The length of wire used for the equilateral triangle is approximately 5.61 meters.
The remaining length of wire used for the circle will be 9 - 5.61 ≈ 3.39 meters.
Here,
To minimize the total area of both figures, we need to find the optimal cut point for the wire.
Let's assume the length of the wire used for the equilateral triangle is x meters, and the remaining length of the wire used for the circle is (9 - x) meters.
For the equilateral triangle:
An equilateral triangle has all three sides equal in length.
Let's call each side of the triangle s meters. Since the total length of the wire is x meters, each side will be x/3 meters.
The formula to find the area of an equilateral triangle with side length s is:
Area = (√(3)/4) * s²
Substitute s = x/3 into the area formula:
Area = (√(3)/4) * (x/3)²
Area = (√(3)/4) * (x²/9)
Now, for the circle:
The circumference (perimeter) of a circle is given by the formula:
Circumference = 2 * π * r
Since the remaining length of wire is (9 - x) meters, the circumference of the circle will be 2π(9 - x) meters.
The formula to find the area of a circle with radius r is:
Area = π * r²
To find the area of the circle, we need to find the radius.
Since the circumference is equal to 2πr, we can set up the equation:
2πr = 2π(9 - x)
Now, solve for r:
r = (9 - x)
Now, substitute r = (9 - x) into the area formula for the circle:
Area = π * (9 - x)²
Now, we want to minimize the total area, which is the sum of the areas of the triangle and the circle:
Total Area = (√(3)/4) * (x²/9) + π * (9 - x)²
To find the optimal value of x that minimizes the total area, we can take the derivative of the total area with respect to x, set it to zero, and solve for x.
d(Total Area)/dx = 0
Now, find the critical points and determine which one yields the minimum area.
Taking the derivative and setting it to zero:
d(Total Area)/dx = (√(3)/4) * (2x/9) - 2π * (9 - x)
Setting it to zero:
(√(3)/4) * (2x/9) - 2π * (9 - x) = 0
Now, solve for x:
(√(3)/4) * (2x/9) = 2π * (9 - x)
x/9 = (8π - 2πx) / (√(3))
Now, isolate x:
x = 9 * (8π - 2πx) / (√(3))
x(√(3)) = 9 * (8π - 2πx)
x(√(3) + 2π) = 9 * 8π
x = (9 * 8π) / (√(3) + 2π)
Now, we can calculate the value of x:
x ≈ 5.61 meters
So, the length of wire used for the equilateral triangle is approximately 5.61 meters.
The remaining length of wire used for the circle will be 9 - 5.61 ≈ 3.39 meters.
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Find the area of the triangle which the line 2x – 3y +6=0 forms with the coordinate axis.
2x-3y+6=0 has an x intercept of 2 and a y intercept of -3.
That means the 2 sides of the right triangle are 2 and -3
Area of triangle= 1/2×base×height
= 1/2×-3×2
=-3
∴ Area of the triangle=-3
The area of the asked triangle is 3 sq units.
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, a triangle is formed by the line 2x – 3y +6=0 and the coordinate axis.
When we plot the graph of the line, we get, y-intercept = 2 and x-intercept = -3
Hence, the height and base of the triangle will be 2 and 3 respectively.
Area of a triangle = 1/2 (base) (height)
Area = 1/2 (2)(3)
Area = 3
Hence, the area of the asked triangle is 3 sq units.
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The California State University (CSU) system consists of 23 campuses, from San Diego State in the south to Humboldt State near the Oregon border. A CSU administrator wishes to make an inference about the average distance between the hometowns of students and their campuses. Describe and discuss several different sampling methods that might be employed. (Select all that apply.) There are no potential problems with self reporting of distances.
Answer:
1)The sample could be generated by taking a stratified random sample by taking a simple random sample from each of the 23 campuses and again asking each student in the sample to report the distance from their hometown to campus.
2)One could take a simple random sample of students from all students in the California State University system and ask each student in the sample to report the distance from their hometown to campus.
