Answer:
ones
Step-by-step explanation:
The temperature of a cup of coffee varies according to Newton's Law of Cooling: -"dT/dt=k(T-A), where 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
Answer:
B) 67°C.
Step-by-step explanation:
Newton's Law of Cooling is given by:
[tex]\displaystyle \frac{dT}{dt}=k(T-A)[/tex]
Where T is the temperature of the coffee, A is the room temperature, and k is a positive constant.
We are given that the coffee cools from 100°C to 90°C in one minute at a room temperature A of 25°C.
And we want to find the temperature of the coffee after four minutes.
First, solve the differential equation. Multiply both sides by dt and divide both sides by (T - A). Hence:
[tex]\displaystyle \frac{dT}{T-A}=k\, dt[/tex]
Take the integral of both sides:
[tex]\displaystyle \int \frac{dT}{T-A}=\int k\, dt[/tex]
Integrate:
[tex]\displaystyle \ln\left|T-A\right| = kt+C[/tex]
Raise both sides to e:
[tex]|T-A|=e^{kt+C}=Ce^{kt}[/tex]
The temperature of the coffee T will always be greater than or equal to the room temperature A. Thus, we can remove the absolute value:
[tex]\displaystyle T=Ce^{kt}+A[/tex]
We are given that A = 25. Hence:
[tex]\displaystyle T=Ce^{kt}+25[/tex]
Since the coffee cools from 100°C to 90°C, the initial temperature of the coffee was 100°C. Thus, when t = 0,T = 100:
[tex]100=Ce^{k(0)}+25\Rightarrow C=75[/tex]
Hence:
[tex]T=75e^{kt}+25[/tex]
We are given that the coffee cools from 100°C to 90°C after one minute at a room temperature of 25°C.
So, T = 90 given that t = 1. Substitute:
[tex]90=75e^{k(1)}+25[/tex]
Solve for k:
[tex]\displaystyle e^k=\frac{13}{15}\Rightarrow k=\ln\left(\frac{13}{15}\right)[/tex]
Therefore:
[tex]\displaystyle T=75e^{\ln({}^{13}\! /\!{}_{15})t}+25[/tex]
Then after four minutes, the temperature of the coffee will be:
[tex]\displaystyle \begin{aligned} \displaystyle T&=75e^{\ln({}^{13}\! /\!{}_{15})(4)}+25\\\\&\approx 67^\circ\text{C}\end{aligned}[/tex]
Hence, our answer is B.
What is the least possible value of (x +1)(x+2)(x+3)(x +4)+2019 where x is a real
number?
MANY POINTS
Answer:
f(x)=(x+1)(x+2)(x+3)(x+4)+2019
f(x)=(x2+5x+4)(x2+5x+6)+2019
Suppose that y=x2+5x
Hence we have f(y)f(y)=(y+4)(y+6)+2019=y2+10y+24+2019=y2+10y+25+2018=(y+5)2+2018≥2018[∵(y+5)2≥0,∀y∈R]
and therefore…. min (f(x))=2018
ANSWER = 2018
Step-by-step explanation:
hope that helps >3
Answer:
2018
Step-by-step explanation:
By grouping the first, last and two middle terms, we get ([tex]x^{2}[/tex]+5x+4)([tex]x^{2}[/tex]+5x+6) + 2019. This can then be simplified to ([tex]x^{2}[/tex]+5x+2)^2 - 1 + 2019 Noting that squares are nonnegative, and verifying that [tex]x^{2}[/tex] + 5x + 5 = 0 for some real x, the answer is 2018.
consider the two triangles shown below are the two triangles congruent
Answer: Yes
Step-by-step explanation: Let's first find the missing angle in the second triangle and to find this angle, remember that the sum of the measures of a triangle is 180 degrees so you should find that our missing angle is 67°.
Now, notice that we have two angles and the included side of one triangle
congruent to two angles and the included side of a second triangle.
Therefore, we can say the triangles are congruent by ASA.
