The temperature of a cup of coffee varies according to Newton's Law of Cooling: dT dt equals negative k times the quantity T minus A, where T is the temperature of the coffee, A is the room temperature, and k is a positive constant. If the coffee cools from 100°C to 90°C in 1 minute at a room temperature of 25°C, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes.

74
67
60
42

Answers

Answer 1

Answer:

67.3°C

Step-by-step explanation:

A = 25, T(0) = 100, T(1) = 90, find T(4)

dT/dt = -k(T - A)

d(T - A)/dt = -k(T - A)

d(T - A)/(T - A) = -k dt

ln(T - A) = lnC - kt

[tex]T(t) -A=Ce^{-kt}\\T(t) = A + Ce^{-kt} = 25 + Ce^{-kt}\\T(0) = 25 + C = 100\\C=75[/tex]

[tex]T(t) = 25 + 75e^{-kt}\\T(1) = 25 + 75e^{-k} = 90\\75e^{-k} = 65\\e^{-k} = \frac{65}{75}, k = ln\frac{75}{65} = 0.1431\\T(t) = 25+75e^{-0.1431t}\\T(4) = 25+75e^{-0.1431\times4} = 67.3[/tex]


Related Questions

8. Find GH,
E
3-4
HY
-
H
2
3x - 4
G
SI
F
9x - 59
D

Answers

Answer:

GH= 47

Step-by-step explanation:

[tex]2(3x - 4) = 9x - 59[/tex]

[tex]6x - 8 = 9x - 59[/tex]

[tex]6x - 9x = - 59 + 9[/tex]

[tex] \cfrac{ - 3x}{ - 3} = \cfrac{ - 51}{ - 3} [/tex]

[tex]x = 17[/tex]

[tex]gh = 3(17) - 4[/tex]

[tex]51 - 4[/tex]

[tex] = 47[/tex]

~

Calculus 3.10 Linearization (a) y=x^2sin2x (b) y=ln sqrt(1+t^2) find the differential of each.

Answers

Answer:

Below in bold.

Step-by-step explanation:

(a) y=x^2sin2x

Using the Product Rule:

dy/dx = x^2*2cos2x + 2xsin2x

dy/dx = 2x(xcos2x + sin2x).

(b) y=ln sqrt(1+t^2)

     y = ln (1 + t^2)^1/2

Using the chain rule:

dy/dx =  1 / (1 + t^2)^1/2 * 1/2(1 + t^2)^-1/2 * 2t

=  2t/(1 + t^2)^1/2 * 1/ (2(1 + t^2)^1/2

=   2t / 2(1 + t^2)

= t / ( 1 + t^2).

Help math math math

Answers

Hello.

In order to convert this equation into slope intercept form, we need to divide the entire equation by 7:

[tex]\tt{8x-7y=13[/tex]

[tex]\tt{\displaystyle\frac{8x}{7} -\frac{7y}{7}=\frac{13}{7}[/tex]

Simplify:

[tex]\tt{\displaystyle\frac{8x}{7}-y=\frac{13}{7}[/tex]

Add y to both sides:

[tex]\Large\boxed{\sf{y=\displaystyle\frac{8x}{7} -\frac{13}{7}}}[/tex]

I hope it helps.

Have an outstanding day. :)

[tex]\boxed{imperturbability}[/tex]

Hey there!

8x - 7y = 13

8x - 13 = 7y

(8x - 13)/ 7 = y

8x/7 - 13/7 = y

Hope it helps ya!

Help me solve this PLS

Answers

Answer:

Ok so what you have to do to is basically apply Pythagoras Theorem

Step-by-step explanation:

The hypotenuse squared is equal to the sum of the squares of the legs of a right-angle triangle.

[tex]c^2 = a^2 + b ^2[/tex]

Assuming:

c = 10 [tex]\rightarrow[/tex] hypotenuse

a = 6.84 [tex]\rightarrow[/tex] adjacent leg (base of the triangle)

b = ? [tex]\rightarrow[/tex] opposite leg (height of triangle)

[tex]10^2 = 6.84^2 + b^2[/tex]

[tex]b^2 = 10^2 - 6.84^2[/tex]

[tex]b = \sqrt{(10)^2-(6.84)^2}[/tex]

[tex]b = 7.295[/tex]

With that, you can calculate the area of the triangle:

[tex]A_{triangle} = \frac{a*b}{2}[/tex]

[tex]A_{triangle} = \frac{6.84*7.295}{2}[/tex]

[tex]A_{triangle} = 24.95[/tex]

And as your polygon has 9 sides, you can assume that you have 9 of this triangles, so the total area would be:

[tex]A = 9*24.95[/tex]

[tex]A = 224.55[/tex]

And rounding this result to the nearest hundreth:

[tex]A = 220[/tex]

please answer these 3 equations fast pls

Answers

Answer:

15: 10.99

2(3.14)r

3.5/2 = 1.75

2(3.14)1.75

10.99

16: 50.24

2(3.14)8

50.24

17: 260%

2 = 200%

3/5 = 60%

200 + 60 = 260%

Have an amazing day!

