Determine the maximum rate of change of f at the given point P and the direction in which it occurs (a) f(x,y) = sin(xy), P(1,0) (b) f(x,y,z) = P(8,1.3)
The maximum rate of change occurs in the direction of this unit vector.
(a) To find the maximum rate of change of f at point P(1,0), we need to find the gradient of f at that point and then find its magnitude. The direction of maximum increase is given by the unit vector in the direction of the gradient.
The gradient of f is:
∇f(x,y) = <y cos(xy), x cos(xy)>
At point P(1,0), we have:
∇f(1,0) = <0, cos(0)> = <0, 1>
The magnitude of the gradient is:
||∇f(1,0)|| = sqrt([tex]0^2[/tex] +[tex]1^2[/tex]) = 1
Therefore, the maximum rate of change of f at point P is 1, and it occurs in the direction of the unit vector in the direction of the gradient:
u = <0, 1>/1 = <0, 1>
So the maximum rate of change occurs in the y-direction.
(b) To find the maximum rate of change of f at point P(8,1.3), we need to find the gradient of f at that point and then find its magnitude. The direction of maximum increase is given by the unit vector in the direction of the gradient.
The gradient of f is:
∇f(x,y,z) = <2x, 2y, 2z>
At point P(8,1.3), we have:
∇f(8,1.3) = <16, 2.6, 2(1.3)> = <16, 2.6, 2.6>
The magnitude of the gradient is:
||∇f(8,1.3)|| = sqrt[tex](16^2 + 2.6^2 + 2.6^2)[/tex]= sqrt(275.56) ≈ 16.6
Therefore, the maximum rate of change of f at point P is approximately 16.6, and it occurs in the direction of the unit vector in the direction of the gradient:
u = <16, 2.6, 2.6>/16.6 ≈ <0.963, 0.157, 0.157>
So the maximum rate of change occurs in the direction of this unit vector.
Learn more about maximum rate
https://brainly.com/question/19153235
#SPJ4
A. johnny translated abcd 3 units to the right and 4 units up to a new position, efgh. draw and label efgh.
b. tom rotated abcd to a new position, ijkl, 90º clockwise about the origin, o. draw and label ijkl.
c. tony placed a smaller car, represented as mnop, on the coordinate plane. mnop is a dilation of abcd with its center at the origin and a scale factor of -0.5. draw and label mnop.
A. To obtain the position of EFGH, Johnny translated ABCD by 3 units to the right and 4 units up. To draw and label EFGH, simply shift each vertex of ABCD by this translation vector (3, 4).
B. Tom rotated ABCD by 90º clockwise about the origin, O, to get the position of IJKL. To draw and label IJKL, rotate each vertex of ABCD 90º clockwise around the origin. This can be achieved by switching the x and y coordinates of each vertex and negating the new x value.
C. Tony placed a smaller car, MNOP, on the coordinate plane. MNOP is a dilation of ABCD with its center at the origin and a scale factor of -0.5. To draw and label MNOP, multiply the coordinates of each vertex of ABCD by the scale factor -0.5, keeping the origin as the center.
Find the surface area of this regular pyramid
The surface area be 243 square feet.
Hence option (d) is correct.
In the given regular pyramid
Slant height = l = 6 ft
Edge of base = s = 9ft
Then,
Area of base = a = 9x9 = 81 square ft
Perimeter of base = p = 4x9 = 36 ft
Since surface area of regular pyramid = A = a + (1/2)ps
= 81 + (36x9)/2
= 81 + 162
= 243
Hence, A = 243 square ft.
To learn more about surface area of pyramid visit:
https://brainly.com/question/1503383
#SPJ1
Answer:
The surface area be 243 square feet.
Step-by-step explanation:
Samantha is told that sin (O) = and tan (0)<0, and was asked to determine the value of cos (©).
• She uses the Pythagorean identity and defines it to be sin() + cos2 ( 0 )= 1.
