Answer:
7.36
Step-by-step explanation:
7.3564 would round to 7.36
Answer:
7.36
Step-by-step explanation:
To round off a decimal to the hundredths or a number to the right you do this, if the number to the right of the hundredths is 4 or less you remove all the other digits including the hundredths, if the number is 5 or more you add one to the digit in the hundredths.
Please help and show the steps
Answer:
≈ 2.8 units
Step-by-step explanation:
Calculate the distance d using the distance formula
d = [tex]\sqrt{x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (3, - 3)
d = [tex]\sqrt{(3-1)^2+(-3+1)^2}[/tex]
= [tex]\sqrt{2^2+(-2)^2}[/tex]
= [tex]\sqrt{4+4}[/tex]
= [tex]\sqrt{8}[/tex] ≈ 2.8 ( to the nearest tenth )
Answer: The answer is 2.8
Step-by-step explanation:
(1,-1)(3,-3) (those are the points shown in the graph)
The formula for finding distance is √(x2-x1)^2+(y2-y1)^2
= √(3-1)^2+(-3-(-1)^2
= √(2)^2+(-3+1)^2
= √4+(-2)^2
= √4+4
= √8
=2.828427125 (to the nearest tenth)
Find an equation of the line graphed below: (picture included)
Answer:
Step-by-step explanation:
1/x + 1/y =9/11 (x+y)/x.y=9/11 11x+11y=9x.y
F(x)=11x/(9x-1)
Answer:
Step-by-step explanation:
(-5,-3) (1,0)
(0+3)/(1+5)= 3/6 = 1/2
y - 0 = 1/2(x - 1)
y = 1/2x - 1/2
if D equals 4x + 10 e f equals 2x - 1 + d f equals 9 x - 15 find DF
Answer:
4x+10+2x-1=9x-15;
6x+9=9x-15;
6x-9x=-15-9;
-3x=-24;
3x=24;
from which
x=24:3=8
Then:
DF=9x-15=(9×8)-15=72-15=57
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coulomb’s law given by F= kq1q2 for r2, where F is force, K is constant, q1 and q2 are changes on the two bodies and r is the distance between them. rewrite the formula for coulomb’s law to solve for r.
Answer:
(Kq_1q_2/F)^(1/2).
Step-by-step explanation:
Coulomb's law is a fundamental tenet of several branches of physics, including electromagnetic, electrostatics, and electronics, and it holds true for both positive and negative charges.
What is Coulomb's law?The electrostatic force that exists between two charged particles is described by Coulomb's law, a basic tenet of physics. It asserts that the force between two point charges is inversely proportional to the square of the distance between them and directly proportional to the product of their charges.
Coulomb's law can be expressed mathematically as follows:
F = k(q₁q₂)/r²
Where q₁ and q₂ are the charges' magnitudes, r is the distance between them, and k is the Coulomb constant, F denotes the force acting between the two charges.
The electrostatic constant, commonly referred to as the Coulomb constant, is a proportionality constant that establishes the magnitude of the electrostatic force. Its worth is roughly 8.99 x 109 Nm2/C2.
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Which expression represents the following calculation? Add the product of 7 and 5 to the quotient of 288 and 18.
The expression is 7 * 5 + 288/18.
How to determine the expression?The statement is given as:
Add the product of 7 and 5 to the quotient of 288 and 18.
Add means +.
So, we have:
The product of 7 and 5 + The quotient of 288 and 18.
Product means *
So, we have:
7 * 5 + The quotient of 288 and 18.
Quotient means /.
So, we have:
7 * 5 + 288/18.
Hence, the expression is 7 * 5 + 288/18.
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Given that M< PQR=102, find M
I hope this helps you...
Elsa's fish tank has 19 liters of water in it. She plans to add 4 liters per minute until the tank has more than 47 liters. What are the possible numbers of
minutes Elsa could add water?
Use t for the number of minutes.
Write your answer as an inequality
Leila's fish tank has 18 liters of water in it. She plans to add 5 liters per minute until the tank has more than 58 liters. What are the possible numbers of minutes Leila could add water? Use t for the number of minutes.
Write your answer as an inequality solved for t.
