The y-coordinate of center of mass is 1.2819 kg.
Describe Center of mass?The center of mass, also known as the center of gravity, is a point in a system of objects where the total mass of the objects is concentrated. It represents the balance point of the system and is the point at which the system would balance if it were suspended from that point. The position of the center of mass is dependent on the distribution of mass in the objects making up the system.
The centre of mass of region R is given by
[tex]$\mathrm{\bar{y}=\frac{\int_{R}\rho y_{e}dA}{Mass_{regionR}} \ \ where \ y_{e} \ center \ of \ mass \ of \ element}[/tex]
For the vertical element,
[tex]\mathrm{y_{e}=\dfrac{y}{2}}[/tex]
Find the numerator of the y coordinate of Center of Mass
[tex]$\mathrm{\frac{1}{2}\int_{R}\rho yydx=\frac{\rho}{2} \int_{\frac{-\pi}{3}}^{\frac{\pi}{3}} (3cosx)^2dx=\frac{9\rho}{2} \int_{\frac{-\pi}{3}}^{\frac{\pi}{3}} cos^2xdx=\frac{9\rho}{2} \int_{\frac{-\pi}{3}}^{\frac{\pi}{3}} (\frac{1+cos(2x)}{2})dx}[/tex]
[tex]$\mathrn{\frac{9\rho}{4} \int_{\frac{-\pi}{3}}^{\frac{\pi}{3}} (1+cos(2x))dx=\frac{9\rho}{4} [x+\frac{sin(2x)}{2}]_{\frac{-\pi}{3}}^{\frac{\pi}{3}}}[/tex]
[tex]$\mathrm{\frac{9\rho}{4} \left[\frac{\pi}{3}+\frac{sin(2(\frac{\pi}{3}))}{2}\right ]-\frac{9\rho}{4} \left[\frac{-\pi}{3}+\frac{sin(2(\frac{-\pi}{3}))}{2}\right ]}[/tex]
[tex]$\mathrn{\frac{9\rho}{4} \left[\frac{\pi}{3}+\frac{\sqrt{3}}{4}\right ]-\frac{9\rho}{4} \left[\frac{-\pi}{3}-\frac{\sqrt{3}}{4}\right ]=\frac{9\rho }{4} \left[\frac{2\pi}{3}+\frac{\sqrt{3}}{2}\right ]}[/tex]
Therefore, the y-coordinate of center of mass is
[tex]$\mathrm{\bar{y}=\frac{\dfrac{9\rho }{4}\left [\dfrac{2\pi}{3}+\dfrac{\sqrt{3}}{2}\right ]}{3\rho \sqrt{3}}=\frac{\sqrt{3}}{4}\left [\frac{2\pi}{3}+\frac{\sqrt{3}}{2}\right ]=\frac{3}{8}+\frac{\sqrt{3}\pi}{6}=1.2819}[/tex]
Thus, The y-coordinate of center of mass is 1.2819 kg
To know more about coordinates visit:
brainly.com/question/27749090
#SPJ4
The center of mass of a thin plate of constant density is determined by its area and the distribution of its mass.
How will you find the center of the mass?To find the center of mass of this plate, we first need to calculate its area. We can do this by using the formula for the area of a region bounded by the x-axis and a curve y=f(x):
A = ∫[tex]a^{b}[/tex] ydx = ∫-pi/3^pi/3 3cosx dx
A = 3∫-pi/3^pi/3cosx dx
A = 3(sin(pi/3) - sin(-pi/3))
A = 3(sin(pi/3) + sin(pi/3))
A = 6sin(pi/3)
A = 6*(1/2)
A = 3
Now that we know the area of the plate, we can calculate its center of mass. To do this, we need to use the formula for the center of mass of a region bounded by the x-axis and a curve y=f(x):
xcm = 1/A ∫[tex]a^{b}[/tex] xydx
xcm = 1/3 ∫-pi/3^pi/3 x(3cosx) dx
xcm = 1/3 ∫-pi/3^pi/3 3xcosx dx
xcm = 1/3(3(sin(pi/3) - sin(-pi/3)) - 3xsin(pi/3) + 3xsin(-pi/3))
xcm = 1/3(6sin(pi/3) - 3pi/3sin(pi/3) + 3(-pi/3)sin(-pi/3))
xcm = 1/3(6sin(pi/3) - 3pi/3sin(pi/3) + 3pi/3sin(pi/3))
xcm = 0
Therefore, the center of mass of the plate is located at (0, 0).