• She substitutes į into the equation for sin (0)
• She then looks at values of sin ( ) and tan () and says that the only quadrant in which sin() is positive and
tan() is negative is the first quadrant.
Samantha determines that the answer is
cos () =
(21)
Samantha determines the answer as cos(θ) = -√(3/4).
Based on the information given, I can help you with this problem. Samantha is correct in using the Pythagorean identity and substitution, but she made an error in identifying the quadrant. Here's the correct process:
1. Given sin(θ) = 1/2 and tan(θ) < 0.
2. The correct quadrant where sin(θ) is positive and tan(θ) is negative is the second quadrant, not the first.
3. Using the Pythagorean identity: sin^2(θ) + cos^2(θ) = 1.
4. Substitute sin(θ) = 1/2 into the equation: (1/2)^2 + cos^2(θ) = 1.
5. Simplify: 1/4 + cos^2(θ) = 1.
6. Solve for cos^2(θ): cos^2(θ) = 3/4.
7. Since we are in the second quadrant, cos(θ) is negative: cos(θ) = -√(3/4).
Your answer: cos(θ) = -√(3/4).
To learn more about quadrant, refer below:
https://brainly.com/question/7196312
#SPJ11
Graph a right triangle with the two points forming the hypotenuse. Using the sides,
find the distance between the two points in simplest radical form.
(-5, -9) and (-7,-2)
Answer:
I believe the distance between these points is (2, 7), because the difference between -5 and -7 is 2, and the for -9 and -2, it's 7. Hope I helped.
There is a line through the origin that divides the region bounded by the parabola y = 2x − 7 x^2 and the x-axis into two regions with equal area. What is the slope of that line?
The slope of the line that divides the region into two equal parts is 8/7.
How to find the slope of that line?We begin by finding the x-coordinates of the points where the parabola intersects the x-axis. Setting y = 0, we get:
[tex]2x - 7x^2 = 0[/tex]
x(2 − 7x) = 0
x = 0 or x = 2/7
Thus, the parabola intersects the x-axis at x = 0 and x = 2/7.
We want to find the slope of the line through the origin that divides the region bounded by the parabola and the x-axis into two regions with equal area.
Let's call this slope m.
We know that the area under the parabola from x = 0 to x = 2/7 is:
A = ∫[0,2/7] (2x − 7[tex]x^2[/tex]) dx
A = [[tex]x^2[/tex] − (7/3)[tex]x^3[/tex]] from 0 to 2/7
A = (4/21)
Since we want the line to divide this area into two equal parts, the area to the left of the line must be (2/21).
Let's call the x-intercept of the line h. Then the equation of the line is y = mx, and the area to the left of the line is:
(1/2)h(mx) = (1/2)mhx
We want this to be equal to (2/21), so we can solve for h:
(1/2)mhx = (2/21)
h = (4/21m)
The x-coordinate of the point of intersection of the line and the parabola is given by:
2x − 7[tex]x^2[/tex] = mx
Simplifying, we get:
[tex]7x^2 - (2 + m)x = 0[/tex]
Using the quadratic formula, we get:
[tex]x = [(2 + m) \pm \sqrt((2 + m)^2 - 4(7)(0))]/(2(7))[/tex]
x = [(2 + m) ± √(4 + 4m + [tex]m^2[/tex])]/14
x = [(2 + m) ± (2 + m)]/14
x = 1/7 or x = −(2/7)
Since we want the line to pass through the origin, we must choose x = 1/7, and we can solve for m:
[tex]2(1/7) - 7(1/7)^2 = m(1/7)[/tex]
m = 8/7
Therefore, the slope of the line that divides the region into two equal parts is 8/7.