Carmen likes to ski. The ski resort where she goes to ski got 3.2 feet of snow during a 5 day period. The average daily snowfall for a given number of days is the quotient of the total amount of snow and the number of days. Estimate the average daily snowfall.
Answer:
0.64 feet or 7.68 inches of snow on average over the 5 days.
Step-by-step explanation:
3.2/5
0.64ft
7.68in.
Sam studied guinea pigs for his science fair project. He found that the amount of weight the guinea pigs gained varied directly with the number of calories they consumed.
The guinea pigs gained 1 ounce for every additional 218 calories in their diet. How many additional ounces would they gain if their diet was increased by 1,090 calories? Let W represent the weight in ounces, and let C represent the number of calories.
Answer: C= 1,090 and the W= 5.
Assistance pleaseeees?!!
Answer:
Step-by-step explanation:
What is the slope of the graph shown below
Answer:
B=-5
Step-by-step explanation:
Slope=rise/run
The line passes in
P1(-1,3)
and
P2(0,-2)
So slope=(3-(-2))/(-1-0)=5/-1=-5
FACTOR....
x^2 + 10× - 2400 = 0
Answer:
x= -5 + 5[tex]\sqrt{97}[/tex], x= -5 - 5[tex]\sqrt{97}[/tex]
Step-by-step explanation:
Since this quadratic is set to zero, we can use the quadratic formula to solve this.
x^2 + 10x - 2400 = 0
Quadractic formula = x= -b +- [tex]\sqrt{b^2 - 4ac}[/tex] /2a
For this equation:
a= 1, b=10, c=-2400
Plug these numbers into the equation and solve.
x= -10 +- [tex]\sqrt{10^2 - 4(1)(-2400}[/tex])/2(1)
x= -10 +- [tex]\sqrt{100 + 9,600}[/tex]/2
x= -10 +- [tex]\sqrt{9,700}[/tex]/2
x= -10 +- [tex]\sqrt{2^2 * 5^2 * 97}[/tex]/2
x= -10 +- 5 * 2[tex]\sqrt{97}[/tex]/2
x= -10 +- 10[tex]\sqrt{97}[/tex] / 2
Divide by 2.
x= -5 +- 5[tex]\sqrt{97}[/tex]
Answer:
x= -5 + 5[tex]\sqrt{97}[/tex] or x= -5 - 5[tex]\sqrt{97}[/tex]
Write L if it is Likely to happen and Write U if it is unlikely to happen. Topic is probability
1. 2:3
2. 4:15
3. 3/10
4. 13/21
5. 6/16
6. 8:11
7. 9:20
8. 11:25
9. 5/16
10. 7/12
11. 6:13
12. 4:9
13. 2:5
14. 19/45
15. 12/25
Please make it quick
Answer
15. 12/25
Step-by-step explanation:
Because the surface value of this question
Can someone help me with this math homework please!
Solve the equation and enter the value of x below. -4(x - 5) = 60
Answer:
The value of x is 10.
Step-by-step explanation:
By question,
-4(x - 5) = 60
or,-4x + 20 = 60
or,-4x = 60 -20
or, -4x = 40
or, x =40/-4
Hence,x=10
Answer:
x = 10
Step-by-step explanation:
-4(x - 5 ) = 60
Solve for x.
-4(x - 5 ) = 60
Step 1 :- Distribute -4.
-4 × x - 4 × -5 = 60
-4x + 20 = 60
Step 2 :- Move constant to the right-hand side and change their sign.
-4x = 60 - 20
Step 3 :- Subtract 20 from 60.
-4x = 40
Step 4 :- Divide both side by -4.
[tex] \frac{ - 4x}{ - 4} = \frac{40}{ - 4} \\ [/tex]
Hence , x = 10
Log problem below in the picture
Your answer is 2.98004491789381.
