Answer:
[tex]M(7 ; 4)[/tex]
Step-by-step explanation:
midpoint -M
[tex]M(\frac{x_{1}+x_{2}}{2} ; \frac{y_{1}+y_{2}}{2} )[/tex]
[tex]M(\frac{9+5}{2} ; \frac{6+2}{2} )[/tex]
[tex]M(7 ; 4)[/tex]
Answer:
(7, 4 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
Here (x₁, y₁ ) = (9, 6) and (x₂, y₂ ) = (5, 2) , then
midpoint = ( [tex]\frac{9+5}{2}[/tex] , [tex]\frac{6+2}{2}[/tex] ) = ([tex]\frac{14}{2}[/tex] , [tex]\frac{8}{2}[/tex] ) = (7, 4 )
Find the Laplace transform of the following functions.(8 pts/each x 8 = 64 pts) a. a(t) = 28(t) + 3+ 4u(t) b. b(t) = 5 – 5e-2t(1 + 2t)
a. the Laplace transform of a(t) is (28/s^2) + (3/s) + (4/s). b. the Laplace transform of b(t) is 5/s - 10/(s + 2) - 10/(s^3 + 2s^2).
a. To find the Laplace transform of a(t) = 28t + 3 + 4u(t), where u(t) is the unit step function, we can apply the linearity property and the transform of elementary functions.
Applying the linearity property, we can split the transform into three parts:
L{28t} + L{3} + L{4u(t)}
Using the transform of t (L{t} = 1/s^2), we get:
28/s^2 + 3/s + 4/s
Simplifying, we can combine the terms:
(28/s^2) + (3/s) + (4/s)
Therefore, the Laplace transform of a(t) is:
(28/s^2) + (3/s) + (4/s).
b. To find the Laplace transform of b(t) = 5 - 5e^(-2t)(1 + 2t), we can again apply the linearity property and the transform of elementary functions.
Applying the linearity property, we can split the transform into two parts:
L{5} - L{5e^(-2t)(1 + 2t)}
The transform of 5 is simply 5/s.
For the second part, we need to use the transform of e^(-at) and t.
The transform of e^(-at) is 1/(s + a), and the transform of t is 1/s^2.
Using these formulas, we get:
-5/(s + 2)(1 + 2/s^2)
Simplifying and combining terms, we have:
5/s - 10/(s + 2) - 10/(s^3 + 2s^2)
Therefore, the Laplace transform of b(t) is:
5/s - 10/(s + 2) - 10/(s^3 + 2s^2).
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Expert Answer Please! If The Area Of A 60 Sector In A Circle Is 75.4,Find The Diameter Of The Circle.
Answer:
multiply 75.4 by 60 =4,524
How many permutations of S9, have cycle strucrure 3^3?
There is only 1 permutation in S9 with a cycle structure of [tex]3^3[/tex].
To find the number of permutations of S9 with a cycle structure of [tex]3^3[/tex], we can use the concept of cycle index.
In a permutation with a cycle structure of[tex]3^3[/tex], we have three cycles of length 3. The cycle index of S9 with respect to cycles of length 3 can be determined using the Polya enumeration theorem.
The cycle index of S9 with respect to cycles of length 3 is given by:
[tex]Z(S9, t1, t2, t3) = (t1^3 + t3^3)^3[/tex]
Expanding this expression, we get:
[tex]Z(S9, t1, t2, t3) = (t1^3 + t3^3)^3\\\= (t1^9 + 3t1^6t3^3 + 3t1^3t3^6 + t3^9)[/tex]
To count the number of permutations with the desired cycle structure, we need to find the coefficient of the term [tex]t1^9t3^9[/tex].
From the expanded form, we see that the coefficient [tex]t1^9t3^9[/tex] is 1.
Therefore, there is only one permutation in S9 with a cycle structure of [tex]3^3[/tex]
In summary, there is 1 permutation of S9 that has a cycle structure of [tex]3^3[/tex].
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Find the flux of the given vector field F across the upper hemisphere x^2 + y^2 + z^2 = a^2, z >= 0. Orient the hemisphere with an upward-pointing normal.
19. F= yj
20. F = yi - xj
21. F= -yi+xj-k
22. F = x^2i + xyj+xzk
6πa² is the flux of F across the upper hemisphere.