Learn more about slope of line
brainly.com/question/16180119
#SPJ11
(1 point) Write an equivalent integral with the order of integration reversed g(y) I hope F(x,y) dydt = F(x,y) dedy f(y) a = b= f(y) = g(y) =
The missing values are:
a = 0b = 1c = 1f(y) = yg(y) = 2 - yh(y) = 0k(y) = yGiven Integral:
[tex]\int\limits^1_0 \int\limits^{2-x}_x {F(x,y)} \, dydx = \int\limits^b_a \int\limits^{g(y)}_{f(y)} {F(x,y)} \ dxdy + \int\limits^c_b \int\limits^{h(y)}_{k(y)} {F(x,y)} \ dxdy \\[/tex]
To write the equivalent integral with the order of integration reversed, express the limits of integration and functions appropriately.
Reversed integral:
[tex]\int\limits^b_a \int\limits^{g(y)}_{f(y)} {F(x,y)} \ dxdy + \int\limits^c_b \int\limits^{h(y)}_{k(y)} {F(x,y)} \ dxdy \\[/tex]
Now, let's determine the values of the variables:
a = 0: The lower limit of the outer integral remains the same as the original integral.
b = 1: The upper limit of the outer integral also remains the same as the original integral.
c = 1: The upper limit of the second inner integral is determined by the limits of integration of the original integral, which is 1.
f(y) = y: The lower limit of the first inner integral is the same as the original integral, which is y = x.
g(y) = 2 - y: The upper limit of the first inner integral is determined by the limits of integration of the original integral, which is 2 - x.
h(y) = 0: The lower limit of the second inner integral remains the same as the original integral.
k(y) = y: The upper limit of the second inner integral remains the same as the original integral.
Learn more about reversed integration here:
https://brainly.com/question/30286960
#SPJ12
What are the operations in the equation 4x – 5 = 7? What operations do you need to use to solve for x?
Answer:
x=3, Adding and dividing. (Im not too sure how to answer that question, Are there some options that you learned in class?)
Step-by-step explanation:
4x-5=7
+5 +5
4x=12
/4 /4
x=3
Ms. paquette put one coat of paint on a rectangular wall that measured 25 1/2 feet by 10 feet. the paint that she bought was sold in 1-gallon containers.
Ms. Paquette used approximately 0.73 gallons of paint for one coat on the rectangular wall.
To determine how many gallons of paint Ms. Paquette used for one coat on the rectangular wall, we first need to calculate the total area of the wall.
Area of the wall = length x width
= 25.5 feet x 10 feet
= 255 square feet
Now, to find out how many gallons of paint are needed for one coat, we need to know the coverage rate of the paint. This information is usually provided on the paint can label. Let's assume that the coverage rate for the paint Ms. Paquette used is 350 square feet per gallon.
To calculate how many gallons of paint are needed, we can divide the total area of the wall by the coverage rate of the paint:
255 square feet ÷ 350 square feet per gallon = 0.7286 gallons
This means that Ms. Paquette used approximately 0.73 gallons of paint for one coat on the rectangular wall. Since paint is typically sold in 1-gallon containers, she would need to purchase at least one gallon of paint to complete one coat on this wall.
To know more about "Rectangle" refer here:
https://brainly.com/question/24364874#
#SPJ11
A woman bought 130kg of tomatoes for 52. 0. She sold half of them at a profit of 30%. The rest of the tomatoes started to go bad. She then reduced the selling price per kg by 12%. Calculate
i. The new selling price per kg
ii. The percentage profit on the whole transaction if she threw away 5kg of bad tomatoes
(I) The new selling price per kilogram of the tomatoes is 0.4576.
(II) The percentage profit on the whole transaction is 24.77% if she threw away 5kg of bad tomatoes.
