[tex]\left \{ {{x=3} \atop {y+1=0}} \right.[/tex] solve graphically this linear system of equations
Answers
Answer:
The solution is the point (3, -1)
Step-by-step explanation:
We have the system of equations:
x = 3
y + 1 = 0
To solve this graphically, we need to graph these two lines and see in which point the lines intersect.
To graph the line x = 3, we need to draw a vertical line that passes through x = 3.
To graph y + 1 = 0
First we should isolate y.
y = -1
This is graphed as a horizontal line that passes through y = -1
The graph of these two lines can be seen in the image below.
Where the green line is x = 3, and the blue line is y = -1
Now, looking at the graph we can see that the lines do intersect in the point (3, -1)
Then the solution of the system is the point (3, -1)
![[tex]\left \{ {{x=3} \atop {y+1=0}} \right.[/tex] Solve Graphically This Linear System Of Equations](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/AEr9r0IZ5mjNAIt4LjQW1oPlkO6mn8Jv.png)
Related Questions
Identify the two types of incorrect decisions in a hypothesis test. For each incorrect decision, what symbol is used to represent the probability of making that type of error?
Choose the correct answer below.
A. A Type 1 error is rejecting a true null hypothesis, whose probability is denoted α
A Type Il error is not rejecting a false null hypothesis, whose probability is denoted β
B. A Type 1 error is not accepting a true null hypothesis, whose probability is devoted α
A Type Il error is accepting a false null hypothesis, whose probability is denoted β
C. A Type I error is not rejecting a false null hypothesis, whose probability is denoted α.
A Type Il error is rejecting a true null hypothesis, whose probability is denoted β
D. A Type 1 error is accepting a false null hypothesis, whose probability is denoted α
A Type Il error is not accepting a true null hypothesis, whose probability is denoted β
Answers
The two types of incorrect decisions in a hypothesis test and the symbol used to represent the probability of making that type of error are as follows:
A. A Type 1 error is rejecting a true null hypothesis, whose probability is denoted α.
A Type II error is not rejecting a false null hypothesis, whose probability is denoted β.
What are Type I and Type II errors?A Type I error occurs when the null hypothesis is rejected, even though it is actually true.
The probability of committing a Type I error is denoted by α (alpha), which is the significance level of the test.
A Type II error occurs when the null hypothesis is not rejected, even though it is actually false.
The probability of committing a Type II error is denoted by β (beta).
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The original price of a camera was $60. It was
on sale at a 20% discount. Later, the price of the
camera was reduced by an additional 25% of the
sale price. What was the final price of the camera?
Answers
Answer:
$36
Step-by-step explanation:
60-12 is 48 (20%)
And 75% Of 48 Is 36
Given the ellipse (x-8)² (y + 1)² 1. 16 4 what are the vertices and co-vertices of the ellipse? Select the correct answer below: The vertices are (12, -1) and (4, -1). The co-vertices are (8, 1) and (8, -3). The vertices are (8, 1) and (8, -3). The co-vertices are (12, -1) and (4, -1). The vertices are (8, 3) and (8,-5). The co-vertices are (10, -1) and (6, -1). O The vertices are (10, -1) and (6, -1). The co-vertices are (8, 3) and (8,-5). +
Answers
The vertices of the ellipse are (12, -1) and (4, -1), and the co-vertices are (8, 1) and (8, -3).
To find the vertices and co-vertices of the given ellipse, we can use the equation of an ellipse in standard form:
((x-h)²/a²) + ((y-k)²/b²) = 1
Comparing this with the given equation ((x-8)²/(16)) + ((y+1)²/(4)) = 1, we can identify the values of h, k, a, and b.
From the equation, we can see that the center of the ellipse is at (h, k) = (8, -1). The value of a is the square root of the denominator of the x-term, which is 4, so a = 4. Similarly, the value of b is the square root of the denominator of the y-term, which is 2, so b = 2.
The vertices of the ellipse are located at a distance of a units from the center along the major axis, which is the x-axis. Therefore, the vertices are (8+a, -1) and (8-a, -1), which simplifies to (12, -1) and (4, -1).
The co-vertices of the ellipse are located at a distance of b units from the center along the minor axis, which is the y-axis. Therefore, the co-vertices are (8, -1+b) and (8, -1-b), which simplifies to (8, 1) and (8, -3).
Hence, the correct answer is: The vertices are (12, -1) and (4, -1). The co-vertices are (8, 1) and (8, -3).
