Problem 2. Find the center of mass of a uniform mass distribution on the 2-dimensional region in the Cartesian plane bounded by the curves y = = √1-x², y = 0, x=0, x= 1.
Answers
By considering infinitesimally small areas and their corresponding masses, we can calculate the x-coordinate and y-coordinate of the center of mass separately. The x-coordinate of the center of mass is found to be 2/π, and the y-coordinate is 4/(3π).
To determine the x-coordinate of the center of mass, we need to integrate the product of the x-coordinate and the infinitesimal mass element over the given region, divided by the total mass. Since the mass distribution is uniform, the infinitesimal mass element can be expressed as dm = k * dA, where k is the constant mass density and dA is the infinitesimal area element.
The region of interest is bounded by the curves y = √(1-x²), y = 0, x = 0, and x = 1. By solving the equation y = √(1-x²) for x, we find that x = √(1-y²). Thus, the limits of integration for y are from 0 to 1, and for x, it ranges from 0 to √(1-y²).
To find the total mass, we can evaluate the integral ∬ k * dA over the given region. Since the mass distribution is uniform, k can be factored out of the integral, and we are left with ∬ dA, which represents the area of the region. Using a change of variables, we can integrate over y first and then x. The resulting integral evaluates to π/4, representing the total mass of the region.
Next, we calculate the x-coordinate of the center of mass using the formula x_c = (1/M) * ∬ x * dm, where M is the total mass. Substituting dm = k * dA and integrating over the given region, we find that the x-coordinate of the center of mass is (1/π) * ∬ x * dA. Using a change of variables, we integrate over y first and then x. The resulting integral evaluates to 2/π, indicating that the center of mass lies at x = 2/π.
Similarly, we can find the y-coordinate of the center of mass using the formula y_c = (1/M) * ∬ y * dm. Substituting dm = k * dA and integrating over the given region, we find that the y-coordinate of the center of mass is (1/π) * ∬ y * dA. Again, using a change of variables, we integrate over y first and then x. The resulting integral evaluates to 4/(3π), indicating that the center of mass lies at y = 4/(3π).
In conclusion, the center of mass of the uniform mass distribution on the 2-dimensional region bounded by the curves y = √(1-x²), y = 0, x = 0, and x = 1 is located at (2/π, 4/(3π)).
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Related Questions
from the top of mt washington, which is 6288 feet above sea level, how far is it to the horizon? assume that the earth has a 3960-mile radius (one mile is 5280 feet), and give your answer to the nearest mile.
Answers
The distance to the horizon from the top of Mt. Washington is approximately 97 miles.
To calculate the distance to the horizon from a certain height above the Earth's surface, you can use the Pythagorean theorem.
In this case, the height of Mt. Washington (6288 feet) above sea level is the height of a right triangle, and the radius of the Earth (3960 miles x 5280 feet/mile) is the base of the right triangle.
The distance to the horizon is the hypotenuse of this right triangle.
Let's set up the Pythagorean theorem:
Distance to horizon = √(radius² - height²)
Where:
Radius = 3960 miles
Height = 1.190909 miles [6288 feet = 1.190909 miles]
Plugging in the values:
Distance to horizon = √((3960 + 1.190909)² - 3960²)
Calculating this:
Distance to horizon ≈ 97 miles.
Hence, the distance to the horizon from the top of Mt. Washington is approximately 97 miles.
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Find the area of hexagon DEFGHI.
Answers
Step-by-step explanation:
Break it up into two trapezoids as shown
area = trap1 + trap2
= 2 * (7+3) / 2 + 3 * ( 7 + 3) / 2 = 10 + 15 = 25 units^2
can you apply the properties of rational exponents to an example?
Answers
We can simplify \((16x^4)^(-1/2) to 1/(4x^2)\) using the properties of rational exponents.
Certainly! Here's an example:
Simplify the expression: \((16x^4)^(-1/2)\)
We can apply the property of rational exponents which states that \((a^m)^n = a^(m*n)\). Using this property, we get:
\((16x^4)^(-1/2) = 16^(-1/2) * (x^4)^(-1/2)\)
Next, we can simplify \(16^(-1/2)\) using the rule that \(a^(-n) = 1/a^n\):
\(16^(-1/2) = 1/16^(1/2) = 1/4\)
Similarly, we can simplify \((x^4)^(-1/2)\) using the rule that \((a^m)^n = a^(m*n)\):
\((x^4)^(-1/2) = x^(4*(-1/2)) = x^(-2)\)
Substituting these simplifications back into the original expression, we get:
\((16x^4)^(-1/2) = 1/4 * x^(-2) = 1/(4x^2)\)
Therefore, the simplified expression is \(1/(4x^2).\)
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An endurance athlete jogs at a rate of 8 miles per hour. How many minutes does it take for the athlete to jog 2.4 miles?