What is the new selling price?The new selling price is calculated as follows;
The cost per kilogram of the tomatoes is;
Cost per kg = Total cost / Total weight
Cost per kg = 52 / 130
Cost per kg = 0.4
Selling price per kg = Cost per kg + (Profit percentage x Cost per kg)
Selling price per kg = 0.4 + (0.3 x 0.4)
Selling price per kg = 0.52
The new selling price per kilogram is:
= Selling price per kg - (Reduction percentage x Selling price per kg)
= 0.52 - (0.12 x 0.52)
= 0.4576
The total revenue from selling the tomatoes is calculated as;
The woman sold half of the 130kg of tomatoes, = 130 / 2 = 65kg
Revenue = (amount sold x selling price per kg) + (amount left x new selling price per kg)
Revenue = (65 x 0.52) + (65 x 0.4576)
Revenue = 33.8 + 29.68
Revenue = 63.48
New total cost = Total cost / Total weight x (Total weight - Bad tomatoes)
New total cost = 0.4 x (130 - 5)
New total cost = 50.6
The profit on the whole transaction is calculated as;
Profit = Total revenue - New total cost
Profit = 63.48 - 50.6
Profit = 12.88
The profit percentage on the whole transaction is calculated as;
Profit percentage = (Profit / Total cost) x 100%
Profit percentage = (12.88 / 52) x 100%
Profit percentage = 24.77%
Learn more about selling price here: https://brainly.com/question/1153322
#SPJ4
Riya has pens and pencils, which together are 40 in number. If she had 5 more pencils and 5 less pens, then the number of pencils would become four times the number of pens. Find the original number of pens and pencils.
Answer:
Pens=13
Pencils=27
Step-by-step explanation:
1. Pens = x, Pencils = y
x+y=40
2. y+5 & x-5 --> y=4x
3. Rearrange the x+y=40 to y=40-x. Then substitute y=4x and y=40-x to 4x=40-x.
4. Solve. 4x=40-x, 5x=40, x=8
5. Plug in x=8 to y=4x -> y=32.
6. Reverse the y+5 & x-5. y=27, x=13.
Dado y = 1 / 3x3 +7x dy encontrar dy/dx
To find dy/dx for y = 1/3x³ + 7x, we need to take the derivative with respect to x using the power rule and the sum rule, which gives dy/dx = x² + 7.
The given equation is y = 1/3x³ + 7x. To find dy/dx, we need to take the derivative of y with respect to x. We can do this by using the power rule and the sum rule of differentiation.
Using the power rule, the derivative of x³ is 3x². Using the sum rule, the derivative of 7x is 7. Therefore, the derivative of y with respect to x is:
dy/dx = d/dx (1/3x³ + 7x)
= d/dx (1/3x³) + d/dx (7x)
= (1/3) d/dx (x³) + 7 d/dx (x)
= (1/3) (3x²) + 7
= x² + 7
Hence, we have found that the derivative of y with respect to x is x² + 7.
For more questions like Derivative click the link below:
https://brainly.com/question/25324584
#SPJ11
plss helpppssss
6 th grade math
Answer:
Step-by-step explanation:
By the figure, it would mean:
67, 67, 68
72, 72, 73, 76, 76, 77, 78
80, 81, 83, 83, 85, 85, 85, 87, 88
91, 91, 93, 95, 99
a) 2 students
b) 9 students
c) 2 students
Explanation : 5 students (90s) - 3 students (60s) = 2 students
d) 81
Explanation : (67 + 67 + 68 + 72 + 72 + 73 + 76 + 76 + 77 + 78 + 80 + 81 + 83 + 83 + 85 + 85 + 85 + 87 + 88 + 91 + 91 + 93 + 95 + 99) ÷ 24 = 81.33
HELP PLEASE I AM STRUGGLING!!!!!!!!!!!!
Calculate the costs of these home improvement and maintenance costs.
Annual real estate taxes on a property are $2046. Insurance premiums total $1236. Required flood insurance protection premiums are $380 annually. The county assesses an annual special assessment landfill fee of $125. Trash collection costs $65 quarterly. Annual homeowner's association is $720 for common area maintenance of the subdivision. The pool company charges $45 quarterly to maintain the pool. Ongoing termite and pest protection costs $39 monthly. How much should a buyer save each month to cover these fees?