58<18+5t
40<5t
8
JUST LIKE THIS U CAN SOLVE...
ITS BETTER TO NOT GIVE STRAIGHT ANSWERS
The concentration C (in mg/cc) of a drug in a patient's bloodstream is related to the time t (in hours) after injection in such a way that as t changes from 0 to 12, C changes from 0.7 to 0.1. Find the average rate of change of C with respect to t.
I have a calculus question similar to this one and I am unsure of how to begin working on this problem.
Answer: -0.05 mg/cc*h
Step-by-step explanation:
Here we have the relation:
ConcentrationVsTime.
If we want to find the average rate of change, we can find the slope of a line that passes through the extremes of each interval: (tmin, Cmin) and (tmax, Cmax)
The interval for the time is:
0h to 12h.
The interval for the concentration is:
0.7 mg/cc to 0.1mg/cc.
Then we can use the points:
(0h, 0.7mg/cc) and (12h, 0.1mg/cc)
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Then in this case the slope (or rate of change) is:
a = (0.1mg/cc - 0.7mg/cc)/(12h - 0h) = (-0.6mm/cc)/12h = -0.05 mg/cc*h
Weights and heights of turkeys tend to be correlated. For a population of turkeys at a farm, this correlation is found to be 0.64. The average weight is 17 pounds, SD is 5 pounds. The average height is 28 inches and the SD is 8 inches. Weight and height both roughly follow the normal curve. For each part below, answer the question or if not possible, indicate why not. A turkey at the farm which weighs more than 90% of all the turkeys is predicted to be taller than % of them. The average height for turkeys at the 90th percentile for weight is Of the turkeys at the 90th percentile for weight, roughly what percent would you estimate to be taller than 28 inches?
Answer:
a turkey at the farm which weighs more than 90% of all the turkeys is predicted to be taller than 79.37 % of them.
The average height for turkeys at the 90th percentile for weight is 34.554
Of the turkeys at the 90th percentile for weight, roughly the percentage that would be taller than 28 inches 79.37%
Step-by-step explanation:
Given that:
For a population of turkeys at a farm, the correlation found between the weights and heights of turkeys is r = 0.64
the average weight in pounds [tex]\overline x[/tex] = 17
the standard deviation of the weight in pounds [tex]S_x[/tex] = 5
the average height in inches [tex]\overline y[/tex] = 28
the standard deviation of the height in inches [tex]S_y[/tex] = 8
Also, given that the weight and height both roughly follow the normal curve
For this study , the slope of the regression line can be expressed as :
[tex]\beta_1 = r \times ( \dfrac{S_y}{S_x})[/tex]
[tex]\beta_1 = 0.64 \times ( \dfrac{8}{5})[/tex]
[tex]\beta_1 = 0.64 \times 1.6[/tex]
[tex]\beta_1 = 1.024[/tex]
To the intercept of the regression line, we have the following equation
[tex]\beta_o = \overline y - \beta_1 \overline x[/tex]
replacing the values:
[tex]\beta_o = 28 -(1.024)(17)[/tex]
[tex]\beta_o = 28 -17.408[/tex]
[tex]\beta_o = 10.592[/tex]
However, the regression line needed for this study can be computed as:
[tex]\hat Y = \beta_o + \beta_1 X[/tex]
[tex]\hat Y = 10.592 + 1.024 X[/tex]
Recall that;
both the weight and height roughly follow the normal curve
As such, the weight related to 90th percentile can be determined as shown below.
Using the Excel Function at 90th percentile, which can be computed as:
(=Normsinv (0.90) ; we have the desired value of 1.28
∴
[tex]\dfrac{X - \overline x}{s_x } = 1.28[/tex]
[tex]\dfrac{X - 17}{5} = 1.28[/tex]
[tex]X - 17 = 6.4[/tex]
X = 6.4 + 17
X = 23.4
The predicted height [tex]\hat Y = 10.592 + 1.024 X[/tex]
where; X = 23.4
[tex]\hat Y = 10.592 + 1.024 (23.4)[/tex]
[tex]\hat Y = 10.592 + 23.9616[/tex]
[tex]\hat Y = 34.5536[/tex]
Now; the probability of predicted height less than 34.5536 can be computed as:
[tex]P(Y < 34.5536) = P( \dfrac{Y - \overline y }{S_y} < \dfrac{34.5536-28}{8})[/tex]
[tex]P(Y < 34.5536) = P(Z< \dfrac{6.5536}{8})[/tex]
[tex]P(Y < 34.5536) = P(Z< 0.8192)[/tex]
From the Z tables;
P(Y < 34.5536) =0.7937
Hence, a turkey at the farm which weighs more than 90% of all the turkeys is predicted to be taller than 79.37 % of them.
