To find the mass of the lamina, we need to integrate the density function over region D. The density function is given by? (x, y) = 7ky, where k is a constant. The region D is bounded by y = [tex](1 ? x^2)[/tex] and y = 0, and the limits of integration are [tex]0 < = y < = (1 - x^2)[/tex] .
So, the mass of the lamina is:
[tex]m = ∫∫?(x, y) dx dy = ∫∫ 7ky dx dy\\= 7k ∫∫ y dx dy = 7k * ∫ (1 - x^2) dy dx\\= 7k * ∫(0 to 1 - x^2) y dy\\= 7k * (1/2 * ∫(0 to 1 - x^2) y^2 dy)\\= 7k * (1/2 * [y^3/3] evaluated at y = (1-x^2) and y=0)\\= 7k * (1/2 * [((1-x^2)^3/3] - 0))= 7k * (1/2 * (1/3 - x^6))[/tex]
To find the center of mass (x bar, y bar) of the lamina, we need to find the x and y coordinates of the center of mass.
The x-coordinate is given by
[tex](x bar) = 1/m * ∫∫ x ?(x, y) dx dy = 1/m * ∫∫ x * 7ky dx dy \\= 7k * ∫ (x * y) dx dy\\= 7k * (x * 1/2 * ∫(0 to 1 - x^2) y^2 dy)\\= 7k * (x * 1/2 * [y^3/3] evaluated at y = (1-x^2) and y=0)\\= 7k * (x * (1/2 * (1/3 - x^6))\\The y-coordinate is given by\\(y bar) = 1/m * ∫∫ y ?(x, y) dx dy = 1/m * ∫∫ y * 7ky dx dy= 7k * ∫ (y^2) dx dy\\= 7k * (1/3 * ∫(0 to 1 - x^2) y^3 dy)\\= 7k * (1/3 * [y^4/4] evaluated at y = (1-x^2) and y=0)\\= 7k * (1/3 * (1/4 - x^6/2))[/tex]
It's worth noting that the mass and center of mass of the lamina depend on the constant k, which is not specified in the problem.
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Jordan is making a paddleball court. The court consists of a wall outlined by 40 m of paint. What dimensions
will maximize the area of the paddleball court?
Length
Width
L
а length - 20 m, width - 20 m
b. length - 13.33 m, width = 1334 m
C length - 10 m, width - 10 m
d. length - 10 m, width 20 m
Answer:
ffhhfhhfhhfhfhfhfhhfhhfhfhfhfhfhfhfhfhfhhfhfhfhfh
Answer:
lnfadvogbfvuvgayuvgalof
Step-by-step explanation:
asdbujvygadsoufyudgasoufgaedoy(b) 33 is 75% of what number?
How do I find the measure of each marked angle question 14
Answer:
x=38
Step-by-step explanation:
hope this helps!
if angles are on a line like that, both equations added up together will always be equal to 180.
like this:
2x-10+3x = 180
5x-10=180 (combine)
5x=190 (subtract 10 on both sides)
x=38 (divide both sides by 5)
The radius of a cylindrical water tank is 4.5ft, and its height is 11ft. What is the volume of the tank?
Use the value 3.14 for π, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
494.8
Step-by-step explanation:
Volume of cylinder = 2pierh + 2pier^2
= 2*3.14*4.5*13 + 2*3.24*4.5^2
= 494.8
4. The area of a rectangle is (x2+8x + 12) cm. If the
length of the rectangle is (x + 6) cm, show that is
breadth is (x + 2) cm.
Answer:
★ Given :
Area of triangle = x² + 8x + 12 cm²
length = (x+6)cm
★ To show :
breadth = (x+2) cm
★ Solution :
We know that,
Area of a rectangle = length × breadth
by putting values
(x² + 8x + 12) = (x+6) × breadth
by diving (x² + 8x + 12) into factors
using middle term splitting
x² + 6x + 2x + 12
x(x+6) + 2(x+6)
= (x+2)(x+6)
(x+2)(x+6) = (x+6) × breadth
Hence, verified..
