Newton's Law of Cooling:
[tex]T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}[/tex]
[tex]T(t) =[/tex] Temperature given at a time
[tex]t =[/tex] Time
[tex]T_{s} =[/tex] Surrounding temperature
[tex]T_{o}=[/tex] Initial temperature
[tex]e =[/tex] Constant (Euler's number) ≈ 2.72
[tex]k =[/tex] Constant
Using this information, find the value of [tex]k[/tex], to the nearest thousandth, then use the resulting equation to determine the temperature of the water cup after 4 minutes.
First, plug in the given values in the equation and solve for [tex]k[/tex]:
[tex]T(t) =[/tex] 197°, [tex]t =[/tex] 1.5 minutes, [tex]T_{s} =[/tex] 70° and [tex]T_{o}=[/tex] 210°
[tex]T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\197=70+(210-70)e^{-1.5k} \\197 -70 = (140)e^{-1.5k} \\127 =(140)e^{-1.5k}\\\frac{127}{140}=e^{-1.5k} \\ln(\frac{127}{140})=-1.5k\\-0.097=-1.5k\\0.0649 = k[/tex]
[tex]k[/tex] ≈ [tex]0.065[/tex]
Let the temperature of the water cup after [tex]t = 4[/tex] minutes be [tex]T(t) = x[/tex]
Now, let's plug the new time and [tex]k[/tex] constant in the equation and solve for [tex]x[/tex]:
[tex]T(t)=T_{s}+(T_{o}-T_{s})e^{-kt}\\\\\x=70+(210-70})e^{-0.065*4}\\\\x=70+(140})e^{-0.26}, -0.26=-\frac{26}{100}=-\frac{13}{50} \\[/tex]
[tex]x=70+(140})e^{-\frac{13}{50}}\\\\[/tex]
[tex]x=70+(140})e^{\frac{1}{\frac{13}{50}}\\\\\\[/tex]
[tex]x=70+e^{\frac{140}{\frac{13}{50}}\\\\\\[/tex]
[tex]x=70+{\frac{140}{\sqrt[50]{e^{13}}}\\[/tex]
[tex]x = 70 +\frac{140}{1.3} \\x=70+107.947\\[/tex]
[tex]x=177.95[/tex] ≈ [tex]178[/tex]
Temperature of water after 4 minutes is 178°
sorry if there's any misspelling or wrong step but I hope my answer is correct ':3
PLEASE HELP!! Stuart invested $800 in a computer and now makes $5 a page typing research
papers. Let x represent the number of pages Stuart has typed, and let y
represent his profit.
a. Write an equation for y in terms of x.
Answer:
y = 5x - 800
Step-by-step explanation:
If x represents the number of pages typed, 5x will represent how much money he earns from typing them, since he gets $5 per page.
Then, 800 needs to be subtracted from this because he spent $800 on the computer.
So, the equation will be y = 5x - 800 to represent his profit.
Represent the following sentence as an algebraic expression, where "a number" is the letter x. 8 is decreased by a number.
Answer:
Given, a number is x.
The question says 8 is decreased by a number. So which is x.
Decreased by here means subtracting "a number" from the "other number".
According to the question, the algebraic expression will be given by-
8-x
Regards!
Round this whole number Round 5,165 to the nearest ten.
Answer:
5,170
Step-by-step explanation:use rounding number calculater for extra help
PLZ ANSWER ASAP!!!!!!!
Answer:
u=(9-6w)÷-2
Step-by-step explanation:
Answer:
u = 3w - 4.5
Step-by-step explanation:
Step 1: -2u + 6w = 9 - Solve for u by isolating the variable u.
Step 2: Subtract 6w both sides
-2u = 9 - 6w
Step 3: Divide by -2 both sides
u = ( 9 - 6w ) / ( -2 )
u = 3w - 4.5
Have a good day!! :)
find x (you must show work)
Answer:
x = 30 degrees
Step-by-step explanation:
The sum of the interior angles of a triangle is 180 degrees.
This means that 2x + 2 + 3x + x - 2 = 180.
We can then combine like terms, getting 6x = 180.
We can then divide both sides by 6, getting x = 30 degrees.
Answer:
x = 30
Step-by-step explanation:
Every triangle equals 180. So make an equation first:
2x + 2 + 3x + x - 2 = 180
Next Combine Like Terms:
6x = 180
Then Divide by 6 On Both Sides:
x = 30
PLZ HELP ME PLEASEEEEE ASAP THIS IS SIGN LANGUAGE HELP I GIVE HECKA POINTS 1: Signs made too close to another person's face can be offensive. True False 2: When a joke is interpreted, it is acceptable for the interpreter to smile. True False 3: Total Communication can include elements of ASL and SEE. True False
Answer:
#1 true
#2 false
false
Step-by-step explanation:
This oblique triangular prism has a volume of 63 cm.