To know more about mass, visit
brainly.com/question/30259066
#SPJ4
The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm.
Round the probabilities to four decimal places.
It is possible with rounding for a probability to be 0.0000.
c) Find the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less.
The probability that a randomly selected Atlantic cod has a length of 53.68 cm or less is given by the equation P ( x < 53.68 ) = 0.8439
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
Let the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less be represented as P
Now , the equation will be
The observed value of x = 53.68 cm
The mean of the sample μ = 49.9 cm
The standard deviation of the sample σ = 3.74 cm
Now , z-score is calculated using the formula:
z = (x - μ)/σ
Substituting the values in the equation , we get
z = ( 53.68 - 49.9 ) / 3.74
z = 1.0107
Now ,the p value from the z table is
P ( x < 53.68 ) = 0.84392
And , the probability is P ( x < 53.68 ) = 84.392 %
Hence , the probability is 84.392 %
To learn more about z-score click :
https://brainly.com/question/25638875
#SPJ1
using separation of variable method solve dy/dx=(1-x)(1-y)
Answer:
[tex]y=1-Ae^{\frac{1}{2}x^2-x}[/tex]
Step-by-step explanation:
Given equation:
[tex]\dfrac{\text{d}y}{\text{d}x}=(1-x)(1-y)[/tex]
Separate the variables by moving all the y terms to one side of the equation and all the x terms to the other side:
[tex]\implies \dfrac{1}{(1-y)}\;\text{d}y=(1-x)\;\text{d}x[/tex]
Integrate both sides of the equation separately:
[tex]\implies \displaystyle \int \dfrac{1}{(1-y)}\;\text{d}y= \int (1-x)\;\text{d}x[/tex]
[tex]\implies -\ln |1-y|+C=x-\dfrac{1}{2}x^2+D[/tex]
[tex]\implies \ln |1-y|-C=\dfrac{1}{2}x^2-x-D[/tex]
Write the two constants as one (a = -D + C):
[tex]\implies \ln |1-y|=\dfrac{1}{2}x^2-x+a[/tex]
Take exponents of both sides:
[tex]\implies e^{\ln |1-y|}=e^{\frac{1}{2}x^2-x++a}[/tex]
[tex]\textsf{As }\; e^{\ln y}=y:[/tex]
[tex]\implies 1-y=e^{\frac{1}{2}x^2-x+a}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]
[tex]\implies 1-y=e^{\frac{1}{2}x^2-x}e^{a}[/tex]
As [tex]e^{a}[/tex] is just a constant, replace it with A:
[tex]\implies 1-y=Ae^{\frac{1}{2}x^2-x}[/tex]
Rearrange to make y the subject:
[tex]\implies y=1-Ae^{\frac{1}{2}x^2-x}[/tex]
Can someone help a brothra out
It would be A. y = -log x
I did it on desmos the graph website
A serving is 1/2 of a cookie how many servings can be made from 3/8 cookies
Answer:
3/4 servings
Step-by-step explanation:
Each serving = 1/2
There are 3/8 cookies.
How many times 1/2 "fits" into 3/8 = how many servings.
3/8 / 1/2
= 3/8 * 2
= 3/4 servings
For breakfast, Mr. Hill bought a cup of coffee for $1.39 and a bagel for $1.85. What was his total cost?
Answer:
$3.24
Step-by-step explanation:
Cost for the coffee + Cost for the bagel
$1.39 + $1.85
$3.24
find the root of 4x²-12x+9=0 graphically taken values of x from -1 to + 4
Answer:
To find the roots of 4x² - 12x + 9 = 0 graphically, we need to plot the equation on a graph and find the x-intercepts, which are the roots.
Here are the steps to graph the equation:
Plot the x-axis and y-axis on the graph
Plot the points (x, 4x² - 12x + 9) for several values of x within the range of -1 to 4.
Connect the points to form a smooth curve.
Find the x-intercepts, where the curve intersects the x-axis. These points represent the roots of the equation.
After finding the x-intercepts, we can use the x-value of each intercept to substitute back into the original equation to find the corresponding y-value. This confirms that the x-intercepts are indeed the roots of the equation.
Note: The above steps can also be done using a graphing calculator or software.