Answer:
hope it helped have a good day mate
Fifteen students were registered in Section 1 and 15 students were registered in Section 2 of a research course. They took the same midterm exam, and their exam scores were distributed as follows: Section 1: 89, 56, 45, 78, 98, 45, 55, 77, 88, 99, 98, 97, 54, 34, 94 Section 2: 77, 88, 87, 67, 98, 87, 55, 77, 45, 44, 88, 99, 69, 67, 98 a. Calculate the mode, median, mean, range, variance, and standard deviation for both sections. Include your SPSS output below. (10 pts) b. Which section did better overall on the exam? Fully justify your answer using the concepts in W&G Chapter 3. (3 pts)
Answer:
a)
For Section 1 -
Mode : 45 , 98
Median - 78
Mean - 73.8
Range - 65
Variance - 537.03
Standard Deviation - 23.17
For Section 2 -
Mode : 67 , 77 , 87 , 88 , 98
Median - 77
Mean - 76.4
Range - 55
Variance - 333.11
Standard Deviation - 18.25
b)
Section 2 did better overall on the exam
Step-by-step explanation:
As given,
Section 1: 89, 56, 45, 78, 98, 45, 55, 77, 88, 99, 98, 97, 54, 34, 94
Section 2: 77, 88, 87, 67, 98, 87, 55, 77, 45, 44, 88, 99, 69, 67, 98
a)
For Section 1 -
Mode : 45 , 98
Median - 78
Mean - 73.8
Range - 65
Variance - 537.03
Standard Deviation - 23.17
For Section 2 -
Mode : 67 , 77 , 87 , 88 , 98
Median - 77
Mean - 76.4
Range - 55
Variance - 333.11
Standard Deviation - 18.25
b)
As,
Standard deviation of section 2 < Standard deviation of section 1
⇒ Students of Section 2 are more consistent.
Also,
mean of Section 2 > mean of Section 1,
⇒average score of Section 2 student > Average score of Section 1 student.
∴ we get
Section 2 did better overall on the exam.
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 417 gram setting. It is believed that the machine is underfilling the bags. A 13 bag sample had a mean of 415 grams with a standard deviation of 30. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Answer:
P value = 0.407
Hence, as P-value (0.407) is greater than 0.1
Fail to reject Null hypothesis
Step-by-step explanation:
Given the data in the question;
sample size n = 13
sample mean x" = 415
standard deviation s = 30
level of significance = 0.1
so;
Null hypothesis H₀ : μ = 417
Alternative hypothesis Hₐ : μ < 417
degree of freedom DF = n - 1 = 13 -1 = 12
Rejection Region { level of significance = 0.1, df = 12 }
critical value of t is - 1.356 as { left tailed test }
Test Statistics;
t = (x" - μ) / [tex]\frac{s}{\sqrt{n} }[/tex]
we substitute
t = (415 - 417) / [tex]\frac{30}{\sqrt{13} }[/tex]
t = -2 / [tex]\frac{30}{\sqrt{13} }[/tex]
t = -0.24
so, from table;
P value = 0.407
Hence, as P-value (0.407) is greater than 0.1
Fail to reject Null hypothesis
Five students in the chess club went to the state tournament. If 20% of the chess club went to the tournament, how many students are in the chess club?
Answer:
25 students are in the chess club
Step-by-step explanation:
100×5=500
500÷20=25
I hope it's correct:)
Answer:
25 students
and how?
its 2 5 S T U D E N T S
Pls help I’ll brainlest ASAP
Answer:
$180
Step-by-step explanation:
$180
Find the perimeter P of
JKLM
with vertices J(-3,-2),K(-5,-5),L(1.-5),M(3.-2) Round your answer to the nearest tenth
The temperature early in the morning is 15 °C. The temperature increases by 2 °C for every hour for the
next 5 hours. Write a function for the temperature in degrees Celsius.
f(h)=
What is the solution to 3x - y = 13 and 2x + 5y = 20
Answer:
Step-by-step explanation:
x = 10 - 5/2y
A line passes through the point (8,-5) and has a slope of 3/2
Answer:
y=3/2x-17
Step-by-step explanation:
y-y1=m(x-x1)
y-(-5)=3/2(x-8)
y+5=3/2(x-8)
y=3/2x-24/2-5
y=3/2x-12-5
y=3/2x-17
I really don’t get it!!
Answer:
The answer is b.
Step-by-step explanation:
Square root 124, you'll get 29.10, after that once you simplify it, you will get the answer and you will have to do the formula, a^2 + b^2 = c^2 since it is a triangle.