What is the area of the base of the prism?
Answer:
its 10.5 cm
Step-by-step explanation:
its what I got off of khan
The base area of the oblique triangular prism is 10.5 square cm
How to determine the base area?The volume is given as:
Volume = 63 cubic cm
The height of the prism is:
Height = 6 cm
The base area of the prism is then calculated using:
Area = Volume/Height
So, we have:
Area = 63/6
Evaluate
Area = 10.5
Hence, the base area of the triangular prism is 10.5 square cm
Read more about volume at:
https://brainly.com/question/1972490
#SPJ2
Acquarium workers are making a mixture of salt water. The desired ratio is 90 grams of salt per liter of water. What is the ratio in ounces per gallon?
Answer: 12.07 ounce/gallon.
Step-by-step explanation:
given data:
desired ratio = 90grams / liter of water.
ratio In ounce/ gallon
first we convert our grams to ounce
= 98grams / 28.35
= 3.175 ounce.
converting liter to gallons
= 1/3.8
=0.263 gallons
therefore;
= 3.175 ounce / 0.263 gallons
= 12.07 ounce/gallon.
Suppose x = 7 is a solution to the equation 4x − 2(x + a) = 8. Find the value of a that makes the equation true. A: 2 B: 3 C: -25 D: 6
if x =7 then plug in 7 for x
4(7) - 2((7)+a) = 8
28 - 14 -2a = 8
14 - 2a = 8
-2a = -6
a = 3
Answer:
Step-by-step explanation:
Can someone please help me with this question? I REALLY need help.
What is the value of [tex]$ \sum_{n=1}^\infty (\tan^{-1}\sqrt{n}-\tan^{-1}\sqrt{n+1})$[/tex]? The answer should be in radians.
Answer:
-45
Step-by-step explanation:
The question is asking for the sum of the sequence. Therefore, there is no such thing as a "radians" answer.
When you evaluate the sum, you should get -45 as your answer. To find so, you simply plug in 1 as n and other numbers then add the result.
The sum telescopes. Consider the N-th partial sum of the series,
[tex]S_N=\displaystyle\sum_{n=1}^N\bigg(\tan^{-1}\sqrt n-\tan^{-1}\sqrt{n+1}\bigg)[/tex]
[tex]S_N=\bigg(\tan^{-1}\sqrt1-\tan^{-1}\sqrt2\bigg)+\bigg(\tan^{-1}\sqrt2-\tan^{-1}\sqrt3\bigg)+\bigg(\tan^{-1}\sqrt3-\tan^{-1}\sqrt4\bigg)+\cdots+\bigg(\tan^{-1}\sqrt N-\tan^{-1}\sqrt{N+1}\bigg)[/tex]
Notice how [tex]\tan^{-1}\sqrt2[/tex] is added, then immediately subtracted. The same goes for [tex]\tan^{-1}\sqrt3[/tex], then [tex]\tan^{-1}\sqrt4[/tex], and so on, up to [tex]\tan^{-1}\sqrt N[/tex]. This leaves us with
[tex]S_N=\tan^{-1}\sqrt1-\tan^{-1}\sqrt{N+1}[/tex]
The value of the given sum is obtained as [tex]N\to\infty[/tex]. We get
[tex]\displaystyle\sum_{n=1}^\infty\bigg(\tan^{-1}\sqrt n-\tan^{-1}\sqrt{n+1}\bigg)=\lim_{N\to\infty}S_N=\tan^{-1}1-\lim_{N\to\infty}\tan^{-1}\sqrt{N+1}[/tex]
To compute the limit, recall that [tex]\tan^{-1}x[/tex] has a range of [tex]\left(-\frac\pi2,\frac\pi2\right)[/tex]; in particular, [tex]\tan^{-1}x\to\frac\pi2[/tex] as [tex]x\to\infty[/tex]. So we have
[tex]\displaystyle\sum_{n=1}^\infty\bigg(\tan^{-1}\sqrt n-\tan^{-1}\sqrt{n+1}\bigg)=\frac\pi4-\frac\pi2=\boxed{-\frac\pi4}[/tex]
What is the distance between the points (5, 1) and (-3, -5)?
2
2
10
4
Step-by-step explanation:
Hey, there!!