Samara wants to cut out fabric in the shape of S to sew onto back of a shirt. How much fabric will Samara use to make S?
The area of the alphabet S that it covers on a square sheet is 12.375 in²
What is a formula of area of square?Area of a Square = Side × Side. Therefore, the area of square = Side2 square units. and the perimeter of a square = 4 × side units.
Given here: The letter S drawn on a square sheet with each square with length 1.5 inch.
Now the letter S includes 2 full squares and 7 half-squares.
Thus the total Area= 2×1.5²+7×1/2 ×1.5²
A=12.375 inch²
Thus the area of the alphabet S that it covers on a square sheet is 12.375 in²
Learn more about area of a square here:
https://brainly.com/question/20693059
#SPJ1
Find the volume of the figure. Express answers in terms of pi, then round to the nearest whole number.
Answer: V=144π cm³
Step-by-step explanation:
) The cycle shop changes their payment policy. Instead of R30 per hour, they pay Luthando R100 per day and commission of R15 per bicycle that he sells. Draw a new table showing Luthando's income based on the number of bicycles he sells (start with zero bicycles).
The table showing Luthando's income based on the number of bicycles he sells:
No. of bicycle. Income
0 R100
1. R115
2. R130
3. R145
4. R160
Luthando's income based on the number of bicycles he sellsAmount Luthando receives per day= R100
Commission on each bicycle = R15
Number of bicycles sold = x
The equation:
100 + 15x
When x = 0
100 + 15x
= 100 + 15(0)
= 100 + 0
= R100
When x = 1
100 + 15x
100 + 15(1)
= 100 + 25
= R115
When x = 2
100 + 15x
= 100 + 15(2)
= 100 + 30
= R130
When x = 3
100 + 15x
= 100 + 15(3)
= 100 + 45
= R145
When x = 4
100 + 15x
= 100 + 15(4)
= 100 + 60
= R160
Therefore, Luthando earned the following income R100, R115, R130, R145, R160
Read more on commission:
https://brainly.com/question/26283663
#SPJ2
two cards are chosen at random from a deck of 52 what is the probability that they have the same value? Answe choice a1/17. b.3/17 c.5/17 d.7/17
The probability will be 1/17 i.e. A.
What exactly is probability?
Probability expresses the likelihood of an event. This mathematical branch of study is concerned with the occurrence of a random event. The value ranges from zero to one. Probability is used in mathematics to anticipate the possibility that events will occur.
Probability refers to the possibility of something happening. This fundamental idea in probability theory is also used by the probability distribution. Before determining the chance of a certain event occurring, we must first determine the total number of possibilities.
The probability that an event will occur P(E) = the number of positive outcomes divided by the total number of outcomes.
Now,
Total cards =52
No. of ways to select 2 cards=52C₂
=52*51*50!/50!*2!=51*26
Now to select two cards with same values we have no. of ways =13*6
so probability that two cards are chosen at random from a deck of 52 and they have the same value=13*6/26*51=3/51=1/17
Hence,
The probability will be 1/17.
To know more about probability visit the link
https://brainly.com/question/30034780?source=aidnull
#SPJ4
Write an equation that is perpendicular to
y
=
−
6
x
+
3
y=−6x+3 and goes through the point
(
12
,
10
)
(12,10).
The equation of the required perpendicular line is 6y = x - 48
With an example, define perpendicular line?
Lines at right angles to one another are referred to as perpendicular lines (90 degrees). A parallel line is shown as "||," which stands for the symbol. Perpendicular lines are denoted with the symbol "". Illustration of parallel lines The opposite sides of a rectangle.
equation = y =−6x+3
m₁ = -6
Let's consider the slope of the line perpendicular to the given line as m₂
m₁ * m₂ = -1
-6 * m₂ = -1
m₂ = 1/6
The equation of the line perpendicular to the given line and passing through the point (12,10)
y - y₁ = m (x - x₁ )
y - 10 = 1/6( x - 12 )
6( y - 10 ) = (x- 12 )
6y - 60 = x - 12
6y = x - 12 + 60
6y = x - 48
Thus, the equation of the required line is 6y = x - 48
Learn more about perpendicular line
brainly.com/question/18271653
#SPJ1
find a formula for the probability distribution of random variable X representing the outcome when a single die is rolled once
When a singular die is rolled once, the results are represented by the probability distribution P(X = x) = 1/6, 1,2,3,4,5,6 for random variable X.
