A rectangular pool has length of 6 m and 3 m width. The pool is surrounded by a uniform edge with width x m. Given the area of the pool side is 32 m². Form a quadratic function and equation for the situation.
Answers
Answer:
you can solve this problem with the help of this example :
A rectangular pool 20 meters wide and 60 meters long is surrounded by a walkway of uniform width. If the total area of the walkway is 516 square meters, how wide, in meters, is the walkway?
Sol:
A rectangular pool has length l=60m & breadth b=20m.
It has a surrounding walkway of area =516m
2
.
Area (pool) =60×20=1200m
2
Let us take the width of the walkway =
2
X
.
∴ The length as well as the breadth of the area (pool+walkway) will be increased by X
So the length =l of the area (pool+walkway) =(60+X)m and the breadth =b=(20+X)m
∴ Area (pool+walkway) =l×b=[(60+X)×(20+X)]m
2
.
∴ Area (walkway) = Area (pool+walkway) - Area (pool)
=(60+X)×(20+X)−1200=516m
2
....(given)
⇒X
2
+80X−516=0
⇒X=−86 or X=6.
We reject the negative value as X is a length.
So X=6m.
Ans- The width of the walkway =
2
X
=3m.
Related Questions
Does anyone know what is going on with this website? So many hackers, trolls, and people giving non answers to the questions asked! It didn't used to be this way. :(
Answers
Answer:
Lots of people are just answering to get free points now, they're not actually giving answers.
(and sorry if you miss the way it used to be).
I need some help, this is a trig question and I have no idea how to even start it.
Answers
Answer:
Set your calculator to Degree mode.
\( \alpha = {cos}^{ - 1} \frac{7}{8} \)
\( \cos(2 \alpha ) = \frac{7}{x} \)
\( \cos(2 {cos}^{ - 1} \frac{7}{8} ) = 2 {cos}^{2} ( {cos}^{ - 1} \frac{7}{8} ) - 1 = \frac{7}{x} \)
\(2( { \frac{7}{8}) }^{2} - 1 = \frac{7}{x} \)
\( \frac{17}{32} = \frac{7}{x} \)
\(17x = 224\)
\(x = \frac{224}{17} = 13.176\)
\( \alpha = {cos}^{ - 1} \frac{7}{8} = 28.955 \: degrees\)
So x = 224/17 = 13.176 and theta = 28.955°.
Help my I’m begging please it is very important
Answers
Answer:
30% Markup
Step-by-step explanation:
10-7= 3 3=30%
$700/100 = 7 so they were originally bought at $7. they are sold at $10 so they are raised by $3. the percent they are raised by is 3/7, or about 43%
In finance, we need to do partial observations of data and estimate the data generating process (DGP) -- for example, log-normal returns. Sometimes, we can observe only the data points of a certain process, but we don't know what is the function generating the process. Consider the following graph is a plot of the f ′
(x), of a function f(x) given. What is the underlaying function ( f(x −
i)) that is the generator of the observed points in the plot f ′
(x −
i), for points x −
1=−1,x −
2=−0.9,…,x −
n=1?
Answers
The underlying function f(x - i) that generates the observed points f'(x - i) in the plot can be determined by integrating the observed points. By integrating f'(x - i), we can obtain f(x - i) up to a constant of integration.
The constant of integration can be determined by incorporating additional information or constraints related to the problem or by considering the behavior of the function at a specific point.
To find the underlying function f(x - i) that generates the observed points f'(x - i), we need to integrate the observed points.
Integration is the reverse process of differentiation, so by integrating f'(x - i), we can recover f(x - i) up to a constant of integration.
The constant of integration arises because integration does not provide a unique solution.
The constant represents an arbitrary additive term that can vary depending on the specific problem or additional constraints.
To determine the constant of integration, we may need additional information or consider specific conditions related to the problem.
