the vertical asymptotes are x = -1 and x = 4, and there is no horizontal asymptote.
what is vertical asymptotes ?
Vertical asymptotes are vertical lines on a graph where a function approaches infinity or negative infinity as the input (x) approaches a certain value. In other words, vertical asymptotes occur when the denominator of a function becomes zero and the function is undefined at that point
In the given question,
To find the horizontal and vertical asymptotes of the function f(x) = 3x²/[(x+1)(x-4)], we need to analyze the behavior of the function as x approaches infinity or negative infinity and as x approaches the vertical asymptotes (if any).
Vertical asymptotes occur at the values of x that make the denominator of the fraction equal to zero. In this case, we have vertical asymptotes at x = -1 and x = 4.
To find the horizontal asymptote, we need to divide the leading term of the numerator by the leading term of the denominator when x approaches infinity or negative infinity. Since the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. However, we can use long division or synthetic division to write the function in the form of a polynomial plus a proper fraction:
f(x) = 3x²/[(x+1)(x-4)] = (3x + 15)/(x² - 3x - 4)
As x approaches infinity or negative infinity, the fraction approaches the value of 3/1 (the ratio of the leading terms of the numerator and denominator), but there is no horizontal asymptote.
Therefore, the vertical asymptotes are x = -1 and x = 4, and there is no horizontal asymptote.
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what is the range of data?
40
42
54
96
what is the median of the data?
64.5
72.5
74.5
75
what is the mode of the data?
5
70
75
88
The range, median and mode of the data-set are given as follows:
Range: 42.Median: 74.5.Mode: 75.How to obtain the features?Considering the stem-and-leaf plot, the data-set is given as follows:
54, 55, 60, 66, 69, 72, 73, 74, 75, 75, 81, 82, 88, 89, 95, 96.
The range of a data-set is calculated as the difference between the highest value and the lowest value in the data-set, thus:
96 - 54 = 52.
The data-set has an even cardinality of 16, hence the median is calculated as the mean of the two middle elements as follows:
Median = (74 + 75)/2
Median = 74.5.
The mode of a data-set is the observation that appears the most times in the data-set, hence it is of 75, which is the only observation that appears twice in the data-set.
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SOLVE THE FOLLOWING INEQUALITY: x^3-5x^2+10 > 0
________________________________
x³ - 5x² + 10 > 0 = x³ - 5x² + 10 = 0= x² - 5x² + 10 - 10 = 0 - 10= x² - 5x² = - 10 = x² - 5x² = - 4x² - 4x² = - 10= - 4x² = - 10 = - 4x² / - 4 = - 10 / - 4x² = 5 / 2 x = √ 5 / 2________________________________
the function g(x) = 12x^2-sinx is the first derivative of f(x). If f(0)=-2 what is the value of f(2pi
Answer:
[tex]f(2\pi) = 32\pi^3 - 2[/tex]
Step-by-step explanation:
Main steps:
Step 1: Use integration to find a general equation for f
Step 2: Find the value of the constant of integration
Step 3: Find the value of f for the given input
Step 1: Use integration to find a general equation for f
If [tex]f'(x) = g(x)[/tex], then [tex]f(x) = \int g(x) ~dx[/tex]
[tex]f(x) = \int [12x^2 - sin(x)] ~dx[/tex]
Integration of a difference is the difference of the integrals
[tex]f(x) = \int 12x^2 ~dx - \int sin(x) ~dx[/tex]
Scalar rule
[tex]f(x) = 12\int x^2 ~dx - \int sin(x) ~dx[/tex]
Apply the Power rule & integral relationship between sine and cosine:
Power Rule: [tex]\int x^n ~dx=\frac{1}{n+1}x^{n+1} +C[/tex]sine-cosine integral relationship: [tex]\int sin(x) ~dx=-cos(x)+C[/tex][tex]f(x) = 12*(\frac{1}{3}x^3+C_1) - (-cos(x) + C_2)[/tex]
Simplifying
[tex]f(x) = 12*\frac{1}{3}x^3+12*C_1 +cos(x) + -C_2[/tex]
[tex]f(x) = 4x^3+cos(x) +(12C_1 -C_2)[/tex]