The given points are A(5,1) and B(-3,-5)
We have, distance formulae for AB is,
[tex]ab = \sqrt{ {(x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]
[tex]ab = \sqrt{( { - 3 - 5)}^{2} + ( { - 5 - 1)}^{2} } [/tex]
[tex]ab = \sqrt{( { - 8)}^{2} + ( { - 6)}^{2} } [/tex]
[tex]ab = \sqrt{64 + 36} [/tex]
[tex]ab = \sqrt{100} [/tex]
Therefore, the distance between AB points is 10 units.
Hope it helps...
the banana is 8 inches long how many 0.4 inch slices can be cut from the banana
Answer:20
Step-by-step explanation:
Please help I will give out brainliest
Answer:
a. L.B. = 20.5
b. U.B. = 21.5
Step-by-step explanation:
Length is measured 21 cm correct to 2 significant figures
a. Lower bound of 21
= 20.5 < 21
= 20.5
b. Upper bound of 21
= 21 < 21.5
= 21.5
Answer:
a. L.B. = 20.5
b. U.B. = 21.5
Step-by-step explanation:
Which of the following expressions has a value of 26.48?
26,480 ÷ 104
2,648 ÷ 102
264.8 ÷ 103
2.648 ÷ 101
Answer:
none of them are right
Step-by-step explanation:
a is 254.6153846153846.
b is 25.96078431372549
c is 2.570873786407767
d is 0.0262178217821782
if b would to be 2,648 divided by 100* it would correct but sadly none of them are correct.
Answer:
The only option that comes close is option 2.
Explanation:
Put everything into your calculator as you see it:
26,480 / 104 = 254.61
2,648 / 102 = 25.96
264.8 / 103 = 2.57
2.648 / 101 = 0.02
in smithville. there were 230 teachers in 1990 and 324 teachers in 2000. find the percent of increase in the number of teachers in the smithville during this time period. Round to the nearest tenth of a percent.
Answer:
40.8696% increase (40.9%)
plz, help ASAP!!! WILL MARK YOU BRAINLIEST IF UR ANSWER IS CORRECT QUESTION #5
Answer:
D.
Step-by-step explanation:
The domain remains the same [a, b) and the range is [mc + n,md + n).
What would be the constant in this problem? 20c+5w+95.50
Answer:
95.50
Step-by-step explanation:
a constant is a number not attached to a variable
in this case the variables are c and w
95.50 is the only one without a variable
20 POINT AND WILL MARK BRAINY Which properties can be used to solve 7y − 15 = −29? Select all that apply.
Answer:
addition property of equality
inverse property of multiplication
Step-by-step explanation:
7y − 15 = −29
Add 15 to each side using the addition property of equality
7y -15+15 = -29+15
7y = -14
Divide each side by 7 using the inverse property of multiplication
7y/7 = -14/7
y =2
Answer:
[tex]\Large \boxed{\mathrm{Addition \ Property \ of \ Equality}} \\\\\\ \Large \boxed{\mathrm{Inverse \ Property \ of \ Multiplication}}[/tex]
Step-by-step explanation:
[tex]\sf 7y-15=-29[/tex]
Using the additive property of equality, we add 15 to both sides of the equation.
[tex]\sf 7y-15+15=-29+15[/tex]
[tex]\sf 7y=-14[/tex]
Using the inverse property of multiplication, we divide both sides of the equation by 7.
[tex]\displaystyle \sf \frac{7y}{7} =\frac{-14}{7}[/tex]
[tex]\sf y = -2[/tex]
how do i write numbers in standard form?
Answer:
For Example say a number is in scientific form, 4.10x10^5, to write this in standard form you can either do 10^5=100,000x4.10=410,000, or you could simply take 4.10 and move the decimal place 5 places to the right, and you would get the same answer, 410,000.
Step-by-step explanation:
is it possible to have a regular polygon whose each exterior angle measure 57 degree justify your answer
Answer:
NoStep-by-step explanation:
The sum of all exterior angles of any regular polygon is 360°.
= [tex]\frac{360}{57} \\\\= 120/19\\or\:6.315[/tex]
The number of sides should be a natural number not in fraction or decimal
What is the common ratio of the geometric sequence below?
18, -6, 2. - ...
Answer:
C
Step-by-step explanation:
The solution is Option C
The common ratio of the geometric sequence is -1/3
What is Geometric Progression?
A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the geometric sequence be represented by A
Now , the value of A is
A = 18 , -6 , 2 , -2/3
Let the first term of the geometric sequence be = a₁
The value of a₁ = 18
Let the second term of the geometric sequence be = a₂
The value of a₂ = -6
And , the common ratio r is given by the formula
Common ratio r = second term / first term
Substituting the values in the equation , we get
Common ratio r = -6/18
On simplifying the equation , we get
Common ratio r = -1/3
Therefore , the ratio is -1/3
Hence , The common ratio of the geometric sequence is -1/3
To learn more about geometric progression click :
https://brainly.com/question/1522572
#SPJ2
Please help!!!