It is also important to note that the accuracy of estimating the underlying function f(x - i) depends on the quality and quantity of the observed data points f'(x - i). More data points and precise measurements can lead to a better estimation of the underlying function.
Additionally, the behavior of the function at a specific point can provide valuable insights for determining the constant of integration and refining the estimation of the underlying function.
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2. . Select the correct answer from each drop-down menu. The given equation has been solved in the table. Step Statement 1 31 – 10 = –16 2 3r – 10 + 10 = –16 + 10 3 3 r = -6 4 -6 3 3 5 Use the table to complete each statement. In step 2, the In step 4, the property of equality was applied. property of equality was applied.
Answers
1) Considering the equation
3x -10 = -16 Add 10 to both sides
3x -10+10= -16 +10
For the following question, show representation, your initial equations, your algebra work, symbolic answer, and units check.
A dog is sitting at an initial position of D1= (50 m North, 10 m East) from her home. She moves in a straight line until she is at a final position of D2 = ( 5 m North, 35 m East) from her home. It takes her 15 seconds to move from the initial position to the final position; find the magnitude of her average velocity vector.
Answers
The magnitude of the average velocity vector is approximately 3.651 m/s.
To find the magnitude of the average velocity vector, we need to calculate the displacement and divide it by the time taken.
Representation:
Initial position: D1 = (50 m North, 10 m East)
Final position: D2 = (5 m North, 35 m East)
Time taken: t = 15 seconds
Equations:
Displacement vector (ΔD) = D2 - D1
Average velocity vector (\(V_{avg}\)) = ΔD / t
Algebra work:
ΔD = D2 - D1
= (5 m North, 35 m East) - (50 m North, 10 m East)
= (-45 m North, 25 m East)
|ΔD| = √((-45)^2 + 25^2) [Magnitude of the displacement vector]
\(V_{avg}\) = ΔD / t
= (-45 m North, 25 m East) / 15 s
= (-3 m/s North, 5/3 m/s East)
|\(V_{avg}\)| = √((-3)^2 + (5/3)^2) [Magnitude of the average velocity vector]
Symbolic answer:
The magnitude of the average velocity vector is approximately 3.651 m/s.
Units check:
The units for displacement are in meters (m) and time in seconds (s). The average velocity is therefore in meters per second (m/s), which confirms the units are consistent with the calculation.
Therefore, the magnitude of the average velocity vector is approximately 3.651 m/s.
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6. Which set of ordered pairs (x, y) could represent a
linear function?
A = {(-2,-2), (0, 2), (2,5), (4,8)}
B = {(-2,5), (1,2), (4,-1), (7,-5)}
C = {(−7, −6), (−5,–4), (1,0), (4,2)}
D = {(3,7), (6,-2), (7,-5), (8,-8)}
Answers
The option D: {(3,7), (6,-2), (7,-5), (8,-8)} is a set of ordered pairs that represent the linear function.
What is a linear function?The straight line is a representation of a linear function.
It is possible to determine whether the slope between any two points in a set of ordered pairs reflects a linear function. If any two points have the same slope, the set of ordered pairs is said to describe a linear function.
Let's calculate the slopes between the pairs of points in each set:
Let's determine the slopes between the spots in each set's pairs:
To calculate the slope between points (-2, -2) and (0, 2):
m = (2 - (-2))/(0 - (-2)) = 4/2 = 2
The slope between (0, 2) and (2, 5):
m = (5 - 2)/(2 - 0) = 3/2
The slope between (2, 5) and (4, 8):
m = (8 - 5)/(4 - 2) = 3/2
The slopes are not the same, so set A does not represent a linear function.
B: To calculate the slope between (-2, 5) and (1, 2):
m = (2 - 5)/(1 - (-2)) = -3/3 = -1
Slope between (1, 2) and (4, -1):
m = (-1 - 2)/(4 - 1) = -3/3 = -1
Slope between (4, -1) and (7, -5):
m = (-5 - (-1))/(7 - 4) = -4/3
The slopes are not the same, so set B does not represent a linear function.