The average height for turkeys at the 90th percentile for weight is :
[tex]\hat Y = 10.592 + 1.024 X[/tex]
where; X = 23.4
[tex]\hat Y = 10.592 + 1.024 (23.4)[/tex]
[tex]\hat Y = 10.592 + 23.962[/tex]
[tex]\mathbf{\hat Y = 34.554}[/tex]
Of the turkeys at the 90th percentile for weight, roughly what percent would you estimate to be taller than 28 inches?
i.e
P(Y >28) = 1 - P (Y< 28)
[tex]P(Y >28) = 1 - P( Z < \dfrac{28 - 34.554}{8})[/tex]
[tex]P(Y >28) = 1 - P( Z < \dfrac{-6.554}{8})[/tex]
[tex]P(Y >28) = 1 - P( Z < -0.8193)[/tex]
From the Z tables,
[tex]P(Y >28) = 1 - 0.2063[/tex]
[tex]\mathbf{P(Y >28) = 0.7937}[/tex]
= 79.37%
The tank of a small airplane holds 48 gallons of fuel. Seven gallons will be used for takeoff and landing. While in the air, the plane will consume an average of 10 gallons of fuel per hour. What is the maximum number of hours the plane can remain in the air?
A. 5.5
B. 4.8
C. 6.0
D. 4.1
Step-by-step explanation:
If x is the number of hours, then:
48 = 10x + 7
41 = 10x
x = 4.1
George went to The Clothes Shack and bought 4 pairs of jeans for $30, 2 pairs of T-shirts for $15, and 3 pairs of shorts for $20. Write an expression that can be used to find the total amount that George spent. How much did George spend?
Answer:
210
Step-by-step explanation:
| 1) Simplify: 12+8/2x3-(42+3)
2) Simplify: 3
1 3
—+-
5
с
3) What is 23% of 80?
а
5/6
b
4) Using the image, name a
pair of corresponding angles.
I
5) Simplify: V169
Answer:
1 no. answer is -21
Step-by-step explanation:
According to BODMAS
12 + 8 / 2 * 3 - (42 + 3)
= 12 + 8 / 2 * 3 - 45
= 12 + 4 * 3 - 45
= 12 + 12 - 45
= 24 - 45
= -21
Vivian is getting a pet snake. She is choosing between the ball python and the corn snake. the ball python is 4 1/2 ft long and the corn snake is 45 in. long. Vivian wants the shorter snake. Which snake should she get? Show your work. (12 in. = 1 ft)
Answer:
The 45 in snake is the shorter one.
Step-by-step explanation:
Which is shorter, 45 in or 4 1/2 ft?
12 in
Convert 4 1/2 ft into inches by multiplying 4 1/2 ft by --------- = 54 in.
1 ft
Thus, the 45 in snake is shorter than the 54 in one and should b e V's first choice.
The shorter snake will be a corn snake. Then she will get a corn snake.
What is conversion?Conversion means to convert the same thing into different units.
Vivian is getting a pet snake. She is choosing between the ball python and the corn snake. The ball python is 4 1/2 feet long and the corn snake is 45 inches long.
Convert inches into feet. Then the length of a corn snake will be
45 inches = 45/12 feet
45 inches = 3 3/4 feet
Vivian wants the shorter snake.
Thus, the shorter snake will be a corn snake. Then she will get a corn snake.
