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MY NOTES Two stoves are located 45 feet apart, one giving out]] 4 times as much heat as the other. If you stand at a point on the line between the stoves at a distance x from the less powerful stove, the temperature of the air is given by H(x)=100 + 60 x2 + 240 (45−x)2 . Assume you move back an forth between the two stoves, always at least 4 ft from either stove.
Answers
Missing Part of the question:
a) Assume you wish to determine the maximum and minimum temperatures you would experience. the domain to study for the function H(x) would be?
b)The is one critical number for the function on the domain in part a and it is?
c) The maximum temperature you would experience is ?
d) The minimum temperature you would experience is ?
Answer:
a. Domain : [tex]4 \leq x \leq 41[/tex]
b. Critical point: [tex]x = 12.33[/tex]
c. The maximum is 115.09
d. The minimum is 100.62
Step-by-step explanation:
Given
[tex]H(x) = 100 + \frac{60}{x^2} + \frac{240}{(45 - x)^2}[/tex]
Solving (a): The domain of H(x)
From the question, we understand that the distance between the two stores is 45ft
Let the first stove be at point A (0 ft) and
the second stove be at point B (45ft)
Since you move back and forth within 4ft from either stoves, then
Your maximum distance at A is (0 + 4) ft = 4ft
Your minimum distance at B is (45 - 4) ft = 41ft
Hence, the domain is: [tex]4 \leq x \leq 41[/tex]
Solving (b): Critical Value
First, we have to differentiate H(x) w.r.t x
[tex]H(x) = 100 + \frac{60}{x^2} + \frac{240}{(45 - x)^2}[/tex]
Differentiate
[tex]H'(x) = 0 -\frac{120}{x^3} + \frac{480}{(45- x)^3}[/tex]
[tex]H'(x) = -\frac{120}{x^3} + \frac{480}{(45- x)^3}[/tex]
Equate H'(x) to 0
[tex]0 = -\frac{120}{x^3} + \frac{480}{(45- x)^3}[/tex]
Rewrite as:
[tex]\frac{120}{x^3} = \frac{480}{(45- x)^3}[/tex]
Cross Multiply
[tex]480 * x^3 = 120 * (45 -x)^3[/tex]
[tex]480 * x^3 = 120 * (45 -x)*(45 -x) * (45 -x)[/tex]
[tex]480 * x^3 = 120 * (2025 -90x +x^2) * (45 -x)[/tex]
[tex]480 * x^3 = 120 * (91125 -4050x +45x^2 -2025x - 90x^2 - x^3)[/tex]
[tex]480 * x^3 = 120 * (91125 -4050x -2025x+45x^2 - 90x^2 - x^3)[/tex]
[tex]480 * x^3 = 120 * (91125 -6075x-45x^2 - x^3)[/tex]
Divide both sides by 120
[tex]4x^3 =91125 -6075x-45x^2 - x^3[/tex]
[tex]4x^3 +x^3-91125 +6075x+45x^2= 0[/tex]
[tex]5x^3-91125 +6075x+45x^2= 0[/tex]
[tex]5x^3+45x^2 +6075x-91125= 0[/tex]
Divide through by 5
[tex]x^3+9x^2 +1215x-18225= 0[/tex]
Solving for x, we have that
[tex]x\approx \:12.33067[/tex]
[tex]x = 12.33[/tex]
Hence, the critical point is 12.33
Solving (x): Maximum temperature
Here, we simply substitute the endpoints of the domain in [tex]H(x) = 100 + \frac{60}{x^2} + \frac{240}{(45 - x)^2}[/tex]
Let x = 4
[tex]H(4) = 100 + \frac{60}{4^2} + \frac{240}{(45 - 4)^2}[/tex]
[tex]H(4) = 100 + \frac{60}{16} + \frac{240}{(41)^2}[/tex]
[tex]H(4) = 100 + \frac{60}{16} + \frac{240}{1681}[/tex]
[tex]H(4) = 100 + 3.75+ 0.14277215942[/tex]
[tex]H(4) = 103.892772159[/tex]
[tex]H(4) = 103.89[/tex] --- approximated
Let x = 41
[tex]H(41) = 100 + \frac{60}{41^2} + \frac{240}{(45 - 41)^2}[/tex]
[tex]H(41) = 100 + \frac{60}{41^2} + \frac{240}{4^2}[/tex]
[tex]H(41) = 100 + \frac{60}{1681} + \frac{240}{16}[/tex]
[tex]H(41) = 100 + 0.03569303985 + 15[/tex]
[tex]H(41) = 115.03569304[/tex]
[tex]H(41) = 115.04[/tex] ---- approximated
Compare both values: The maximum is 115.09
Solving (d): The minimum temperature
In (b), we have that:
[tex]x = 12.33[/tex] --- critical point
The minimum occurs at this point
Substitute 12.33 for x in [tex]H(x) = 100 + \frac{60}{x^2} + \frac{240}{(45 - x)^2}[/tex]
[tex]H(12.33) = 100 + \frac{60}{12.33^2} + \frac{240}{(45 - 12.33)^2}[/tex]
[tex]H(12.33) = 100 + \frac{60}{12.33^2} + \frac{240}{32.67^2}[/tex]