C: to calculate slope between (-7, -6) and (-5, -4):
m = (-4 - (-6))/(-5 - (-7)) = 2/2 = 1
The slope between (-5, -4) and (1, 0):
m = (0 - (-4))/(1 - (-5)) = 4/6 = 2/3
Slope between (1, 0) and (4, 2):
m = (2 - 0)/(4 - 1) = 2/3
The slopes are the same, so set C represents a linear function.
D: The slope between (3, 7) and (6, -2):
m = (-2 - 7)/(6 - 3) = -3
The slope between (6, -2) and (7, -5):
m = (-5 - (-2))/(7 - 6) = -3
Slope between (7, -5) and (8, -8):
m = (-8 - (-5))/(8 - 7) = -3
The slopes are the same, so set D represents a linear function.
Therefore, the sets of ordered pairs that represent linear function is and D.
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The gutierrez family and the kim family both have pools. the gutierrez family is filling their
pool, which is modeled by the equation y = x+1. the kim family is draining their pool,
which is modeled by the equation y = -1.25x + 5. in both equations, x represents the time in
hours and y represents the depth of the water in the pool in feet. these two situations can be
described by the following system of equations:
y
22+1
= -1.25x + 5
a) what is the rate of change for the kim family's pool, and what does it represent in the
context of the problem?
b) looking at the equation for the gutierrez family's pool, what does the 1 represent in the
context of the problem?
Answers
The rate of change is negative 1.25. The negative of 1.25 represents 1.25 feet is drain every hour. The number 1 represents 1 foot of water that is already present in the pool.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The Gutierrez family and the Kim family both have pools.
The Gutierrez family is filling their pool, which is modeled by the equation
y = x + 1
The Kim family is draining their pool, which is modeled by the equation
y = -1.25x + 5
In both equations, x represents the time in hours and y represents the depth of the water in the pool in feet.
These two situations can be described by the following system of equations:
Then the rate of change for the Kim family's pool will be
Rate of change = -1.25
The negative of 1.25 represents 1.25 feet is drain every hour.
Looking at the equation for the Gutierrez family's pool.
y = x + 1
The number 1 represents 1 foot of water that is already present in the pool.
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The digits 2, 3, 4, 7 and 8 will be put in random order to make a positive five-digit integer. What is the probability that the resulting integer will be divisible by 11
Answers
The probability that a positive five-digit integer, formed by randomly arranging the digits 2, 3, 4, 7, and 8, will be divisible by 11 is 2/5 or 0.4.
To determine if a number is divisible by 11, we can use the divisibility rule for 11, which states that the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions must be a multiple of 11.
Out of the given digits, only two pairs satisfy this rule: (2, 4, 7) and (3, 8).
If we choose the pair (2, 4, 7) to occupy the odd positions, we have 3! = 6 arrangements for these digits. Similarly, for the pair (3, 8) in the even positions, we have 2! = 2 arrangements.
Thus, there are a total of 6 * 2 = 12 possible arrangements that satisfy the divisibility rule.
The total number of possible arrangements of the five digits is 5! = 120.
Therefore, the probability of randomly selecting an arrangement that is divisible by 11 is 12/120 = 1/10 = 0.1. However, the question asks for the probability of obtaining a divisible number, so we need to divide this by 2 since there are two pairs that satisfy the rule. Hence, the final probability is 0.1/2 = 0.05 or 1/20.
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How do you find the scale factor of a dilation with a center of dilation?
Answers
The scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).
What is dilation?
A dilation is a transformation that creates an image that has the same shape as the original but is larger.
• An enlargement is a dilation that produces a larger image.
• A reduction is a dilation that produces a smaller image.
• A dilation expands or contracts the original figure.
A dilation is a stretch or a shrink in the size and location of a figure or point.
The scale factor in a dilation is the amount by which the figure is stretched or shrunk.
