Answer:
18 ft
Step-by-step explanation
1. Put 8/16 like a fraction and since we do not know the height of the tree yet we put the height as 9/d.
2. We have to cross multiply so we multiply 8 by d and we get 8d. Then we multiply 9 by 16 and we get 144.
3. We divide both sides by 8 so we can get (d) by itself and we divide 144 by 8 also.
4. We get d = 18
The answer is correct but my explanation is a little hard to read so sorry about that :)
Suppose you have just poured a cup of freshly brewed coffee with temperature 90∘C in a room where the temperature is 20∘C.
Newton's Law of Cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. Therefore, the temperature of the coffee, T(t), satisfies the differential equation
dT/dt=k(T−Troom)
where Troom=20 is the room temperature, and k is some constant.
Suppose it is known that the coffee cools at a rate of 1∘C per minute when its temperature is 70∘C.
A. What is the limiting value of the temperature of the coffee?
limt→[infinity]T(t)= ________
B. What is the limiting value of the rate of cooling?
limt→[infinity]dT/dt= _________
C. Find the constant k in the differential equation.
k= _________
D. Use Euler's method with step size h=2 minutes to estimate the temperature of the coffee after 10 minutes.
T(10)= _________
Solution :
A). As the time passes the temperature of the coffee tends to acquire the temperature of the room, so the limiting value of the temperature of the coffee is 20°C. i.e.
[tex]$\lim_{t \to \infty} T(t)=20$[/tex]
B). And limiting value of rate of cooling is given by :
[tex]$\lim_{t \to \infty} \ \frac{dT}{dt} =\lim_{t \to \infty} \ [k(T-T_{room})] $[/tex]
[tex]$=k . \lim_{t \to \infty} (T-T_{room})$[/tex]
[tex]$=k .[ \lim_{t \to \infty} T-\lim_{t \to \infty} T_{room}]$[/tex]
[tex]$=k.[T_{room}-T_{room}]$[/tex]
= k. 0
= 0
C). Given, [tex]$\frac{dT}{dt} = -1, $[/tex] when T(t) = 70° using this in the given equation,
-1 = k.(70-20)
k = -0.02
D). By Euler method, we get
[tex]$T_{n+1}=T_n + h \ f(t_n, T_n)$[/tex]
[tex]$t_{n+1}=t_n +h$[/tex]
where, [tex]$f(t,T) =k(T-T_{room})$[/tex]
= -0.02(T - 20)
We have [tex]$T_0 = 90^\circ$[/tex] at t = 0 and h = 2.
So [tex]$t_1 = 0+2 = 2$[/tex]
∴ [tex]$T_1=T_0 + h \ f(t_0,T_0)$[/tex]
= 90+2[-0.02(90-20)]
= 87.2
At [tex]$t_2 = 2+2 = 4$[/tex]
[tex]$T_2=T_1 + h \ f(t_1,T_1)$[/tex]
= 87.2+2[-0.02(87.2-20)]
= 84.51
At [tex]$t_3 = t_2+2 = 4+2=6$[/tex]
[tex]$T_3=T_2 + h \ f(t_2,T_2)$[/tex]
= 84.51+2[-0.02(84.51-20)]
= 81.93
At [tex]$t_4 = t_3+4 = 6+2=8$[/tex]
[tex]$T_4=T_3 + h \ f(t_4,T_4)$[/tex]
= 81.93+2[-0.02(81.93-20)]
= 79.45
At [tex]$t_5 = t_4+2 = 8+2=10$[/tex]
[tex]$T_5=T_4 + h \ f(t_4,T_4)$[/tex]
= 79.45+2[-0.02(79.45-20)]
= 77.07
So after 10 minutes, the temperature of the coffee will be 77.07°C.
A contractor is required by a county planning department to submit one, two, three, four, five, six, or seven forms (depending on the nature of the project) in applying for a building permit. Let Y = the number of forms required of the next applicant. The probability that y forms are required is known to be proportional to y—that is, p(y) = ky for y = 1, , 7.
A) What is the value of c?