Answers
Answer:
0.3
Step-by-step explanation:
Brandon and Chloe ride their bikes for 4 hours along a flat, straight road. Brandon's velocity, in miles per hour, at time t hours is given by a differentiable function B for 0≤t≤4. Values of B(t) for selected times t are given in the table above. Chloe's velocity, in miles per hour, at time t hours is given by the piecewise function C defined by C(t)={
te ^(4−t^2)
12−3t−t^2
for 0≤t≤2
for 2
(a) How many miles did Chloe travel from time t=0 to time t=2 ? (b) At time t=3, is Chloe's speed increasing or decreasing? Give a reason for your answer. (c) Is there a time t, for 0≤t≤4, at which Brandon's acceleration is equal to 2.5 miles per hour per hour? Justify your answer. (d) Is there a time t, for 0≤t≤2, at which Brandon's velocity is equal to Chloe's velocity? Justify your answer.
Answers
(a) Chloe traveled 6 miles from time t=0 to time t=2. (b) Chloe's speed is decreasing at time t=3. (c) There is a time t = 0.25, for 0≤t≤4, at which Brandon's acceleration is equal to 2.5 miles per hour per hour. (d) It is not possible to determine if there is a time t, for 0≤t≤2, at which Brandon's velocity is equal to Chloe's velocity without additional information or calculations.
(a) To find the distance traveled by Chloe from time t=0 to time t=2, we need to calculate the definite integral of her velocity function C(t) over the interval [0, 2]. Thus, we have:
∫0^2 C(t) dt = ∫0^2 te^(4−t^2) dt + ∫0^2 (12−3t−t^2) dt
Evaluating the integrals, we get:
∫0^2 C(t) dt = [(−1/2) e^(4−t^2)] 0^2 + [(6t−(1/2)t^2)] 0^2 = 6
Therefore, Chloe traveled 6 miles from time t=0 to time t=2.
(b) To determine whether Chloe's speed is increasing or decreasing at time t=3, we need to look at the sign of her acceleration function C'(t) at t=3. Taking the derivative of C(t) with respect to t, we get:
C'(t) = e^(4−t^2) − 6 − 2t
Evaluating C'(3), we get:
C'(3) = e^(4−3^2) − 6 − 2(3) = e−5 < 0
Since C'(3) is negative, Chloe's speed is decreasing at time t=3.
(c) To find out if there is a time t, for 0≤t≤4, at which Brandon's acceleration is equal to 2.5 miles per hour per hour, we need to find the derivative of his velocity function B(t) and set it equal to 2.5. Thus, we have:
B'(t) = d/dt B(t)
At time t, for 0≤t≤4, B'(t) is the instantaneous rate of change of Brandon's velocity, or his acceleration. Setting B'(t) = 2.5, we get:
d/dt B(t) = 2.5
Differentiating B(t), we get:
B'(t) = d/dt B(t) = 2.6 − 0.4t
Setting this equal to 2.5, we get:
2.6 − 0.4t = 2.5
Solving for t, we get:
t = 0.25
Therefore, there is a time t = 0.25, for 0≤t≤4, at which Brandon's acceleration is equal to 2.5 miles per hour per hour.
(d) To find out if there is a time t, for 0≤t≤2, at which Brandon's velocity is equal to Chloe's velocity, we need to solve the equation B(t) = C(t) for t. However, since B(t) and C(t) are given as different functions, we cannot solve this equation analytically. Therefore, we can only approximate the solution by graphing the two functions and looking for their intersection. From the given table, we know that B(0) = 20 and B(4) = 10, so Brandon's velocity decreases over the time interval [0, 4]. Chloe's velocity function C(t) is a bit more complicated, but we can still graph it. Doing so, we see that her velocity starts at 9 mph and increases to about 10.5 mph over the interval [0, 2], then decreases back to 9 mph over the interval [2, 4].
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4x+10 + 6x+13 + 2= 180
Answers
Answer:
x=1.45
Step-by-step explanation:
4x+10+6x+13+2=180
10x+25=180
-25 -25
10x=145
10x/10=145/10
x=14.5
Ricardo is talking to his parents about saving for retirement. Which of the following is NOT a good way to save for retirement, and why?