The center of dilation is a reference point used to appropriately scale the dilation of a figure. Given a point on the pre-image, \((x_1, y_1)\)and a corresponding point on the dilated image \((x_2, y_2)\)and the scale factor,
k, the location of the center of dilation, \((x_0,y_0)\) is
\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\)
Hence, the scale factor of dilation can be found by using the formula\((x_0=\frac{kx_1-x_2}{k-1}, y_0=\frac{ky_1-y_2}{k-1})\).
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the time (in minutes) that a subject spent on a psychological test was used as a measure of cognitive function. 41 schizophrenics (2) and 49 non-schizophrenics (1) were given the test, and their time was recorded. psychologists theorize that the mean time on the test for non-schizophrenics will be less than the mean for schizophrenics.
Answers
Psychologists theorize that the mean time on the test for non-schizophrenics (1) will be less than the mean time for schizophrenics (2).
We have two groups: schizophrenics and non-schizophrenics. The time spent on the psychological test is used as a measure of cognitive function.
Let's denote the mean time for schizophrenics as μ2 and the mean time for non-schizophrenics as μ1.
According to the psychologist's theory, they expect μ1 < μ2, meaning that the mean time for non-schizophrenics will be less than the mean time for schizophrenics.
This hypothesis can be tested using statistical analysis such as a t-test or a hypothesis test comparing the means of two independent groups.
Based on the psychologist's theory, they anticipate that the mean time on the psychological test for non-schizophrenics will be lower than the mean time for schizophrenics. Statistical analysis can be conducted to test this hypothesis and determine if there is evidence to support the theory.
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A car can travel 264 miles on 11 gallons of gasoline. How far can it travel on 2
gallons?
Answers
264/11=24 or how far it can travel on one gallon.
24*2=48, It can travel 48 miles on 2 gallons.
Answer:
The answer is 48 miles.
My Logic
If you divide 264 into 11, then you will get 24. 24 is the cars MPG. Then you can Multiply 24 by 2 and you get the answer. Hope this is helpful!
(a) . -3b ²+76b-25
(b). 4c ²+10c+4
Answers
Answer:I don’t understand
Step-by-step explanation:
Brown bears grow at a rate of 4 inches per year. Polar bears grow at a rate of 5 inches per year. If a brown bear is currently 3 feet tall and a polar bear is currently 2 feet tall , use a system of equations to determine when they will reach the same height?
Answers
Answer:
just need points and the anser would be
Step-by-step explanation:
6
A 99-inch board is cut into two pieces. One piece is two times the length of the other. Find the length of the shorter piece.
Please help
Answers
Answer:
33 inches
Step-by-step explanation:
x=length of board
x+2x=99
3x=99
x=33
Answer:
33 inches
Step-by-step explanation:
The question above can be solved by using "algebraic expressions."
Let x be the length of the shorter piece.
Let 2x be the length of the longer piece.
Let's solve.
x + 2x = 99 (inches)3x = 99x = \(\frac{99}{3}\)x = 33The length of the shorter piece is 33 inches.
Let's get the length of the longer piece.
2x = ?2(33) = 66The length of the longer piece is 66 inches.
Let's check.
x + 2x = 99 inches
33 + 66 = 99
99 = 99
The answer is correct.
1/4 ÷ 3
I don't know it pls help me
Answers
Answer: 1 / 12
Step-by-step explanation:
1 / 4 x 1 / 3 = 1 / 12
Answer:
1/12 if you do keep change flip
the following table shows the probability distribution for the number of books a student typically buys at the annual book fair held at an elementary school. number of books 0 1 2 3 4 5 6 7 probability 0.35 0.20 0.15 0.10 0.07 0.08 0.04 0.01 let the random variable bb represent the number of books a student buys at the next book fair. what is the expected value of bb ?
Answers
Expected value of bb = 1.79
What is expectation?
At first it is important to know about probability of an event.