B) What is the probability that at most three forms are required?
C) What is the probability that between two and four forms (inclusive) are required?
D) Could pX(x) = x^2/50 for x = 1, . . . , 5 be a probability distribution of X? Explain.
Answer:
Step-by-step explanation:
Given that:
P(Y) = ky
where;
y =1,2,...7
To find the value of c or k (constant)
[tex]\sum P(Y) = 1[/tex]
[tex]\sum \limits_{y \to 1}^7 k*y = 1[/tex]
= k(1+2+3+4+5+6+7) = 1
28k = 1
[tex]k = \dfrac{1}{28}[/tex]
b) The required probability is P ( X ≤ 3)
[tex]P(X \le 3) = \sum \limits^3_{y=1 } P(y)[/tex]
[tex]P(X \le 3) = \sum \limits^3_{y=1 } \dfrac{1}{28}(y)[/tex]
[tex]P(X \le 3) = \dfrac{1}{28} (1 +2+3)[/tex]
[tex]P(X \le 3) = \dfrac{6}{28}[/tex]
P ( X ≤ 3) = 0.2143
c) The required probability P(2 ≤ Y ≤ 4)
[tex]P(2 \le Y \le 4) = \sum \limits ^4_{y=2} P(Y)[/tex]
[tex]P(2 \le Y \le 4) = \sum \limits ^4_{y=2} \dfrac{1}{28}(Y)[/tex]
[tex]P(2 \le Y \le 4) = \dfrac{1}{28}(2+3+4)[/tex]
[tex]P(2 \le Y \le 4) = 0.3214[/tex]
d) The required probability:
[tex]P(X) = \dfrac{x^2}{50} ; \ \ \ \ where; \ x= 1,2,...5[/tex]
[tex]\sum \limits ^5_{y =1} P(Y)= \sum \limits ^5_{y =1} \dfrac{1}{50}(x)^2[/tex]
[tex]\sum \limits ^5_{y =1} P(Y)= \sum \limits ^5_{y =1} \dfrac{1}{50}(1+4+9+16+25)[/tex]
[tex]\sum \limits ^5_{y =1} P(Y)=1.1[/tex]
what is 3,000 + 200 + .4 + .06 in standard from
Answer:
3,200.406
I think
Step-by-step explanation:
Answer:
Hello! :) have a good day!
3000 + 200 + .4 + 0.6 in standard form is 3201
PLEASE HELP PLEASEEEE
PLEASE I WILL GIVE YOU COOKIES.
Find the range of the function f(g)=3g-5 for the domain {-2,0,2}
{-9, -4, 5}
{-2, 0, 2}
{ -13, -7, -3}
{-11, -5, 1}
Answer:
option 4 {-11, -5, 1}
Step-by-step explanation:
range: set of output
f(-2)=3(-2)-5=-11
f(0)=3(0)-5=-5
f(2)=3(2)-5=1
Can someone help me with this? #1 first please
Answer:
Ok so you did the first box of statements and reasons correct. Now let us look at the second box of statements and reasons. There is also one more given statements and reasons and it is RS is congruent to TS. That is going to be a given one. Now if you look at the prove sections, it says to prove angle RSV is congruent to angle TSV. In the comments section let us find the answer together. I know the answers, but you give it a try too. I will give you a hint that the triangle is a AAS postulate (Angle-Angle-Side).
The average temperature on the surface of the earth is 15 degrees. On the surface of Mars, the average temperature is -50 degrees. What is the difference in these two temperatures? degrees
Answer:
65
Step-by-step explanation:
the difference is 65 degrees fahrenheit
Find the perimeter and area of a rectangle of cardboard measuring 14.1 cm by 6.5 cm
Answer:
perimeters =41.2
area=91.65
Step-by-step explanation:
rectangle Perimeter(p) Area (A)
L=length 2 (L+W) L×W
W=width
Answer:
14.1*6.5= your area
6.5+6.5+14.1+14.1=perimeter
Step-by-step explanation:
hope this helps!