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the sum of fifty and a
Answer:
a + 50
Step-by-step explanation:
Step 1: Translate word into math
sum = +
fifty = 50
a = a
Step 2: Combine
a + 50
Answer:
a + 50
Step-by-step explanation:
Step 1: Translate word into math
sum = +
fifty = 50
a = a
Step 2: Combine
a + 50
please help me
what is the radical expression that is equivalent 27 ⅕?
enter your answer as a radical
Answer:
[tex]\sqrt[5]{27}[/tex]
Step-by-step explanation:
a¹/ᵇ = [tex]\sqrt[b]{a}[/tex]
Radical expression of 27 ⅕ is
27 ⅕ = [tex]\sqrt[5]{27}[/tex]You want to go to graduate school, so you ask your math professor, Dr. Emmy Noether, for a letter of recommendation. You estimate that there is a 80% chance that you will get into a graduate program if you receive a strong recommendation, a 60% chance that you will get into a graduate program if you receive a moderately good recommendation, and 5% chance that you will get into a graduate program if you receive a weak recommendation. Furthermore, you estimate that the probabilities that a recommendation will be strong, moderately good, and weak are 0.7, 0.2, and 0.1, respectively. Based on these estimates, what is the probability that you will get into a graduate program. Given that you did receive an offer to attend a graduate program, what is the probability that you received a strong recommendation? Suppose you didn't receive an offer to attend a graduate program. Given that, what is the probability that you received a moderately good recommendation?
Answer:
a
[tex]P(G) = 0.69[/tex]
b
[tex]P(S | G) = 0.81[/tex]
c
[tex]P(M|G') = 0.26[/tex]
Step-by-step explanation:
From the question we are told the
The probability of getting into getting into graduated school if you receive a strong recommendation is [tex]P(G |S) = 0.80[/tex]
The probability of getting into getting into graduated school if you receive a moderately good recommendation is [tex]P(G| M) = 0.60[/tex]
The probability of getting into getting into graduated school if you receive a weak recommendation is [tex]P(G|W) = 0.05[/tex]
The probability of getting a strong recommendation is [tex]P(S) = 0.7[/tex]
The probability of receiving a moderately good recommendation is [tex]P(M) = 0.2[/tex]
The probability of receiving a weak recommendation is [tex]P(W) = 0.1[/tex]
Generally the probability that you will get into a graduate program is mathematically represented as
[tex]P(G) = P(S) * P(G|S) + P(M) * P(G|M) + P(W) * P(G|W)[/tex]
=> [tex]P(G) = 0.7 * 0.8 + 0.2 * 0.6 + 0.1 * 0.05[/tex]
=> [tex]P(G) = 0.69[/tex]
Generally given that you did receive an offer to attend a graduate program, what is the probability that you received a strong recommendation is mathematically represented as
[tex]P( S|G) = \frac{ P(S) * P(G|S)}{ P(G)}[/tex]
=> [tex]P(S|G) = \frac{ 0.7 * 0.8 }{0.69}[/tex]
=> [tex]P(S | G) = 0.81[/tex]
Generally given that you didn't receive an offer to attend a graduate program the probability that you received a moderately good recommendation is mathematically represented as
[tex]P(M|G') = \frac{ P(M) * (1- P(G|M))}{(1 - P(G))}[/tex]
[tex]P(M| G') = \frac{ 0.2 * (1- 0.6)}{ (1 - 0.69)}[/tex]
[tex]P(M|G') = 0.26[/tex]
What is the answer? Step by step.
Answer:
420 in^2
Step-by-step explanation:
The area of the rectangle before removing the circles is
A = l*w
A = 24*22
=528
The area of one of the circles is
A = pi r^2
The diameter is 6 so the radius is 6/2 = 3
= 3.14 * ( 3) ^2
=28.26
There are 4 circles
4* 28.26
113.04
Subtract the area of the 4 circles from the rectangle
528-113.04
414.96
415 in ^2
The best estimate is 420
The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.3 inches. What is the probability that the average length of a steel sheet from a sample of 9 units is more than 29.95 inches long
Answer:
62.93%
Step-by-step explanation:
Z score is a score used in statistics to measure by how many standard deviations that the raw score is above or below the mean. A positive z score means the raw score is above the mean and a negative z score means the raw score is below the mean. The z score is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given that:
Mean (μ) = 30.05 inches, standard deviation (σ) = 0.3 inches
For x > 29.95
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{29.95-30.05}{0.3} =-0.33[/tex]
From the normal distribution table, P(x > 29.95) = P(z > -0.33) = 1 - P(z < 0.33) = 1 - 0.3707 = 0.6293 = 62.93%
What is the product of the polynomials below?