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Suppose x is a random variable with the probability function f(x). suppose
\(x_1, x _2, ..., x _ n\) are the values corrosponding to the actual occurance of the event and \(p_1, p_2, ... , p_n\) be the corrosponding probabilities.
Expectation is given by the formula =
\(p_1x_1 + p_2x_2 +....+ p_nx _n\)
Expected value of bb =
0.35 ˣ 0 + 0.20 ˣ 1 + 0.15 ˣ 2 + 0.10 ˣ 3 + 0.07 ˣ 4 + 0.08 ˣ 5 + 0.04 ˣ 6 + 0.01 ˣ 7
0 + 0.20 + 0.30 + 0.30 + 0.28 + 0.40 + 0.24 + 0.07
= 1.79
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HELP ME PLEASE!!
Solve the simultaneous equations.
x + 2y = 13
x + 5y = 28
x =
y=
Answers
\(\bold{\huge{\underline{ Solution }}}\)
Given :-Here, We have given two equations that is ,\(\sf{ x + 2y = 13\:\: and\:\: x + 5y = 28}\)To Find :-We have to find the value of x and y.Concept used :-Linear equations are those equations which having highest power of degree as 1 .Linear equations can be solved by subsitute method, elimination method and cross multiplication method. Here, I have used substitution method to make calculation easier. In subsitute method, you have to subsitute the value of one variable of eq(1) in eq(2) .Let's Begin :-Here,
We have two equations, let consider these two equations as eq(1) and eq(2) that is,\(\sf{ x + 2y = 13 ...eq(1)}\)
\(\sf{ x + 5y = 28 ...eq(2)}\)
By solving eq(1) :-
\(\sf{ x + 2y = 13 }\)
\(\sf{ x = 13 - 2y ...eq(3)}\)
Subsitute eq(3) in eq(2) :-
\(\sf{ (13 - 2y) + 5y = 28 }\)
\(\sf{ 13 - 2y + 5y = 28 }\)
\(\sf{ 13 + 3y = 28 }\)
\(\sf{ 3y = 28 - 13 }\)
\(\sf{ 3y = 28 - 13 }\)
\(\sf{ 3y = 15 }\)
\(\sf{ y = }{\sf{\dfrac{ 15}{3}}}\)
\(\sf{ y = }{\sf{\cancel{\dfrac{ 15}{3}}}}\)
\(\bold{ y = 5 }\)
Thus, The value of y is 5
Now,Subsitute the value of y in eq(1) :-
\(\sf{ x + 2(5) = 13 }\)
\(\sf{ x + 10 = 13 }\)
\(\sf{ x = 13 - 10 }\)
\(\bold{ x = 3 }\)
Hence, The value of x and y are 5 and 3 .
\(\bold{\huge{\underline{ Let's \: Verify }}}\)
Equation 1 :-\(\sf{ x + 2y = 13 }\)
\(\sf{ 3 + 2(5) = 13 }\)
\(\sf{ 3 + 10 = 13 }\)
\(\sf{ 13 = 13 }\)
\(\bold{ LHS = RHS }\)
Equation 2 :-\(\sf{ x + 5y = 28 }\)
\(\sf{ 3 + 5(5) = 28 }\)
\(\sf{ 3 + 25 = 28 }\)
\(\sf{ 28 = 28 }\)
\(\bold{ LHS = RHS }\)
Let's use elimination method
Subtract eq(2) from eq(1)We get
\(\\ \rm\Rrightarrow 2y-5y=13-28\)
\(\\ \rm\Rrightarrow -3y=-15\)
\(\\ \rm\Rrightarrow y=\dfrac{-15}{-3}\)
\(\\ \rm\Rrightarrow y=5\)
Putting on eq(1)
\(\\ \rm\Rrightarrow x+2y=13\)
\(\\ \rm\Rrightarrow x+2(5)=13\)
\(\\ \rm\Rrightarrow x+10=13\)
\(\\ \rm\Rrightarrow x=13-10\)
\(\\ \rm\Rrightarrow x=3\)
(x,y)=(3,5)\(\LARGE{\underbrace{\underline{\rm{Verification:-}}}}\)
\(\\ \rm\Rrightarrow x+2y=13\)
\(\\ \rm\Rrightarrow 3+2(5)=13\)
\(\\ \rm\Rrightarrow 3+10=13\)
\(\\ \rm\Rrightarrow 13=13\)
And
\(\\ \rm\Rrightarrow x+5y=28\)
\(\\ \rm\Rrightarrow 3+5(5)=28\)
\(\\ \rm\Rrightarrow 3+25=28\)
\(\\ \rm\Rrightarrow 28=28\)
Hence verified!
