Answer:
[tex]\iint_D 8y^2 \ dA = \dfrac{88}{3}[/tex]
Step-by-step explanation:
The equation of the line through the point [tex](x_o,y_o)[/tex] & [tex](x_1,y_1)[/tex] can be represented by:
[tex]y-y_o = m(x - x_o)[/tex]
Making m the subject;
[tex]m = \dfrac{y_1 - y_0}{x_1-x_0}[/tex]
∴
we need to carry out the equation of the line through (0,1) and (1,2)
i.e
y - 1 = m(x - 0)
y - 1 = mx
where;
[tex]m= \dfrac{2-1}{1-0}[/tex]
m = 1
Thus;
y - 1 = (1)x
y - 1 = x ---- (1)
The equation of the line through (1,2) & (4,1) is:
y -2 = m (x - 1)
where;
[tex]m = \dfrac{1-2}{4-1}[/tex]
[tex]m = \dfrac{-1}{3}[/tex]
∴
[tex]y-2 = -\dfrac{1}{3}(x-1)[/tex]
-3(y-2) = x - 1
-3y + 6 = x - 1
x = -3y + 7
Thus: for equation of two lines
x = y - 1
x = -3y + 7
i.e.
y - 1 = -3y + 7
y + 3y = 1 + 7
4y = 8
y = 2
Now, y ranges from 1 → 2 & x ranges from y - 1 to -3y + 7
∴
[tex]\iint_D 8y^2 \ dA = \int^2_1 \int ^{-3y+7}_{y-1} \ 8y^2 \ dxdy[/tex]
[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \int ^{-3y+7}_{y-1} \ y^2 \ dxdy[/tex]
[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( \int^{-3y+7}_{y-1} \ dx \bigg) dy[/tex]
[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( [xy^2]^{-3y+7}_{y-1} \bigg ) \ dy[/tex]
[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( [y^2(-3y+7-y+1)]\bigg ) \ dy[/tex]
[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ([y^2(-4y+8)] \bigg ) \ dy[/tex]
[tex]\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( -4y^3+8y^2 \bigg ) \ dy[/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [\dfrac{ -4y^4}{4}+\dfrac{8y^3}{3} \bigg ]^2_1[/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [ -y^4+\dfrac{8y^3}{3} \bigg ]^2_1[/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [ -2^4+\dfrac{8(2)^3}{3} + 1^4- \dfrac{8\times (1)^3}{3}\bigg][/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [ -16+\dfrac{64}{3} + 1- \dfrac{8}{3}\bigg][/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{64-8}{3}\bigg][/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{56}{3}\bigg][/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [ \dfrac{-45+56}{3}\bigg][/tex]
[tex]\iint_D 8y^2 \ dA =8 \bigg [ \dfrac{11}{3}\bigg][/tex]
[tex]\iint_D 8y^2 \ dA = \dfrac{88}{3}[/tex]
Plzzz help. Giving 20 pts
Answer:
The ratio of the similar triangles is 6/4=3/2. Since BC-YZ in this case, 3*3/2=9/2=4.5 which is B.
Answer:
b
Step-by-step explanation:
The equation (x – 5)2 = –2(y + 1) represents a parabola. Complete the statements describing the graph.
The vertex is
(5,1)
(5,-1)
(-5,1)
(-5,-1)
The graph opens
up
left
right
down
Answer:
(5,-1)
Step-by-step explanation:
TAKE ONE SIDE
(X-5)2=0
2X-10= 0
2X=10
X=10/2
X=5
THEN TAKE OTHE SIDE
-2(y+1) =0
-2y-2=0
-2y=2
y=2/-2
y=-1
So the answer is (5,-1)
And it should be in right down
(-5,1) , the graph opens down
What is an equation?
'An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.'
.Given equation: 2(x-5) = -2(y+1)
Evaluating left-hand side,
⇒ (x-5)2 = 0
⇒2x-10 = 0
⇒2x = 10
⇒x =10/2
⇒x = 5
Evaluating RHS,
⇒-2(y+1) = 0
⇒-2y-2 = 0
⇒-2y = 2
⇒y = 2/-2
⇒y = -1
Hence, we can conclude the vertex is at (-5,1) and the graph opens down.
Learn more about graphs here: https://brainly.com/question/4074088
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Find the slope on the graph
Solve the Compound Interest Formula for time given:
250,000 = 12,000e^.125t
ILL MARK AS BRAINLIEST!! PLEASE HELP FAST!!
Answer:
neither
Step-by-step explanation:
The table below shows the distribution of students by age in a high school
with 1500 students. What is the probability that a randomly chosen student is
14 years old?