Answer: To calculate the total amount a buyer should save each month to cover these fees, we need to add up all the costs and divide by 12 (the number of months in a year).
Annual real estate taxes = $2046
Insurance premiums = $1236
Flood insurance premiums = $380
Annual special assessment landfill fee = $125
Quarterly trash collection costs = $65 x 4 = $260
Annual homeowner's association fee = $720
Quarterly pool maintenance costs = $45 x 4 = $180
Monthly termite and pest protection costs = $39 x 12 = $468
Total annual costs = $2046 + $1236 + $380 + $125 + $260 + $720 + $180 + $468 = $5405
Total monthly costs = $5405 / 12 = $450.42
Therefore, a buyer should save $450.42 each month to cover these fees.
Step-by-step explanation:
How do you do this problem?
Answer: 135 and 45
Step-by-step explanation:
We can read off from these equations the gradients of the two lines: (3) and (-2).
Then we quote the trigonometric identity tan(A-B) = [tan(A)-tan(B)] / [1+tan(A)tan(B)]
Substituting tan(A)=3 and tan(B)=-2 gives tan(A-B) = [(3)-(-2)] / [1+(3)(-2)] = 5/-5 = -1
So A-B = 135°.
That is the obtuse angle between the two lines, so the acute angle is 45°.
What is the average rate of change of the function g(x)=6x from x=-1 to x=3? show your work or explain how you obtained your response
The average rate of change of the function g(x)=6x from x=-1 to x=3 is found to be 6.
The function g(x) = 6x describes a relationship between x and the value of 6 times x. We want to find the average rate of change of this function from x = -1 to x = 3. The average rate of change tells us the average amount by which the function changes per unit of change in x over this interval.
In this case, by using the function g(x) = 6x and evaluating it for x = 3 and x = -1, a difference of 18 - (-6) = 24 is found. The difference in x's values is equal to 3 - (-1) = 4. We divide these to get an average rate of change of 6.
To know more about average rate change, visit,
https://brainly.com/question/2170564
#SPJ4
What kind of triangle has angles that measure 47, 70, and 63 degrees
Answer:
Acute triangle
Step-by-step explanation:
angles that are less than 90° are called acute
This triangle has 3 acute angles, so it is an acute triangle
What is the slope of y = 3x - 2?
A Film crew is filming an action movie where a helicopter needs to pick up a stunt actor located on the side of a canyon actor is 20 feet below the ledge of the canyon the helicopter is 30 feet above the canyon. Which of the following expressions represents the length of rope that needs to be lowered from the helicopter to reach the stunt actor
The expression that represents the length of rope that needs to be lowered is 30 - -20
Which expression represents the length of rope that needs to be loweredFrom the question, we have the following parameters that can be used in our computation:
canyon actor is 20 feet below the ledge of the canyon Helicopter is 30 feet above the canyonUsing the above as a guide, we have the following:
Length of rope = helicopter - canyon
So, we have
Length of rope = 30 - -20
Evaluate
Length of rope = 50
Hence, the length of rope is 50 feet
Read more about lengths at
https://brainly.com/question/24487155
#SPJ1
Students in Mr. Jeffer’s class write down how many hours each student studies math per week. The results are 3, 4, 4, 3, 5, 4, 6, 3, 2, 2, 4, 6, 5, 7, 5, 3, 3, 4, and 5. Which box plot represents these data?
The box plot that represents these data is Option B because the centre of measure falls on 4.
What is the median study hours for Mr. Jeffer’s math class?To find the median, we first arrange the study hours in ascending order:
2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7.
From here, we have 15 numbers, so the median is the 8th number in the list which is 4.
As the median study hours for Mr. Jeffer's math class is 4 hours per week, then, the box plot that represents these data is B because the centre of measure falls on 4.
