Answer:
a
f'(t) is negative
b
The unit is degC/min
c
At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
Step-by-step explanation:
From the question we are told we are told that
The equation for the temperature of a cup of coffee place on a counter is
[tex]H= f(t)[/tex]
Here t is the time in minutes the coffee was put on the counter
Generally f(t)' is the derivative of f(t) at it represents the change of the temperature of the cup of coffee with respect to time
Generally for the coffee placed on the counter after a couple of minutes the temperature will decrease hence f(t)' is negative
Generally the unit of the temperature is in degrees Celsius while that of time is in minutes
So the change in temperature with time f(35)' will be in degrees Celsius/minutes (i.e degC/min)
From the question we are told that
[tex]|f(35)'| = 1.5[/tex]
i.e the rate of change of temperature after 35 minutes is 1.5
and
[tex]|f(35)| = 68[/tex]
i.e the temperature of the cup of coffee after 35 minutes is 67 degC
Now after another t= 30 seconds = [tex]\frac{30}{60}= 0.5 \ minutes[/tex] the rate of change of the temperature of the cup of coffee is
[tex]R = |f(35)'| * t[/tex]
=> [tex]R = 1.5 * 0.5 [/tex]
=> [tex]R = 0.75 [/tex]
So
At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
The value of f'(t) is negative because as the cup of coffee is placed on the counter there is a loss of heat from the cup of coffee to the surroundings as t increases hence f'(t) is negative.
The units of f'(35) = degC/min.
At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
Given
The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in minutes since the coffee was put on the counter.
1. The value of f'(t) is negative because as the cup of coffee is placed on the counter there is a loss of heat from the cup of coffee to the surroundings as t increases hence f'(t) is negative.
2. What are the units of f'(35)?
The units of f'(35) = degC/min.
3. At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
At ║f'(35)║ = 1.5 and f'(35) = 68
|f'(35)| = 1.5 represents the rate of change of temperature every 35 minutes = 1.5.
To know more about Temperature click the link given below.
https://brainly.com/question/16045110
What is the volume of a cube that measures 3.5 inches on each edge?
72.5 in
35 in?
none of these
42.9 in
Answer:
42.9 in
Step-by-step explanation:
Volume of a cube = side cubed
V = (3.5)^3
V = 42.875
5 2/5 as a mixed number
Answer:
Mixed numbers have a whole number followed by the fraction (2 1/2). You would say "two and one half." The other format is an improper fraction where the numerator is greater than the denominator (5/2). Mathematicians would say that is five halves.
Answer:
27/5 I think um I have to fill out the question so ya
In the triangle below, what is the length of the side opposite the 60° angle?
Answer:
3
Step-by-step explanation:
Answer:
3 sqrt3
Step-by-step explanation:
AP3X
Need help I am stuck, I would like to see if my work matches someone else's to check it over.
Answer:
i think its 45
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
I'm pretty sure but sorry if its incorrect.
which one is the coldest AMD why
Answer:
Raleigh.
Step-by-step explanation:
Just look for the Fahrenheit with the smallest number.
Answer:Raleigh
Step-by-step explanation:Your going to go for the smallest and I just took the quiz
The formula for converting miles into feet is F=5280m. If m=3, evaluate to find F, the number of feet in 3 miles
Answer:
15,840?
Step-by-step explanation:
if f=5280m and m=3 then 5280x3= 15,840
Good luck!
Task: Use the following situation to answer Parts A and B Instructions At noon, a tank contains 100 gallons of water. The table shows the input and output of water from pipes A, B, and C. The pipes begin operating simultaneously at noon. A B C Pipe Flow IN (gallons per minute) a (2) = 172 6(2) = 80 Flow OUT (gallons per minute) c (2)=30r Complete each of the 2 activities for this Task. Activity 1 of 2 Let T (2) represent the amount of water in the tank x minutes after all of the pipes A, B, and C are opened. Which of the following functions represents T (x)? O A T (2) = 100 + a(z) +b(2) - c(x) OCT (x) = 100 + a (x) +b(2) + c(2) OBT () = a (x) + b() +(2) ODT (2) = a (x) +b(x) - c(:) Activity 2 of 2 Using the equation, after how many minutes will the tank be empty?
Answer:
1. Option C2. NeverStep-by-step explanation:
Refer to attached for the table and clearer version of the question
As per table A and B pipes feed the tank and C is the outlet
Considering initial volume of 100 gallons, the amount of water in the tank after x minutes is:
T(x) = 100 + a(x) + b(x) - c(x), this is option C.We can calculate when tank is going to be empty:
0 = 100 + 25x + 10x - 30x0 = 5x + 1005x = -100x = -20Since we got negative number, the tank is not going to be empty when all 3 pipes are open.
The function which represent T (x) for the tank which contains 100 gallons of water and input and output of water from pipes A, B, and C is,
[tex]T(x)=100+a(x)+b(x)-c(x)[/tex]
The tank will not be empty when all the three pipes are in operation.