Ultimately, all of the constant of integration terms at the end can combine into one single unknown constant of integration:
[tex]f(x) = 4x^3 + cos(x) + C[/tex]
Step 2: Find the value of the constant of integration
Now, according to the problem, [tex]f(0) = -2[/tex], so we can substitute those x,y values into the equation and solve for the value of the constant of integration:
[tex]-2 = 4(0)^3 + cos(0) + C[/tex]
[tex]-2 = 0 + 1 + C[/tex]
[tex]-2 = 1 + C[/tex]
[tex]-3 = C[/tex]
Knowing the constant of integration, we now know the full equation for the function f:
[tex]f(x) = 4x^3 + cos(x) -3[/tex]
Step 3: Find the value of f for the given input
So, to find [tex]f(2\pi)[/tex], use 2 pi as the input, and simplify:
[tex]f(2\pi) = 4(2\pi)^3 + cos(2\pi) -3[/tex]
[tex]f(2\pi) = 4*8\pi^3 + 1 -3[/tex]
[tex]f(2\pi) = 32\pi^3 - 2[/tex]
Answer:
[tex]f(2 \pi)=32\pi^3-2[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given:
[tex]g(x)=12x^2-\sin x[/tex][tex]f(0)=-2[/tex]If g(x) is the first derivative of f(x), we can find f(x) by integrating g(x) and using f(0) = -2 to find the constant of integration.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $\sin x$}\\\\$\displaystyle \int \sin x\:\text{d}x=-\cos x+\text{C}$\end{minipage}}[/tex]
[tex]\begin{aligned} \displaystyle f(x)&=\int f'(x)\; \text{d}x\\\\&=\int g(x)\;\text{d}x\\\\&=\int (12x^2-\sin x)\;\text{d}x\\\\&=\int 12x^2\; \text{d}x-\int \sin x \; \text{d}x\\\\&=12\int x^2\; \text{d}x-\int \sin x \; \text{d}x\\\\&=12\cdot \dfrac{x^{(2+1)}}{2+1}-(-\cos x)+\text{C}\\\\&=4x^{3}+\cos x+\text{C}\end{aligned}[/tex]
To find the constant of integration, substitute f(0) = -2 and solve for C:
[tex]\begin{aligned}f(0)=4(0)^3+\cos (0) + \text{C}&=-2\\0+1+\text{C}&=-2\\\text{C}&=-3\end{aligned}[/tex]
Therefore, the equation of function f(x) is:
[tex]\boxed{f(x)=4x^3+ \cos x - 3}[/tex]
To find the value of f(2π), substitute x = 2π into function f(x):
[tex]\begin{aligned}f(2 \pi)&=4(2 \pi)^3+ \cos (2 \pi) - 3\\&=4\cdot 2^3 \cdot \pi^3+1 - 3\\&=32\pi^3-2\\\end{aligned}[/tex]
Therefore, the value of f(2π) is 32π³ - 2.
algebra pls helpppppppppp
The correct answers are:
They are inverses of one another
They are symmetric over the line y=x
What is exponential form?When a number is too big or too little, exponential notation can express it as a single number and 10 increased to the power of the appropriate exponent.
The exponential form [tex]y=5^x[/tex]
The logarithmic form [tex]y = log_5\ x[/tex] are inverse functions of each other.
If we [tex]y = 5^x[/tex], then [tex]x = log_5\ y[/tex].
As long as x is a real number and y is positive, this is true for any value of x and y.
The graphs of [tex]y = 5^x[/tex] and [tex]y = log_5\ x[/tex] are symmetric over the line y = x.
We obtain the other graph by reflecting the first graph across this line.
Over the line y = x, the inverse functions are always symmetric.
If we swap the x and y coordinates of any point on one graph, we get a comparable position on the other graph.
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Find the probability that
event A or B takes place.
The probability that event A or B takes place is P ( A ∪ B ) = 6/17
Given data ,
Let the probability that event A or B takes place is P ( A ∪ B )
Now , the probability of A is P ( A ) = 2/17
And , the probability of B is P ( B ) = 4/17
where P ( A ∩ B ) = 0
On simplifying the equation , we get
P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B )
So , P ( A ∪ B ) = 2/17 + 4/17
P ( A ∪ B ) = 6/17
Hence , the probability is 6/17
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Find the slope of the tangent to f(x)=x^2 at the point (3,9).
Answer:
f'(x) = 2x, so f'(x) = f'(3) = 2(3) = 6.
Pls Help Parallelogram PQRS is shown in the coordinate plane below. What is the perimeter of parallelogram PQRS?