(6x2-3x-6)(4x2 +5x+4)
A. 24x4 +18x2 – 15x2 - 42x-2
B. 24x4 +18X? – 15x? - 36x - 24
C. 24x4 +18x3 - 15x2 - 42x - 24
D. 24x4 +18x? - 15x2 - 36x-2
Answer:
C :) try the box method! it always works for alot of people but i prefer diatrubuative method
Mrs. McAlister wrote the equation 10 t minus 4 t + 3 t = 8 on the board and asked students to write an equivalent equation. The table below shows the responses from four students.
Answer:
t = 8/9
Step-by-step explanation:
There are many possible solutions that could be expressed as equivalent to the equation 10t - 4t + 3t = 8. With that being said, here is a simplified form, solved for t.
10t - 4t + 3t = 8
6t + 3t = 8
9t = 8
t = 8/9
Each of these form's is an equivalent equation to the one written by Mrs. McAlister.
If you can provide the table of student answers, we could answer which students were correct or wrong. Without the table, we can only guess.
Cheers.
Answer:
9t=8
Step-by-step explanation:
As a fraction what is 5/8+3/5
Answer:
49/40
Step-by-step explanation:
By using the LCD method 49/40 is the equivalent fraction by adding 5/8 and 3/5 your welcome
Answer:
5/8 + 3/5 = 49/40
Step-by-step explanation:
(5 x 40)/(8 x 40)
(3 x 40)/(5 x 40)
25/40
24/40
25 + 24/40
7. Eva bought popcorn, candy and a drink at
the movies. The popcorn was three times as
expensive as the candy and the drink was
twice as expensive as the candy. Eva spent a
total of $10.50.
a. Write an equation to represent the situation.
Let c represent the cost of the candy.
b. Find the value of c.
c. How much did Eva's
drink cost?
Answer:
Step-by-step explanation:
let $p, $c and $d represents the costs of popcorn, candy and a drink respectively. If the popcorn was three times as expensive as the candy then;
p = 3c.... 1
If the drink was twice as expensive as the candy then d = 2c .... 2
If Eva spent a total sum of $10.50 at the movies, the equation that represents the situation will be p + c + d = $10.50 .... 3
Substituting equation 1 and 2 into 3;
3c + c + 2c = $10.50
6c = $10.50
Hence the equation to represent the situation is 6c = $10.50 where c represents the cost of the candy.
b) To get c from the equation 6c = $10.50, we will simply divide both sides by the coefficient of c i.e 6 as shown
6c/6 = $10.50/6
c = $1.75
Hence the value of c is $1.75
c) The equation representing Eva's drink in terms of the candy is expressed as d = 2c
Substituting c = $1.75 into the equation will give;
d = 2(1.75)
d = 3.5
Hence the cost of Eva's drink is $3.50
Kate gets a paycheck twice a month. Every
month, a total of $345.67 is deducted from her
paycheck for taxes. If she has been paid 8
paychecks so far this year, how much money
has been deducted for taxes?
Answer:
1382.68
Step-by-step explanation:
not sure if im right
Answer:
–$2,419.69Step-by-step explanation:
I got it right on edgenuity
The GCF is 3x...
Express each term as the product of the GCF and its other factors.
15x^2+6x=3x(__)+3x(__)
8+(-8) + a = simplified
Answer:
Just a
Step-by-step explanation:
8+(-8) they cancel each other out so 0+a = a
What is (2x + 3)??
(2x + 3)?
1x2 +
Answer:
4x^2+12x+9
Step-by-step explanation:
(2x+3)(2x+3)
Multiply 2x by 2x first.
then 2x by 3
and then repeat that step and you add like terms
then recieve your answer.
Answer:
4x^2 + 12x + 9
Step-by-step explanation:
Actually, you are to find (2x + 3)^2, which is "the square of 2x + 3."
