Anne Kates house is 20c. She had just made a fresh cup of tea (100c). Five minutes after she made her mad scientist nephew came in,stuck a thermometer in the cup and announced that the tea was now only 70c Write the possible equation with asymptotes
Answer:
The possible equation is; T(t) = 20 + 80·[tex]e^{(-0.094 \cdot t)}[/tex]
The horizontal asymptotes is Lim(t → ∞), T → 20°C
The vertical asymptote is Lim(t → 0) T → 100°C
Step-by-step explanation:
The given parameters are;
The temperature of the house = 20°C
The initial temperature of the tea = 100°C
The temperature of the tea after 5 minutes = 70°C
From Newton's law of cooling, is given as follows;
[tex]T(t) = T_s + (T_0 - T_s) \cdot e^{k \cdot t}[/tex]
[tex]\dfrac{dT}{dt} = -k(T - T_a)[/tex]
Where;
T(t) = The temperature after time, t =
[tex]T_s[/tex] =The room temperature = 20°C
T₀ = The initial temperature of the tea = 100°C
k = Constant
T(5) = 70°C, therefore, we have;
[tex]70 = 20 + (100 - 20) \cdot e^{k \cdot 5}[/tex]
50/80 = [tex]e^{k \cdot 5}[/tex]
5·k = ㏑(5/8)
k = ㏑(5/8)/5 ≈ -0.094
Therefore, the possible equation is given as follows;
T(t) = 20 + 80·[tex]e^{(-0.094 \cdot t)}[/tex]
The asymptotes are Lim(t → ∞), T → 20°C and Lim(t → 0) T → 100°C
What is the vertex of the function (X) = -x + 71 - 4?
O A. (-7,-4)
B.
(7,4)
O C. (-7,4)
OD. (7,-4)
Answer:
C
Step-by-step explanation:
Hope this Helps.
The coordinate of the vertex is ( 7 ,4), the correct option is B.
What is an Absolute value function?An absolute value function is a function that gives positive value for a number or variable. It has a V shaped graph, it is also called as a modulus function.
The absolute function is y = | -x +7| +-4
The v shaped curve has a vertex and it can be determined by following method.
The value of the x coordinate is determined by equating the modulus to 0, the point at which the modulus is zero.
-x +7 = 0
Adding -7 to both sides.
-x = -7
x = 7
The value of y at this point is the y coordinate of the vertex.
y = 0 +4
y = 4
(x,y) = ( 7,4)
To know more about Absolute value function
https://brainly.com/question/10664936
#SPJ5
A company charges a flat fee of 1500 dollars to rent a yacht in addition renters must pay 100 dollars per hour
Answer:
[tex]y= 1500+100x[/tex]
Step-by-step explanation:
Given data
Flat fee= $1500
additional fee= $100 per hour
let the number of hours be x
Hence the total charges for x hours y is given as
[tex]y= 1500+100x[/tex]
(3/4)^-1 (4/3)^-2 exponent solving
Answer:
7/12
Step-by-step explanation:
3/4 - 4/3 = 7/12 or 0.583
HELP WILL MARK BRAINLIEST IF GOTTEN RIGHT!!! GET IT WRIBNG ON PURPOSE I REPORT YOU!
Answer:
A
Step-by-step explanation:
Can anyone help my little sister with her math I tried helping her but I couldn’t figure out how to do the math!!
Answer:
1: the wooden part is 3.725 kilograms.
2: 10 Children
Answer:
1 3.725 kg of wood
2 10
Step-by-step explanation:
For question 1 you multiply the total weight by 3/4 to find the weight of the metal, you then subtract this from the total to find the weight of the wood
For question 2 you look at it as a fraction 1/3 kids + 2/3 adults equal 30, since there are twice as many adults. Then you multiply 30 by 1/3 and get 10
Which value of x from the set { 8 , 11 , 61 , 67 } makes the equation ( x − 3 )² = 64 true?
8
11
61
or 67
Answer:
I
Step-by-step explanation:
this its 61 ok thanks you
Estimate the sum of 872 and 121 by rounding both values to the nearest hundred. What is the best estimate of the sum?
Answer:
872
Step-by-step explanation:
Joe made a frozen yogurt shake with 10 ounces of milk and some strawberry frozen yogurt. He used the mixture to fill three 5-ounce glasses and had 2 ounces left over. How much-frozen yogurt did he use?
Answer:
2x - 9y = 23
5x - 3y = -1
Step-by-step explanation:
Alyssa had 191 dollars to spend on 6 books. after buying them she had 17 dollars. how much did each book cost?
Calculate the sum of the first n terms of the arithmetic progression (an)
a) a, = -4; d = 2; n = 16
please help me
Answer:
n²-5n
Step-by-step explanation:
The sum of the nth term is expressed as;
Sn =n/2[2a+(n-1)d]
Given
a, = -4; d = 2; n = 16
Sn = n/2[2(-4)+(n-1)2]
Sn =n/2[-8+2n-2]
Sn = n/2[2n-10]
Hence the sum of the nth term is 2n²-10n/2
2n(n-5)/2
= n(n-5)
= n²-5n
The sum of the nth term is n²-5n
What is
h(x) = 1/(x-5)3
Answer:
lim_( 3\/(-5 + x) = 0
Step-by-step explanation:
h(x) = 1\/(x - 5)×3
{x element R : x!=5}
{h element R : h!=0}
d\/dx(3\/(x - 5)) = -3\/(x - 5)^2
integral 3\/(x - 5) dx = 3 log(x - 5) +
Lauren got 321$ for her birthday. She wants to put 20% in her savings account. How much will she have left over to buy new clothes?