Answers
Answer:
There is nothing to refer to
Step-by-step explanation:
The endpoints of GH are G(3,3) and H(-7,7).
Find the coordinates of the midpoint M.
Answers
Step-by-step explanation:
Hey there!!
You can simply use midpoint formulae to find midpoint of the coordinates.
Here, Given that;
G(3,3) and H(-7,7).
Using midpoint formulae,
\(midpoint \: of \: gh = (\frac{x1 + x2}{2} ,\frac{y1 + y2}{2} \))
\(midpoint \: of \: gh = (\frac{3 - 7}{2} ,\frac{3 + 7}{2} \))
After simplifying it we get,
= (-2,5).
Therefore, midpoint of GH is M(-2,5).
Hope it helps....
Nevaeh read 49 1/2 pages in 2 1/4 hours. If she continues reading at the same rate, how many pages will she read in an hour?
Answers
Nevaeh reads 22 pages in a hour.
Step-by-step explanation:
49.5/9 is 5.5x4=22
PLEASE HELP AND SHOW WORK
write an equation in slope intercept form that passes through the points (-4,6) and (-5,-2)
Answers
The required equation in slope intercept form is given by y = 8x + 36.
What is the intercept in the equation?In the equation intercept is the value of the linear function where either of the variables is zero.
Here,
Points are (-4,6) and (-5,-2)
The slope of the line is given as,
M = (y₂ - y₁) / (x₂ - x₁)
m = -2 - 6 / -5 + 4
m = -8/-1
m = 8
Now,
The Equaiton of the line is given as,
y - y₁ = m (x - x₁)
y - 6 = 8 (x + 4)
y = 8x + 32 + 6
y = 8x + 36
Thus, the required equation in slope intercept form is given by y = 8x + 36.
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. If tanx=3.5 then tan(−x)=
2. If sinx=0.7 then sin(−x)= 0[infinity]
3. If cosx=0.2 then cos(−x)=
4. If tanx=0.5 then tan(π+x)=
Answers
The equation for the function g(x) is g(x) = -f(x + 6) + 2, which simplifies to g(x) = -(x + 6)^3 + 2.
The equation for the function g(x) can be derived based on the given transformations: a shift of two units down, reflection in both the x-axis and y-axis, and the shape described as f(x) = sqrt(x).
For the given function f(x) = sqrt(x), let's apply the transformations step by step:
1. Shift two units down: To shift the graph of f(x) down by two units, we subtract 2 from the function: f(x) - 2.
2. Reflect in the x-axis: To reflect the graph in the x-axis, we take the negative of the function obtained in the previous step: -(f(x) - 2) = -f(x) + 2.
3. Reflect in the y-axis: To reflect the graph obtained so far in the y-axis, we take the negative of the entire expression: -(-f(x) + 2) = f(x) - 2.
Therefore, the equation for the function g(x) is g(x) = f(x) - 2, which simplifies to g(x) = sqrt(x) - 2.
Now, let's move on to the second part of the question:
For the given function f(x) = x^3, we need to apply the transformations of shifting six units to the left, two units down, and reflecting in the y-axis to obtain the equation for g(x).
1. Shift six units to the left: To shift the graph of f(x) six units to the left, we replace x with (x + 6) in the function: f(x + 6).
2. Shift two units down: To shift the graph obtained in the previous step down by two units, we subtract 2 from the function: f(x + 6) - 2.
3. Reflect in the y-axis: To reflect the graph obtained so far in the y-axis, we take the negative of the entire expression: -(f(x + 6) - 2) = -f(x + 6) + 2.
Therefore, the equation for the function g(x) is g(x) = -f(x + 6) + 2, which simplifies to g(x) = -(x + 6)^3 + 2.
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3/24 simplified fraction
Answers
Answer:
1/8
Step-by-step explanation:
1/8 is equivalent to 3/24 because you can divide both 24 and 3 by 3 which will make the equivalent fraction 1/8. please mark me as brainliest
The simplified form of the given fraction is 1/8.
The given fraction is 3/24.
Here, numerator of the fraction is 3 and the denominator of the fraction is 24.
To write fraction is simplified form, divide both numerator and denominator by same number.
Here, divide both numerator and denominator by 3, we get
(3÷3)/(24÷3)
= 1/8
Therefore, the simplified form of the given fraction is 1/8.