Age
13, 14, 15, 16, 17, 18
Number of Students
15,375,450,420,225,15
A. 0.15
B. 0.30
C. 0.28
D. 0.25
Answer: 28
Step-by-step explanation:
Answer:
it is .28
Step-by-step explanation:
ayepexs
A local little league has a total of 60 players, of whom 20% are right-handed. How many right-handed
players are there?
There are right-handed players.
Answer:
12
Step-by-step explanation:
Step one:
given data
total players in the league
60
we are told that 20% are right-handed.
Required
The number of right-handed players
Step two:
=20/100*60
=0.2*60
=12
There are 12 right-handed players.
Choose the scenario that describes a proportional relationship.
Miguel earns $7.50 per hour while babysitting.
A hotel charges a flat rate of $12.00 to park in their parking lot.
A cellphone plan is $25 plus $0.05 per megabyte, MB, of data usage.
Raphael sells paintings for $200 each at a market but has to pay $100 to reserve a table.
Answer:
Raphael sells paintings for $200 each at a market, but has to pay $100 to reserve a table. :)
Step-by-step explanation:
The scenario that describes a proportional relationship is D; Raphael sells paintings for $200 each at a market but has to pay $100 to reserve a table.
What is directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex]where that middle sign is the sign of proportionality.
This inversely proportional relationship is denoted by;
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
Thus, the scenario that describes a proportional relationship is D; Raphael sells paintings for $200 each at a market but has to pay $100 to reserve a table.
Learn more about directly inversely proportional relationship variable here:
https://brainly.com/question/13082482
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can someone please help me with this question??
Answer:
2nd one
Step-by-step explanation:
Evaluate 2k + 3m if k= 1 and m=5
17
2(1) + 3(5) = 2+15 = 17
2x+3y
help me please
Answer:
2 x + 3 y
Step-by-step explanation:
A poll asked 325 people whether they would support a certain amendment to the state constitution. 58% of people said they would.
Write a 95% confidence statement.
whats 9+10 ? ;) im dumb so i dont know simple mafs
Answer:
the answer is 100% = 21
Step-by-step explanation:
find the slope please help!
Answer:
-3/4
Step-by-step explanation:
Get the coordinates of the two points and use the slope formula to find the slope.
We'll call the points point A and point B.
Point A's coordinates are (-3,1) and point B's coordinates are (1,-2)
Now, plug the numbers into the slope formula
Slope formula is: y2-y1/x2-x1
-2-1/1--3
-3/4
Let v(t) = 1/π + sin(3t) represent the velocity of an object moving on a line. On the interval [π/2, π], what is the velocity when the acceleration is 3?
Answer:
[tex]\displaystyle \frac{1}{\pi}\approx0.318[/tex]
Step-by-step explanation:
The velocity of an object moving on a line is given by the function:
[tex]\displaystyle v(t)=\frac{1}{\pi}+\sin(3t),\; \frac{\pi}{2}\leq x\leq\pi[/tex]
And we want to determine the velocity of the object when its acceleration is 3.
So, we will need to determine our acceleration function. Remember that acceleration is simply the derivative of speed. Therefore, our acceleration function a(t) will be:
[tex]\displaystyle a(t)=v^\prime(t)=\frac{d}{dt}[\frac{1}{\pi}+\sin(3t)][/tex]
Differentiate. We will use the chain rule on the second part. Hence, our acceleration function is:
[tex]\displaystyle a(t)=3\cos(3t)[/tex]
We want to find the velocity when the acceleration is 3.
So, let’s set a(t) equal to 3 and determine at what time t our function equals 3. Hence:
[tex]3=3\cos(3t)[/tex]
Divide both sides by 3:
[tex]\cos(3t)=1[/tex]
Take the inverse cosine of both sides.
Remember that cosine is 1 for every 2π. Hence:
[tex]3t=2\pi n[/tex]
Where n is an integer.
Divide both sides by 3. Therefore, our solutions are:
[tex]\displaystyle t=\frac{2\pi n}{3}[/tex]
However, our domain was π/2≤x≤π.
Hence, we can test values of n such that it is within our domain.
Testing for n=0, 1, and 2, we see that:
[tex]\displaystyle t=0, \, t=\frac{2\pi}{3},\, t=\frac{4\pi}{3}...[/tex]
However, the only solution that is within our domain is the second solution.
Hence, the acceleration is 3 when the t is 2π/3.
