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# the temperature is 66°,3 hours of time, 2/3 degree per hour

Distributive property

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### Math Forum - Ask Dr. Math

How many degrees did the temperature drop per hour? ... Search Dr. Math. Equations from Word Problems, and Units ... You are given the total time, 2 1/4 hours ...
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### the temperature has been dropping 3 degrees per hour. at ...

at noon the temperature is .6.f but the temperature drops 2 degrees per hour for the next few hours?what is ... at what time would the temperature be -3 degree C ...
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### what temperature - page 2 - jiskha.com

Time, min Temperature, °F 15 ... at a steady rate of −3 °C per hour. Let t represent temperature in ... by 11 degree Celsius per hour for 2 ...
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### Basal Body Temperature (BBT) Stirrup Queens

Basal Body Temperature (“BBT”) ... (3 hours uninterrupted sleep minimum). ... Your temperature rises approximately .2 degrees per hour throughout the morning ...
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### How Long Does It Take Your Home to Warm Up by 10 Degrees F ...

My initial answer to "How Long Does It Take Your Home to Warm ... about 3 degree per hour during ... still maintain your set temperature by a certian time, ...
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### Hourly Weather Forecast for Chicago, IL - The Weather Channel ...

Hourly Local Weather Forecast, weather conditions, precipitation, ... 66 ° 66 ° 0 % 64 % SSW 4 ... Next 8 Hours Today's Top ...
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### How quickly should the temperature drop if a Central AC unit ...

I have to run the system for hours to get the temperature to drop a degree. ... Ask Your Question. ... hour or two of running time should result in a 10 degree ...
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### New York Hourly Weather - AccuWeather Forecast for NY 10007

Get the New York hour-by-hour weather forecast including temperature, ... NY 10007 from AccuWeather.com. ... 66%: 31%: 17%: 11%: 11%: 11%: 11%: 11%:
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### 3.4 Rates of Change - dnichols30582.edublogs.org

SECTION3.4 Rates of Change ... change of Martian temperature with respect to time (in degrees Celsius per hour) ... 3:2 D #1:5625ıC=hour: 14. The temperature (in ...
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### Chicago Hourly Weather - AccuWeather Forecast for IL 60608

Get the Chicago hour-by-hour weather forecast including temperature, ... IL 60608 from AccuWeather.com. ... 66°F. Local Weather.
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## Suggested Questions And Answer :

### The temperature in a greenhouse from 7:00p.m. to 7:00a.m. is given by f (t)= 96 - 20sin (t/4), where f (t) is measured in Fahrenheit, and t is the number of hours since 7:00 p.m.

The temperature in a greenhouse from 7:00p.m. to 7:00a.m. is given by f (t)= 96 - 20sin (t/4), where f (t) is measured in Fahrenheit, and t is the number of hours since 7:00 p.m. A) What is the temperature of the greenhouse at 1:00 a.m. to the nearest Fahrenheit? (B) Find the average temperature between 7:00 p.m. and 7:00 a.m. to the nearest tenth of a degree Fahrenheit. (C) When the temperature of the greenhouse drops below 80 degreeso Fahrenheit, a heating system will automatically be turned on a maintain the temperature at minimum of 80 degrees Fahrenheit. At what values of the to the nearest tenth is the heating system turned on? (D) The cost of heating the greenhouse is \$0.25 per hour for each degree. What is the total cost to the nearest dollar to heat the greenhouse from 7:00 p.m. and 7:00 a.m.?   The equation is: f(t) = 96 – 20sin(t/4), 0 <= t <= 12 (A)  At 1.00 a.m. t = 6 f(6) = 96 – 20.sin(6/4) = 96 – 20*0.99749 = 96 – 19.9499 f(6) = 76 ⁰F (B)  The average temperature would need to be worked out by sampling the temperature at different times throughout the night. Divide the temperature range into N equal intervals, giving N+1 sampling points. We would then have T1 = f(δt), T2 = f(2δt), T3 = f(3δt), ... ,Tn = f(nδt) Where δt = range/N = 12/N, and n = 0..N Giving Tn = 96 – 20.sin((12n/N)/4) = 96 – 20.sin(3n/N) Then Tav = (1/N)*sum(Tn, n = 0 .. N) i.e. Tav = (1/N)*sum(96 – 20.sin(3n/N), n = 0 .. N Tav = 96 – 20. (1/N)*sum(sin(3n/N), n = 0 .. N I used Maple to evaluate the above summation. The results are tabulated as follows.                                  Average Temperature Num Intervals            3       4        6       10       20      50     100    200 Tav over the range 83.39 83.01 82.78 82.69 82.69 82.71 82.72 82.73 As can be seen from the table the temperature is averaging out at:  Tav = 82.7 ⁰F (C)  T = f(t) = 96 – 20sin(t/4), 0 <= t <= 12 At T = 80 ⁰F,            96 – 20sin(t/4) = 80 20.sin(t/4) = 96 – 80 = 16 sin(t/4) = 0.8 t/4 = 0.927295 t = 3.70918 t = 3.7 (to nearest tenth) (D)  The temperature will (normally) drop to 80 ⁰F after t = 3.7 hours and rise again to 80 ⁰F when t = 12 – 3.7 = 8.3 hours. Heating system is turned on for 8.3 – 3.7 = 4.6 hours Cost of heating is 4.6*80*0.25 = 4.6*20 = 92 Cost = \$92
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### If oil is leaking out at 53 milliliters per hour, what is the operating temperature of the tractor?