Please rate and mark brainliest!!

if a printer prints 36 pages in 12 minutes, how many pages per minute?

Answers

3 pages per minute. all u have to do is divide 36 by 12

Step-by-step explanation:

The key word "per" hints at a ratio

A ratio is represented by ?:?, ?/?, etc

So, we can divide the two

pages. 36 pages

----------- = ------------- = 3 pages per min minute 12 minutes

can someone help me with this I already answered half of all of them but I need to make sure It's right?

Answers

Answer:

yes 0.265 is correct it is your answer

Rewrite the absolute value function as a piecewise function.
a
f(x) = -3x +11 – 2
-

Answers

y=-3x+9 that is the answer

Ivan rented a truck for the day. There is a base fee of $17.95, and there was an additional charge of 91 cents for each mile driven. Ivan had to pay $284.58 when he returned the truck. For how many miles did he drive the truck?

Answers

Answer:

293 miles

Step-by-step explanation:

284.58-17.95=266.63

266.63/0.91=293

293 miles

If 6 - 8 = 28, what is the value of y?

Answers

if there is supposed to be a “y” after 6 the answer would be y=6 but if it isnt the answer is y= - 26

my past Is about to be here What subjects do I need to start studying??? btw I'm a sphomore.

Answers

The psat has evidence based reading/ writing and math on it. The college board website has helpful info and practice tests that you can take

what Is the remainder when the polynomial p(x) = 5x^3 + x^2 + 10 Is divided by (x + 2)?

Answers

Answer:

its not showing up on the screen

someone please help​

Answers

Answer:

C

Explanation:

I think you’re asking what graph goes with D = {x|x≠0} and R = {all real numbers}, which would be C. The reason being is that because x≠0, you need an open dot to represent 0 not being on the line. B has a closed dot, meaning 0 is included, which isn’t what it’s asking for.

Find the value of |5|-4(3^2 - 2).
-11
-33
7
-23

Answers

Answer:

-23

Step-by-step explanation:

I dont really know how to explain this sorry. but I hope it some what helps

a car travels at a speed of 85 mph how far will it travel in 15 minutes ​

Answers

Answer:

106.25 mph

Step-by-step explanation:

since the car travels at 85 miles per hour we divide it by 60 seconds in order to find how many miles is it to get in a minute

=> 85mph ÷ 60

divide 85 by 60

=> 1.416

multiply 1.416 by 15 to get how many miles it to go in 15 minutes

=> 21.25

then add it to 85

=> 106.25


[tex] \frac{x}{4} + 3 = \frac{x}{2} + 3[/tex]

Answers

Answer:I think it’s 7...

Step-by-step explanation:

Lucy walks one time around the lake. She walks for 1.5 hours at an average rate of 3 miles per hour. What is the distance, in miles, around the lake?

Im stuck on this one, please help!

Answers

Answer:

4.5 miles

Step-by-step explanation:

Since she walked at a rate of 3 miles for 1.5 hours, you have to multiply both together (1.5 x 3) and you get 4.5 miles

Simplify.
-4(y+6)+5y

Answers

-4(y + 6) + 5y

= -4y - 24 + 5y

= y - 24 (simplified)

Answer:

9y+24

Step-by-step explanation:

Line L in the figure below is parallel to the line y=5x+3. Find the coordinates of the point P.

Answers

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{5}x+3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

that means that the slope of line L is also 5, or 5/1 or   [tex]slope=\cfrac{\stackrel{rise}{5}}{\underset{run}{1}}[/tex]

Check the picture below.

Math workshops and final exams: The college tutoring center staff are considering whether the center should increase the number of math workshops they offer to help students improve their performance in math classes. Faculty would like to know if requiring student attendance at these math workshops will improve overall passing rates for their students in their math classes. They plan to use the number of workshops attended to predict the final exam score and regression analysis to determine the effectiveness of the mandatory workshop attendance policy. Which is the response variable

Answers

Answer:

Final Exam score is the response variable.