What are examples and probability?Probability is the potential outcome of any random occurrence. This expression relates to estimating the chance that any certain event will take place. How likely are we to get a head, for example, if we flip the coin into the air? The solution to this question is based on the potential number of occurrences.
When one die is rolled, there are only six possible outcomes: 1, 2, 3, 4, and 5. Due to the equal likelihood of each scenario, its sp risk is 1/6. The following is true for the required posterior distribution of the random variable x:
P(X = x) = 1/6, 1,2,3,4,5,6
To know more about Probability visit:
https://brainly.com/question/24756209
#SPJ1
A sine function has the following key features:
Period =12
Amplitude=4
Midline:y=1
y-intercept: (0, 1)
The function is not a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the grapn closest to the first point.
Please show me on a graph how to do this.
Compared with the parent function y= sin(x), the graph of 4 sin[ (π/6)x ] + 1 will be stretched vertically by a scale factor of 4, translated 1 unit up, and with a shorter distance between the peaks.
What is a function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between varied quantities and other variables.
Here, we have
1) The parent function is sin(x)
2) sin(x) has:
Middle line: y = 0
Amplitude: 1 because the function goes from 1 unit up to 1 unit down the middle line.
Period: 2π because the sine function repeats every 2π unit.
y-intercept: (0,0) because sin(0) = 0.
Now look at how these changes in the function reflect on the parameters:
A sin (ωx + B) + C:
That function will have:
amplitude A, because the amplitude is scaled by that factor
Period: 2π / ω, because the function is compressed horizontally by that factor.
It will be translated B units to the left
It will be translated C units up.
And you need
Period = 12 => 2π / ω = 12 => ω = π/6
A = 4
Translate the midline from y = 0 to y = 1 => shift the function 1 unit up => C = 1.
Translate the y-intercept from y = 0 to y = 1, which is already accomplished when you translate the function 1 unit up.
So, this is the function searched
y = A sin (ωx + B) + C = 4 sin[ (π/6)x ] + 1
Now you can check the amplitude, the period, the middle line, and the y-intercept of that y = 4 sin[ (π/6)x ] + 1.
Hence, compared with the parent function y= sin(x), the graph of 4 sin[ (π/6)x ] + 1 will be stretched vertically by a scale factor of 4, translated 1 unit up, and with a shorter distance between the peaks.
To learn more about the function from the given link
https://brainly.com/question/10439235
#SPJ1
Help please!
Slope of one of the dotted lines:
Slope of the line of reflection:
The slope of one of the dotted lines is equal to 1.
The slope of the line of reflection is equal to -1.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, the slope of one of the dotted lines include the following;
Slope, m = (4 - 1)/(-1 - (-4))
Slope, m = 3/(-1 + 4)
Slope, m = 3/3.
Slope, m = 1.
For the line of reflection, the slope is given by:
Slope, m = (2 - 4)/(1 - (-1))
Slope, m = -2/(1 + 1)
Slope, m = -2/2.
Slope, m = -1.
Read more on slope here: brainly.com/question/3493733
#SPJ1
Write the proposition "I come to class whenever there is going to be a quiz" in the form "if p then q" then state its converse, contrapositive, and inverse.
The proposition "I come to class whenever there is going to be a quiz" can be written as "If there is going to be a quiz, then I come to class."
The converse of this proposition is "If I come to class, then there is going to be a quiz."
The contrapositive of this proposition is "If there is not going to be a quiz, then I do not come to class."
The inverse of this proposition is "If I do not come to class, then there is not going to be a quiz."
What is proposition?A mathematical proposition is a statement such as "3 is bigger than 4," "an infinite set exists," or "7 is prime." A proposition that is presumed to be true is referred to as an axiom. A proposition is an either true or incorrect statement. A mathematical assertion will be referred to as a theorem throughout our course. A theorem is a significant result. A lemma is a claim that serves primarily to establish a bigger theorem.
Here,
The proposition "I come to class whenever there is going to be a quiz" can be written as "If there is going to be a quiz, then I come to class."
The converse of this proposition is "If I come to class, then there is going to be a quiz."
The contrapositive of this proposition is "If there is not going to be a quiz, then I do not come to class."
The inverse of this proposition is "If I do not come to class, then there is not going to be a quiz."