2x + 3 is a binomial. There is a formula for the square of a binomial:
(a + b)^2 = a^2 + 2ab + b^2
Following this pattern,
(2x + 3)^2 becomes:
[2x]^2 + 2[2x][3] + [3^2], or
4x^2 + 12x + 9
In evaluating a double integral over a region D, a sum of iterated integrals was obtained as follows:
∬Df(x,y)dA=∫5_0∫(2/5)y_0 f(x,y)dxdy+∫7_5∫(7−y)_0 f(x,y)dxdy.
Sketch the region D and express the double integral as an iterated integral with reversed order of integration.
∫b_a∫g2(x)_g1(x) f(x,y)dydx
a= b=
g1(x)= g2(x)=
Answer
[tex]a=0[/tex], [tex]b=2[/tex]
[tex]g_1(x)=\frac{5x}{2}[/tex], [tex]g_2(x)=7-x[/tex]
Step-by-step explanation:
Given that
[tex]\int \int Df(x,y)dA=\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy+\int_5^7\int_0^{7-y} f(x,y)dxdy\; \cdots (i)[/tex]
For the term [tex]\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy[/tex].
Limits for [tex]x[/tex] is from [tex]x=0[/tex] to [tex]x=\frac {2y}{5}[/tex] and for [tex]y[/tex] is from [tex]y=0[/tex] to [tex]y=5[/tex] and the region [tex]D[/tex], for this double integration is the shaded region as shown in graph 1.
Now, reverse the order of integration, first integrate with respect to [tex]y[/tex] then with respect to [tex]x[/tex] . So, the limits of [tex]y[/tex] become from [tex]y=\frac{5x}{2}[/tex] to [tex]y=5[/tex] and limits of [tex]x[/tex] become from [tex]x=0[/tex] to [tex]x=2[/tex] as shown in graph 2.
So, on reversing the order of integration, this double integration can be written as
[tex]\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy=\int_0 ^2\int _ {\frac {5x}{2}}^5 f(x,y)dydx\; \cdots (ii)[/tex]
Similarly, for the other term [tex]\int_5 ^7\int _0 ^ {7-y} f(x,y)dxdy[/tex].
Limits for [tex]x[/tex] is from [tex]x=0[/tex] to [tex]x=7-y[/tex] and limits for [tex]y[/tex] is from [tex]y=5[/tex] to [tex]y=7[/tex] and the region [tex]D[/tex], for this double integration is the shaded region as shown in graph 3.
Now, reverse the order of integration, first integrate with respect to [tex]y[/tex] then with respect to [tex]x[/tex] . So, the limits of [tex]y[/tex] become from [tex]y=5[/tex] to [tex]y=7-x[/tex] and limits of [tex]x[/tex] become from [tex]x=0[/tex] to [tex]x=2[/tex] as shown in graph 4.
So, on reversing the order of integration, this double integration can be written as
[tex]\int_5 ^7\int _0 ^ {7-y} f(x,y)dxdy=\int_0 ^2\int _5 ^ {7-x} f(x,y)dydx\;\cdots (iii)[/tex]
Hence, from equations [tex](i)[/tex], [tex](ii)[/tex] and [tex](iii)[/tex] , on reversing the order of integration, the required expression is
[tex]\int \int Df(x,y)dA=\int_0 ^2\int _ {\frac {5x}{2}}^5 f(x,y)dydx+\int_0 ^2\int _5 ^ {7-x} f(x,y)dydx[/tex]
[tex]\Rightarrow \int \int Df(x,y)dA=\int_0 ^2\left(\int _ {\frac {5x}{2}}^5 f(x,y)+\int _5 ^ {7-x} f(x,y)\right)dydx[/tex]
[tex]\Rightarrow \int \int Df(x,y)dA=\int_0 ^2\int _ {\frac {5x}{2}}^{7-x} f(x,y)dydx\; \cdots (iv)[/tex]
Now, compare the RHS of the equation [tex](iv)[/tex] with
[tex]\int_a^b\int_{g_1(x)}^{g_2(x)} f(x,y)dydx[/tex]
We have,
[tex]a=0, b=2, g_1(x)=\frac{5x}{2}[/tex] and [tex]g_2(x)=7-x[/tex].