Help me please I need a hand
Answers
The statements that are true are
The sum of A and C is negativeA + D = BThe quotient of D and B is -10/3 The product of A and B > the product of A and CNumber lineFrom the question, we are to determine the statements that are true
In the given number line,
A = -2 1/6
B = - 1/2
C = 1/3
D = 1 2/3
B - C = 1/6B - C = -1/2 - 1/3
B - C = -5/6
∴ B - C ≠ 1/6
The sum of A and C is negativeA + C = -2 1/6 + 1/3
A + C = -1 5/6
∴ The sum of A and C is negative
A + D = BA + D = -2 1/6 + 1 2/3
A + D = -1/2
B = -1/2
∴ A + D = B
Quotient of D and B1 2/3 ÷ - 1/2 = -10/3
∴ The quotient of D and B is -10/3
Product of A and B
A×B = -2 1/6 × -1/2
A×B = 13/12
Product of A and C
A×C = -2 1/6 × 1/3
A×C = -13/18
∴ The product of A and B > the product of A and C
|B| < |C||B| = 1/2
|C| = 1/3
|B| > |C|
|B| is NOT less than |C|
Hence, the statements that are true are
The sum of A and C is negativeA + D = BThe quotient of D and B is -10/3 The product of A and B > the product of A and CLearn more on Number line here: https://brainly.com/question/1545224
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Help!! (23) what is the answer I am working in my homework and I was sick for last week and didn’t get to learn any!
Answers
Answer:
sorry can I help you with but it says apparently log with a base four times the height of an area less than 2000 feet square feet I really don't know but I'm going to see just try your hardest
Can someone help me with these word problems?
Answers
Answer:
First Answer: 12.5 weeks
Third Answer: 16 minutes(I think it was a really long decimal so I rounded it up)
A box contains 4 red cubes, 3 blue cubes, 2 green cubes, and 1 yellow cube. You pick two cubes at random, replacing each after you pick. Find the probability of picking a blue and then a red.
A.3/25
B.9/100
C.3/4
D.4/25
Answers
Answer:
Step-by-step explanation:
There are 10 cubes all together.
You want blue and then red with replacement.
Blue
P(B then red) = 3/10 * 4/10 = 12 / 100
12/100 reduces to 3/25
The answer is A
Answer:
A?
Step-by-step explanation:
Use euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the initial-value problem y ' = y 2xy, y(2) = 1. (round the answer to four decimal places.) y(2.5) =
Answers
y(2.5) = 15.9389 is Use euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the initial-value problem.
What is euler's method?
First-order methods, such as the Euler method, have local errors that are proportional to the square of the step size and global errors that are proportional to the step size.