[tex]H(12.33) = 100 + \frac{60}{152.0289} + \frac{240}{1067.3289}[/tex]
[tex]H(12.33) = 100 + 0.39466180443 + 0.22486039682[/tex]
[tex]H(12.33) = 100.619522201[/tex]
[tex]H(12.33) = 100.62[/tex] --- approximated
Hence, the minimum is 100.62
The quality-control manager of a large factory is concerned about the number of defective items produced by workers. Thirty workers at the factory agree to participate in a study of three different incentive plans to help reduce the number of defective items produced. The plans will be randomly assigned to the workers so that 10 workers received each plan. The reduction in the number of defective items produced by each worker will be recorded two weeks after the plans are implemented.
Answers
Answer:
There is no blocking variable, and incentive plans will be randomly assigned to the workers.
Step-by-step explanation:
The options are missing and they are;
A ) There is no blocking variable, and incentive plans will be randomly assigned to the workers.
B ) There is no blocking variable, and the workers were selected at random.
C) Each incentive plan is a block, and a completely randomized design is not blocked.
D ) Each plan will be randomly assigned to 10 pairs of workers who share a similar characteristic.
E ) The number of workers participating in the study was greater than or equal to 30.
The option that best describes why a completely randomized design is an appropriate design to use in this situation is;
Option A; There is no blocking variable, and incentive plans will be randomly assigned to the workers.
A blocking variable is a variable used by an experimenter or a researcher to block out nuisance variables and test the treatments that are of utmost importance to him.A blocking variable is a continuous variable like weight, age e.t.c. From the question, the treatments, that are the incentive plans, are being randomly assigned to the 30 workers without consideration of specific treatments via blocking variable and as such a completely randomized design would solve that problem.Thus, we can conclude that the reason why a completely randomized design is important to use in this case is because there is no blocking variable and as such the treatments are randomly assigned to the workers.
Read more at; https://brainly.com/question/9606278
A chemist is raising the temperature of a liquid. The temperature is now --8.4 degrees Celsius and is increasing by 1.6 degrees Celsius per minute. How many minutes will it take it for it to take to get to 0 degrees Celsius thiz is due 3
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Which angle is not supplementary to angle 6?
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Answer:
These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°:
Notice that together they make a straight angle.
supplementary angles 60 and 120
But the angles don't have to be together.
These two are supplementary because
60° + 120° = 180°
Step-by-step explanation:
he map shows some geographic features of ancient Egypt.
A map titled Ancient Egypt. It has a scale from 0 to 100 kilometers and 0 to 60 miles. The Mediterranean Sea is at the top of the map. The Nile River flows north through Kush, Upper Egypt, and Lower Egypt. The Nile River Delta is in Lower Egypt next to the Mediterranean Sea. The Red Sea begins south of the Mediterranean Sea.
What does the map demonstrate about the importance of the Nile River to trade in ancient Egypt?
The Nile River allowed ancient Egyptians to export mud bricks across the region.
The Nile River gave ancient Egyptians access to trade opportunities in the Red Sea.
The Nile River allowed the ancient Egyptians to provide for their needs without trade.
The Nile River gave ancient Egyptians access to trade opportunities in the Mediterranean Sea.