Read more about Box plot
brainly.com/question/14277132
#SPJ4
Hamid's soccer game will start at 10:00 am but the players must arrive to the field three quarters of an hour early to warm up. the game must end by 1:15
Hamid's soccer game starts at 10:00 am with players warming up 45 minutes earlier and ends by 1:15.
How long is Hamid's soccer game?Hamid's soccer game is scheduled to start at 10:00 am, but the players must arrive at the field 45 minutes early to warm up. This means that they need to be there at 9:15 am. The duration of the game is not given, but we know that it must end by 1:15 pm.
Assuming that the game will last for 90 minutes, it would end at 11:30 am. This would give the players ample time to change, clean up, and leave the field by 12:00 pm. However, if the game were to last longer, say for 2 hours, it would end at 12:00 pm, leaving only 15 minutes for the players to get ready to leave.
Therefore, it is important for the players to play efficiently and within the time allotted so that they have enough time to change and leave before the deadline. It is also important for the players to arrive at the field on time to ensure that they have enough time to warm up and prepare for the game.
Learn more about soccer game
brainly.com/question/31078315
#SPJ11
Please upload a picture of a piece of paper with the problem worked out, and draw the graph for extra points, there will be 6 of these, so go to my profile and find the rest, and do the same, for extra points. solve the system using the ELIMINATION method.
The solution to this system of equations are x = 7 and y = -3.
How to solve these system of linear equations?In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.
Given the following system of linear equations:
3y = 26 - 5x .........equation 1.
6x + 7y = 21 .........equation 2.
Rewriting in standard form, we have:
5x + 3y = 26
6x + 7y = 21
By multiplying equation 1 by 6 and dividing by 5, we have:
6x + 3.6y = 31.2 .........equation 3.
By subtracting equation 3 from equation 2, we have:
3.4y = -10.2
y = -3.
x = (26 - 3y)/5
x = (26 - 3(-3))/5
x = 7
Read more on elimination method here: brainly.com/question/28405823
#SPJ1
Match each equation to its graph and table representation
Answer:
The first one is B & H
2nd one is A & G
3rd one is D & E
4th one is C & F
Step-by-step explanation:
Cher is making hotdogs for her coworkers to celebrate their 5 year
anniversary. Hotdogs come in packs of 6, while the buns come in
packs of 10. How many hotdogs should Cher cook to have the
smallest number of hotdogs and hotdog buns?
The Bayview community pool has a snack stand where Juan works part time he tracks his total sales during each shift last month this box plot shows the results what fraction of Juan’s shifts had a total sales of $225 or more
The fraction of Juan's shifts with a total sales of $225 or more can be found by looking at the box plot.
We can see that the top line of the box represents the third quartile (Q3) which is the value where 75% of the data falls below.
In this case, Q3 is at approximately $250. This means that 75% of Juan's shifts had total sales less than $250. To find the fraction of shifts with sales of $225 or more, we need to determine how many shifts fall within the range of $225 to $250.
Looking at the box plot, we can see that the distance between Q1 and Q3 (the interquartile range) is approximately $100. Therefore, the distance between Q1 and $225 is approximately one-third of the interquartile range or $33.33. So, any shift with total sales of $225 or more would fall within one-third of the distance between Q1 and Q3.
Therefore, the fraction of Juan's shifts with total sales of $225 or more is approximately one-third of 75%, which is 25%.
In summary, approximately 25% of Juan's shifts at the Bayview community pool had total sales of $225 or more, based on the box plot.