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guys please help me with this question
Answers
Answer:
= 15/20 + 1 10/20 + 4 4/20
= 5 29/20
= 6 9/20
Exact Form:
[tex]\frac{3}{4}[/tex]
Decimal Form:
6.45
Mixed Number Form:
6[tex]\frac{9}{12}[/tex]
This equation shows how the size of Terrence's sticker collection is related to the number of sticker packs he buys.
s = 20p
The variable p represents the number of sticker packs he buys, and the variable s represents the total number of stickers he has. How many sticker packs does Terrence have to buy to have a total of 20 stickers?
Answers
Answer:
400
Step-by-step explanation:
Which distribution do you use when you are testing a population mean and the standard deviation is known? Assume sample size is large.
O normal distribution
O uniform distribution
O Student's t-distribution
O binomial distribution
O Poisson distribution
Answers
The option A is correct answer which is Normal distribution.
What is Normal distribution?
A sort of continuous probability distribution for a random variable with a real value is called a normal distribution or a Gaussian distribution in statistics.
When testing a population mean and the standard deviation with large sample size so we used Normal distribution.
Hence, the option A is correct answer which is Normal distribution.
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ASAP What is 94737638 x -9376383889483 this is a real question plz help!!!
Answers
Answer:
-8.8829646e+20
Step-by-step explanation:
Answer:
Step-by-step explanation:
Remark
94737638 x -9376383889483
The exact answer can be found by using the calculator that comes with windows (windows 7 if you are using that. Windows 10 for sure.). It can give exact answers up to 18 digits (or that's what I thought. This question is an astonishing 21 digits). The answer to this question is
-888,296,462,670,872,461,154
I don't know if Apple has a calculator that comes with its operating system. I would think so, but I don't know. I use a PC.
Proving parallel lines. Find the value of x so that l // m. State the converse worksheet due tomorrow help please.
Answers
Answer:
x = 17Step-by-step explanation:
Find the diagram attached
The sum of the two adjacent angles is 180 degrees. Hence;
8x-9 + 53 = 180
8x + 44 = 180
Subtract 44 from both sides of the equation
8x + 44 - 44 = 180 - 44
8x = 136
Divide both sides by 8
8x/8 = 136/8
x = 17
Hence the value of x is 17
What is the area of the shaded triangle?
Answers
A= 30m
Solve d/4+7/8=6
What is d?
Answers
Answer:
the answer is d=20.5 hope this helped
Answer:
d= 20.5
Step-by-step explanation:
d/4+7/8=6
(we know that to add fractions, we have to have both denomiators the same number. We aslo know that that means 8. Using that information, we know that to top number must be 48. 48/8 = 6. We can substract)
48-7= 41
(we then need to divide by 2 as we would have had to already multiplyed 4 by 2.)
41/2 = 20.5
Sean is employed as a truck driver. He drives x hours a week and is paid $21.60 per hour. Also he is paid $250 for food per week. This week he earned a total of $1,114. How many hours did he drive?
Answers
Answer:
Hours driven= 40 hours
Step-by-step explanation:
Giving the following information:
Variable income= $21.6 per hour
Fixed income= $250
Total income= $1,114
To calculate the number of hours driven, we need to use the following formula:
Total income= fixed income + hourly rate*number of hours
1,114 = 250 + 21.6*x
864 = 21.6x
864 / 21.6 = x
40=x
Hours driven= 40 hours
A cylinder has a radius of 15 feet. Its volume is 5,652 cubic feet. What is the height of the cylinder?
Answers
Answer:
8
Step-by-step explanation:
I just put it in the calculator thint
Label each statement as true or false regarding the zeros/roots of a quadratic function. The roots zeros of a quadratic function are the same as the factors of the quadratic function. The roots zeros are the spots where the quadratic function intersects with the y-axis. The roots zeros are the spots where the quadratic function intersects with the x-axis. There are not always two roots/zeros of a quadratic function,
Answers
Answer:
True, false, true, true.
Step-by-step explanation:
The roots zeros of a quadratic function are the same as the factors of the quadratic function. This is true because your roots are your factors—>(x-3) is a factor, x=3 is the root.
The roots zeros are the spots where the quadratic function intersects with the y-axis. No! Those are called y-intercepts!
The roots zeros are the spots where the quadratic function intersects with the x-axis. True. X-intercepts are your solutions. (x-3) graphed would the (3,0). That’s a solution.
There are not always two roots/zeros of a quadratic function, True. No solution would be when your quadratic doesn’t intersect the x-axis. One solution would be when your vertex would be on the x-axis. Two solutions is when your quadratic intersects the x-axis twice. Can there be infinite solutions? No. It’s either 0, 1, or 2 solutions.