1) Find the missing side using the right triangle shown. 2) Then find the perimeter by adding all four sides of the parallelogram!
Note that the perimeter of the parallelogram is 42
How is this so?recall that opposite sides of a parallelogram are congruent always
We have to to find the distance between the points Q(6, 6 ) and R(1, -6) using the distance formula which is
d = √[(x2 - x1) ² + (y2 - y 1)²]
where d is the distance between two points with paris (x1 , y1)
and (x2, y2).
PS = QR = √(6-1)² + (6+6)²
= √5² + 12²
= √(25+144
= √(169)
= 13
PQ = SR = 8
Perimeter = 13 + 13 + 8 + 8
Perimeter = 42.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
Guys can someone help me with these 2 problems please that's the matrix
The solution of the matrix is [tex]4G + 2F = \begin{bmatrix}32 &-20 &-32& -8 &-40 \\-24& -28 &4 &36 &8 \\16& 24 &12 &28 &20 \\-16&-12 &0 &-40 &-36\end{bmatrix}[/tex]
A matrix is a rectangular array of numbers arranged in rows and columns. The size of a matrix is given by its dimensions, which indicate the number of rows and columns in the matrix. In this question, both matrices G and F have 4 rows and 5 columns, so we say that they are 4x5 matrices.
Scalar multiplication is performed by multiplying each element of a matrix by a scalar, which is simply a number.
Now, to find the value of 4G + 2F, we need to perform scalar multiplication on each matrix and then add the results. We get:
[tex]4G = 4 * \begin{bmatrix}8 &-5 &-8& -2 &-10 \\-6& -7 &1 &9 &2 \\4& 6 &3 &7 &5 \\-4&-3 &0 &-10 & -9\end{bmatrix}\\= \begin{bmatrix}32 &-20 &-32& -8 &-40 \\-24& -28 &4 &36 &8 \\16& 24 &12 &28 &20 \\-16&-12 &0 &-40 & -36\end{bmatrix}[/tex]
[tex]2F = 2 * \begin{bmatrix}1 &8 &-2& -5 &9 \\-9& 10 &6 &-3 &0 \\4& 5 &-4 &3 &7 \\2&-10 &-6 &-1 & -8\end{bmatrix}= \begin{bmatrix}2 &16 &-4& -10 &18 \\-18& 20 &12 &-6 &0\\8& 10 &-8 &6 &14 \\4&-20 &-12 &-2 & -16\end{bmatrix}[/tex]
Now, we can perform matrix addition on 4G and 2F to get:
[tex]4G + 2F = \begin{bmatrix}32 &-20 &-32& -8 &-40 \\-24& -28 &4 &36 &8 \\16& 24 &12 &28 &20 \\-16&-12 &0 &-40 &-36\end{bmatrix}[/tex]
Therefore, the value of 4G + 2F is the 4x5 matrix given above.
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‼️‼️‼️‼️‼️WILL MARK BRAINLIEST IF HELPFUL‼️‼️‼️‼️‼️
A spherical balloon has a 20-in. diameter when it is fully inflated. Half of the air is let out of the balloon. What is the volume of the fully-inflated balloon?
The volume of the fully - inflated balloon is 4186.67 cubic inches. The solution has been obtained by using the formula for sphere.
What is a sphere?
The geometric equivalent of a circle in two dimensions in three dimensions is a sphere. A collection of three-dimensional points with the same r separation between them are referred to as a sphere.
We are given diameter as 20 inches.
So, the radius is half of the diameter which comes out to be 10 inches.
From this, we get the volume as
⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]r^{3}[/tex]
⇒ Volume = [tex]\frac{4}{3}[/tex] π [tex]10^{3}[/tex]
⇒ Volume = [tex]\frac{4000}{3}[/tex] π
⇒ Volume = 4186.67 cubic inches
Hence, the volume of the fully - inflated balloon is 4186.67 cubic inches.
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If g(x) = 3x -2 and (gof)(x) = 15x + 10, find f(x).
Answer:
the function f(x) is f(x) = 5x + 4.
Step-by-step explanation:
To find f(x), we need to use the formula:
(gof)(x) = g(f(x)) = 3f(x) - 2
We are given that (gof)(x) = 15x + 10, so we can substitute this expression into the formula to get:
3f(x) - 2 = 15x + 10
Simplifying this equation, we get:
3f(x) = 15x + 12
Dividing both sides by 3, we get:
f(x) = 5x + 4
Therefore, the function f(x) is f(x) = 5x + 4.