What is a function?If we have two sets A and B as:
[tex]A = \{a_1, a_2, ... \}\\B = \{b_1, b_2, ... \}[/tex]
Then, function
[tex]f:A \rightarrow B[/tex]
is a connection of elements of A to B such that one element of A is connected to only single element of B, and not many.
The connected pairs are then written as:
[tex]\{(a_i_1,b_j_1), (a_i_2, b_j_2), ... \}[/tex]
Under the function f.
The table shows the input and output of water from pipes A, B, and C.
Pipe A B C
Flow In (gallons/minute) a(x)=25x b(x)=10x
Flow Out (gallons/minute) c(x)=30x
The pipes begin operating simultaneously at noon. Let T (2) represent the amount of water in the tank x minutes after all of the pipes A, B, and C are opened.
At noon, a tank contains 100 gallons of water. In the above table A and B shows the inlet of water while C shows the out let of the water.
So, 100, A and B added in the function while C will be subtracted as,
[tex]T(x)=100+a(x)+b(x)-c(x)[/tex]
Thus, the function in option C represents T (x).
Now use this equation, to find the number of minutes for the tank be empty. For this equation, the equation equal to zero as,
[tex]T(x)=100+25x+10x-30x[/tex]
[tex]0=100+25x+10x-30x\\-100=5x\\x=-20[/tex]
This negative value of x tells that if all the three pipes are open, the tank is never become empty completely.
Thus, the function which represent T (x) for the tank which contains 100 gallons of water and input and output of water from pipes A, B, and C is,
[tex]T(x)=100+a(x)+b(x)-c(x)[/tex]
The tank will not be empty when all the three pipes are in operation.
Learn more about the function here;
https://brainly.com/question/13395697
help pleaseeeeeeee :$))$$$$
Answer:6
Step-by-step explanation: I don't really know how to explain this...
Answer:
6
Step-by-step explanation:
hi! absolute value is defined as the number of units away from zero on the number line. distance is always positive, so absolute value is always positive. therefore, the answer is 6 since you just take the negative sign away.
hope this helps!
One night in January, the temperature in Alaska is -16℉. The next day, the temperature is half of what it was the night before. What is the temperature? One night in January, the temperature in Alaska is -16℉. The next day, the temperature is half of what it was the night before. What is the temperature?
Answer:
-8 degrees
Step-by-step explanation
Half of negative 16 would be negative 8.
Answer:
-8
Step-by-step explanation:
-16 ÷ 2 = -8
You could also do:
16 ÷ 2 = 8
and then put a negative in front of 8
And to prove it's true,
8 x 2 = 16
-8 x 2 = -16
Tim's holds a fishing line at the surface of a lake, and it sinks 10 feet below the surface of the water. Tim then pulls the lure up 4 feet.which of the following statements about this situation are true?select all that apply
Answer:
Where are the answers to choose from?
Evaluate:
54 - 75 + 81 - (-27) + 53
Answer:
140
Step-by-step explanation:
Answer:
140.
Step-by-step explanation:
PEMDAS.
Since there isn't any problems that aren't adding, we can just do it step by step.
54 - 75.
-21.
Add 81.
60.
Subtract -27.
87.
Add 53.
140.
Brainiest?
Greta can bike 6 miles in 30 minutes. At that rate, how many miles can she bike in 45 minutes?
Answer: 9 miles
Step-by-step explanation:30 divided by 6 is 5. So the was biking 1 mile every 5 minutes. 45 divided by 5 is 9.
Feet up a ratio for miles over time:
6/30 = x/45
Cross multiply:
30x = 270
Divide both sides by 30:
X = 270/30
X = 9 miles
Denise spent $56.48 at the grocery store while Michael spent $74.06. How much more money did Michael spendthan Denise?A.$17.58B.$37.03C.$65.27D.$130.54
Answer:
A 17.58
Step-by-step explanation:
Can someone help please
Find the perimeter and area of the figure if each unit on the graph measures 1 centimeter. Round answers to the nearest tenth, if necessary.
Answer:
The perimeter of the figure is : 22.4 cm
The area of the figure is : 30.2 cm²
Step-by-step explanation:
From the diagram, the figure is a rectangle.
Use the coordinate points to find the lengths of each side.
Side length AD = side length BC
Apply the Pythagoras relationship to find length BC as;
a² + b²= c² where a=2 cm and b = 4 cm and c =BC
2² + 4² = c²
4+16 = c²
20 = c²
c= √20 = 4.4721
Length BC = Length AD = 4.5 cm
Side length AB = Side length DC
Apply the Pythagoras relationship to find length DC as;
a² + b²= c² where a=6 cm and b = 3 cm and c =DC
6² + 3² =c²
36 + 9 = c²
45 = c²
√45 = c
c= 6.7082
c = DC = 6.7 cm
Now you have measurements of the rectangle as;
Length = 6.7 cm and width = 4.5 cm
The perimeter will be ;
P= 2{l +w} --------- where l is length and w is width and P is perimeter of the rectangle
P=2{6.7 + 4.5}
P=2{11.2}
P= 22.4 cm
The area will be ;
A= l*w
A= 6.7 * 4.5 = 30.15 = 30.2 cm²
The perimeter of the figure is : 22.4 cm
The area of the figure is : 30.2 cm²
Answer:
its wrong
Step-by-step explanation:
A rectangular garden is 10 2/7 feet by 5 4/9 . What is the area of the garden?