Question on a Oil Leak  A tractor has an oil leak. The amount of oil, L(t), in milliliters per hour that leaks out is a function of the tractor's operating temperature, t, in degrees Celsius. The function is  L(t)= 0.0004t^2+0.16t+20,100 degrees Celsius<_t<_160 degrees Celsius  a) How many milliters of oil will leak out in 1 hour if the operating temperature of the tractor is 100 degrees C?  b) If oil is leaking out at 53 milliliters per hour, what is the operating temperature of the tractor? a) t = 100 ºC L = 0.0004(100)^2+0.16*100+20 L = 4 + 16 + 20 = 40 L = 40 ml/hr b) L = 53 ml/hr 53 = 0.0004t^2+0.16t+20   <--- let t = 100T 53 = 4T^2 + 16T + 20 4T^2 + 16T - 33 = 0 (2T - 3)(2T + 11) = 0 T = 1.5, T = -5.5 t = 150, t = -550  (ignore the negative temperature) t = 150 º
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### What's a function of function?

If you just mean the purpose of a function then see immediately below. If you mean f of g where f and g are two functions, go to the end. The purpose of a function is like giving someone a to-do list. A function (normally shown as f(x)= meaning "function of x", or y=) will usually contain one variable, usually represented by x. Some functions may have more than one variable. If x isn't the variable, it will usually be a different letter like t or a or any letter. Let's say it is x. This variable will appear in a formula with numbers. The formula is the function and it contains instructions in symbols telling you what to do with the variable. For example, multiply the variable by 2 then add 3 and divide the result by 4. This would be written f(x)=(2x+3)/4 or y=(2x+3)/4. The equals sign means that the function is defined as the expression on the right. Just like someone might say to you, think of a number (that's x), but don't tell me what it is, then double it and add 3 and divide the result by 4. Functions can be plotted on a graph. The idea of this is that on the horizontal axis (x axis) you have markers for 0, 1, 2, etc. On the vertical axis (y or f(x)) you also have markers. The graph is usually a continuous line, and every point on the line is made by putting a different value for x and marking the point (on a rectangular grid f(x) units vertically and x units horizontally) for the result of working out the value of the function for different values of x. The points make up the graph. You can use the graph to find the value of x for any value of the function, and the value of the function for any value of x, provided the graph extends far enough. This is just a brief example of the purpose of a function. A practical example is the conversion of temperature in degrees Fahrenheit (F) to degrees Celsius: C=5(F-32)/9. This function tells you what do with the value of the temperature. You could plot this as a straight line graph and you can read off degrees C for any temperature in degrees F, and vice versa. Another example is d=30t where d=distance, speed=30mph, t=time. The function is 30t, and from it you can work out the distance a car moves in a particular time t when its speed is 30mph. Function of a function: this simply means you work out the value of applying one function and then feed this answer as the variable into the other function. An example could be that one function is used to find out how many miles a car travelling at an average speed of 30mph in a given time. The second function could be to find out how much fuel is used to travel that distance. So g(t)=30t is the first function. The second function is h(d)=d/24 where fuel consumption is 24 miles per gallon. h of g is h(g(t))=30t/24=5t/4.
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### The dropping at the rate of g (t)=10e^(-0.1t) for 0 is less than or = to t less than or = 10, where g is measured in degrees in Fahrenheit and t in minutes.