To know more about proposition,
https://brainly.com/question/13011669
#SPJ4
Can someone tell me how i find this problem?
Answer:
9.80
Step-by-step explanation:
x²=14²-10² = 196-100 = 96
x=√96 = √(16*6 ) = 4*√6 =4*2.45=9.80
I need help with this problem
Using Trigonometric identities, On the interval 0 2, we wish to locate all solutions to the equation 2sin() = 3. The sole answer is = 1.05.
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
what is the solutions of 2sin(θ)=−√3 on the interval 0≤θ 2π?Determining the answer to the following equation is therefore important: 2sin(θ) = √3
To begin, split both sides by two to obtain:
sin(θ) = (√3)/2
Now consider the behavior of the inverse sine function:
Asin(x) = sin(x) and Asin(x) = x
We can therefore apply this to both sides to obtain:
Asin(sin(s)) = Asin(sin(s))/3)
θ = Asin((√3)/2) = 1.05
The single solution in the interval is: because we know that the sine function's period is 2 and that there is only one solution on the range between 0 and 2:
θ = 1.05
sin(3θ) = √3/2
θ = π/9 + 2kπ/3, 2π/9 + 2kπ/3
We obtain = /9, 2/9 if k = 0.
We obtain = 7/9 and 8/9 if k = 1.
We obtain = 13/9 and 14/9 if k = 2.
Other values of k produce values of beyond the range [0, 2].
To learn more about trigonometric identities from given link
https://brainly.com/question/24496175
#SPJ1
Show that if f is a function from S to T, where S and T are finite sets with |S| > |T|, then there are elements s1 and s2 in S such that f(s1) = f(s2), or in other words, f is not one-to-one.
Hence proved f is not one-to-one.
What do you mean by function?A function is a mathematical concept that assigns a unique output value for each input value.
In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.
Functions play a central role in mathematics and are used to model real-world phenomena and to study the relationships between variables. They are also used in computer programming to perform specific tasks, such as converting temperatures from Celsius to Fahrenheit or calculating the square root of a number.
Suppose that f is a function from S to T, where |S| > |T|. This means that there are more elements in S than there are in T.
Since f maps elements of S to elements of T, we can think of f as pairing elements of S with elements of T. However, since |S| > |T|, there will be at least two elements of S that are paired with the same element of T, and these two elements are s1 and s2.
Therefore, f is not one-to-one, as f(s1) = f(s2), meaning that two different elements of S are mapped to the same element of T.
This shows that if f is a function from S to T, where |S| > |T|, then there must exist elements s1 and s2 in S such that f(s1) = f(s2), and hence f is not one-to-one.
To know more about function visit:
https://brainly.com/question/29796477
#SPJ4
A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of
gold in each bracelet is 4 grams and the amount of gold in each necklace is 20 grams.
The jeweler made a total of 14 bracelets and necklaces using 120 grams of gold.
Graphically solve a system of equations in order to determine the number of bracelets
made, «, and the number of necklaces made, y. I need the graph
Answer:
10 bracelets4 necklacesStep-by-step explanation:
You want the number of bracelets (x) and the number of necklaces (y) made from 120 grams of gold when a total of 14 were made with 4 grams in each bracelet and 20 grams in each necklace.
EquationsThe equations describing the numbers can be written as ...
4x +20y = 120 . . . . . . amount of gold used
x + y = 14 . . . . . . . . . number of items made
GraphThe first equation can be graphed by plotting its x-intercept at (30, 0) and its y-intercept at (0, 6). The line between these points is the graph.
The graph of the second equation is the line between the two intercepts at 14: (14, 0) for the x-intercept, and (0, 14) for the y-intercept.
The lines cross at (x, y) = (10, 4).
The number of bracelets made was 10; the number of necklaces, 4.
O
x (x² - x - 6) = 0
Answer:
The equation has 3 solutions x(1) = -2 x(2) = 0 x(3) = 3
Step-by-step explanation:
1.When the product of the factor equals 0, atleast one of the factors is 0
x=0
x^2 - x - 6 = 0
2.solve the equation for x
x = 0
x = -2
x = 3
hope this helped :D
Keshawn is selling lollipops and candy bars for the PHS football team fundraiser this year. The lollipops are $2, and the candy bars are $4. He is hoping to raise $180 on his own. Define the variables. Write an Inequality to represent the situation.
The variables are the number of candy bars and lollipops and their prices. The possible equality is 2x + 4y ≥ 180.