Find the volume of the composite solid. Round your answer to the nearest hundredth.
Therefore, the volume of the composite solid is approximately 1357.28 cubic feet, rounded to the nearest hundredth.
What is volume?Volume is a measure of the amount of space occupied by an object or a substance. In other words, it is the three-dimensional space that an object or substance occupies. The SI unit for volume is cubic meters (m³), although other units such as cubic centimeters (cm³) and liters (L) are also commonly used.
Here,
The composite solid is made up of a hemisphere and a cone with the same base radius and height. The volume of the hemisphere is given by (2/3)πr³, and the volume of the cone is given by (1/3)πr²h, where r is the radius and h is the height. Given that the radius is 6 feet and the height is 12 feet, we can find the volumes of the hemisphere and the cone as follows:
Volume of hemisphere = (2/3)π(6³)
= 288π cubic feet
Volume of cone = (1/3)π(6²)(12)
= 144π cubic feet
The total volume of the composite solid is the sum of the volumes of the hemisphere and the cone, which is:
Total volume = Volume of hemisphere + Volume of cone
= 288π + 144π
= 432π
To find the numerical value of this volume, we can use the approximation π ≈ 3.14 and round the result to the nearest hundredth:
Total volume ≈ 432(3.14)
= 1357.28 cubic feet
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Please answer if you know this one with the steps thank you.
Step-by-step explanation:
T = 5200 = .2 ( E - 10600)
5200 / .2 = E - 10600
E = 5200/.2 + 10 600 = 36600 pounds
-(9-6)+(-1-2)-(3+4)+(5-6)=
Answer:
Step-by-step explanation:
-9+6-1-2-3-4+5-6
-3-3-7-1
-6-8
-14
Answer:
The answer is -14.
Step-by-step explanation:
-(9 - 6) + (-1 -2) - (3 + 4) + (5 - 6)
Subtract 6 from 9 to get 3.
-3 -1 -2 - (3 + 4) + 5 - 6
Subtract 1 from -3 to get -4.
-4 - 2 - (3 + 4) + 5 - 6
Subtract 2 from -4 to get -6.
-6 - (3 + 4) + 5 - 6
Add 3 and 4 to get 7.
-6 - 7 + 5 - 6
Subtract 7 from -6 to get -13.
-13 + 5 - 6
Add -13 and 5 to get -8.
-8 - 6
Subtract 6 from -8 to get -14.
-14.
14). Find the measures of both angles.
xo
(3x +20)°
Answer:
40 degrees and 140 degrees
Step-by-step explanation:
To solve this problem you can add x+3x+20 and set that equal to 180. (We can do this because angle x and angle 3x + 20 make a linear pair. Knowing this we can estimate that both angles added together will equal 180)
Let us add x + 3x + 20 = 180 to find x. We can then substitute that into the equation.
[tex]x+3x+20=180 :a\\\\4x+20=180 :b\\\\4x + 20 -20=180-20:c\\\\4x=160:d\\\\\frac{4x}{4} = \frac{160}{4}:e\\\\x=40:f[/tex]
a: So in this part, we have rewritten the equation to make it easier to solve
b: In this step, you combine the like terms x+3x to get 4x
c: In step c, you are subtracting 20 from both sides to keep constants on one side and variables on the right
d: In this last step the equation has been simplified to make it easier to solve.
e: To isolate x you have to divide both sides by 4, we do this because the coefficient of x is 4 so you divide the equation by 4 to cancel it out.
f: You rewrite and simplify the equation.
Now to find the measure of both angles you substitute x into the equation.
The first angle's value is 40 degrees and the second is 140 degrees.
These are our answers.
A gas can hold 10 L of gas how many cans could we filled filled with 7 L of
Answer:
2 cans
Step-by-step explanation:
Miguel is 3 years older than Katrice. In 9 years the sum of their ages will be 51. How old is Miguel now?
Malaika has a number of candies. She can give out 12 to each of her friends and have 3 left over. or she can give 9 out to each of her friends and have 12 left over. How many friends can receive candy?
If she can give out 12 to each of her friends and have 3 left over. or she can give 9 out to each of her friends and have 12 left over, Malaika has 3 friends who can receive candies.
Let's suppose Malaika has "c" candies, and "f" is the number of friends she has.