To know more about interquartile range click on below link:
https://brainly.com/question/29173399#
#SPJ11
Find the smallest whole number that is divisible by both 720 and 1575
Answer:
LCM = 2^4 x 3^2 x 5^2 x 7 = 25200
Step-by-step explanation:
Prime factorization of 720:
720 = 2^4 x 3^2 x 5
Prime factorization of 1575:
1575 = 3^2 x 5^2 x 7
Answer:
720 = 2 × 2 × 2 × 2 × 3 × 3 × 5
1,575 = 3 × 3 × 5 × 5 × 7
LCM of 720 and 1,575 =
2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 × 7 = 25,200
Express the area of the entire rectangle. your answer should be a polynomial in standard form. x+6 x+2 area=
The formula for the area of a rectangle is length times width, or in this case (x+6)(x+2) or x^2 + 8x + 12 in standard form.
To simplify this expression, we can use the distributive property to multiply the two binomials:
(x+6)(x+2) = x(x+2) + 6(x+2)
= x² + 2x + 6x + 12
= x² + 8x + 12
To express the area of the entire rectangle, we need to multiply the length (x + 6) by the width (x + 2). This will give us a polynomial in standard form.
Step 1: Write down the expression for the area of the rectangle.
Area = (x + 6)(x + 2)
Step 2: Use the distributive property (also known as the FOIL method) to expand the expression.
Area = x(x + 2) + 6(x + 2)
Step 3: Continue to expand and simplify the expression.
Area = (x² + 2x) + (6x + 12)
Step 4: Combine like terms.
Area = x² + 8x + 12
So the area of the entire rectangle is expressed as the polynomial x² + 8x + 12 in standard form.
Know more about area here:
https://brainly.com/question/27683633
#SPJ11
In ARST, r = 58 cm, m/S=48° and m/T=29°. Find the length of s, to the nearest
centimeter.
The value of length 's' is 44.3 cm
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
The measure of angle R = 180-( 48+29)
R = 180- 77
R = 103°
sinR/ r = sinS/s
sin103 / 58 = sin48/s
s × sin103 = 58 × sin48
s × 0.974 = 43.1
s = 43.1/0.974
s = 44.3 cm
therefore the value of length is is 44.3 cm
learn more about sine rule from
https://brainly.com/question/20839703
#SPJ1
Recommendations for safely thawing frozen turkey are provided on the packaging.
a. What is the thaw rate of the turkey for refrigerator thawing?
For cold water thawing?
b. What could the initial value represent?
c. Write a linear function in the form y = mx + b to model the time t, in hours, it takes to thaw turkey in the refrigerator as a function of the weight w, in pounds, of the turkey.
a. The thaw rate of the turkey for refrigerator thawing is day(s) per pound.
(simplify your answer.)
(1) it takes about 10 hours to thaw a 20-pound turkey in cold water.(2) it takes an additional 0.25 hours (or 15 minutes) to thaw in the refrigerator.
What is a linear function and examples?A linear function is a function that represents a straight line in the coordinate plane. For example, y = 3x - 2 represents a straight line in the coordinate plane and thus a linear function. Since y can be replaced by the function f(x), this function can be written as f(x) = 3x - 2.
a. A typical thawing rate when thawing in the refrigerator is about 1 day per 4-5 kilograms of turkey meat. So if you have a 20 pound turkey, it will take about 4-5 days to thaw in the fridge. In cold water, the thawing rate is about 30 minutes per pound, so it takes about 10 hours to thaw a 20-pound turkey in cold water.
b) The initial value may represent the weight of the frozen turkey before thawing begins. c. Let y be the time it takes to thaw the turkey in hours and let x be the weight of the turkey in pounds. Assuming a linear relationship between melting time and weight, we can write:
y = mx + b
where m is the thaw rate (in hours per pound) and b is the intercept (the time it takes to thaw a 0-pound turkey, which is 0). From part a, we know that the refrigerator thaw rate is about 1 day per 4-5 pounds of turkey, or about 0.25-0.2 hours per pound. So we can use m = 0.25 in our linear function:
y = 0.25x + 0
This means that for every additional pound of turkey, it takes an additional 0.25 hours (or 15 minutes) to thaw in the refrigerator.
Learn more about coordinate plane here
https://brainly.com/question/13611766
#SPJ1