The dropping at the rate of g (t)=10e^(-0.1t) for 0 is less than or = to t less than or = 10, where g is measured in degrees in Fahrenheit and t in minutes. If the metal is initially 100 degrees Fahrenheit, what is the temperature to the nearest degree Fahrenheit after 6 minutes? I'm  stuck with this problem. The equation is: g (t)=10e^(-0.1t),  0 <=  t  <= 10 g(t) is the dropping rate, which I assume means the rate at which the temperature drops. Let T(t) be the temperature of the metal over time. Then dT/dt = g(t) Now, a differential quotient, such as dT/dt, is by definition, the rate of increase of T wrt t. Since we know that the Temperature is actually dropping over time, the dropping rate, g(t), must be negative. i.e. g (t) = -10e^(-0.1t),  0 <=  t  <= 10 So, dT/dt = -10e^(-0.1t) Integrating wrt t, T(t) = 100e^(-0.1t) + const We are given that initially (at t = 0), the temperature of the metal is 100 degrees. i.e. 100 = 100e^(0) + const 100 = 100 + const Const = 0 Our expression for the temp of the metal then is T(t) = 100e^(-0.1t) At t = 6, T(6) = 100e^(-0.6) T(6) = 100*0.5488 T(6) = 54.88 The temperature of the metal after 6 minutes is 55 degrees Fahrenheit
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### linear How many bags and how many jackets should be made per week to maximize profit?

Bag sewing time=4 mins, jacket sewing time=2 mins; bag pressing time=1 min, jacket pressing time=3 mins. Available sewing time=2,000 mins per week, available pressing time=1,500 mins per week. Profit=5RM per bag, 6RM per jacket. Call B=number of bags per week and J=number of jackets per week. Plot two lines on the same graph if available time for pressing and sewing is fully utilised. The first equation is based on the sewing time: 4B+2J=2000, and the second on the pressing time: B+3J=1500. Let B be the vertical axis and J the horizontal axis. Plot the first equation: draw a line between 1500 on B axis and 500 on J axis. These are the points where no jackets are made, just bags (B=1500 and J=0) and where no bags are made, just jackets (B=0 and J=500). Plot the second equation similarly with a line joining 500 on B to 1000 on J. Where they cross shows how many bags and jackets can be made to optimise the time available and maximise profit. The two equations can be solved by substituting B=1500-3J into 4B+2J=2000, giving us 6000-12J+2J=2000. So J=400, therefore B=300. The intersection point is (400,300) for (J,B). The profit from this optimisation would be 300*5+400*6 RM = 3,900 RM.
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### ring of terror

Diameter of the wheel is 25-1=24m. When t=0 y=1.5m. Angular speed is 540 degrees (1.5*360) per minute or 9 degrees per second. A complete revolution is 360 degrees so it takes 40 seconds for one revolution. When t=0 and t=40 the trig function will have the same value. The minimum value of sin or cos is -1 and the maximum is 1. The difference between max and min has to be 24m. Assume the first option is y=13sin(...)-12 rather than y=13sin(...)=12and the others are as shown, we have: ±13-12=-25 to 1 as the range - eliminate option1 ±12+13=1 to 25 possible option Ditto Ditto Eliminate option5 because range would be 14 to 38, and 38 is higher than the wheel Possible option The trig function must have the same value for t=0 and 40: Option1 already eliminated Same value for t=0 and 40 Ditto Different value for t=0 and 40-eliminate option4 Option5 already eliminated Possible option The only options left are 2, 3 and 6. Minimum is t=0 and maximum is t=20 (highest point): Option 2 min: 1.48; max: 24.52 Option 3 min: 1.48; max: 24.52 Option 6 min: 1.48; max: 24.52. So these options provide reasonable models for the height of the platform. The three curves have identical periods and amplitudes. The only difference is that they are phase-shifted with respect to one another. The factor of 9 degrees per second in the arguments confirms this. The time base, t, for each of them has a different reference point: -1.8, 11.8 and 38.2 seconds (38.2-(-1.8)=40 seconds, the cycle time). For options 2 and 6 only the value of y, the height of the platform is 1.5m (approximately); at t=0, option 3 is at the maximum platform height of about 24.5m (the average of 38.2 and -1.8), corresponding to the lowest point of about 1.5m for options 2 and 6. The reverse is true at t=20.
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### what is the formula to find right angles between minute & hour hand in one hour