The problem requires us to compute the flux of the given vector field F across the upper hemisphere x² + y² + z² = a², z ≥ 0. We are to orient the hemisphere with an upward-pointing normal. The four vector fields are:
F = yj
F = yi - xj
F = -yi + xj - kz
F = x²i + xyj + xzk
To begin with, we'll make use of the Divergence Theorem, which states that the flux of a vector field F across a closed surface S is equivalent to the volume integral of the divergence of the vector field over the region enclosed by the surface, V, that is:
F · n dS = ∭V (div F) dV
where n is the outward pointing normal unit vector at each point of the surface S, and div F is the divergence of F.
We'll need to write the vector fields in terms of i, j, and k before we can compute their divergence. Let's start with the first vector field:
F = yj
We can rewrite this as:
F = 0i + yj + 0k
Then, we compute the divergence of F:
div F = d/dx (0) + d/dy (y) + d/dz (0)
= 0 + 0 + 0 = 0
So, the flux of F across the upper hemisphere is 0. Now, let's move onto the second vector field:
F = yi - xj
We can rewrite this as:
F = xi + (-xj) + 0k
Then, we compute the divergence of F:
div F = d/dx (x) + d/dy (-x) + d/dz (0)
= 1 - 1 + 0 = 0
So, the flux of F across the upper hemisphere is 0. Let's move onto the third vector field:
F = -yi + xj - kz
We can rewrite this as:
F = xi + y(-1j) + (-1)k
Then, we compute the divergence of F:
div F = d/dx (x) + d/dy (y(-1)) + d/dz (-1)
= 1 - 1 + 0 = 0
So, the flux of F across the upper hemisphere is 0. Lastly, let's consider the fourth vector field:
F = x²i + xyj + xzk
We can compute the divergence of F directly:
div F = d/dx (x²) + d/dy (xy) + d/dz (xz)
= 2x + x + 0 = 3x
Then, we express the surface as a function of spherical coordinates:
r = a, 0 ≤ θ ≤ 2π, 0 ≤ φ ≤ π/2
Note that the upper hemisphere corresponds to 0 ≤ φ ≤ π/2.
We can compute the flux of F over the hemisphere by computing the volume integral of the divergence of F over the region V that is enclosed by the surface:
r² sin φ dr dφ dθ
= ∫[0,2π] ∫[0,π/2] ∫[0,a] 3r cos φ dr dφ dθ
= ∫[0,2π] ∫[0,π/2] (3a²/2) sin φ dφ dθ
= (3a²/2) ∫[0,2π] ∫[0,π/2] sin φ dφ dθ
= (3a²/2) [2π] [2] = 6πa²
Therefore, the flux of F across the upper hemisphere is 6πa².
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IM GIVING BRAINLIEST!!PLEASE HELP!!
Answer: c
Step-by-step explanation:
This equation shows how the amount of time that a receptionist named Terrence spends on the phone is related to the number of phone calls he routes to employees.
t = p + 17
The variable p represents the number phone calls he routes, and the variable t represents the number of minutes he is on the phone. In all, how many phone calls does Terrence have to route to spend a total of 20 minutes on the phone?
phone calls
hmmm I dunno sorry ......
1. Identify the Parent function related to the given function. Choose the correct answer from the choices below:
f(x)=1/2x-9 4/5
Linear Function
Not a Function
Absolute Value Function
Quadratic Function
help with questions 10-13 plz!!
Answer:
._. ;
._. ;
._. ;
A Susan B. Anthony dollar coin has a diameter of 26.5 millimeters. Round your final answers to the nearest hundredth. Show your steps. 7. What is the radius? 8. What is the circumference? 9. What is the area?
Answer:
7. 13.25mm
8. 83.25 mm
9. 551.55 mm²
Step-by-step explanation:
The shape of a coin is circular.
A Susan B. Anthony dollar coin has a diameter of 26.5 millimeters. Round your final answers to the nearest hundredth. Show your steps.
7. What is the radius?
The formula for radius = Diameter/2
= 26.5 mm/2
= 13.25 mm
8. What is the circumference?
The formula for the circumference of a circle = 2πr
= 2× π × 13.25mm
= 83.25220532 mm
Approximately to the nearest hundredth = 83.25 mm
9. What is the area?
The formula for the area of a circle = πr²
= π × (13.25mm)²
= 551.54586025 mm²
Approximately to the nearest hundredth = 551.55 mm²
A triangle has three angles that measure 15 degrees, 85 degrees and (4x - 20). What is the value of x?
y=Ax^2 + Bx + C is the solution of the DEQ: y'=87x. Determine A,B. A 'C' is the constant of integration.