Answers
Answer:
i think it is b
Step-by-step explanation:
plz mark brainliest
Answer:
b
Step-by-step explanation:
math need help asap 20 points
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Step-by-step explanation:
Step 1: List out all of the formulas for the trigonometric functions
sin(x) = opposite/hypotenuse
cos(x) = adjacent/hypotenuse
tan(x) = opposite/adjacent
Step 2: Find the values for the given numbers
sin(J) = opposite/hypotenuse = 24/25
tan(J) = opposite/adjacent = 24/7
sin(K) = opposite/hypotenuse = 7/25
tan(K) = opposite/adjacent = 7/24
Step 3: Check if the answers match
24/25 = 24/25 So it is TRUE
24/7 != 7/25 So it is FALSE
7/25 != 24/25 So it is FALSE
7/24 = 7/24 So it is TRUE
Answer: TRUE, FALSE, FALSE, TRUE
PLS I NEED YOUR HELP!!!!!!!
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Answer:
[tex] R_2 = \dfrac{R_1R_T}{R_1 - R_T} [/tex]
Step-by-step explanation:
[tex] R_T = \dfrac{R_1R_2}{R_1 + R_2} [/tex]
[tex] (R_1 + R_2)R_T = R_1R_2 [/tex]
[tex] R_1R_T + R_2R_T = R_1R_2 [/tex]
[tex] R_2R_T - R_1R_2 = -R_1R_T [/tex]
[tex] R_2(R_T - R_1) = -R_1R_T [/tex]
[tex] R_2 = \dfrac{-R_1R_T}{R_T - R_1} [/tex]
[tex] R_2 = \dfrac{R_1R_T}{R_1 - R_T} [/tex]
3 1/4 divided by 3 1/2 in simplest form.
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Answer:
3/14
Step-by-step explanation:
First off, we will turn the fractions into a different form. 3 1/4 will be 13/4 and 3 1/2 will be 7/3
Then, you want to turn 7/3 into 3/7 and multiply them
1/2 x 3/7 = 3/14
sharon pays $78 sales tax on a new camera. If the sales tax rate is 6.5% what was the cost of the camera
Answers
Answer:
83.07
Step-by-step explanation:
If you multiple the original price $78 times the sale tax in decimal form 0.065 you get 5.07, $78 + $5.07 = 83.07.
De
11/9/2015
00:00
Danielle picks 744 apples at an apple orchard. She divides the apples equally into 40 baskets
Part A
Drag a word to the box to make a true statement
ones
tens
hundreds
When dividing 744 – 40, the first digit of the quotient will be in the
place.
00:00
Part B
How many apples will be in each basket? Enter your answer in the box,
18.6
apples
00:00
Part C
How many apples will be left? Enter your answer in the box.
apples
Back
of 22
Next
Answers
Answer:
Tens
PART B: 18
PART C: 24
Step-by-step explanation:im pretty sure
On Monday, Greg walks the entire length of a trail that is 3 1/2 miles long. On Tuesday he walks the entire length of a trail that is 4.6 miles long. On Wednesday, he starts out on a trail that is 2 1/5 miles long, but he does not walk the final 1.7 miles. How many miles does Greg walk in total on Monday, Tuesday, and Wednesday? *
A. 8 3/5
B. 8 3/50
C. 10 3/10
D. 10 3/100
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brainlist asap !!
___________
1) find the simple interest: ____
principal: $6000
interest rate: 5%
time: 6 months
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Answer:
150 dollars in 6 months
Step-by-step explanation:
5% of 6000 is 300 cut a year in half you get half of 300 which is 150
Solve the missing tables.
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Answer:
Step-by-step explanation:
1 4(1) + 2 6
3 4(3) + 2 14
6 4(6) + 2 26
0 0 + 3 3
2 2 + 3 5
4 4 + 3 7
1 1 - 1 0
3 3 - 1 2
5 5 - 1 4
m − 56/–7 = –6
solve for m
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Gregory rode his scooter 2 miles in 30 minutes. At this rate, how far would he ride in
45 minutes?
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It would be 3 miles.
A grocery store is making fruit baskets using 144 apples, 108 oranges, and 90 pears. Each basket will be identical. What is the greatest number of fruit baskets the store can make using all the fruit?
⇒ 6
⇒ 9
⇒ 16
⇒ 18
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Answer:
18
Step-by-step explanation:
just divided so ye .........