What are the variables?In mathematics, the variables are factors that might change. Due to this, in maths variables are often expressed using letters as their exact value is not known. Then the variables are:
Number of candy bars = xNumber of lollipops = yWhat inequality represents this situation?Based on the previous information, the correct inequality would be:
2x + 4y ≥ 180
Learn more about inequalities in https://brainly.com/question/30231190
#SPJ1
8. The equation of a straight line is 3x - 2y = 6 i. Find whether the point (0, 3) lies on it or not. ii .Find the equation of the straight line having the same slope and passing through the point (0, 3).
Answer:
3x-2y=-6
Step-by-step explanation:
I recommend using desmos graphing calculator to find the answer
The table shows input and output values of a function given a rule. Which function represents the rule?
The table shows input and output values of a function given a rule. Which function represents the rule?
Input: x, a number; Output: y, 3 less than 2 times x
a. y = 2x - 3
b. y = -2x + 3
c. y = -3x - 2
d. y = 3x + 2
Answer:
YStep-by-step explanation:
Solve the following system using the elimination method. Enter your answer as an ordered form (x,y) if there is one unique solution. Enter all is there are infinite solutions and enter none if there are none.
The elimination method involves adding or subtracting the two equations to cancel out one of the variables and obtain a single equation in one variable. We can then solve for that variable, and then use the original equations to find the other variable.
What does "system of equations" mean?
simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
Here's the work for the given system of equations:
7x - 2y = 35
4x + 5y = -23
Multiplying the second equation by 2:
8x + 10y = -46
Adding the two equations to eliminate x:
15y = -11
Dividing both sides by 15 to solve for y:
y = -11/15
Using the first equation to find x:
7x - 2(-11/15) = 35
Expanding and solving for x:
7x + 22/15 = 35
Subtracting 22/15 from both sides:
7x = 35 - 22/15
Simplifying the right side:
7x = 35 - 22/15
7x = 77/15
Dividing both sides by 7 to solve for x:
x = 11/15
The solution to the system is (x,y) = (11/15, -11/15).
Learn more about system of equations
https://brainly.com/question/25976025
#SPJ1
Mrs. Farley made 24 meat patties out of 72 ounces of hamburgers. How many ounces of hamburgers are in each meat patty?
Answer: Each meat patty would have 72 ounces of hamburger divided by 24 patties, which is equal to 3 ounces per patty.
Step-by-step explanation:
Find x rounded to one decimal place.
x =
Answer:
x≅101.5
Step-by-step explanation:
(88×cot60° + x)tan 30°=88
(88/√3 + x)1/√3 = 88
88/3 + x/√3= 88
x/√3=176/3
x= 176×1.73/3
x= 101.49
x≅101.5
the value of x will be 101.61 units.
What is the right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
Given two right-angle triangles with the same height of 88 units
Let the adjacent side of a triangle with a leg angle of 60 be "h"
From the general formula of a tangent:
Tan A = opposite side/ adjacent side
For the triangle with a leg angle of 60
tan 60 = 88/h
√3 = 88/h
h = 88/√3
For the triangle with a leg angle of 30
tan 30 = 88/(x +h)
1/ √3 = 88(x + h)
x +h = 88 * √3
x = 88*√3 - 88/√3
x = 101.613
therefore, the value of x will be 101.61 units.
Learn more about right-angle triangles here:
https://brainly.com/question/3770177
#SPJ1
True or False?. Pie graphs are best with progression of amounts over time, whereas line graphs are better in showing parts of a whole or percentages.
Answer:
false
Step-by-step explanation:
write an equation for a line perpendicular to y=3x+2 and passing through the point (-9,6)
y=
Answer:
y = - [tex]\frac{1}{3}[/tex] x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 2 ← is in slope- intercept form
with slope m = 3
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex] , then
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (- 9, 6 ) into the partial equation
6 = - [tex]\frac{1}{3}[/tex] (- 9) + c = 3 + c ( subtract 3 from both sides )
3 = c
y = - [tex]\frac{1}{3}[/tex] x + 3 ← equation of perpendicular line
find the vaule of the varibles if the answer is not an integer express it in simplest radical form
Therefore, in this sort of triangle with angles 30-60-90, the value of y is 10√3 and the value of x is 10.
what is variables ?In algebra, a logo (typically a letter) used to represent an undetermined numerical score in a calculation or algebraic expressions. Simply put, a variable is an amount that may have been changed and is not fixed. Categorical and numeric elements are the two main types of variables. Then, discrete and continuous subcategories are made for each category for the categorical and numerical elements, respectively. An overview of various types is given in this section. a metric that has a wide range of values. Someone that can change; a variable's sign; an element of a laboratory test that could vary.
given
As a result, this is a "special triangle." According to the 30-60-90 triangle, if the short leg is x, the hypotenuse will be 2x, and the long leg will be x√3.