The exact value of A in the general solution is 87/2 and B is 0
How to determine the value of A and B in the general solutionFrom the question, we have the following parameters that can be used in our computation:
y = Ax² + Bx + C
The differential equation is given as
y' = 87x
When y = Ax² + Bx + C is differentiated, we have
y' = 2Ax + B
So, we have
87x = 2Ax + B
By comparing both sides of the equation, we have
2Ax = 87x
B = 0
So, we have
2A = 87
B = 0
Divide both sides of 2A = 87 by 2
A = 87/2
B = 0
Hence, the value of A in the general solution is 87/2 and B is 0
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What is the lyrics for its good to be alive by among us?
Answer:
HEHEHEHEHEH
I've been waiting for this moment
Feels good to be alive right about now
Good, good, good, good to be alive right about now
Good, good, good, good to be alive right about now
Hallelujah, let that bass line move ya, say hey
Step-by-step explanation:
Have fun
The price of fuel may increase due to demand and decrease due to overproduction. Marco is studying the change in the price of two types of fuel. A and B. over time.
The price in dollars of fuel A after x months is represented by the function below.
10 = 2.961.04)
Part A: is the price of the increasing or decreasing and by what percentage per month? Justify your answer. (5 points)
Part 8: The table below shows the price 9m) in dollars of fuels afer m months
64
m (number of months) 1
3
sim) (price in dollars) 3.04 3.22 3.41 3.61
Which ope of fuel recorded a greater percentage change in pace over the previous month? Justity your answer. (5 points)
Answer:
A. Increasing by 4%.
Step-by-step explanation:
Answer:
A) The price of product A is increasing by 3% per year.
(B) The product A recorded a greater percentage change in price over the previous year.
Step-by-step explanation:
(A)
The function representing the price, in dollars, of product A after x years is:
FA(x)=0.69*(1.03)x
The function FA(x)can be written as:
FA(x)=0.69*1+(0.03)x
The function FA(x) is similar to the exponential growth function, y=a(1+r)x .
Here r is the growth rate.
Thus, it can be said that the price of product A is increasing by 3% per year.
(B)
Consider the data of product B for the year 3 and 4.
The price of product B for year 3 and 4 are 10,303.01 and 10,406.04.
Compute the percent price change from year 3 to 4 as follows:
10406.04-10303.01/10303.01*100
which is 0.999%
~1%
The price of product B is increasing by 1% per year.
Thus, the product A recorded a greater percentage change in price over the previous year.
Select all the figures that are shaded to represent 60% of the whole. Whoever answers correctly and first will be marked as brainliest!!!!
Answer:
the first one
Step-by-step explanation:
PLEASE HELP ME!!!! I WILL MARK!!!
Answer:
6(x - 3 ) = 6x - 18
2(3x - 3) = 6x - 6
Step-by-step explanation:
I need help on the circled problem please
Answer:
There would be infinite solutions because the equations are exactly the same.
I hope this answered your question
Which of the following equations? (picture included)
Answer:
B
Step-by-step explanation:
A medical team randomly selects people in an area, until he finds a person who has a corona virus, Let p is the probability that he succeeds in finding such a person, is 0.2 and X denote the number of people asked until the first success. (i) What is the probability that the team must select 4 people until he finds one who has a corona virus? (ii) What is the probability that the team must select more than 6 people before finding one who who has a corona virus?
Answer : i) The probability of finding the first case in 4 trials is 0.1024 ii) The probability that the team must select more than 6 people before finding one who has a corona virus is 0.4095.
Explanation : Given information:Let p is the probability that he succeeds in finding such a person, is 0.2 and X denote the number of people asked until the first success.
(i) What is the probability that the team must select 4 people until he finds one who has a corona virus?
The number of trials required until the first success follows geometric distribution.
The probability of finding the first case in 4 trials is: P(X = 4) = q^3p, where q = 1 - p. We have p = 0.2 and q = 0.8. So, P(X = 4) = 0.8^3 × 0.2 = 0.1024
(ii) What is the probability that the team must select more than 6 people before finding one who who has a corona virus? P(X > 6) = 1 - P(X ≤ 6) The probability of finding the first case in the first 6 trials is:P(X ≤ 6) = 1 - q^6p= 1 - 0.8^6 × 0.2= 0.59049P(X > 6) = 1 - P(X ≤ 6)= 1 - 0.59049= 0.4095 Therefore, the probability that the team must select more than 6 people before finding one who has a corona virus is 0.4095.