Anna, Bob and Chris are altogether 31 years old. How old will all three be altogether in three years time? (A)32 (B)34 (C)35 (D)37 (E)40
Answer:
40
Step-by-step explanation:
A+B+C = 31
Add 3 years to each age
A+3 +B+3 + C+3 = 31 +3+3+3
They will be
A+3 +B+3 + C+3 = 40
Answer:
it will be 40
Step-by-step explanation:
If they are altogether 31 years old now in 3 years we just add 9 thus it is 40
Can someone explain how to do this please?
for the columns where is less than or equal zero, use the first line of the function to calculate the value of f(x)
[tex] { ( \frac{1}{3} ) }^{ - 2} - 1 = 9 - 1 = 8 \\ { ( \frac{1}{3} ) }^{ - 1} - 1 = 3 - 1 = 2 \\ { ( \frac{1}{3} ) }^{ 0} - 1 = 1 - 1 = 0[/tex]
for every x greater than zero, use the second line to determine the value
[tex] {3}^{1} - 2 = 3 - 2 = 1 \\ {3}^{2} - 2 = 9 - 2 = 7[/tex]
hope this helps and gives some insight what to do.
if there are open questions left, feel free to ask them in the comments
have a beautiful day
-Alex
Como Determinar a equação da reta que passa pelos pontos A(-1, -2) e B(5,2)
Answer:
A equação da reta é dada por: [tex]y = \frac{2}{3}x - \frac{4}{3}[/tex]
Step-by-step explanation:
Equação de uma reta:
A equação de uma reta tem o seguinte formato:
[tex]y = ax + b[/tex]
Em que a é o coeficiente angular e b é o coeficiente linear.
Coeficiente angular:
Com posse de dois pontos, o coeficiente angular é dado pela mudança em y dividida pela mudança em x.
A(-1, -2) e B(5,2)
Mudança em y: 2 - (-2) = 2 + 2 = 4
Mudança em x: 5 - (-1) = 5 + 1 = 6
Coeficiente angular: [tex]m = \frac{4}{6} = \frac{2}{3}[/tex]
Então:
[tex]y = \frac{2}{3}x + b[/tex]
Coeficiente linear:
Substituindo um ponto na equação, encontra-se o coeficiente linear.
B(5,2)
Quando [tex]x = 5, y = 2[/tex]. Então:
[tex]y = \frac{2}{3}x + b[/tex]
[tex]2 = \frac{2}{3}5 + b[/tex]
[tex]b = 2 - \frac{10}{3} = \frac{6}{3} - \frac{10}{3} = -\frac{4}{3}[/tex]
Então:
[tex]y = \frac{2}{3}x - \frac{4}{3}[/tex]
HELP TIMED QUESTION. Determine whether the equation is an identity or not an identity.
Answer:
It is not an identity.
Step-by-step explanation:
COS2A+ cos2 A cot2A =cot 2 A
Answer:
a= (π/4) + (kπ/2)
Step-by-step explanation:
I have attached the explanation above. hopefully this will help
9514 1404 393
Explanation:
This is an identity.
cos²(A) +cos²(A)cot²(A) = cot²(A)
Transforming the left side, we have ...
= cos²(A)(1 +cot²(A))
= cos²(A)csc²(A)
= (cos(A)/sin(A))²
= cot²(A)
Which graph represents the function of f(x) = 4x² - 4x -8/2x+2.
Answer:
I think that second option represents the function of f(x) = 4x² - 4x -8/2x+2.
At a local Brownsville play production, 420 tickets were sold. The ticket
prices varied on the seating arrangements and cost $8, $10, or $12. The
total income from ticket sales reached $3920. If the combined number
of $8 and $10 priced tickets sold was 5 times the number of $12 tickets
sold, how many tickets of each type were sold?
Answer:
jsdcjdvnjkdnjnjdanskcbanknqnjfkrbgiyrwhgondfkv
Step-by-step explanation:
The parallel chord lie on opposite sides of the center of a circle of radius 13cm. Their lengths are 10cm and 24cm respectively. What is the between the chords
We are required to find the distance between both chords.
Answer:
17 cm
Step-by-step explanation:
The two chords are parallel to each other.
This means that a perpendicular line drawn from the centre of the circle will divide both of them into 2 equal sides.
This is depicted in the image attached.
From the Image,the diagonal drawn from one end of either chord through the centre will form the hypotenuse side of either chords.