In 60 minutes the minute hand moves 360 degrees, while the hour hand moves 30 degrees (5 mins=360/12=30). The minute hand moves 12 times faster than the hour hand. Let the angle of the minute hand from 12 o'clock be m degrees and the hour hand from 12 o'clock be h degrees. Starting with the hands showing 3 o'clock, we can write the equation m=12(h-90). When h=90 m=0, representing 3 o'clock. We want to find the next time the hands are exactly 90 degrees apart, so that's m-h=90. We have two equations and two variables. m=90+h, so we can write 90+h=12(h-90). So 90+h=12h-1080. 11h=1170, so h=106.3636... the next time the hands are at 90 degrees and m=196.3636... What time is this? Divide by 360 and multiply by 60 (therefore divide by 6 to convert degrees to clock minutes). t=m/6, where t is the time in minutes past the hour. The minutes are 32.7272... after the hour, so if we started at 3 o'clock the time would be 3:32.7272 or 3:32:44 approx. The minutes would be the same for other starting times, like 9 o'clock, for example.
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### Creata a fraction story

FIVE LITTLE PIGS GO TO THE MALL Mama Pig gave her five little pigs seven and a half dollars between them to spend at the mall. It was a cold day, twenty-three Fahrenheit, minus five Celsius, or five degrees below freezing. Off they trotted at a quarter to three in the afternoon. "How far is it?" the youngest pig asked after a while. "One point seven five miles from home," said the eldest. "What does that mean?" asked the youngest. "Well," explained the eldest, "if we divide the distance into quarter miles, it's seven quarters." "How long will it take to get there?" asked the pig in the middle. Her twin sister replied, "It's five past three now, so that means we've taken twenty minutes to get here. Remember the milestone outside our house? There's another one here, so we've come just one mile and we've taken a third of an hour. [That means our speed must be three miles an hour.] "How much longer?" the youngest asked. "Three quarters of a mile to go," the next youngest started. "Yes," said the eldest, "we get the time by dividing distance by speed, so that means three quarters divided by three, which is one quarter of an hour [which is fifteen minutes]." ["So what time will we arrive?" the youngest asked. "About twenty past three," all the other pigs replied together.] "That's thirty-five minutes altogether," the eldest continued, "which means that - let me see - seven quarters divided by three is seven twelfths of an hour. One twelfth of an hour is five minutes [so seven twelfths is thirty-five minutes]. Yes, that's right." When they got to the mall, it had started to snow. Outside there was a big thermometer and a sign: "COME ON IN. IT'S WARMER INSIDE!" The eldest observed: "It shows temperature in Fahrenheit and Celsius. See, there's a scale on each side of the gauge. It's warmer now than it was when we left home. The scales are divided into tenths of a degree. It says twenty-seven Fahrenheit exactly, and, look, that's the same as minus two point eight Celsius," speaking directly to the youngest, "because the top of the liquid is about eight divisions between minus two and minus three. Our outside thermometer at home is digital, but this is analogue." The youngest stuttered: "What's 'digital' and 'analogue'?" "Well," began one of the twins, "your watch is analogue, because it has fingers that move round the watch face. Our thermometer at home is digital, because it just shows the temperature in numbers." ["Yes," said the eldest, "it would show thirty-seven point zero degrees Fahrenheit, four degrees warmer, and minus two point eight Celsius, two point two degrees warmer than when we left."] Continued in comment...
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### \$8 per hour mowing lawns and & \$12 per hour babysitting. she wants at LEAST \$100 per week but can't won't more than 12 hours a weeks write a graph & system of lines inequalities