The number 2A5A0A2 is divisible by 99. What is the digit A
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Answer:
A = 3
2A5A0A2 = 2353032
Step-by-step explanation:
Given:
2A5A0A2 is divisible by 9
2A5A0A2 can be divisible by 99 if the sum of the digits can be divided by 9
Digits A is between 0 to 9
2 + A + 5 + A + 0 + A + 2 = 9x
Where,
x = multiples of 9
9 + 3A = 9x
Make A the subject
A = (9x - 9) / 3
When x = 0
A = {9(0) - 9} / 3
= (0 - 9) /3
= -9/3
= -3
When x = 1
A = (9x - 9) / 3
= 9(1) - 9 /3
= 9-9/3
=0/3
A = 0
When x = 2
A = (9x - 9) / 3
= 9(2) -9 / 3
= 18-9/3
= 9/3
A = 3
When x = 3
A = (9x - 9) / 3
= 9(3) - 9 / 3
=27 - 9 /3
= 18/3
A = 6
When x = 4
A = (9x - 9) / 3
= 9(4) -9 /3
= 36-9/3
= 27/3
= 9
Recall, Digits A is between 0 to 9
Substituting A = 0
2050002 ÷ 99
= 20707.09
Substituting A = 3
2A5A0A2
2353032 ÷ 99
= 23,768
Substituting A = 6
2A5A0A2
2656062 ÷ 99
= 26,838.91
Substituting A = 9
2A5A0A2
2959092 ÷ 99
= 29,889.82
Therefore, the only A digit that will not give a decimal number when divided by 9 is 3
A = 3
Larijah is creating a circular board game with a spinner with four regions that players use to determine what happens on their turns.
She wants to meet these requirements:
- Exactly half of the circle should contain the “Lose a Turn” region.
- “Move One Space” should be two times the angle as “Move Two Spaces”.
- “Move Two Spaces” should be four the angle as “Trade Places With Any Opponent”.
Answer choices:
A)14
B)27
c)48
d)66
E)51
Answers
Answer:
A. 14
Step-by-step explanation:
A circle has 360 degrees. Lose a turn region is half, so 180. 360-180=180
If the answer is A, move two spaces region would be 56 degrees because 14*4=56
56+14=70
Move one space is 2 times move two spaces so 56*2=112
112+70=182
182+180=362
182 is the closest you can get to 180 without having a decimal.
HELP ME PLEASEEEEEEE
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Answer:a
Step-by-step explanation:The temperature rose by 80 so up the number line and dropped 20 so down the number line to 60
Answer:
A because there's 2 arrows
The table shows one point from the given graph. How could you find more ordered pairs to create a graph and table of equivalent fractions? Check all that apply. O Include the point (0, 0), which is on every graph of equivalent ratios. Multiply both 2 and 3 by 4. O Multiply 2 by 2 and 3 by 3. O Start at the point on the grid. Move right 2 and up 3 and plot the point. O Multiply 2 by 3 and 3 by 2.
Answers
Answer:
A,B,D
Step-by-step explanation:
JUST TOOK THE QUIZ
Answer:
ABD :)
Step-by-step explanation:
dan deposits $4000 into an account that pays simple interest at a rate of 4% per year. how much interest will he be paid in 6 years
Answers
Answer:
$9,600 is what he'll earn in all but the interest that he will earn is $5600
Step-by-step explanation:
To find out the interest earned in all you multiply 4000 times .4 times 6 which is 9600 so if you want to figure out the interest paid it is 9600 - 4000 which is 5600
Given g(x) = f(x) + k. Identify a value of k that transforms finto g. Round your answer to the nearest integer. g 2 X - 14 -2 O 2 2 f k =
Answers
Answer:
k = -5Step-by-step explanation:
We can see the lines are parallel
The function f(x) has y-intercept of 2 at point (2, 0) and the function g(x) has y-intercept of -3 at point of (-3, 0)
If f(x) = mx + 2, then g(x) = mx - 3
The value of k is the difference of y-intercepts as slopes are same due to lines being parallel:
g(x) = f(x) + kk = g(x) - f(x) k = (mx - 3) - (mx + 2) k = -3 - 2 k = -5So the answer is k = -5
After going through this module, you are expected to:
1. Describe principal roots and tells whether they are rational or irrational
2. Determine between what two integers the square root of a number is.
3. Plot irrational numbers on the number line.
1
Square Root
WEEK
3
6
Count the total number of squares of the
chess board. Prove that it has a total of 204
squares.