Since we have the short leg, we can divide it by 2 to determine the hypotenuse, or y in this case:
20 /2 = 10
Next, divide the short leg by 3 to determine the long leg, or x in our case:
10 × √3 = 10√3
Therefore, in this sort of triangle with angles 30-60-90, the value of y is 10√3 and the value of x is 10.
To know more about variable visit :-
https://brainly.com/question/2466865
#SPJ1
Microeconomics
A firm producing leather shoes has a production function given below: = 2√ , in the short run, the firm's amount of capital equipment is fixed at = 100. The interest rate for K is $1 and the wage rate for L is$4. Based on this:
A. Calculate the firm’s short-run total cost curve and calculate the short-run average cost curve function
B. What is the firm’s short-run marginal cost function? Determine the Short-run Total cost (), short-run Average cost (), and short-run marginal cost () at twenty-five (25) and two hundred (200) levels of output.
C. Draw a graph for (, and )
D. Where does the curve intersect the curve? Explain why the curve always intersects the SAC curve at its lowest or minimum points
A. The firm's short-run total cost (TC) is given by TC = rK + wL, where r is the interest rate for capital and w is the wage rate for labor.
B. The short-run total cost at 25 units of output: TC = $100 + 4((25/2)^2) = $100 + 100 = $200
The short-run total cost at 200 units of output: TC = $100 + 4((200/2)^2) = $100 + 1600 = $1700
Please let's go ahead with the explanation to fully understand the solution,
How the solution was obtainedA. To calculate the firm's short-run total cost curve and average cost curve function, we need to know the amount of labor (L) the firm uses at each level of output (Q). We can use the production function to find the optimal combination of L and Q given the fixed amount of capital (K = 100).
The firm's short-run total cost (TC) is given by TC = rK + wL, where r is the interest rate for capital and w is the wage rate for labor.
The short-run average cost (SAC) can be calculated by dividing the short-run total cost by the level of output (Q): SAC = TC/Q
B. The short-run marginal cost (SMC) is the change in the total cost per unit change in the level of output. The SMC can be calculated as the derivative of the short-run total cost function with respect to Q.
At a level of output of 25, we have: TC = $100 + 4L, and Q = 2√L. So we can substitute L = (Q/2)^2 into the short-run total cost equation to find the short-run total cost at 25 units of output: TC = $100 + 4((25/2)^2) = $100 + 100 = $200
At a level of output of 200, we have: TC = $100 + 4L, and Q = 2√L. So we can substitute L = (Q/2)^2 into the short-run total cost equation to find the short-run total cost at 200 units of output: TC = $100 + 4((200/2)^2) = $100 + 1600 = $1700
The short-run average cost at 25 units of output is SAC = TC/Q = $200/25 = $8, and the short-run average cost at 200 units of output is SAC = TC/Q = $1700/200 = $8.5
The short-run marginal cost at 25 units of output is the derivative of the short-run total cost with respect to Q evaluated at 25 units of output. Since the short-run total cost is linear in Q, the short-run marginal cost is constant and equal to the wage rate, which is $4. The short-run marginal cost at 200 units of output is also constant and equal to $4.
C. A graph of the short-run total cost, short-run average cost, and short-run marginal cost functions can be plotted on the same graph, with Q on the x-axis and the corresponding cost on the y-axis.
D. The short-run average cost curve intersects the short-run marginal cost curve at the minimum point of the short-run average cost curve. This is because the short-run average cost is the derivative of the short-run total cost with respect to Q, and the short-run marginal cost is the derivative of the short-run total cost with respect to Q. At the minimum point of the short-run average cost curve, the first derivative (the short-run marginal cost) is equal to zero, and the second derivative (the short-run average cost) is negative.
Learn more on cost calculations here https://brainly.com/question/25109150
#SPJ1