3)Certain problems arise with self reporting of distances, such as recording error or poor recall.
Step-by-step explanation:
1)The sample could be generated by taking a stratified random sample by taking a simple random sample from each of the 23 campuses and again asking each student in the sample to report the distance from their hometown to campus.
2)One could take a simple random sample of students from all students in the California State University system and ask each student in the sample to report the distance from their hometown to campus.
3)Certain problems arise with self reporting of distances, such as recording error or poor recall.
If anyone can give me the answer that will be greatly appreciated :)
42-x=58
or, -x=58-42
with change in side sign also chamges we change sides to make like terms in one side and unlike in amother side.
or, -x= 16
or,x=-16.
therefore x=-16...
Hope this helps you.
Under which transformation can the image be a different size than the original
figure?
A. translation
B. rotation
C. dilation
D. reflection
C. Dilation.
Dilation can resize the image.
Translation will shift the imagine's position but won't change its actual size.
Rotation will mangle with image's orientation but also won't change its size.
Reflection is just a type of rotation which as established, also won't change its size.
Hope this helps.
Let sin A = -5/13 with 270 degrees < A < 360 degrees and cos B = -15/17 with 90 degrees < B < 180 degrees find sin (A+B)
Answer:
Step-by-step explanation:
Find m These questions getting hard
Answer:
the
Step-by-step explanation:
it's fairly easy actually. You just have to use sin
The hypotenuse of a right triangle is 16 units and the length of one of the legs is 12 units. What is the length of the other leg in simplest radical form?
A. 2√13
B. 4√11
C. 2√17
D. 4√7
Answer:
D, 4√7
Step-by-step explanation:
Answer:
Step-by-step explanation:
c = 16
a = 12
b = ?
a^2 + b^2 = c^2
12^2 + b^2 = 16^2
144 + b^2 = 256
b^2 = 256 - 144
b^2 = 112
b^2 = 16 * 7
sqrt(b^2) = sqrt(16)*sqrt(7)
b = 4 * sqrt(7)
Sudhanshu is solving a system representing a race between two remote control cars. The variable x is defined as time in seconds, and y is the distance in meters from the starting line.
Red car: y = 3 x + 5. Blue car: y = 4 x.
How many solutions should Sudhanshu find?
zero
one
two
infinite
Answer:
One
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptSolving systems of equations
Step-by-step explanation:
Step 1: Define
Identify systems
y = 3x + 5
y = 4x
Step 2: Solve
If we compare the 2 lines, we can see that they both have a different slope. If they had the same slope but different y-intercepts, then they would be parallel and have no solution. We can also see that the 2 lines aren't the same. If they were, then they would have infinite solutions.
∴ the systems should have only one solution.
Answer:
B
Step-by-step explanation:
You have 8 quarts of milk. You need 1.25 cups to make one serving of deep fried chicken. How many servings can you make?
Answer: 25.6 servings (partial serving) / 25 servings (whole serving)
Step-by-step explanation:
Concepts:
As we can see from the question, there are two units applied. [Quarts] and [cups]; therefore, we need to do the unit conversion.
1 quart = 4 cups
Solve:
Step one: Convert quarts into cups
1 quart = 4 cups8 quarts = 4 × 8 = 32 cupsStep two: Divide the cups to find the number of servings
32 cups / 1.25 cups = 25.6 servings**Disclaimer** I am not sure about the rules that you apply in mathematics. Here, the answer is not an integer. I am concerned whether you would allow partial servings. In my understanding, the servings shall be a whole, thus should be rounded. However, if you are fine with decimals, then you have the choice.
Hope this helps!! :)
Please let me know if you have any questions
Which equation has a constant of proportionality equal to 2?
Answer:
[tex]{ \tt{y = 2x}}[/tex]
Answer:
2y=x
Step-by-step explanation:
If x = y, then x – a = y – a represents the ________ property of equality.