Therefore, our velocity at that time t is:
[tex]\begin{aligned}\displaystyle v(\frac{2\pi}{3})&=\frac{1}{\pi}+\sin(3(\frac{2\pi}{3}))\\ &=\frac{1}{\pi}+\sin(2\pi)\\&=\frac{1}{\pi}+0\\&=\frac{1}{\pi}\approx 0.318\end{aligned}[/tex]
GIVING BRAINLIEST PLEASE HELP!!!!!!!!!!!!!!!! Calculate the correlation coefficient of the following data: (1,1) (2,3) (3,6) (4,2) (7,9) (8,6) (10,7)
Answer:
The value of R is 0.7482.
Step-by-step explanation:
X Values
∑ = 35
Mean = 5
∑(X - Mx)2 = SSx = 68
Y Values
∑ = 34
Mean = 4.857
∑(Y - My)2 = SSy = 50.857
X and Y Combined
N = 7
∑(X - Mx)(Y - My) = 44
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = 44 / √((68)(50.857)) = 0.7482
r = 0.7482
Sorry if I get this wrong Because not for sure how you need the awnsers I dont know if this is the right way
Mx: 5.000
My: 4.857
Sum: 68.000
Sum: 50.857
sum: 44.000
X Values
∑ = 35
Mean = 5
∑(X - Mx)2 = SSx = 68
Y Values
∑ = 34
Mean = 4.857
∑(Y - My)2 = SSy = 50.857
X and Y Combined
N = 7
∑(X - Mx)(Y - My) = 44
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = 44 / √((68)(50.857)) = 0.7482
Meta Numerics (cross-check)
r = 0.7482
Consider the equation 6*e^{0.25t}=9
Solve the equation for t. Express the solution as a logarithm in base-e.
Approximate the value of t. Round your answer to the nearest thousandth
Answer:
t = ln1.5/0.25
t = 1.622
Step-by-step explanation:
Gives the equation, 6*e^{0.25t}=9
We are to find t
6*e^{0.25t}=9
e^{0.25t}=9/6
e^{0.25t}= 1.5
Apply ln to both Sides
ln( e^{0.25t) = ln1.5
0.25t = ln1.5
t = ln1.5/0.25
t = 1.622
5) Tyra went to the movies and bought a coke for $1.25, popcorn for $4.25 and peanut butter M&Ms for $3. How much did Tyra spend in I
True or False
1. We find the x-intercepts of a function fby evaluating f(0).
2. The solutions of a function are the first coordinates of the
x-intercepts of the function.
3. We can use completing the square to solve any quadratic equation.
4. The function f(x)=-3(x+4)2-5 has a maximum value.
what word problem would fit for 7x+10=-3x-2
Answer:
A number is multiplied by 7 and the added to 10 and it is equal to when -3 is multiplied by the same number and then 2 is taken away. Find the number.
Step-by-step explanation:
interpretation: 7x+10=-3x-2
B is a number larger than 1
Answer:
b= infinity
Step-by-step explanation:
Because is b>1 than b can be 2, 3, 44, 100, 1000, 100000000213981623 and higher. There is no way to find the exact number though.
4/5 divided by 1/5 in unit form
Answer:
answer to your question is 4
14.
Find the sum of the expression: 87.75 – 7.25 =
A. 80.50
B. 79.25
C. 80.25
D. 80.80
Answer:
A
Step-by-step explanation:
87.75-7.25=80.50
Answer:
A. 80.50
Step-by-step explanation:
The owner of an apartment building can rent all 50 apartments if she charges $600 per month, but she rents one fewer apartment for each $20 increase in monthly rent. Identify the maximum revenue for this function?
Answer:
30,000
Step-by-step explanation:
If she gets all 50 at 600 per month, 50x600 is 30,000.
I hope this helped!
Help plz that would be great
Answer:
-8
Step-by-step explanation:
I got 8 from my calculations so im sure thats the anwser
Could I get help with this ?
Answer:
top is -2,4 and bottom is 3,-2 ??
hope that what u need
Step-by-step explanation:
???
1/3 + a = 5/4
A=? ..........................................................
If f(x) = 3x + 2, what is f(5)?
Answer:
The 5 in the () is what the x is
Step-by-step explanation:
3(5)+2=17
Answer:
Step-by-step explanation:
Replace the X with 5
3(5)+2
Follow PEMDAS
so multiplication goes first
15+2
Then add
17
If there are 2.54 centimeters in an inch and 12 inches in a foot, how many centimeters in 3 feet
Answer:
91.44
Step-by-step explanation:
Answer:
3 ft = 91.44 cm
Step-by-step explanation:
We want to convert 3 ft to cm.
So we need a conversion factor.
Multiplying 3 ft by (12 in / 1 ft results in 36 in (this is equivalent to 3 ft).
Next, we convert 36 in to cm:
36 in 2.54 cm
-------- * ------------- = 91.44 cm
1 1 in
I don’t get this please help me