According to the problem statement, we have two equations:
c = 12f + 3
c = 9f + 12
To solve for "f", we can set the two equations equal to each other:
12f + 3 = 9f + 12
Simplifying the equation, we get:
3f = 9
Dividing both sides by 3, we get:
f = 3
We can verify our solution by plugging "f=3" back into one of the original equations:
c = 12f + 3
c = 12(3) + 3
c = 39
So, Malaika has 39 candies in total. We can also check the other equation to make sure it is true:
c = 9f + 12
c = 9(3) + 12
c = 39
Both equations are true, so our solution of "f=3" is correct.
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Use the given feasible region to find the maximum possible value of the objective function f=5x+6y
The calculated value of the maximum possible value of the objective function is 46
Finding the maximum possible value of the objective functionFrom the question, we have the following parameters that can be used in our computation:
Objective function, F = 5x + 6y
The coordinates of the feasible region are
(0, 6), (1, 6.5) and (2, 6)
Substitute (0, 6), (1, 6.5) and (2, 6) in the above equation, so, we have the following representation
F(0, 6) = 5(0) + 6(6) = 36
F(1, 6.5) = 5(1) + 6(6.5) = 44
F(2, 6) = 5(2) + 6(6) = 46
The maximum value above is 46 at (2, 6)
Hence, the maximum possible value of the objective function is 46
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Christian earned a grade of 67% on his multiple choice science final that had a total of 200 problems. How many problems on the final exam did Christian answer correctly?
Answer: 134.
Step-by-step explanation:
First revert 67% into it's decimal form. You get 0.67. Then, multiply 0.67 by 200 because there were 200 problems.
0.67 x 200
67 x 2
134
So, christian got 134 out of 200 problems correct.
Need the right answer for problem 12
The distance of the point from the line is d =
Given data ,
Let the point be P ( 1 , 1 )
Let the equation of line be represented as e
where A ( -5 , 0 ) and B ( 1 , -2 ) lies on the line
So , slope m = ( 0 + 2 ) / ( -5 - 1 )
m = 2/-6
m = -1/3
So , the equation of line is
y - 0 = ( -1/3 ) ( x + 5 )
y = ( -1/3 ) ( x + 5 )
( 1/3 )x + y + 5/3 = 0
Now , the Distance of a point to line D = | Ax₀ + By₀ + C | / √ ( A² + B² )
On simplifying , we get
D = | ( 1/3 )( 1 ) + ( 1 ) ( 1 ) + ( 5/3 ) | / √[ ( 1/3 )² + ( 1 )² ]
D = | ( 6/3 ) + 1 | / √ [ ( 1/9 ) + 1 ]
D = 3 / ( 10 ) / 9
D = 27/10
D = 2.7 units
Hence , the distance is 2.7 units
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Assume the random variable x is distributed with mean of 50 and a standard deviation of 7. Compute the probability.
P(x > 38)
Using the given random variable and the mean the required probability in the given situation is 0.9772.
What is probability?A probability is a numerical representation of the likelihood or chance that a specific event will take place.
Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
= P(x>36) = P(X-μ/σ>36-50/7)
= P(Z>-14/7) Z=X-μ/σ
= P(Z>-2)
= P(Z<2) [P(Z<z) = P(Z>-z)]
= 0.9772 by the p-value table
Therefore, using the given random variable and the mean the required probability in the given situation is 0.9772.
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Correct question:
Assume the random variable x is normally distributed with mean 50 and a standard deviation 7. Find the indicated probability. P(X>36)
Which number is irrational?
0.020202
0.8
0.333...
All the numbers are rational numbers.
We have,
Rational numbers are those numbers that are terminating and recurring non-terminating.
Irrational numbers are those numbers that are non-terminating and non-recurring.
The numbers are:
1)
0.020202
This is non terminating recurring number.
It is a rational number.
2)
0.8
This is a terminating number.
It is a rational number.
3)
0.020202
This is non terminating recurring number.
It is a rational number.
Thus,
All the numbers are rational numbers.
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I have two similar triangles and can't find x. since I'm too lazy to download the app, the larger one has two sides of 6 and 12 and the smaller has two sides of x-3 and x+1. what is x??
Answer:
7
Step-by-step explanation:
We can use the fact that the corresponding sides of similar triangles are in proportion to each other.