Answer:
x = 11,
m∡LMN = 124°
Step-by-step explanation:
since NO bisects ∡LMN, then ∡LMO = ∡NMO
so we can do the following to solve for 'x':
8x - 26 = 2x + 40
6x = 66
x = 11
now, plug 11 in for 'x' into either expression and double it, since ∡LMN is made up of two equal angles
8(11) - 26 = 88 - 26 = 62
62 x 2 = 124
solve for each quotient 2 1/2+7 1/3
The quotient of the given fractions is 9/44.
Given that, [tex]1\frac{1}{2}\div 7\frac{1}{3}[/tex].
How to divide the fractions?The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.
The given mixed fractions can be written as, [tex]1\frac{1}{2}=\frac{3}{2}[/tex] and [tex]7\frac{1}{3}=\frac{22}{3}[/tex]
Now, 3/2 ÷ 22/3
=3/2 × 3/22
=9/44
Therefore, the quotient of the given fractions is 9/44.
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Lattice Arena sold a total of 150 tickets to a basketball game. 90 of the tickets were sold to fans of the home team. What percent of the tickets were sold to fans of the home team?
60 percentage of the tickets were sold to fans of the home team.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
To find the percentage of tickets sold to fans of the home team,
we need to divide the number of tickets sold to home team fans by the total number of tickets sold, and then multiply by 100 to convert the fraction to a percentage:
Percentage of tickets sold to home team fans = (Number of tickets sold to home team fans / Total number of tickets sold) x 100%
Number of tickets sold to home team fans = 90
Total number of tickets sold = 150
Percentage of tickets sold to home team fans = (90 / 150) x 100%
Percentage of tickets sold to home team fans = 0.6 x 100%
Percentage of tickets sold to home team fans = 60%
Therefore, 60% of the tickets were sold to fans of the home team.
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Estimate the average rate of change from x=2 to x=5
Answer:
5x3x2y
Step-by-step explanation:
The average rate of change for the graph is 4/3 from x = 2 to x = 5.
What is Lagrange mean value theorem?Lagrange mean value theorem states that, if a function f is continuous over the closed interval [a, b] and differentiable over the open interval (a, b), then there must be at least one point c in the interval (a, b) where the slope of the tangent at the point c is equal to the slope of the tangent through the curve's endpoints, resulting in the expression f'(c) = {F(b) -F(a)}/(b-a)
According to the given graph,
At point x = 2,
F(2) = 3
At point x = 5,
F(5) = 7
Since the formula for the average rate of change of the function between x = a and x = b is,
The average rate of change = {F(b) -F(a)}/(b-a)
Here a = 2, b = 5 and F(2) = 3, F(5) = 7
Substitute the values in the formula,
So the average rate of change = (7 - 3)/(5 - 2) = 4/3.
Hence, the average rate of change of the function is 4/3.
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A) Find the area of the shaded region
ill give you brainliest
Answer:
2.0
Step-by-step explanation:
Area of Shaded Region = Area of square – Area of circle
Area of square = 3×3 = 9
Area of circle = π×r² = π×1.5² ≈ 7.068
(radius of circle is half of the side length)
9–7.068≈2.0
A universitys freshman class has 8900 students. 3471 of those students are majoring in Engineering. What percentage of the frehman class are Engineering majors?
Answer:
39%
Step-by-step explanation:
Helpppp!!!!!! After a few rides, your friends are ready for some ice cream! You stop into Scoops to You for some ice-cream. Which is the better deal?
3 scoops for $3.69
2 scoops for $2.69
1 scoop for $1.79
Answer:
3 scoops for $3.69 is better deal.
Step-by-step explanation:
Given that,
There are 3 deals to buy icecram.
3 scoops for $3.69
2 scoops for $2.69
1 scoop for $1.79
We can find the cost of 1 scoop for each deal. So,
First deal,
1 scoop = 3.69/3 = $1.23
Second deal,
1 scoop = 2.69/2 = 1.345
We can see that the cost of 1 scoop for deal 1 is less than others. It means first deal is best.
4/4 times 1/2 PLEASE HURRY ILL MARK BRAINLIEST
Answer: 1/2
Step-by-step explanation:4
4
×
1
2
=
1
2
Result in decimals: 0.5
Calculation steps:
4
4
×
1
2
=
4 × 1
4 × 2
=
4
8
=
4 ÷ 4
8 ÷ 4
=
1
2
Further explanation
For the problem:
4
4
×
1
2
= ?