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 7(1.06)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 13,29 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Answers
The y-intercept of the graph of the function f(d) would represent 7 and a reasonable domain to plot the growth function is 0 ≤ d ≤ 18 because the number of days is a whole number.
Part A: When the biologist concluded her study, the radius of the algae was approximately 13,29 mm.
What is a reasonable domain to plot the growth function?The given equation is,f(d) = 7(1.06)d
The radius of the algae was approximately 13.29 mm, which is the value of f(d).Thus, f(d) = 13.29
Substitute this value in the equation to find the value of d.13.29 = 7(1.06)dlog(13.29/7)/log(1.06) = dd = 17.19
Hence, a reasonable domain to plot the growth function is 0 ≤ d ≤ 18 because the number of days is a whole number.
Part B: What does the y-intercept of the graph of the function f(d) represent?The y-intercept of the graph of the function f(d) represents the initial value of the function when x = 0. The given function is,f(d) = 7(1.06)d
Substitute 0 in the above function and solve for f(0).f(0) = 7(1.06)0f(0) = 7
Hence, the y-intercept of the graph of the function f(d) represents 7.
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What is the value of y when
IN
The value of y varies directly with x. When y = 75, x =
x is 2
A 84
B 337
С
- 162
D 168
4
В.
Answers
Answer:
I think that the answer is B , 337/5 i mean .
Good luck ^^
What is the probability that the sample mean life span of 64 calculators from Caseo will exceed the sample mean life span of 81 calculators from Sharpy by greater than 6 months?
Answers
Answer:
it would be 64-81 than answer devide by 6.
Find the eigenvalues and the corresponding eigenspaces for the matrix -2 0 1 1 0 -1 0 1 - 1 Here the characteristic polynomial should be cubic. You may use a calculator or Wolfram Alpha to factor the characteristic polynomial if you wish.
Answers
The eigenvalues of the matrix -2 0 1 1 0 -1 0 1 -1 are λ₁ = -1, λ₂ = 1, and λ₃ = -1. The corresponding eigenspaces are E₁ = span{[-1, 1, 0]}, E₂ = span{[1, 1, 1]}, and E₃ = span{[-1, 1, 2]}.
Eigenvalues and eigenvectors play a fundamental role in linear algebra, particularly in the study of matrices.
The eigenvalues of a matrix are the values λ for which the equation A = λ has nontrivial solutions, where A is the given matrix and is a non-zero vector. The eigenspace associated with an eigenvalue is the set of all eigenvectors corresponding to that eigenvalue.
To find the eigenvalues of the matrix -2 0 1 1 0 -1 0 1 -1, we need to solve the characteristic equation det(A - λI) = 0, where A is the given matrix, λ is an eigenvalue, and I is the identity matrix.
The characteristic equation in this case is (-2 - λ)(λ² + 1) + (1 - λ)(-1) = 0. Simplifying this equation yields λ³ - 2λ² - 2 = 0. This is a cubic equation, and we can use a calculator or Wolfram Alpha to find its roots, which are λ₁ = -1, λ₂ = 1, and λ₃ = -1.
Once we have the eigenvalues, we can find the corresponding eigenvectors by solving the equation (A - λ) = 0 for each eigenvalue.
For λ₁ = -1, solving (A + ) = 0 gives us the eigenvector [-1, 1, 0]. For λ₂ = 1, solving (A - ) = 0 gives us the eigenvector [1, 1, 1].
Finally, for λ₃ = -1, solving (A + ) = 0 gives us the eigenvector [-1, 1, 2]. These eigenvectors span the eigenspaces E₁, E₂, and E₃, respectively.
In summary, the eigenvalues of the matrix -2 0 1 1 0 -1 0 1 -1 are λ₁ = -1, λ₂ = 1, and λ₃ = -1. The corresponding eigenspaces are E₁ = span{[-1, 1, 0]}, E₂ = span{[1, 1, 1]}, and E₃ = span{[-1, 1, 2]}.
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What number could replace t below?
\dfrac{1}{3} = \dfrac{2}{t}
3
1
=
t
2
Answers
Answer:
If you go to this link it'll give you a whole explanation and walk how to get your answer:
https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-visualizing-equiv-frac/a/equivalent-fractions-common-denominator-review
Step-by-step explanation:
Hope that this helps! :)
Have a great rest of your day/night!
Round to the nearest tenth, if necessary.