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The volume of this cylinder is 4,939.22 cubic millimeters. What is the height? Use a 3.14 and round your answer to the nearest hundredth.
Answer:
13 mm
Step-by-step explanation:
V = πr²h
4,939.22 mm³ = 3.14 × (11 mm)²h
4,939.22 mm³ = 3.14 × (11 mm)²h
h = 13 mm
Answer: 13 mm
select the correct answer. which expression is equivalent to x 3x2−2x−3÷x2 2x−3x 1 if no denominator equals zero? a. 1x2−2x−3 b. 1x2−4x 3 c. 1x2 2x−3 d. x 3x 1
The correct answer is option c. 1/(x² + 2x - 3). To determine which expression is equivalent to the given expression, let's simplify it step by step:
The given expression is (x³ - 2x - 3) ÷ (x² + 2x - 3).
Option a. 1/(x² - 2x - 3):
This option is not equivalent to the given expression because it represents the reciprocal of the quadratic denominator, which is different from the given expression.
Option b. 1/(x² - 4x + 3):
This option is not equivalent to the given expression because the signs of the quadratic terms are different. The given expression has a positive quadratic term, while this option has a negative quadratic term.
Option c. 1/(x² + 2x - 3):
This option is equivalent to the given expression because it represents the reciprocal of the quadratic denominator with the same signs for the quadratic terms.
Option d. x/(3x - 1):
This option is not equivalent to the given expression because it lacks the term x³ in the numerator.
Therefore, the correct answer is option c. 1/(x² + 2x - 3).
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state four reasons why choice should be made in satisfaction human wants
A bakery produces five types of bagels, two of which are chocolate chip and cinnamon raisin.
(a) If there are at least 10 bagels of each type, how many different selections of 10 bagels are there?
(b) Suppose there are only 3 chocolate chip and 2 cinnamon raisin bagels, but at least 10 of the other three types. How many different selections of 10 bagels are there?
a) If there are at least 10 bagels of each type, we can calculate the number of different selections of 10 bagels by using the concept of combinations. Since there are 5 types of bagels and we need to select 10 bagels, the calculation can be done as follows:
[tex]\(\binom{10+5-1}{10} = \binom{14}{10}\)[/tex]
b) If there are 3 chocolate chip and 2 cinnamon raisin bagels, and at least 10 of the other three types, we can calculate the number of different selections of 10 bagels using the same concept of combinations. In this case, we have 3 types of bagels (excluding chocolate chip and cinnamon raisin) with at least 10 bagels each. So the calculation becomes:
[tex]\(\binom{10+3-1}{10} = \binom{12}{10}\)[/tex]
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Find the surface area of the prism.
7 cm
13 cm
5 cm
12 cm
The surface area is
Answer:
please give more information
Step-by-step explanation:
can i get an owa owa ?????
owa owa???
owa owa??
OWA OWA??
OWA OWA??
OWA OWA?ms.Rivera went to dinner for new year's eve the meal and sodas cost a total of $138 the sales tax in new york state is about 8% and ms Rivera wanted to leave a 20% tip because the service was good. What was the total cost of the meal
Answer:
138 + 27.6 = 165.6
Step-by-step explanation:
Please give brainliest
2. Find the area of a circle with a diameter of 10
feet.
Step-by-step explanation:
d=2r
πr^2
10/2=r
5=r
5^2π
25π=78.5398
Hope that helps :)
hi i need help again
(I need help on number 9) ty
Answer:
You did not take the picture correctly, try taking it again
Step-by-step explanation:
I can’t seeeee
Can someone help me find and answer an equation to the following math question : Natalie earns 5% commission on all electronics she sells.On Monday she sold a television for $1130 and a DR that cost $325. What was the total she earned in commission?
Answer:
She will make a total commission of $1130+$325=$1445
Then 5% of $1445= $1445×5%=$72,75
NOLINKS ..................
Answer:
The answer is in the link
Step-by-step explanation:
quntyfcjb/crown!.com :))))
The starting salary of a starting teacher is $40,000, which will increase by 2% each year.
Which of the following is the function that models the teacher salary scenario?
The answer choices are in the picture.
Answer:
The first choice is the correct one.
Step-by-step explanation:
The first choice is the correct one. It starts with the base salary and then is multiplied by (1 + 0.02)^t, which is the correct formula for compounding once per year.