Answer:
Subtractive Property of equality
Step-by-step explanation:
Since x = y, When you subtract anything from x, you must do the same to y for them to stay equal.
Answer:
Subtraction property of equality
Malingo read 3/8 of a book on Friday, 1/4 on Saturday and the rest on Sunday. what fraction did he read on Sunday?
Answer:
3/8
Step-by-step explanation:
We can write the entire book with the number 1. Now we can write this operation
3/8 + 1/4 + x = 1
3 + 2 + 8x = 8
5 + 8x = 8
8x = 3
x = 3/8
(c³d)a(cd⁷)a
Simplify
Answer:
= c^4 d^8 a^2
Step-by-step explanation:
Apply exponent rule: aa= a^2
= c^3 da^2 cd^7
= c^4 da^2 d^7
= c^4 d^8 a^2
During a certain 9-year period, the Consumer Price Index (CPI) decreased by
45%, but during the next 9-year period, it decreased by only 5%. Which of
these conditions must have existed during the second 9-year period?
A. Deflation
B. Stagnation
C. Conflation
D. Inflation
Answer:
deflation ,,,,
Step-by-step explanation:
I hope it's helpful for you ☺️Deflation must have existed during the second 9-year period.
What is deflation?Deflation is a decrease in the general price level of goods and services in an economy over a period of time. This means that the purchasing power of money increases, as the same amount of money can buy more goods and services.
The opposite of inflation, which is an overall rise in the cost of goods and services over time, is deflation. Money loses value due to inflation, whereas it gains value due to deflation. Deflation can reduce demand for goods and services, though, if it lasts for a long time. This is because customers may put off purchases in expectation of cheaper costs. A downturn in economic activity may follow, which would be bad for the economy.
Given data ,
Deflation is a decrease in the general price level of goods and services in an economy over a period of time. A decrease in the Consumer Price Index (CPI) is a measure of deflation.
In the first 9-year period, the CPI decreased by 45%, which indicates a significant deflationary period. In the next 9-year period, the CPI decreased by only 5%, which still indicates a deflationary period, but not as severe as the previous one.
Hence , the process is deflation in the second year
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Solve for X. Round to the nearest tenth, if necessary. Please help
Answer:
X=1.2/1.3
answérica is 1.25, depends on how you want to round
Step-by-step explanation:
Can someone please help me with this.
How many gallons each of 25% alcohol and 5% alcohol should be mixed to obtain 20 gal of 16% alcohol?
Answer:
✓ x gal of 25% 20-x gal of 5% pure alcohol is x(.25)+(20-x)(.05)=20*.16=3.2 so .25x+1-.05x=3.2 gallons of 25% .20x=2.2 gallons of 5% x=11 gallons of 25%.
Step-by-step explanation:
Hope this helps~ ;D
SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the 82% confidence interval to 25 points, how many students should the administrator sample
Answer:
The appropriate solution is "259".
Step-by-step explanation:
According to the question,
[tex]\sigma = 300[/tex]
[tex]M.E=25[/tex]
At 82% CI,
[tex]\alpha = 0.18[/tex]
Critical value,
[tex]Z_c=1.341[/tex]
Now,
The sample size will be:
⇒ [tex]n=(Z_c\times \frac{\sigma}{E} )^2[/tex]
By substituting the values, we get
[tex]=(1.341\times \frac{300}{25} )^2[/tex]
[tex]=(1.341\times 12)^2[/tex]
[tex]=259[/tex]
(9,2) and (5,-4) find the slope of the line containing the pair of points
Answer:
3/2
Step-by-step explanation:
We can use the slope formula
m = (y2-y1)/(x2-x1)
= ( -4-2)/(5-9)
= -6/-4
=3/2
What is the constant of variation k of the direct variation y=KP through (-3, 2)
Answer:
isisis
Step-by-step explanation:
ISO’s
Answer:
-2/3
Answer: The constant of variation k for y = kx through (-3, 2) is k = -2/3.