D
Recall that a rati
Answers
Answer:
See below
Step-by-step explanation:
Number of squares:
1x1 squares = 8*8 2x2 squares = 7*73x3 squares = 6*64x4 squares = 5*55x5 squares = 4*46x6 squares = 3*37x7 squares = 2*28x8 square = 1Total number:
8² + 7² + 6² + 5² + 4² + 3² + 2² + 1 =64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 =204squares numbers:
1x1 squares = 8*8
2x2 squares = 7*7
3x3 squares = 6*6
4x4 squares = 5*5
5x5 squares = 4*4
6x6 squares = 3*3
7x7 squares = 2*2
8x8 square = 1
number total:
8² + 7² + 6² + 5² + 4² + 3² + 2² + 1 =
64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 =
204
Solve each system of equations. Equation 1: x+3y=-5 Equation 2: 9x+3y=3
Answers
Answer:
Equation 1: x-3y+5=0
Equation 2: 3x+y-1=0
Step-by-step explanation:
Equation 1: x+3y=-5
x+3y+5=-5+5
x=3y+5=0
Equation 2: 9x+3y-3=0
3x+y-1=0
Help please show your work
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write the equation of the line in slope-intercept form with slope m=4 through the point (-2,5)
Answers
Answer:
i have no idea\
Step-by-step explanation:
:D:/Janie has \$3$3dollar sign, 3. She earns \$1.20$1.20dollar sign, 1, point, 20 for each chore she does and can do fractions of chores. She wants to earn enough money to buy a CD for \$13.50$13.50dollar sign, 13, point, 50.
Write an inequality to determine the number of chores, ccc, Janie could do to have enough money to buy the CD.
Answers
Answer:
9
Step-by-step explanation:
13.50 - 3 = 10.50
1.20×8 = 9.60 = not enough
1.20×9= 10.80 = more than enough
She has to do 9 chores to have enough money including the 3 dollar she already has
Answer:
Inequality:
3+1.20c ≥ 13.5
solution = c ≥ 8.75
On the graph, have the dot closed and have it going from the point between 8.5 and 9 going to the right.
| ------------•---------- | -------------------- | ------------------> |
8.5 9 9.5 10
please help me!!!!!!!!!!
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Another math question:/
Answers
Answer:
Well to start with, a coefficient is a number that is placed before a variable. In this case we have 10x+8, so the coefficient is well 10.
Step-by-step explanation:
Carol is going to be away on vacation for a couple of days. She does not know how long she will be gone. Carol, however, knows that $250 will be enough for the caretaker to feed the cats, Rover and Bobo, while she is away.
How many days can the caretaker feed the cats before Carol returns? Explain your reasoning critically.
Answers
Answer:
The answer is "$150".
Step-by-step explanation:
Please find the complete question in the attached file.
In this question first, we include the quantity of food that these cats eat daily.
[tex]\to \frac{3}{4}= 0.75\\\\\to \frac{1}{2}= 0.5 \\\\ \to 0.75+ 0.5=1.25[/tex]
They are now able to eat the total of meat we consume on a daily basis, that the food we still eat is 1,25 cans each day, and we must have the full 3 cans.
[tex]\to 1.25 \times 2=2.50[/tex]
2.5 cans and they eat 2.5 cans every 2 years with every other day so we'll have to purchase more meat. So let's go to buy some at our favourite place. 2.5 cans one another day to allow us to give the Bobo leftover .5 a can and open the new Rover can.
We also left this meal 1.25 cans, so that we can give it to them tomorrow. The feed time would not allow them to purchase food as we have the right quantity of food left. But we went for 6 cans in 4 days. Let's figure out how we're going to divide 60 by 4 =15
So we have 15 times 6 now, because that will provide us with the answer [tex]\to 15 \times 6=90[/tex]
We finally find out just how much we pay by 90 cans in 60 days so we will find out what it costs us.
That's the number of cans we get from each purchase and we will divide 90 by 3.
[tex]\to \frac{90}{3}=30[/tex]
They are going to multiply 30 times 5 now, since that is the sum of money to buy.
[tex]\to 30 \times 5=150[/tex]