Let's compare the corresponding sides of the two triangles:
Corresponding sides and ratio
larger triangle's side of length 6 larger triangle's side of length 12Ratio
smaller triangle's side of length x-3smaller triangle's side of length x+1Since the triangles are similar, we know that these ratios are equal. That is,
6 / (x-3) = 12 / (x+1)
We can simplify this equation by cross-multiplying:
6(x+1) = 12(x-3)
Expanding and simplifying:
6x + 6 = 12x - 36
42 = 6x
x = 7
Therefore, x has a value of 7.
What is this from vertex to standard form ?
Answer:
y = -x^2-2x-2Step-by-step explanation:
vertex form = y=a(x-h)^2+k
standard form = y=ax^2+bx+c
the most straightforward way to solve it is to expand the vertex form
we get :
-(x+1)(x+1)-1
= -(x^2+x+x+1) - 1
note: remember to leave the negative sign out of the parentheses and distribute it after - otherwise you may mix up signs
= (-x^2-x-x-1) - 1
= -x^2-2x-1-1
= -x^2 - 2x - 2
So, in standard form, it is y=-x^2-2x-2
Hope this helps!
Can you please help me with this?
Answer:
a= Acute
b=Obtuse
c= Acute
d= Right
Help please Given the diagram below, what statement could you make about the relationship between angles 1 and 4?
A) ∠1 is congruent to ∠4.
B) m∠1 is greater than m∠4.
C) m∠1 is less than m∠4.
D) ∠1 and ∠4 cannot be determined.
Answer:
A) angle 1 is congruent (equal size) to angle 4.
Step-by-step explanation:
when 2 lines intersect, then the intersection angles are the same on both sides of any of the lines. they are only left-right mirrored.
Answer:
A) angle 1 is congruent (equal size) to angle 4.
Step-by-step explanation:
pls help with this geometry asap
Area of sector XYZ is 81.45 feet².
Define area of sectorThe area of a sector is a measure of the size of a portion of a circle enclosed by two radii and an arc between them. It is expressed in square units, such as square centimeters, square meters, or square inches.
To find the area of a sector, you need to know the radius of the circle and the central angle of the sector.
The formula for the area of a sector is:
Area of sector = (central angle / 360°) x π x r²
where r is the radius of the circle, π is the mathematical constant pi (approximately 3.14), and the central angle is measured in degrees.
n is the area of sector XYZ
n/360=115/255(X)
n/255=115/360(V)
(The same elements are proportional)
n=115/360×255
n=81.4583≈81.45 feet²
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An angle measures 125°. Through what fraction of a circle does the angle turn?
If an angle measure 125° then the angle measures a fraction of 25/72 of a full circle.
What is a circle?A circle is a two-dimensional geometric shape that is defined as the set of all points that are equidistant from a single point, called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle, passing through the center, is called the diameter. The circumference of a circle is the distance around the edge or perimeter of the circle. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π (pi) is a mathematical constant that represents the ratio of the circumference to the diameter of a circle, approximately equal to 3.14159.
According to the given informationA circle has 360 degrees. To find what fraction of a circle an angle measures, we can divide the angle by 360. In this case, the angle measures 125 degrees, so the fraction of a circle it turns can be calculated as:
125/360 = 0.347222222...
To simplify this fraction, we can multiply both the numerator and denominator by 2:
125/360 = (1252)/(3602) = 250/720
We can further simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 10:
250/720 = (2510)/(7210) = 25/72
Therefore, the angle measures a fraction of 25/72 of a full circle.
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Trey's company makes solid balls out of scrap metal for various industrial uses. For one project, he must make aluminum balls that have a radius of 7.5 in. If
aluminum costs $0.12 per in, how much will the aluminum cost to make one ball?
Use 3.14 for x, and do not round your answer.
Thus, Cost of making 1 solid aluminium ball is found as $211.95.
Explain about the spherical shape:Something spherical is similar to a sphere in three dimensions in that it is round, or somewhat round. Even though they are never exactly round, oranges and apples are both spherical. Since an asteroid is frequently spheroidal—nearly round but lumpy—it has an approximately spherical form.
radius of solid aluminium balls r = 7.5 in.
Cost of of aluminium = $0.12 per cu. in.
Volume of sphere = 4/3 * π * r³
Volume of sphere = 4/3 * 3.14 * 7.5³
Volume of sphere = 1766.25 cu. in.
Cost of making 1 solid aluminium ball = 0.12 * 1766.25
Cost of making 1 solid aluminium ball = $211.95.
Thus, Cost of making 1 solid aluminium ball is found as $211.95.
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