Thus, using pythagoras theorem, we have for the chord that has a length of 10 cm. Perpendicular distance from centre of chord to centre of circle is;
d = √(13² - 5²)
d = √144
d = 12
Similarly, for chord with length = 24 cm, we have;
d' = √(13² - 12²)
d' = √25
d' = 5
Therefore, distance between chords = d + d' = 12 + 5 = 17 cm
A corporate team-building event cost $4, plus an additional $3 per attendee. If there are 39 attendees, how much will the corporate team-building cost?
Answer:
$121
Step-by-step explanation:
Find how much additional money it will cost from the attendees:
39(3)
= 117
Add the other $4:
117 + 4
= 121
So, it will cost $121
The Marked price of an article was fixed to Rs 1380 by increasing 15% on its actual price. Find the actual price.
Answer:
The actual price of the article was Rs. 1200.
Step-by-step explanation:
mp (marked price)
ap (actual price)
[tex]mp = 1380[/tex]
[tex]mp = ap + 15\%(ap)[/tex]
[tex]1 380 = ap + \frac{15}{100} ap[/tex]
[tex]1380 = \frac{100}{100} ap + \frac{15}{100} ap[/tex]
[tex]1380 = \frac{115}{100} ap[/tex]
[tex]1380 \div \frac{115}{100} = ap[/tex]
[tex]1380 \times \frac{100}{115} = ap[/tex]
[tex] \frac{138000}{115} = ap[/tex]
[tex]1200 = ap[/tex]
The actual price of the article is given by the equation A = $ 1,200
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the actual price of the article be A
Now , the equation will be
The marked price of the article be = $ 1380
The percentage of increase from the actual price = 15 %
So , the equation is
The actual price + percentage of increase from the actual price = 1380
Substituting the values in the equation , we get
A + ( 15/100 )A = 1380 be equation (1)
( 115/100 ) A = 1380
Multiply by 100 on both sides of the equation , we get
115A = 138000
Divide by 115 on both sides of the equation , we get
A = $ 1200
Therefore , the value of A is $ 1200
Hence , the actual price of the article is $ 1200
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
Find X in this question
Answer:
Step-by-step explanation:
∠1 = 38 {Vertically opposite angles}
∠2 = 39 + 36 = 75
Exterior angle equals the sum of opposite interior angles.
x = ∠1 +∠2
= 38 + 75
x = 113
Solve for x. Round to the nearest tenth, if necessary.
7r-15/s when r= 3 and s = 5.
Answer:
21-3=18
Hope This Helps!!!
Answer:
18
Step-by-step explanation:
7(3)= 21
15/5=3
21-3=18
please help me solve this
6-4y=8
Step-by-step explanation:
6-4y=8-4y= 8-6y=2/-4y=1/-2hope it helps..stay safe healthy and happy....Answer:
{\color{#c92786}{6-4y}}=8
6−4y=8
−4+6=8
{\color{#c92786}{-4y+6}}=8
−4y+6=82
Subtract from both sides of the equation
=
−
1
2
Which statement about y= 7x2 + 23x + 6 is true?
Answer:
Please include the statements too
A sum of money earns the interest ar the rate of Rs. 5 per Rs.25 in a year. how many years would it trible itself?
a. 5
b. 10
c.15
d. 20
HELP CONGRUENCE BY SAS AND SSS WILL GIVE BRAINLIEST IF CORRECT
Answer:
1. Cong SSS 2.Cong SSS 3.Not Cong 4.Not Cong 5.Cong SAS 6.Cong SSS 7.Cong SAS 8.Cong SSS 9.Cong SSS 10.Cong SAS 11.d 12.a 13.a 14.b 15.a
Step-by-step explanation:
which of the following must be true to prove Δ ABC≅Δ DEF by the AAS theorem?
A. C∠≅∠F
B. ∠B≅∠E
C. ∠E≅∠F
D.∠B≅∠C
Answer:
b must be because the therom is aas so
Answer:
B is answer
Step-by-step explanation:
just did it