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the following stem-and-leaf plot shows scores on a statistics final exam. find the number of outliers. 2 00 3 468 4 357 5 01677 6 235 7 6899 8 233569999 9 01268 10 0
Answers
In the given stem-and-leaf plot, we can conclude that there are at least 5 outliers
The number of outliers in the given stem-and-leaf plot can be determined by identifying values that are significantly higher or lower than the majority of the data.
To find the number of outliers in the stem-and-leaf plot, we need to analyze the data distribution and identify values that deviate significantly from the rest of the scores.
Looking at the stem-and-leaf plot, we observe that the majority of the scores are concentrated between 20 and 90. The numbers 2, 3, 4, 5, 6, 7, 8, 9, and 10 represent the tens digit of the scores, while the leaves represent the ones digit.
Upon examining the plot, we notice that there are a few values that stand out from the rest. These values are 00, 01677, 6899, 233569999, and 01268. Outliers are typically defined as values that fall outside the "typical" range of the data, and these values appear to deviate significantly from the majority of the scores.
To determine the exact number of outliers, we need to apply specific criteria. One common method is to use the 1.5 × IQR (interquartile range) rule. The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of the data. Any values below Q1 - 1.5 × IQR or above Q3 + 1.5 × IQR are considered outliers.
In this case, we don't have the exact raw data to calculate the quartiles and IQR. However, based on visual inspection of the stem-and-leaf plot, we can still identify the values mentioned earlier as outliers due to their significant deviation from the majority of the scores.
Therefore, in the given stem-and-leaf plot, we can conclude that there are at least 5 outliers
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Does anyone know what this is
Answers
Answer:
D. -3 + 6
Step-by-step explanation:
-3 - (-6) = 3 and -3 + 6 also equals 3
how much more can you simplify this
Answers
At 11:00 A.M. the temperature was 37 °F. At 11:00 P.M. the temperature was -6 °F.
What was the change in temperature between 11:00 A.M. and 11:00 P.M.?
Answers
Answer:
The temperature decreased by 43 degrees
-43
Step-by-step explanation:
Difference means subtraction
37 - (-6) = -43
I hope this helps!
Which Statment is True?
a. The data distribution is both symmetric and skewed
b. the data distribution is skewed to the left
c.the data distribution is skewed to the right
d. the data distribution is symmetric
Answers
Given Correct Statement is :- The data distribution is skewed to the right, which means that the right tail of the distribution is longer than the left tail. c. The data distribution is skewed to the right.
It is not possible for a data distribution to be both symmetric and skewed at the same time, as these are mutually exclusive characteristics.
A symmetric distribution is one in which the data is evenly distributed around the mean, with the left and right sides of the distribution being mirror images of each other.
A skewed distribution is one in which the data is not evenly distributed around the mean, with one tail of the distribution being longer than the other.
Based on the given options, only one statement can be true.
Option (c) states that the data distribution is skewed to the right, which means that the right tail of the distribution is longer than the left tail. Therefore, the correct statement is:
c. The data distribution is skewed to the right.
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The equation of circle D is (x + 2)2 + y² = 32.
Select all the points that lie on circle D.
□ (-6,-4)
□ (-2,16)
□ (-4,6)
□ (0,14)
□ (2,4)
Answers
The equation of circle D is (x + 2)2 + y² = 32 then the points (-6,-4) and (-4,6) lie on circle D
The equation of a circle with center (h,k) and radius r is (x - h)² + (y - k)² = r².
This is called the standard form of the equation of a circle.
In the given equation, (x + 2)² + y² = 32, we can see that the center of the circle is (-2, 0) and the radius is √32 = 4√2.
To determine which points lie on the circle, we substitute the x and y coordinates of each point into the equation and check if the equation is true.
If it is true, then the point lies on the circle.
Let us check if (-6, -4) lies on the circle, we substitute x = -6 and y = -4 into the equation:
(-6 + 2)² + (-4)² = 32
(-4)² + (-4)² = 32
16 + 16 = 32
32 = 32
Since the equation is true, (-6, -4) lies on the circle.
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write the fraction
28
32
in simplest form.
Answers
Answer: 7/8 or 0.875
Step-by-step explanation:
28
32
Reduce the fraction
28/32
to lowest terms by extracting and canceling out 4.
7/8
the simplest form of given fraction 28/32 is 7/8.
Given that:
Fraction: 28/32
To write the fraction 28/32 in its simplest form, to find the greatest common divisor (GCD) of the numerator (28) and the denominator (32) and then divide both the numerator and denominator by that GCD.
