
does he need to make the cake? Round your
answer to the nearest gram.
Answers
Answer: 110 grams of the 99% cocoa, and 90 grams of the 70% cocoa.
===================================================
Work Shown:
x = amount of the 99% cocoa
200-x = amount of the 70% cocoa
0.99x = amount of pure coca from the first batch
0.70(200-x) = amount of pure cocoa from the second batch
0.99x+0.70(200-x) = total amount of pure cocoa
0.99x+0.70(200-x) = 200*0.86
0.99x+0.70*200-0.70x = 200*0.86
0.99x+140-0.70x = 172
0.29x+140 = 172
0.29x = 172-140
0.29x = 32
x = 32/0.29
x = 110.344827586207
x = 110
200-x = 200 - 110 = 90
Lyle needs 110 grams of the 99% cocoa, and 90 grams of the 70% cocoa.
Both of these values are approximate.
points A(2, 3) B(-3,4).
area of triangle PAB = 8.5.
Answers
The equation of the locus of the point P so that the area of triangle PAB is 8.5 square units will be 5 k + h = 34.
Let coordinate of P be (h, t)
We are given the coordinates of A and B as:
A = (2,3) and B = (−3,4)
Now, we also know that Area of triangle PAB is:
A = 1 / 2 (h ( 3 − 4 ) + 2 ( 4 − k ) − 3 ( k − 3 ) )
± 8.5 = 1 / 2 ( h ( - 1 ) + 2 ( 4 - k ) - 3 ( k - 3 ) )
± 17 = ( - h + 8 - 2 k - 3 k + 9 )
± 17 = ( 17 - 5 k - h )
When + 17 is there:
5 k + h = 0
When - 17 is there:
5 k + h = 34
So, locus of the point P will be 5 k + h = 34.
Therefore, the equation of the locus of the point P so that the area of triangle PAB is 8.5 square units will be 5 k + h = 34.
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Your question was incomplete. Please refer the content below:
A(2,3) and B(−3,4) be two given points. Find the equation of the locus of P so that the area of triangle PAB is 8.5 square units.
in a survey, 80 people were were questioned to find out how how many people read newspapers, S or D or both both. The survey revealed ya that 45 read D, 30 read read S and 10 read neither
Represents the information in a venn diagram.
Answers
Greetings from Brasil...
In this type of problem, we will use Set Theory
n(D ∪ S) = n(D) + n(S) - n(D ∩ S)
as n(U) - n(D ∪ S) = 10, then
n(D ∪ S) = 70, so
n(D ∩ S) = 5 (read both)
n(D) - n(D ∩ S) = 40 (read only D)
n(S) - n(D ∩ S) = 25 (read only S)
see attached figure
_________________________________
something similar
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Someone help with this, need it for hw,thanks!
Answers
Answer: B
Step-by-step explanation: you see how its by the 2 that means that its going to be where the 3 is
What is the solution set of the quadratic inequality 6x² + 1 ≤0?
O {X[XER}
O
{X1 X=-1}
Answers
Answer:
The empty set
Step-by-step explanation:
The square of a real number is non-negative, and thus the left hand side is always positive.
question 14(multiple choice worth 1 points) (01.05 lc) which calculation can be used to find the value of p in the equation p3
Answers
The response to this question is that p has a value of 8, or the cube root of 8. i.e. p=∛8.
Why do you use the term "Cube roots"?An integer y such that y³ = x is known as the cube root of a number x in mathematics. All nonzero complex numbers have three different complex cube roots, while all nonzero real numbers have exactly one real cube root and two complex conjugate cube roots. When we multiply a factor three times to obtain a number, we have obtained the cube root of that factor. Three cube root of, ending cubic root is the sign for the cube root. In contrast to cubing an integer, finding its cube root is a mathematical operation.
According to the equation, p³=8
We can clearly see that the power of p is 3.
Now by taking cube root on both the sides, we can see that the value of p is
∛p³=∛8
⇒p=∛8
The value of p in the equation cube root of 8.
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What must be added to 3x + y to get 2x + 3y?
Answers
You have 3x+y and you need to make it 2x+3y
The difference between 3x and 2x is 1x(x)
And the difference between y and 3y is 2y
For the x you have to minus x from 3x to get 2x,(3x-x=2x)
For the y you have to add 2y to y to get 3y,(y+2y=3y)
Now add them
=3x+y+-x+2y=2x+3y
Therefore you add -x+2y
Answer:
-x+2yStep-by-step explanation:
What must be added to 3x + y to get 2x + 3y?
3x + y + z = 2x + 3y
3x + z = 2x + 3y - y
3x + z = 2x + 2y
z = 2x-3x+2y
z = -x+2y
-------------------
check
3x + y + (-x) +2y =
2x + 3y
the answer is good
Help please quite immediate am pro
Answers
question the benefit of using inferential statistics is that it allows a researcher to describe the data describe the data find the measures of central tendency find the measures of central tendency find the spread of the data find the spread of the data make generalizations about a population make generalizations about a population visualize the raw data
Answers
A researcher can make generalizations about a population by utilizing inferential statistics, which is a benefit.
What kind of statistics are inferential, for instance?Two purposes dominate the use of inferential statistics: estimating population numbers (for example, the mean SAT score of all 11th graders in the US). testing hypotheses to make population-level judgments (for example, the relationship between SAT scores and family income).
Inferential statistics that are helpful in the design of experimental and quasi-experimental studies or in the assessment of program outcomes.
When comparing the average performance of two groups on a single measure to check if there is a difference, one of the simplest inferential tests may be performed. You might be interested in learning whether math test results between eighth-grade boys and girls differ or if a program group differs from a control group in terms of the outcome measure.
The t-test for differences between groups should always be taken into consideration when comparing the average performance of two groups.
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The following diagram depicts a construction of copying a line segment.
If AB is 6.7 cm, what would the length of line segment CD be?
Answers
The diagram depicting the construction of copying a line segment indicates that AB = CD = 6.7 cm.
How can the length of the constructed line segment, AB be found?A line segment, which can be expressed as a segment of a line, has definite length. It is a line drawn that has two endpoints.
A line segment can be named by the capital letters placed at the endpoints.
Copying a line segment, therefore gives a segment of equal length as the original line segment.
Given that the length of AB = 6.7 cm, and the line segment, CD, is obtained by copying segment AB, we have;
Length of CD = Length of AB = 6.7 cm
Therefore;
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Simplify the following
Need the answer asap pls
Answers
1) 9y-1
2) x ³ - x ² + x
3)-3a²+ a + 2
4) -x ²
5) -4x ⁵ + 16x ³ - 20x ²
6) 8x ³ + 6x ² - 32x + 15
7) x - 6
8) 6x -3
9) x ² - 6x +5
10) 10x ⁵ +3x ³ - 2x ²