The required values are,
[tex]a=0\\b=2\\g_1(x)=\frac{5x}{2} \\g_2(x)=7-x[/tex]
Double Integral:Double integral is mainly used to find the surface area of a 2d figure, and it is denoted using ‘ ∫∫’. We can easily find the area of a rectangular region by double integration.
Given function is,
[tex]\int \int_Df(x,y)dA=\int_{0}^{5}\int_{0}^{2y}f(x,y)dxdy+\int_{5}^{7}\int_{0}^{7-y}f(x,y)dxdy[/tex]
We can write the double integral as a single term by reversing the order as,
[tex]\int_{a}^{b}\int_{g_1(x)}^{g_2(x)}f(x,y)dydx=\int_{0}^{2}\int_{\frac{5x}{2}}^{7-x}f(x,y)dydx)[/tex]
The region D is attached below.
Hence, we get the values,
[tex]a=0\\b=2\\g_1(x)=\frac{5x}{2} \\g_2(x)=7-x[/tex]
Learn more about the topic Double Integral:
https://brainly.com/question/18568839
Write and expression equivalent to (7.5+2)-5
Answer:
4.5
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write expression
(7.5 + 2) - 5
Step 2: Parenthesis
9.5 - 5
Step 3: Subtract
4.5
Answer:
4.5
Step-by-step explanation:
Order of operations rules dictate that we do the operation within the parentheses first: 7.5 + 2 = 9.5.
Then we have 9.5 - 5, or 4.5.
Give Two Other Names For WQ
Answer:
d. Name a ray with endpoint E that is an opposite ray of . Solution a
Consider the first order differential equation
y′ + t/t2 − 25y = et/t − 9
For each of the initial conditions below, determine the largest interval a
a. y(-7) = 6.4.
b. y(-2. 5) = -0.5.
c. y(0) = 0.
d. y(4.5) = -2.1.
e. y(14)= 1.7.
Answer:
For y(-7) =6.4
The largest interval is between
[tex]-\infty \to -5[/tex]
For y(-2.5) = -0.5.
The largest interval is between
[tex]-5 \to 5[/tex]
For y(0) = 0
The largest interval is between
[tex]-5 \to 5[/tex]
For y(4.5) = -2.1.
The largest interval is between
[tex]-5 \to 5[/tex]
For y(14)= 1.7.
The largest interval is between
[tex]9 \to \infty[/tex]
Step-by-step explanation:
From m the question we are told that
The first order differential equation is [tex]\frac{y' - t}{ t^2 -25} = \frac{e^t}{t-9}[/tex]
Now the first step is to obtain the domain of the differential equation
Now to do that let consider the denominators
Now generally
[tex]t^2 - 25 \ne 0[/tex] side calculation
=> [tex]t\ne \pm5[/tex] [tex]t^2 - 25 = 0[/tex]
[tex]t = \pm 5[/tex]
Also [tex]t-9\ne 0[/tex] [tex]t -9 = 0[/tex]
=> [tex]t\ne 9[/tex] [tex]t= 9[/tex]
This means that this first order differential equation is discontinuous at
[tex]t = -5 , \ \ t = 5 \ \ t = 9[/tex]
[tex]This \ is \ illustrated \ below \ \\ ------------------\\\. \ \ \ | \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | \ \ \ \ \ \ \ \ \ \ \ \ \ |\\. \ -5 \ \ \ \ \ \ \ \ \ \ \ \ 5 \ \ \ \ \ \ \ \ \ \ \ \ \ 9[/tex]
So
For y(-7) =6.4
The largest interval is between
[tex]-\infty \to -5[/tex]
For y(-2.5) = -0.5.
The largest interval is between
[tex]-5 \to 5[/tex]
For y(0) = 0
The largest interval is between
[tex]-5 \to 5[/tex]
For y(4.5) = -2.1.
The largest interval is between
[tex]-5 \to 5[/tex]
For y(14)= 1.7.
The largest interval is between
[tex]9 \to \infty[/tex]