Step 1: Find the GCD of 28 and 32.
The factors of 28 are 1, 2, 4, 7, 14, and 28.
The factors of 32 are 1, 2, 4, 8, 16, and 32.
The largest common factor between 28 and 32 is 4.
Step 2: Divide both the numerator and denominator by the GCD (4).
28 ÷ 4 = 7
32 ÷ 4 = 8
Hence, the simplified fraction is 7/8.
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Two more than three times a number is 18.
Answers
Let the number be x
ATQ
\(\\ \sf\longmapsto 3x+2=18\)
Take 2 to right side\(\\ \sf\longmapsto 3x=18-2\)
\(\\ \sf\longmapsto 3x=16\)
\(\\ \sf\longmapsto x=\dfrac{16}{3}\)
\(\\ \sf\longmapsto x=5.3\)
\(\\ \sf\longmapsto x\approx 5\)
Help please I don’t understand this and help me with any question you want thank you!:((
Answers
Answer:
(2/2)*(2/2)=1
(2/2)+(2/2)=2
(2*2)-(2/2)=3
2*2*2/2=4, or 2+2+2-2=4
I hope this helps!
If $15,000 is invested at a rate of 4.75% compounded continuously for 25 years, what is the final value of the investment? Round the answer to the nearest penny. $49,183.11 $48,790.55 $34,183.11 $32,812.5
Answers
The final value of the investment at a rate of 4.75% compounded continuously for 25 years is $49,183.11.
What is the accrued amount of the investment?The formula accrued amount compounded continuously is expressed as;
A = P × e^(rt)
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $15,000 Compounded contiouslyTime t = 25 yearsInterest rate r = 4.75Accrued amount A = ?Plug the given values into the above formula and solve for A.
A = P × e^(rt)
A = $15,000 × e^( 4.75% × 25 )
A = $15,000 × e^( 4.75/100 × 25 )
A = $15,000 × e^( 0.0475 × 25 )
A = $15,000 × (2.71828)^1.1875
A = $49,183.11
Therefore, the accrued amount of the investment is $49,183.11.
Option A is the correct answer.
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Answer:
$49,183.11
Step-by-step explanation:
I got it right.
identify the number of real roots for given function
Answers
The number of real roots for the functions are
Graph 1 = 4Graph 2 = 1Graph 3 = 2Graph 4 = 0Graph 5 = 1Graph 6 = 1How to identify the number of real roots for the functionsFrom the question, we have the following parameters that can be used in our computation:
The graphs
The number of real roots of a function is the number of times the function intersects with the x-axis
This in other words means the zeros of the function
Using the above as a guide, we have the roots of the graphs to be
Graph 1 = 4
Graph 2 = 1
Graph 3 = 2
Graph 4 = 0
Graph 5 = 1
Graph 6 = 1
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2367800 divide by 769231 in long division method
Answers
Answer: 3.078139077
Step-by-step explanation:
Use the 1st digit 2 from dividend 2367800.
Since 2 is less than 769231, use the next digit 3 from dividend 2367800 and add 0 to the quotient.
Use the 2nd digit 3 from dividend 2367800.
Since 23 is less than 769231, use the next digit 6 from dividend 2367800 and add 0 to the quotient.
Use the 3rd digit 6 from dividend 2367800
Since 236 is less than 769231, use the next digit 7 from dividend 2367800 and add 0 to the quotient.
Use the 4th digit 7 from dividend 2367800.
Since 2367 is less than 769231, use the next digit 8 from dividend 2367800 and add 0 to the quotient.
Use the 5th digit 8 from dividend 2367800.
Since 23678 is less than 769231, use the next digit 0 from dividend 2367800 and add 0 to the quotient.
Use the 6th digit 0 from dividend 2367800.
Since 236780 is less than 769231, use the next digit 0 from dividend 2367800 and add 0 to the quotient.
Use the 7th digit 0 from dividend 2367800.
Find closest multiple of 769231 to 2367800. We see that 3×769231=2307693 is the nearest. Now subtract 2307693 from 2367800 to get reminder 60107.
Add 3 to quotient.
Quotient: 3
Reminder: 60107
It's not as difficult as it looks.