Answer:
$256.80
Step-by-step explanation
Change the 20% to a decimal, .20, the multiply it by the total amount of $$$, 321, and you get $64.20. Subtract that by the total amount to get the amount left over for her to get new clothes.
Hope it helps!! :))))
find the slope given the following points (8,-6) (-9,-12)
Please Hurry!!
simplify the expressions
1. 2x + 1 + 3x + 7
2. 5x + 2(3x + 5)
(two different questions)
Answer:
1. 5x + 8
2. 11x + 10
Step-by-step explanation:
1. 2x + 1 + 3x + 7
Combine like terms:
2x + 3x + 1 + 7
Add coefficients
5x + 8
2. 5x + 2(3x + 5)
Distribute the 2 by multiplying by each term inside the parentheses:
5x + 6x + 10
Combine like terms by adding coefficients
11x + 10
The area of a square floor on a scale drawing is 81 square centimeters, and the scale drawing is 1 centimeter:2 ft. What is the area of the actual floor? What is the ratio of the area in the drawing to the actual area?
Answer:
4 sq ft is the answer to your question
I’m trying to figure out #’s 31 and 32. I don’t need the answers I just need guidance on how to figure them out.
Answer:
open circle means less than OR greater to
closed circle means less than or equal to OR greater than or equal to
what is the [?]
which one answers this equation. please help
24 [?] 3/4= -32
answer choices:
x (times)
+ (plus)
- (minus)
/ (divided by)
Answer the photo below thanks
what is the distance between points A(3,-5) and B(-8,2) on the coordinate plane?
Answer:
use distance formula
Step-by-step explanation:
Please help
I will give 40 points ☺️
Answer:
Its 62
Step-by-step explanation:
B Mrs. Sayers made a rectangular fence
around the school vegetable garden so it
would not get destroyed by students. She
constructed a fence that was 4 feet long, 2 feet
wide, and 3 feet high. How much material did
she use to build her fence?
Answer:
Mrs. Sayers utilized 24 sq. ft material to build her fence
Step-by-step explanation:
length x width x height = volume
4 x 2 x 3 = 8 x 3 = 24
If x(x + y) = 3 and y(x + y) = 10, which of the following is a possible value of x + y?
(A) radical 7
(B) radical 13
(C) 6.5
(D) 7
(E) 13
With steps and explanation please.
Answer:
I believe that the answer is D: 7
4(w + 1) = -6; w =
help asap
Answer:
w = -10/4 or -2.5
Step-by-step explanation:
4(w + 1) = -6
4w + 4 = -6
4w = -10
w = -10/4 or -2.5
Answer:
W = 1/2 or 0.5
Step-by-step explanation:
Distribute
4w + 4 = 6
-4. -4
4w/4 = 2/4
W = 1/2
please helpp!!
The exponential function f(x) has a horizontal asymptote at y = 3.
What is the end behavior of f(x)?
A.
As x decreases, f(x) approaches, but never reaches, 3. As x increases, f(x) increases.
B.
As x decreases, f(x) decreases. As x increases, f(x) approaches, but never reaches, 3.
C.
As x decreases, f(x) approaches, but never reaches, 3. As x increases, f(x) decreases.
D.
As x decreases, f(x) approaches, but never reaches, 0. As x increases, f(x) increases.
Answer: A
Step-by-step explanation:
a
Step-by-step explanation:
Please help!! ill give 20pts
1) y=x2+24x+43
find the vertex form by completing the square SHOW ALL WORK!!!
2) Given the function f(x)=−x2+8x+9, state whether the vertex represents a minimum or maximum point for the function. Explain your answer.
Answer:
1. Vertex is (-12, -101)
2. Vertex is (4, 25)
Step-by-step explanation:
1)
[tex]y = x^{2} + 24x + 144 + 43 - 144\\ = (x + 12)^{2} - 101[/tex]
Vertex is (-12, -101)
2)
[tex]y = -x^{2} + 8x + 9\\ = -(x^{2} - 8x + 16) +9 + 16\\ = -(x - 4)^{2} + 25[/tex]
Vertex is (4, 25)
Which expression is equivalent to 8(2x + 4)?
A. 16x + 32
B. 2x + 32
C. 16x + 4
D. 10x + 12
Find another point in the pattern that passes through the points (0, 4) and (2, 12)
Answer:
3
Step-by-step explanation:
In which step did Carson make his first mistake?
1 - 4x = 2/3 (-2 + x)
Step 1: 1 - 4x = - 4/3 + x
Step 2: 1 = -4/3 + 5x
Step 3: 7/3 = 5x
Step 4: 7/15 = x
Answer: the first because he didn’t distribute the 2/3 with all the things in the parentheses
Step-by-step explanation: it’s supposed to be -4/3 + 2/3x the first step
need help from An Expert i really need your help help with the whole thing
Answer:
free points
Step-by-step explanation:
Answer:
etm
Step-by-step explanation:
yc