Multiply all of the numerators by each other. Do the same with the denominators and form a new fraction with these values:
4 × 1
4 × 2
=
4
8
The Greatest Common Factor (GCF) of 4 and 8 is 4. The result can be simplified by dividing both the numerator and denominator by 4.
4
8
=
4 ÷ 4
8 ÷ 4
=
1
2
The result is:
4
4
×
1
2
=
1
2
Answer:
1/2
Step-by-step explanation:
any expression divided by itself is 1
1×1/2
any expression multiplied by 1 remains the same
1/2
increase 2 hour 30 minute by the ratio of 6:5
Answer:
we get 180 minutes; this is equivalent to 3 hours
Step-by-step explanation:
Solving this problem is easier if we convert 2 hr 30 min to min: 150 min.
In the ratio 6:5, the 5 represents the 150 min and we need to determine how long the time interval will be if increased in this ratio.
We write and solve an equation of ratios:
6 x
--- = ------ This becomes 5x = 900 through cross multiplication.
5 150
solving this for x, we get 180 minutes; this is equivalent to 3 hours.
The time taken should be 180 minutes or 3 hours.
Calculation of the time taken:
Since there is an increase of 2 hours 30 minutes by the ratio of 6:5
So here we convert 2 hr 30 min so it comes 150 min.
Now the time taken should be
5x = 900
x = 150 minutes
hence, The time taken should be 180 minutes or 3 hours.
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ples ill give you the brianliest
Answer:
72
Step-by-step explanation:
step 1: 10(4+14/7)+12
step 2: 10(4+2)+12
step 3: 10(6)+12
step 4: 60+12=72
Find the product of (x2 + 2x −3)(4x2 − 5x + 6). (2 points) a 4x4 + 13x3 − 16x2 + 27x − 18 b 4x4 + 3x3 − 28x2 + 27x − 18 c 4x4 + 3x3 − 16x2 + 3x − 18 d 4x4 + 3x3 − 16x2 + 27x − 18
Answer:
D
Step-by-step explanation:
We want to find:
[tex](x^2+2x-3)(4x^2-5x+6)[/tex]
Distribute:
[tex]=(x^2+2x-3)(4x^2)+(x^2+2x-3)(-5x)+(x^2+2x-3)(6)[/tex]
Distribute:
[tex]=(4x^4+8x^3-12x^2)+(-5x^3-10x^2+15x)+(6x^2+12x-18)[/tex]
Rearrange:
[tex]=(4x^4)+(8x^3-5x^3)+(-12x^2-10x^2+6x^2)+(15x+12x)+(-18)[/tex]
Combine like terms:
[tex]=4x^4+3x^3-16x^2+27x-18[/tex]
The answer is D.
Find the area of the figure.
(Simplify Your Answer)
Answer:
7550 meter square
area of rectangle = Length x breadth= 130 x 20
= 2600 meter square
area of triangle = 1/2 x base x height
1/2 x (130-20)m x (130-40)m
1/2 x 110m x 90m
55 x 90
4950 metre square
area of rectangle + area of triangle
4950 + 2600
7550 meter square
(x-4)^2=25 by taking the square root
Answer:
x = -1, 9
Step-by-step explanation:
[tex](x-4)^2=25\\x-4=\sqrt{25}\\[/tex]
x - 4 = ±5 (positive or negative 5, because (-5)^2 = 25)
x - 4 = 5
x = 9
or
x - 4 = -5
x = -1
x = -1, 9
Pleaseeee helpp its due in 6 mins
Answer:
5 8 as decimal is: 0.625
Step-by-step explanation:
What is 5/8 as a decimal?
To write 5/8 as a decimal you have to divide numerator by the denominator of the fraction.
We divide now 5 by 8 what we write down as 5/8 and we get 0.625
And finally we have:
5/8 as a decimal equals 0.625
A diagonal path divides a square park in half. If the park is 50 yards on each side, how long is the path? A. 10 yd. B. 250 C. 50 yd. D. 5000
Answer:
B) 250Step-by-step explanation:
Hope this helps!!
Answer: its 5000 i got it right
Step-by-step explanation:
which correctly shows 5.05 and 5.5
Answer:
how are we gonna answer the question if there is no picture of it
Step-by-step explanation:
Find the whole. 215% of what number is 172