Answers
Answer:
what are we rounding? like what is your question?
Step-by-step explanation:
**if you answer you have my promise and i'll go back and provide an actual answer**
what is the worst thing you can do to a girl but they will like it
Answers
Answer:
KISS THEY BESTFRIEND AND THEY BOTH WANNA CUDDLE
Step-by-step explanation:
Answer:
expressing how you feel even if it comes off wrong because sometimes we understand this based off of a boys actions for example say he gets an attitude because your talking to everyone except him at a party and he came there with you well you have to understand that it could come off as awkward because he standing around looking lonely because your not admiring his presence when he's there with you and 9 times out of 10 your his girl friend
Step-by-step explanation:
Which shows the Commutative Property of Addition?
A 2 (5+6)=2 (5) + 2(6)
B 3+ (7+ -2) = 3 +(-2+ 7)
C 13+ (-13) = 0
D-9+(3+4)= (-9 + 3) + 4
Answers
Answer:
B 3+ (7+ -2) = 3 +(-2+ 7)
Step-by-step explanation:
It shows that the answer is the same even if you switch the problem in the parentheses around
A homeowner installs a solar heating system, which generates 20 savings at a rate of 300e t dollars per year, t years after installation. Find a formula for the total savings after t years. If the system cost 30000 dollars to install, when will the savings match the installation cost
Answers
Answer:
"35.84 years" is the appropriate solution.
Step-by-step explanation:
The given values are:
Rate of savings generation,
[tex]s'(t)=300e^{\frac{t}{20} }[/tex]
System cost to install,
= $30000
Now,
The total savings will be:
⇒ [tex]s(t)=\int\limits s'(t) \ dt[/tex]
On substituting the values, we get
⇒ [tex]= \int\limits 300e^{\frac{t}{20} } \ dt[/tex]
⇒ [tex]s(t)=\frac{300e^{\frac{t}{20} }}{\frac{1}{20} }+c[/tex]
When,
Savings = 0
t = 0, then
⇒ [tex]0=6000e^o+c[/tex]
⇒ [tex]c=-6000[/tex]
The formula will be:
⇒ [tex]s(t)=6000[e^{\frac{t}{20} }-1][/tex]
On putting the values in the above formula, we get
⇒ [tex]30000=6000(e^{\frac{t}{20} }-1)[/tex]
[tex]5=e^{\frac{t}{20}}-1[/tex]
[tex]e^{\frac{t}{20} }=6[/tex]
On taking log, we get
⇒ [tex]\frac{t}{20} =log \ 6[/tex]
[tex]t=20 log 6[/tex]
[tex]=35.84 \ years[/tex]
use the midpoint rule with the given value of n to approximate the integral. round the answer to four decimal places.
Answers
Using the midpoint rule with the given value of n, we can approximate the integral. The answer, rounded to four decimal places, will be explained in the following paragraphs.
The midpoint rule is a numerical method used to approximate definite integrals. It involves dividing the interval of integration into n subintervals of equal width and evaluating the function at the midpoint of each subinterval. The approximated value of the integral is obtained by summing the products of the function values at the midpoints and the width of each subinterval.
To calculate the integral using the midpoint rule, we need to know the value of n, which determines the number of subintervals. The larger the value of n, the more accurate the approximation becomes. However, increasing n also requires more computational effort.
Once we have determined the value of n, we divide the interval of integration into n subintervals of equal width. Then, we evaluate the function at the midpoint of each subinterval and multiply it by the width of the subinterval. Finally, we sum up all these products to obtain the approximate value of the integral.
Rounding the answer to four decimal places ensures that the approximation is presented with a reasonable level of precision. It is important to note that while the midpoint rule provides a reasonable estimate, it may not always yield an exact result due to the inherent limitations of numerical methods for integration.
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Use complete sentences to describe the domain of the consine function.
Answers
Answer:
The domain of a function is the set of the possible input values of the function. For example: consider the function f(x) = cos x, the domain of the function is the set of possible values of x.
The cosine function takes x values from all real numbers.
Therefore, the domain of the cosine function is a real numbers.
Step-by-step explanation:
Find the area of a trapazoid
Answers
Answer:
The formula would be
((a+b) / 2)h = area
In this case a is one side of the base (top parralel or bottom line)
And b is the second one (top or bottom)
You can only choose one for each
You add those two up and divide that by 2
Now you multiply it by “h” or height.