Step-by-step explanation:

The response variable is the variable of interest. It is what is being tested for given the predictor variables. The response variable is also called the dependent variable and from our question we want to predict final exam scores would improve if attendance is made mandatory or as the question says, required. The number of times attended is the independent variable while final exam score is the response variable.

There is a bag filled with 5 blue and 6 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 blue?

Answers

5/11 * 6/11 = 30/121

The value of square root of 20 is between 4.4 and 4.5. Which of the following is a more precise approximation of square root of 20?

Answers

Answer:

4.5

Step-by-step explanation:

the square root of 20 is closer to 4.5 than it is to 4.4

1) Find AB
B
29
41°
С
13
A

Answers

Step-by-step explanation:

See attached image for the answer

A statistician believes that the percent population growth rate of major cities has decreased compared to the last decade. To test his claim, he randomly selects major cities and compares the percent population growth between the years 2007 and 2017 to the percent population growth between the years 1997 and 2007. Suppose that data were collected for a random sample of 17 cities, where each difference is calculated by subtracting the percent growth rate from 1997 to 2007 from the percent growth rate from 2007 to 2017. Assume that the percentages are normally distributed. The statistician uses the alternative hypothesis Ha:μd<0. Using a test statistic of t≈−5.053, which has 16 degrees of freedom, determine the range that contains the p-value.

Answers

Answer:

The range consisting of the p-value is, 0.000001 < p-value < 0.00001.

Step-by-step explanation:

The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.

In this case a paired t-test is used to determine whether the percent population growth rate of major cities has decreased compared to the last decade.

The alternative hypothesis is Hₐ: [tex]\mu_{d}<0[/tex].

The test statistic value is, t = -5.053.

The degrees of freedom is, 16.

Compute the p-value as follows:

[tex]p-value=P(t_{16}<-5.053)=0.000059[/tex]

Thus, the range consisting of the p-value is, 0.000001 < p-value < 0.00001.

HELP ILL MARK BRAINLIEST IF CORRECT!!!

Answers

Answer:

Does y vary directly with x?

•YES

What is the---------------?

•A. k=y

What is the function----------?

•A. y=x

If x = 3i, y = 2i, and z = m + i, the expression xyz equals
1.) -12-12mi
2.)-6-6mi
3.)12-12mi
4.)6-6mi

Answers

Answer:

Step-by-step explanation:

I am assuming that i = √(-1)

3i*2i*(m + i)

= 6i^2(m + i)

= -6(m+ i)

= -6m - 6i.

Which formula can be used to measure the area of a trapezoid?
O Multiply the bases, add the height, then divide by two.
O Add the bases, multiply by the height, then divide by two.
O Add the bases, divide by the height, then multiply by two.

Answers

The correct answer is add the bases multiply height and divide by two

Ok, so Jay has a goal of saving money to buy a handheld game console. Jay has reached 10% of his goal and saved $12. Please explain

Answers

Answer:

$120

Step-by-step explanation:

10% = 1/10

If Jay has only saved 1/10 of his goal, then to find how much the goal is we multiply how much he has by 10. This will convert 1/10 to 1.

12 x 10 = 120

Jay's goal is $120

Answer:

$120

i got on edg 2020 hope this helped you

Need help!
v varies directly as the square of x and inversely as the cube of y. Find v when x=3 and y=2, given that v=2 when x=4 and y=3

Answers

Step-by-step explanation:

If two objects vary directly, we just divide those two objects.

If two objects vary indirectly, we multiply them.

So here we have

[tex] \frac{v}{ {x}^{2} } {y}^{3} = k[/tex]

where k is a constant.

So let analyze when all variables Except k is given.

[tex] \frac{2}{16} (27) = 3.375[/tex]

So k=3.375

[tex] \frac{v}{ {3}^{2} } (2 {}^{3} ) = 3.375[/tex]

[tex] \frac{v}{9} (8) = 3.375[/tex]

[tex] \frac{v}{9} (8) = \frac{27}{8} [/tex]

[tex]v8 = \frac{243}{8} [/tex]

[tex]v = \frac{243}{64} [/tex]

[tex]3.796875[/tex]

Solve the question in the image please.

Answers

Answer:

Where's the image?

cause i can't solve the question without the image

Send the image please
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