Question 5 (4 points)
(06.01)
Evaluate the expression 43 ÷ (7 − 3) × 2. (4 points)
Answer:
21.5
Step-by-step explanation:
(solve in parentheses first)
43/(7-3)x2
(43/4)x2
86/4
21.5
Answer:
[tex]21.5[/tex]
Step-by-step explanation:
First you have to simplify 7 - 4 to 3.
[tex]43 \div 4\times 2[/tex]
Then Simplify 43 ÷ 4 to 10.75.
[tex]10.75 \times 2[/tex]
And lastly, Simplify.
[tex]21.5[/tex]
Therefor, the answer is, 21.5.
1. Given A = {1,2,3,4}, B ={1,2,4,5), C={3,4,6}, D= {7,8}. U={1,2,3,4,5,6,7,8,9}
What is A UB? Bn C? CD? A'? (A U B)
Answer:
Step-by-step explanation:
A∪B = {1,2,3,4,5}
B∩C = {4}
I don't know what CD means.
A' = {5,6,7,8,9}
Instant brainliest please help.
Answer:the second one
Step-by-step explanation:
someone pls answer this-
Elizabeth invested $67,000 in an account paying an interest rate of 4 %
compdunded annually. Aiden invested $67,000 in an account paying an interest rate
of 4 % compounded daily. After 6 years, how much more money would Elizabeth
have in her account than Aiden, to the nearest dollar?
o
Answer: $2066
Step-by-step explanation:
4% of what number is 39
Answer:
975
Step-by-step explanation:
39 ÷ 4% = 975
Answer:
975Step-by-step explanation:
Formula = Number × 100 = 39 × 100
Percent 4
Following shows the steps on how to derive this formula
Step 1 : if 4% of a number is 39, then what is 100% of the number ? Setup the equation.
39 = Y
4% 100 %
Step 2 : Solve for Y
Using cross multiplication of two fractions , we get
4Y = 39 × 100
4Y = 3900 = 975
100
Choose the letter of the correct answer. Write your answer on the line before the number at the back
page write your solution.
1. Which of the following is NOT an algebraic expression?
A. 7x + y
B. 3(m-n)
C. 8+3=1
Da + b
2. Find the value of (1 - 5)2.
A. 36
B. 16
C. -16
D. -36
25
3. Evaluate:
22
A. 64
B. 32
C. 16
D. 8
4. In the expression, m2 - 3, if m= -2, then m-3 = ?
A.-7
B.-1
C. 1
D. 7
5. What is the value of 12 + 13?
A.1
B. 2
C. 3
D.5
6. If x = -2, what is the value of -5x2 ?
A. -20 B. -10 C. 10
D. 20
Answer:
1. C
2. -8 (there are no choices for this)
3. (no question here)
4. -5 (there are no choices for this)
5. 25 (there are no choices for this)
6. D
Step-by-step explanation:
Answer:
i dot know
Step-by-step explanation:
1000-(864%2+336%3+648%2)=
Answer:
959.72
Step-by-step explanation:
you have to simplify
Step-by-step explanation:
=1000-864%2-336%3-648%2
=1000-17.28-10.08-12.96
=-11123.36
please answer the above question
If gasoline costs $3.28 per gallon, how much would 15.5 gallons cost?
Answer:
$50.84
Step-by-step explanation:
By multiplying $3.28 × 15.5 = $50.84
Mother plans to buy 1/2 kilogram of chicken and 2/5 kilogram of beef How many kilograms of meat does she plan to buy?
Answer:
Step-by-step explanation:
aplicaciones de la geometría en la vida
Answer:
I don't understand I'm sorry.....
A 40-foot pipe is cut into three sections. The longest section is three times as long as the shortest, and the middle-sized section is 5 feet longer than the shortest. Complete the diagram
by giving a and b as expressions involving x. Do not solve the problem.