Now you have the area
6. The distribution of the weight of a prepackaged "1-kilo pack" of cheddar cheese is assumed to be N(1.18, 0.072), and the distribution of the weight of a prepackaged *3-kilo pack" of cheese (special for cheese lovers) is N(3.22, 0.09²).
Select at random three 1-kilo packs of cheese, independently, with weights being X1, X2 and X3 respectively. Also randomly select one 3-kilo pack of cheese with weight being W. Let Y = X1 + X2 + X3.
(a) Find the mgf of Y
(b) Find the distribution of Y, the total weight of the three 1-kilo packs of cheese selected.
(c) Find the probability P(Y
Answers
(a) The mgf of Y is M_Y(t) = exp (3.54t + 0.01632t²).
(b) The distribution of Y, the total weight of the three 1-kilo packs of cheese selected is Y ~ N(3.54, 0.216).
(c) The probability P(Y < W) = 0.2808.
(a) The moment generating function (mgf) of Y, the total weight of the three 1-kilo packs of cheese selected is given by:
M_Y(t) = M_X1(t) × M_X2(t) × M_X3(t)
= exp (µ_X1 t + ½ σ²_X1 t²) × exp (µ_X2 t + ½ σ²_X2 t²) × exp (µ_X3 t + ½ σ²_X3 t²)
= exp [(µ_X1 + µ_X2 + µ_X3) t + ½ (σ²_X1 + σ²_X2 + σ²_X3) t²]
Therefore, the mgf of Y is given by:
M_Y(t) = exp [(1.18 + 1.18 + 1.18) t + ½ (0.072 + 0.072 + 0.072) t²]
M_Y(t) = exp (3.54t + 0.01632t²)
(b) The total weight Y of the three 1-kilo packs of cheese is the sum of three independent and identically distributed random variables.
So, the distribution of Y is given by the following normal distribution: Y ~ N (µ_Y, σ²_Y), where µ_Y = µ_X1 + µ_X2 + µ_X3 and σ²_Y = σ²_X1 + σ²_X2 + σ²_X3.
Thus, µ_Y = 3 × 1.18
µ_Y = 3.54 and,
σ²_Y = 3 × 0.072
σ²_Y = 0.216
⇒ σ_Y = √0.216
⇒ σ_Y = 0.4649
Therefore, Y ~ N(3.54, 0.216).
(c) We need to find P(Y < W), where W is the weight of the 3-kilo pack of cheese.
Now, Y and W are independent normal random variables.
Therefore, Y - W is also a normal random variable with the following distribution: Y - W ~ N(µ_Y - µ_W, σ²_Y + σ²_W), where µ_W = 3.22 and σ²_W = 0.09².
We know that µ_Y - µ_W = 3.54 - 3.22
µ_Y - µ_W = 0.32 and,
σ²_Y + σ²_W = 0.216 + 0.09² = 0.301.
Therefore, σ_Y - W = √0.301
σ²_Y + σ²_W = 0.5486.
Now, we need to find P(Y - W < 0), which is equivalent to finding P(Z < -0.5799), where Z = (Y - W - (µ_Y - µ_W))/σ_Y - W.
Substituting the values, we get:
Z = (Y - W - 0.32)/0.5486
⇒ Y - W = -0.5799
Z = (Y - W - 0.32)/0.5486
⇒ Y - W < 0 is equivalent to Z < -0.5799.
Using a standard normal table or calculator, we get: P(Z < -0.5799) = 0.2808.
Hence P(Y < W) = P(Y - W < 0)
P(Y < W) = 0.2808.
Therefore, P(Y < W) = 0.2808, correct to four decimal places.
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4.
Find the area of the shaded region.
A. 5x2 + 16x – 21
B. 7x2 + 28x + 27
C. 5x2 + 28x + 27
D. 5x2 + 28x + 21
Answers
Answer:
yay
Step-by-step explanation:
yayyayyayyayyayyyayyayayayyayaya
Answer:
D. 5x2 + 28x + 21
Step-by-step explanation:
First you want to find the area of the white rectangle
Then find the area of the beings rectangle
Then subtract beings minus white.
Sorry it’s +21. The first answer in your list
then thats correct
...............................................................................................................................................
5x^2+28x+21 confirmed from Cortez himself
What is the radius of a circle with a diameter of 240 mm?
A) 76.43 mm
B) 480.00 mm
C)12.00 mm
D) 120.00 mm
Answers
The radius of a circle is half of its diameter so the radius of a circle with a diameter of 240 mm is 120.00 mm. Option D is the correct answer.