\$8 per hour mowing lawns and & \$12 per hour babysitting. she wants at LEAST \$100 per week but can't won't more than 12 hours a weeks write a graph & system of lines inequalities Mowing a lawn = \$8/hr Babysitting= \$12/hr Work Time = WT <= 12 hrs/wk Income = M >= \$100 / week Let x be the number of hrs mowing lawns.   “   y  “    “         “         “    “   babysitting. Setting up our inequalities, M = 6x + 12 y   à 8x + 12y >= 100,  i.e. 2x + 3y >= 25 WT = x + y     --> x + y <= 12 The system of inequalities is, 2x + 3y >= 25 x + y <= 12 x >= 0, y >= 0 These inequalities can be graphed using the lines, l1: 2x + 3y = 25 l2: x + y = 12 and are shown below, The inequality x + y <= 12 is given by all that area below the line l1, such that both x and y are positive, i.e. the triangle AOB. The inequality 2x + 3y >= 25 is given by all that area above the line l2, such that both x and y are positive, i.e. the triangle COD. The common area satisfying both requirements is the triangle ACE. Only points within the triangle ACE are both below l1 and above l2. Income, M, is maximised for that point within triangle ACE that is furthest from the origin, which is the point A, i.e. where x = 0 and y = 12. M = 6x + 12y 6*9 + 12*12 = 144 Max income: \$144
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### I need help for this problem. Thanks. I really appreciate the help. How do I find theta?

The minute hand moves 12 times as fast as the hour hand, because the hour hand moves 1/12 of the area of the clock face while the minute hand moves the whole area of the clock face. At 4 o'clock, the hands are 120 degrees apart (one third of 360 degrees). The tips of the hands at this time are distance x apart where x is given by the cosine rule: x=sqrt(3^2+4^2-2*3*4cos120)=sqrt(25+12)=sqrt(37), because cos120=-1/2. At time t minutes after 4, the angle between the tips of the hands decreases initially. For example, if t=15 minutes, the hour hand will move 1/4 the distance between 4 and 5, i.e., 30/4=7.5 degrees, while the minute will have moved 90 degrees. The angle between the hands becomes 120-90+7.5=37.5 degrees. For t minutes, then, the angle ("theta") changes to 120-360t/60+30t/60 degrees=120-6t+t/2=120-11t/2. (Theta can be found for any time t minutes after 4 o'clock from this formula. Also, t can be found when theta is zero, the hands being aligned: t=240/11.) So, x=sqrt(25-24cos(120-11t/2))=sqrt(25-24(cos120cos(11t/2)+sin120sin(11t/2)). If t is very small cos(11t/2) is close to 1 and sin(11t/2) is close to 11t/2. sqrt(120)=sqrt(3)/2; x=sqrt(25-24(-1/2+11tsqrt(3)/4))=sqrt(37-264tsqrt(3)/4)=sqrt(37-66tsqrt(3)). The change in x is sqrt(37-66tsqrt(3))-sqrt(37)=sqrt(37)(sqrt(1-66tsqrt(3)/37)-1). We can use the Binomial Theorem to evaluate sqrt(1-66tsqrt(3)/37)=(1-66tsqrt(3)/37)^(1/2). When t is very small we can ignore t^2 terms and higher powers of t, so we get 1-33tsqrt(3)/37 as an approximation. The change in x becomes sqrt(37)(1-33tsqrt(3)/37-1)=-33tsqrt(3/37). The instantaneous rate of change of x at 4 o'clock is found by dividing this expression by t=-33sqrt(3/37)=-9.3967"/minute=-0.1566"/sec. The minus sign indicates that the hands are closing at the rate of 0.1566 inches per second. The solution can also be found applying formal calculus, where dx (the change in x) is related to the angle change (dø) and the angular rate of change dø/dt can be related to the rate of change of x, dx/dt. This involves differentiating the cosine expression. Because a time of 4 o'clock has been specified, the solution has been calculated from first principles, thus avoiding calculus.
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