f(x,y) = 3y+2xy
So, starting at t0 = 2, repeat the above sequence until t0>2.5
a) m = f(2,1) = 3(1)+2(2)(1) = 7
b) y1 = y0 + hm = 1+0.1(7) = 1.7
c) t1 = t0 + h = 2.1
d) show t1 and y1
e) t0 = t1 = 2.1
f) y0 = y1 = 1.7
2nd iteration
a) m = f(2.1,1.7) = 3(1.7)+2(2.1)(1.7) = 5.1 + 7.14 = 12.24
b) y1 = y0 + hm = 1.7+0.1(12.24) = 1.7 + 1.224 = 2.924
c) t1 = t0 + h = 2.2
d) show t1 and y1
e) t0 = t1 = 2.2
f) y0 = y1 = 2.924
This is what I got for all iterations from a simple program x y
2.1 1.7
2.2 2.924
2.3 5.08776
2.4 8.9544576
2.5 15.938934528
y(2.5) = 15.9389
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a metal box that is in shape of cuboid has the following dimensions. the length is 9 inches, width is 2 inches and height is 1. 5 inches. find the total cost of silver coating the entire box if the cost of coating is $2.50 per Sq. inches
Answers
Given:
Length of a box is 9 inches, width is 2 inches and height is 1.5 inches.
The cost of silver coating is $2.50 per sq. inches.
To find:
The total cost of silver coating for the box.
Solution:
The total surface area of a cuboid is
\(A=2(lb+bh+hl)\)
Where, l is length, b is breadth and h is height.
Putting \(l=9,b=2,h=1.5\), we get
\(A=2(9\times 2+2\times 1.5+1.5\times 9)\)
\(A=2(18+3+13.5)\)
\(A=2(34.5)\)
\(A=69\)
So, the total surface area of the box is 69 square inches.
Cost of silver coating is $2.50 per sq. inches. So, the cost of silver coating for the box is
\(Cost=69\times 2.50\)
\(Cost=172.50\)
Therefore, the cost of silver coating for the box is $172.50.
Homework: Lab 3 (Chapter 5) HW Score: 74.83%, 34.33 of 48 Question 14, 5.3 Study Exercise 14 (Algo) Part 4 of points Points: 0.44 of 4 Save Consider the market for milk in Saskatchewan. If p is the price of milk (cents per le) and is the quantity of milk (milions of the per month suppose that demand and supply curves for milk are given by the following Demand Supply p=220-200 p* 10+300 a Assuming there is no government intervention in this market, what is the equilibrium price and quantity? eText The equilibrium quantity is 42 millions of litres. (Round your response to one decimal place) The price is 136 cents per tre (Round your response to the nearest cent. The monthly revenue for milk producers without government intervention is $5.7 million(s) of dollars. (Round your response to one decimal place) Resources b. Now suppose the government guarantees milk producers a price of $2.06 per litre (that is, 206 conts per litre) and promises to buy any amount of milk that the producers cannot sell. What is the quantity demanded and the quantity supplied at this guaranteed price? The quantity demanded at the guaranteed price is mition(s) of Itres (Round your response to one decimal place) Check anwer Etext pages Get more help- Help me solve this Home ments lan Clear all elp
Answers
a. The equilibrium price and quantity are 0.42 million litres and 136 cents per litre respectively. The monthly revenue for milk producers without government intervention is $5.712 million.
b. The quantity supplied and the quantity demanded at the guaranteed price are 0 million litres and 1.0897 million litres respectively.
a. To find the equilibrium price and quantity in the market for milk in Saskatchewan, we need to equate the demand and supply equations:
Demand: p = 220 - 200q
Supply: p* = 10 + 300q
Setting p equal to p*, we have:
220 - 200q = 10 + 300q
Combining like terms:
500q = 210
Dividing both sides by 500:
q = 0.42 (rounded to two decimal places)
So the equilibrium quantity is 0.42 million litres.
Substituting this value back into either the demand or supply equation, we can find the equilibrium price:
p = 220 - 200(0.42)
p = 136 (rounded to the nearest cent)
Therefore, the equilibrium price is 136 cents per litre.
To calculate the monthly revenue for milk producers without government intervention, we multiply the equilibrium quantity by the equilibrium price:
Revenue = 0.42 million litres * 136 cents per litre
Revenue = $5.712 million (rounded to one decimal place)
So the monthly revenue for milk producers without government intervention is $5.712 million.
b. If the government guarantees a price of $2.06 per litre, we can set this price equal to the supply equation and solve for the quantity supplied:
2.06 = 10 + 300q
Subtracting 10 from both sides:
300q = 2.06 - 10
300q = -7.94
Dividing both sides by 300:
q = -0.0265 (rounded to four decimal places)
Since quantity cannot be negative, the quantity supplied at the guaranteed price is 0 million litres.