To find the radius of a circle with a given diameter, you can follow these steps:
Given that the diameter is 240 mm, divide it by 2 to obtain the radius. Recall that the radius is half the length of the diameter.
Radius = Diameter / 2
In this case, Radius = 240 mm / 2 = 120 mm.
Therefore, the radius of the circle with a diameter of 240 mm is 120.00 mm.
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A swimming pool is 20 ft wide and 40 ft long and its bottom is an inclined plane, the shallow end having a depth of 3 ft and the deep end, 9 ft.
Suppose the pool is full of water, and assume that the weight density of water is62.5\,lb/ft^3.
(a) Find the hydrostatic force (in lb) on the shallow end. (include units)
Hydrostatic force = (b) Find the hydrostatic force (in lb) on the deep end. (include units)
Hydrostatic force = (c) Find the hydrostatic force (in lb) on one of the sides that extends from the shallow end to the deep end. (include units)
Hydrostatic force = (d) Find the hydrostatic force (in lb) on the bottom of the pool. (include units)
Hydrostatic force =
Answers
The pool's hydrostatic force is 1,500 pounds at the shallow end, 4,500 pounds at the deep end, 1,500 pounds on each side from shallow to deep, and 0 pounds at the bottom.
(a) To compute the pressure the water exerts at that depth and multiply it by the shallow end's surface area, we must first measure the hydrostatic force on the shallow end. The equation P = gh, pressure is P, is the fluid's density, acceleration from gravity is g, the depth is h, determines the pressure that a fluid exerts at a given depth.
In this case, the depth of the shallow end is 3 ft. The weight density of water is given as 62.5 lb/ft³.
Plugging in these values, we have,
P = (62.5 lb/ft³) * (32.2 ft/s²) * (3 ft)
P = 1,500 lb/ft².
To find the hydrostatic force, we multiply this pressure by the surface area of the shallow end, which is the width times the length,
Hydrostatic force = 1,500 lb/ft² * (20 ft * 40 ft)
Hydrostatic force = 1,500 lb. Therefore, the hydrostatic force on the shallow end is 1,500 lb.
(b) Using the same method as in part (a), we find that the pressure exerted by the water at the depth of the deep end, which is 9 ft, is ,
P = (62.5 lb/ft³) * (32.2 ft/s²) * (9 ft)
P = 4,500 lb/ft².
Multiplying this pressure by the surface area of the deep end (20 ft * 40 ft), we get the hydrostatic force on the deep end,
Hydrostatic force = 4,500 lb/ft² * (20 ft * 40 ft)
Hydrostatic force = 4,500 lb.
Therefore, the hydrostatic force on the deep end is 4,500 lb.
(c) The depth of the side is varying linearly from 3 ft to 9 ft. Taking the average depth, we have (3 ft + 9 ft) / 2 = 6 ft.
Using the formula,
P = (62.5 lb/ft³) * (32.2 ft/s²) * (6 ft),
We find that the pressure is 3,000 lb/ft².
Multiplying this pressure by the surface area of the side (20 ft * 6 ft), we get the hydrostatic force,
Hydrostatic force = 3,000 lb/ft² * (20 ft * 6 ft)
Hydrostatic force = 1,500 lb.
(d) Since the bottom of the pool is horizontal, the depth remains constant throughout, which is 3 ft. Plugging this value into the formul,
P = (62.5 lb/ft³) * (32.2 ft/s²) * (3 ft),
p = 1,500 lb/ft², we find that the pressure is 1,500 lb/ft². However, since the bottom is horizontal, the surface area facing upward cancels out the surface area facing downward, resulting in a net force of 0 lb.
Therefore, the hydrostatic force on the bottom of the pool is 0 lb.
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evaluate the double integral where is the region in the first quadrant enclosed by the circle and the lines and by changing to polar coordinates.
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To evaluate the double integral over the region in the first quadrant enclosed by a circle and lines by changing to polar coordinates, we need to express the integral limits and the integrand in terms of polar coordinates.
The region in the first quadrant enclosed by a circle and lines can be defined as follows: The circle has a radius 'r' centered at the origin, and the lines are given by the equations θ = 0 and θ = π/4, where θ represents the angle in polar coordinates.
In polar coordinates, the limits of integration for 'r' would be from 0 to the radius of the circle, and the limits of integration for θ would be from 0 to π/4.
The integrand, which represents the function being integrated, would be expressed in terms of 'r' and θ.
To evaluate the double integral, we would integrate the function over the defined region using the limits of integration and the appropriate differential element in polar coordinates, which is r dr dθ.
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