Subtract 7 pounds 3 ounces from 10 pounds
Please Help! What's the rule that represents the sequence 13, 27, 41, 55, ...?
Answer:
B
Step-by-step explanation:
an = a+(n-1)d
an=13+(n-1)14
d=14
what is proportion as applied in mathematics
Answer:
como se siente el actor al presentar la obra hola
Someone help please
66 because you have to solve the problem next time
please help, will give brainliest!!!
Answer:
f^-1(x) = sqrt(x+4)
Step-by-step explanation:
y = x^2 -4
Exchange x and y
x = y^2 -4
Add 4 to each side
x+4 = y^2
Take the square root of each side
sqrt(x+4) = y
f^-1(x) = sqrt(x+4)
Answer:
f^-1(x) = sqrt(x+4)
Step-by-step explanation:
21. Gabe Amodeo, a nuclear physicist, needs 80 liters of a 30% acid solution. He currently has a 20% solution and a 60%
solution. How many liters of each does he need make the needed 80 liters of 30% acid solution?
Gabe needs
liters of the 20% solution.
He also needs
liters of the 60% solution.
Let x be the amount (in liters) of 20% solution that Gabe uses, and y the amount (also in L) of the 60% solution.
He needs 80 L of 30% solution, so that
x + y = 80
0.20x + 0.60y = 0.30 (80) = 24
Solve for y in terms of x :
y = 80 - x
Substitute this into the second equation and solve for x :
0.20x + 0.60 (80 - x) = 24
0.20x + 48 - 0.60x = 24
24 = 0.40x
x = 60
Solve for y :
y = 80 - 60
y = 20
Which is the correct calculation of the y-coordinate of point A? 0 (0 - 0)2 + (1 - y2 = 2 O (0 - 1)² + (0- y2 = 22 (0-0)² + (1 - y2 = 2 (0 - 1)2 + (0-y2 = 2
Answer:
The y-coordinate of point A is [tex]\sqrt{3}[/tex].
Step-by-step explanation:
The equation of the circle is represented by the following expression:
[tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]h[/tex], [tex]k[/tex] - Coordinates of the center of the circle.
[tex]r[/tex] - Radius of the circle.
If we know that [tex]h = 0[/tex], [tex]k = 0[/tex] and [tex]r = 2[/tex], then the equation of the circle is:
[tex]x^{2} + y^{2} = 4[/tex] (1b)
Then, we clear [tex]y[/tex] within (1b):
[tex]y^{2} = 4 - x^{2}[/tex]
[tex]y = \pm \sqrt{4-x^{2}}[/tex] (2)
If we know that [tex]x = 1[/tex], then the y-coordinate of point A is:
[tex]y = \sqrt{4-1^{2}}[/tex]
[tex]y = \sqrt{3}[/tex]
The y-coordinate of point A is [tex]\sqrt{3}[/tex].
...............................................................
Function: g(x) = 2x2 - 8
Answer:
f(x)= √ 1 2 x + 4 For x ≤ 0
Step-by-step explanation:
Refer to the values described below, then identify which of the following is most appropriate: discrete random variable, a. Responses to the survey question "How many pets do you have?" b. Exact heights of the next 100 babies born in a region c. Responses to the survey question "What is your eye color?" d. Exact foot length of humans e. Number of people in families a. Since the outcomes are b. Since the outcomes are countable, this is this is a discrete random variable. random variable.
Answer:
Exact heights of the next 100 babies born in a region.
Step-by-step explanation:
A discrete random variable involves two key factors ; discrete and randomness ; Hence, a discrete random variable should have a finite or countable Number of outputs or values. It should also stem from a random procedure. Here, the height of the next hundred babies is a random procedure as the next 100 babies in the region are unknown until Given birth too and as such all pregnant women have the chance of having their babies among. Since, we are dealing with exact height values which are countable (100), then we this is a discrete random variable.