✨
A 3 column table with 4 rows. The first column is labeled Satellite with entries, A, B, C, D. The second column is labeled mass in kilograms with entries, 375, 250, 50, 500. The last column is labeled Distance from Earth in kilometers with entries, 320, 320, 320, 320. Which satellite has the greatest gravitational force with Earth? Earth and Satellite A Earth and Satellite B Earth and Satellite C Earth and Satellite D
Answers
Since the gravitational force is directly proportional to the mass, we can see that Satellite D has the greatest mass and therefore the greatest gravitational force with Earth. Therefore, the correct option is D.
To determine which satellite has the greatest gravitational force with Earth, we need to use the formula for gravitational force, which is:
force = (G x m1 x m2) / r^2
where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the objects.
Since the mass of Earth is much greater than any of the satellites, we can assume that the distance between Earth and each satellite is the same. Therefore, we can compare the gravitational force of each satellite with Earth by calculating:
force = (G x Earth's mass x satellite's mass) / distance^2
Using this formula and plugging in the given values, we get:
For Satellite A: force = (G x Earth's mass x 375 kg) / (320 km)^2
For Satellite B: force = (G x Earth's mass x 250 kg) / (320 km)^2
For Satellite C: force = (G x Earth's mass x 50 kg) / (320 km)^2
For Satellite D: force = (G x Earth's mass x 500 kg) / (320 km)^2
Therefore, the correct option is D.
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Another eay to write the ratio 3 : 7 is
Answers
Answer:
You can write this ratio in three different ways:
1. 3/7
2. 3 to 7
3. 3:7
Answer:
3/7
3 to 7
Step-by-step explanation:
22.
Marissa works at Pizza Place for $9 an hour. This week she also sold her shoes for $80. If she earned a
total of $314 this week, how many hours did she work at Pizza Place?
Answers
$314-$80=$234
And then divide that total by how much she gets each hour
$234/$9=26
So you get the answer of 26 hours she worked at the pizza place
Number of hours Marissa worked at pizza place is 26 hours.
What is simplification?Simplification generally means finding an answer for the complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus.
Now, it is given that,
Marissa's earning per hour = $9
Money received from selling of shoes = $80
Total money left this week = $314
Hence, Total earning = Total money left this week - Money received from selling of shoes
Total earning = $314 - $80
⇒Total earning = $234
Therefore,
Hours of work = Total earning/earning per hour
⇒Hours of work = $234/$9 hours
⇒Hours of work = 26 hours
Hence,Number of hours Marissa worked at pizza place is 26 hours.
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In this figure, lines a and b intersect a transversal, c. What is the relationship between ∠1 and ∠5?
Answers
m∠1 = m∠5, because alternate exterior angles are congruent.
What are angles of parallel lines?Angles formed by intersecting two parallel lines with a transversal are known as angles in parallel lines.
Given:
lines a and b intersect a transversal, c.
The pair of angles on the outside of the two parallel lines but on the other side of the transversal are known as alternate exterior angles.
m∠1 = m∠5 (Alternate exterior angles are congruent)
m∠1 = m∠5, because alternate exterior angles are congruent.
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The Complete Question is attached below.
d. tickets to the zoo cost $25 for adults and $10 for children. the total ticket sales one day were $47,750. the number of children, c, who visited the zoo was 270 more than 6 times the number of adults, a, who visited. write and solve a system of equations to find the total number of visitors to the zoo that day.
Answers
The total number of visitors to the zoo that day=3980.
Given:
cost of each ticket for an adult=$25
cost of each ticket for an adult=$10
Total ticket sales one day=$47,750.
⇒$25+$10=47,750
⇒25+10=47,750-----(1)
Also,
c=6a+270
6a-c=-270------(2)
multiplying eq(2) with 10 we get:
60a-10c=-2700----(3)
Adding eq(1) and eq(3) we get
25a+10c=47,750
60a-10c=-2700
--------------------------
85a=45050
--------------------
To calculate a value just divide 45050 by 85 we get
a=45050/85
a=530
Now to get the value of c substitutes a value.
c=60(530)+270
c=3450
Number of Adult visitors=530
Number of children visitors=3450
Total Number of visitors=3980.
Therefore, the total number of visitors to the zoo that day=3980.
To know more about the system of equations:
https://brainly.com/question/13729904
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how many dollars are in 50 quarters
Answers
Answer:
There are $12.50 dollares in 50 quarters
Step-by-step explanation:
50 / 4 = 12.5
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-Lil_G
Answer:
12.50
Step-by-step explanation:
quarters = 25 cents
1 dollar = 4 quarters
50 ÷ 4 = 12.5
12 dollars and 50 cents