Answer:
50 8/63
Step-by-step explanation:
10*5=50
when multiplying fractions we have to multiply the numerators, then multiply the denominators.
2*4=8
7*9=63
hope this helps =3
sorry if im wrong
Someone answer number 10.(Both parts please.)
why do u not regroup any tens into hundreds? pls i need help
Answer:
You dont regroup any tens into hundreds depended on what Number you have and if your adding and subtracting if you have 375 - 38 then you’ll regroup.
Step-by-step explanation:
Select the term that is suggested by the fugure
Answer:
im pretty sure its line segment if
Step-by-step explanation:
if its not im so sorry!!
How do you do this question?
Answer:
convergent
Step-by-step explanation:
the function increases or decreases or as the number of terms of the series increases.
Answer:
Divergent
Step-by-step explanation:
The series can be written as:
∑ 1 / (4n − 1)
We can compare this to 1 / (5n). 1 / (5n) is smaller and diverges (p-series test). Therefore, the larger function also diverges.
The graph and the table show 2 different bicycle riders. Each rider travels at a constant speed. Compare the speeds of the two riders.
Answer:
C
Step-by-step explanation:
Consider the equation: x^2+10x-24=0 First, use the " completing the square " process to write this equation in the form ( x+D )^2 = E and enter the results below x^2 + 10x -24 = 0is equivalent to......? = ?
Answer:
[tex]x^2 + 10x -24 = 0 \: \\ is \: equivalent \: to \: ( x + 2) {}^{2} + 10x - 36=0[/tex]
Step-by-step explanation:
[tex]x^2 + 10x -24 = 0 \\ x^2 + 12x - 2x -24 = 0 \\x(x + 12) - 2(x + 12) = 0 \\ (x - 2)(x + 12) = 0[/tex]
solving equations 1/2(x+3)=2/5(x+2)
Answer:
x=-7
Step-by-step explanation:
convert to decimals 0.5(x+3)=0.4(x+2)
simplify the brackets 0.5x+1.5=0.4x+0.8
isolate x to one side 0.1x=-1/7
divide both sides by 0.1 x=-7
Can u help me asap please
Answer:
It is for sure a rational # , and whole #, but possibly also a natural#
Step-by-step explanation:
What is 50x50x1x0 =?
What is 0x0 =?
What is 0/0 =?
What is 50x50x1x0 = 0
What is 0x0 = 0
What is 0/0 = it is called undefined and the expression is 00
Answer:
1. 0 2.0 3. impossible
Step-by-step explanation:
1. PEMDAS
50*50=2500
2500*1=2500 idnetification property
2500*0=0 zero property
2. 0*0 =0 zero property
3. 0 can not be a divisor. This leads to the answer being an error
What is the solution of 4+ V5x+88 – X+
10?
X = -10
X = 3
X = -10 or x = 3
O no solution
Answer: no solution
Step-by-step explanation:
The set of all numbers greater than -1 and less than 0.
Answer:
I would just think that it is 0
Step-by-step explanation:
0 is greater then -1 and it is the exact same thing and not less than 0
Answer:
-0.5
Step-by-step explanation:
<________-1_-0.5_0__1_________>
its greater than -1 and less than 0
use point slope form to write an equation of the line with the given slope that passes through the given point.
Answer:
A. y - 0 = 2 ( x + 2 )
Step-by-step explanation:
First you have to isolate y, by using A, the 0 can simply be forgotten about. Next, you must expand the equation, thus with 2 ( x + 2 ), it expands to:
y = 2x + 4
With this in mind, the b value is 4, and with a slope of 2, you can see that the equation eventually crosses the y-axis at 4.
A certain shade of green paint is made by mixing blue and yellow paint. The relationship between the number of quarts of blue paint in the mix, xx, and the number of quarts of yellow paint, yy, is represented by the graph below.
What does the ordered pair (2,102,10) indicate?
Answer:
2 quartz of the blue paint for every 10 quartz of yellow paint
Step-by-step explanation:
The graph shows the possible different amount of yellow paint and blue paint, in quartz, that can be mixed to obtain a shade of green paint.
On the graph, at the point with the coordinates pair of (2, 10), it means for we would require 2 quartz of blue paints to be mixed with every 10 quartz of yellow paint in order to get the shade of the green paint that we are looking for.
Answer: 2 quartz of the blue paint for every 10 quartz of yellow paint
Step-by-step explanation: good luck
Find the measure of the indicated angle.
Answer:
I believe it could be 25
Step-by-step explanation:
Eight angle = 90
1. 38 + 27 = 65
2. 90 - 65 = 25
I haven't done angles for a long time, but I hope my memories serves well. Sorry if it may be wrong, but this is what I remember from doing angles in Year 7