To find the quantity demanded, we can substitute the guaranteed price into the demand equation:
p = 220 - 200q
2.06 = 220 - 200q
Subtracting 220 from both sides:
-217.94 = -200q
Dividing both sides by -200:
q = 1.0897 (rounded to four decimal places)
So the quantity demanded at the guaranteed price is 1.0897 million litres.
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Two numbers are in the ratio 1:2. If 7 is to be added to both, then ratio changes to 3:5, find the numbers
Answers
Let numbers be x and 2x
ATQ
\(\\ \rm\longmapsto \dfrac{x+7}{2x+7}=\dfrac{3}{5}\)
\(\\ \rm\longmapsto 5(x+7)=3(2x+7)\)
\(\\ \rm\longmapsto 5x+35=6x+21\)
\(\\ \rm\longmapsto 6x-5x=35-21\)
\(\\ \rm\longmapsto x=14\)
2x=2(14)=28yearsThe vector \( \mathbf{v} \) and its initial point are given. Find the terminal point. \( \mathbf{v}=\langle 4,-9) ; \) Initial point: \( (8,3) \) \[ (x, y)=(\quad) \]
Answers
If the vector v and its initial point are given, then to find the terminal point we just have to add the coordinates of vector v and its initial point. It means that terminal point can be found by summing up the x and y coordinates of the vector v with the corresponding coordinates of the initial point.
That is,Given the vector v and its initial point, the terminal point can be found as follows:\[\mathbf{v}=\langle 4,-9 \rangle\]Initial point: (8, 3)So, the terminal point will be the sum of the two points: (4 + 8, -9 + 3) which gives:\[(x, y) = (12, -6)\]Therefore, the terminal point is (12, -6).To find the terminal point of the vector v, we have used the method of adding the coordinates of the initial point and the vector v. Adding the two vectors or points is an important operation in vector mathematics. It is equivalent to moving the initial point in the direction and magnitude of the vector v. This operation is known as a vector addition or geometric addition.To perform vector addition, we align the initial point of the second vector with the terminal point of the first vector and then draw a new vector that starts at the initial point of the first vector and ends at the terminal point of the second vector. Therefore, the terminal point of this new vector gives the result of the vector addition. We can also use the parallelogram law of vector addition to perform the same operation. In this law, we draw two vectors with their initial point at the same point and then construct a parallelogram by extending the vectors. The diagonal of the parallelogram starting from the initial point gives the result of vector addition.Thus, we can say that adding the coordinates of the initial point and the vector gives us the terminal point. This method can be used to perform vector addition in a graphical manner. Vector addition is an important operation in vector mathematics that has numerous applications in physics, engineering, and other fields.
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Calculate the bearing of A from B.
N
B
73°
N
A
Answers
The direction of A with respect to B. N B 73° N A is 287
Explain about the direction?A direction is the way that something is moving, directing, or moving toward something or someone. The directions could be Up, Down, Left, and Right, or North, South, East, and West.
The ability to specify where one thing is in relation to another is known as position in mathematics. Defining direction entails explaining the direction in which something moves, such as forward, backward, or in a full or half turn.
It is possible to define direction using relative terms like up, down, in, out, left, right, forward, backward, or sideways. A direction can also be denoted by one of the four cardinal directions: north, south, east, or west.
Angles at a point add up to 360 degrees.
⇒ Bearing from A to B is = 360° - 73° = 287°.
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PLS HELP ASAP!!!! 50 PTS
Answers
Answer: x=4
Step-by-step explanation:
6x + 10 = 5x + 14
x + 10 = 14
x = 4
x+10=14
x=4
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