A pairs of fair die is tossed. What is the probability of not setting a sum 13?
A. 0
B. 1
C. 2
D. 0.5
Answer:
Answer is A the highest number we can get is 12 so its potion A
The both highest numbers are 6 and, 6 6 +6 is 12 so its 0
Find the sum : 1/2( x+7) = 32
Answer:
x=52
I think it is the answer
Hey everyone please I really need your help that idk what to answer this I’m so confused and but please don’t ignore this question
Step-by-step explanation:
The domain of a graph is all of the possible x values, and the range is all possible y values.
7. The graph goes on for both the x and y values, so the domain is (-inf, inf) and the range is (-inf, inf).
8. In this case, the domain is also (-inf, inf), but the range is [-2, inf) as there are no y values less than -2.
9. The domain is [-2, 2], as the x values only range from -2 to 2. The range is [-3, 3] as the y values range from -3 to 3.
10. The domain is (-inf, inf) because all x values are possible. The range is [-1, 1], as there are no y values greater than 1 or less than -1.
-4c^2+7, c=7a^2 solve for c
The answer is explained in the photo I have linked.
Exponential functions help please
Answer:
8400/2 then simplify
Step-by-step explanation:
.
Given g(x)=-x-4, find g(5)
The required g(5) is -9.
Function g(x) = -x-4. g(5) to determine.
The function is a type of mathematical sting that contains an algebraic link.
Here. g(x) = -x-4
Put 5 in place of x.
g(5) = -5-4
g(5) = -9
Thus, g(5) is -9
Learn more about functions here:
https://brainly.com/question/12431044
#SPJ2
Mr. Molesky observes a group of monkeys for 24 hours to learn about their behavior. He records how long they slept (in hours), how many bananas they ate, key
Answer:
Explained below.
Step-by-step explanation:
The complete question is:
Mr. Molesky observes a group of monkeys for 24 hours to learn about their behavior. He records how long they slept (in hours), how many bananas they ate, gender, age (in years), and the specific breed of monkey.
(a) What are the individuals in this data set?
(b) Identify the variables that were recorded, and indicate whether each one is categorical or quantitative?
Solution:
(a)
The term "individuals", in statistics, implies or denotes the objects or people included in a statistical study.
In this case it is provided that Mr. Molesky observes a group of monkeys for 24 hours to learn about their behavior.
So, the "individuals" in this data set are the monkeys.
(b)
Categorical variables belong to a certain category or label values. Such as gender of a person, state from which a person is from, color of the marble and so on.
Quantitative variables are those variables that assume numerical values and represent some sort of measurement. Such as height, weight, annual income of the people working at the same place and so on.
In this case the variables are:
Number of bananas the monkeys ate - Quantitative variable
Gender - Categorical variable
Age (in years) - Quantitative variable
Specific breed of monkey - Categorical variable
The individuals in the data set refers to each monkey used in the experiment.
The variables in the experiment include :
Number of bananas = QUANTITATIVE (DISCRETE) gender = QUALITATIVE (MALE OR FEMALE) Age (in years) = QUANTITATIVE (discrete) and the specific breed of monkey = QUALITATIVE.Individuals used in a research refers to each species or subject used in the research finding.
QUALITATIVE or categorical variables are used as labels rather than numerical values. They include gender, colors , and so on. QUANTITATIVE variables involves numerical variables upon which basic mathematical operations may be performed.DISCRETE variables involves variables whose values or numbers can be obtained by counting.while
CONTINUOUS variables include variable measure are obtained by measurement such as height and weight.
Learn more https://brainly.com/question/10697348
Complete question :
Mr. Molesky observes a group of monkeys for 24 hours to learn about
their behavior. He records how long they slept (in hours), how many bananas they ate, gender, age (in years), and the specific breed of monkey.
(a) What are the individuals in this data set?
(b) Identify the variables that were recorded, and indicate whether each one is categorical or quantitative(continuous), or quantitative(discrete), make sure tell me which one is continuous and which one is discrete
The points (-4,-3) and (2,4) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.
Answer: sqrt(85)/2
Step-by-step explanation:
Remember that the length of the diameter is twice that of the radius.
The first step would be finding the distance between the two points using the distance formula[tex]\sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}[/tex].
The distance of diameter = [tex]\sqrt{85}[/tex]
The distance of the radius would be half that, so [tex]\frac{\sqrt{85}}{2}[/tex]
1. A man is paid $ 600 per week after a pay rise of 20 %. What was he paid before?
Answer:
y. 100
------ = -------
600. 120
120y= 60000
y = 60000÷ 120
= $500