P = 40 ft
12
X
b
21
X
P
1
a
Length of
middle-sized
Length of
shortest
section
Length of
longest
section
section
Answer:
P=40
a + b + x = P
a = 3x
b = x + 5
substitute for b & y
3x + (x+5) + x = 40
Step-by-step explanation:
longest section 1 = a
mid length section 2 = b
shortest section 3 = x
P=40
a + b + x = P
a = 3x
b = x + 5
substitute for b & y
3x + (x+5) + x = 40
5x + 5 = 40
5x = 35
x = 7
b = 12
a = 21
What additional information would allow the triangles to be proven similar by AA?
Question options:
A)
≅
B)
≅
C)
∠M ≅ ∠P
D)
∠Q ≅ ∠P
The additional information would allow the triangles to be proven similar by AA is: C. ∠M ≅ ∠P.
What is the AA Similarity Theorem?The acronym, "AA" stands for "angle-angle". Thus, the AA similarity theorem is a triangle theorem that is used to prove that two triangles that have two pairs of corresponding congruent angles are similar to each other.
The figure given shows two triangles, triangle MNO and triangle PQR, which have a pair of corresponding congruent angles, angle MNO and angle PQR [both are congruent because they are right angles that are equal to angle 90 degrees.]
Thus, this is not enough to prove that both triangles are similar to each other by the AA similarity theorem.
In other to prove that both triangles are similar by AA, we need to be given or shown that both triangles also have another pair of corresponding congruent angles.
Thus, the additional information needed can be: C. ∠M ≅ ∠P.
Learn more about the AA similarity theorem on:
https://brainly.com/question/2166570
#SPJ1
In 2002, the population of a town was approximately 34,050. In 2012,
the population of the town had increased to approximately 56,800. Based
on a linear model, what will be the approximate population of the town
in 2020?
Answer choices
A. 52,250
B. 75,000
C. 79,550
D. 99,850
Hello - I'm trying to find the answer for $6,000 x 10% x (1/12) to find the monthly interest rate
Answer:600
Step-by-step explanation:
Make the number 6 x 1000
Take 10% of the 1000
Now put the 6 and the 100 together
HELP PLZ!!!! I will give brainlest
Mr. Olejnik's son is going for a bike ride on his new bike. The cold weather has the tires deflated. Normal pressure is between 35 psi and 60 psi. (50 is ideal). The back tire is currently at 18 psi. If Mr. Olejnik increase the tire pressure by 250%, will this be too much?
Help Please :)
Answer:
Step-by-step explanation:
2.5*18 = 45
So, the answer would be
Yes, this is in the range between 35 psi and 60 psi.
I'm a Clay student, are you too? :) Good luck!!
which is the product of 15 5\12 A. 5 5\12 B. 6 1\4 C. 7 1\12 D. 7 3\4
Answer:
6 1/4
HOPE THIS HELPS!!!!!
A group of 1,254 people are going on a boat tour. If each boat holds 8 people, how many boats will they need?
Answer:
Step-by-step explanation:
1254p(b/(8p))=156.75b
The number of boats must be an integer because you can’t have a fraction of a boat so
b=157
Please please give answer for this question
Can someone pls help lol I rlly do need help on this :)
Answer:
a+51=90
a+51+90=180
39
Step-by-step explanation:
hope this helped :)
solve
1. 1/3n=4
what is n?
If a restaurant purchases organic food there is a 66% chance it will go bankrupt. If a restaurant does not purchase organic food there is a 64% chance it will go bankrupt. Only 12% of businesses purchase organic food. When a restaurant goes bankrupt what is the probability it purchased organic food
Answer:
0.1233 = 12.33% probability it purchased organic food
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Goes bankrupt
Event B: Purchase organic food.
Probability it goes bankrupt:
66% of 12%(purchases organic food)
64% of 88%(dont purchase organic food).
So
[tex]P(A) = 0.66*0.12 + 0.64*0.88 = 0.6424[/tex]
Intersection of A and B:
Bankrupt when purchases organic food. So
66% of 12%
[tex]P(A \cap B) = 0.66*0.12 = 0.0792[/tex]
When a restaurant goes bankrupt what is the probability it purchased organic food
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0792}{0.6424} = 0.1233[/tex]
0.1233 = 12.33% probability it purchased organic food
