Answer:
[tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]
Step-by-step explanation:
Explanation
Given function f(r) = r² log r ....(i)
Apply derivatives formula
[tex]\frac{d}{dx} UV = U^{l} V + V^{l} U[/tex]
[tex]\frac{d}{dx}x^{n} = nx^{n-1}[/tex]
[tex]\frac{d}{dx}log x = \frac{1}{x}[/tex]
Differentiating equation (i) with respective to 'r' , we get
[tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )\frac{d}{dr} (\frac{1}{r } )+ log(\frac{1}{r} ) 2 r[/tex]
[tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )(\frac{-1}{r^{2} } )+ log(\frac{1}{r} ) 2 r[/tex]
Final answer:-
[tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]
What is the area of the region bounded by the lines x= 1 and y= 0 and the curve y=xe^x^2?
Answer:
A = 0.859
Step-by-step explanation:
We want to find the area of the region bounded by the lines x = 1 and y = 0 and the curve y = xe^(x²).
At y = 0, let's find x;
0 = xe^(x²)
Solving this leads to no solution because x is infinity. Thus we can say lower bound is x = 0.
So our upper band is x = 1
Thus,lets find the area;
A = ∫xe(x²) dx between 1 and 0
A = (e^(x²))/2 between 1 and 0
A = ((e¹)/2) - (e^(0))/2)
A = 1.359 - 0.5
A = 0.859
The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 50.8 and 51 min.
Answer: the probability that the class length is between 50.8 and 51 min is 0.1 ≈ 10%
Step-by-step explanation:
Given data;
lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min
hence, height = 1 / ( 52.0 - 50.0) = 1 / 2
now the probability that the class length is between 50.8 and 51 min = ?
P( 50.8 < X < 51 ) = base × height
= ( 51 - 50.8) × 1/2
= 0.2 × 0.5
= 0.1 ≈ 10%
therefore the probability that the class length is between 50.8 and 51 min is 0.1 ≈ 10%
Please help ASAP!!!!!!!!!
______________________________
1.) Plug our numbers into the formula:[tex]B[/tex] × [tex]H[/tex][tex]6[/tex] × [tex]4=24[/tex]______________________________
HELP NOW PLSSSSS
(where the longer it takes to solve a problem and the fewer people who answer it correctly, the more difficult it is). On each subsection, question 1 will be "easy" and question 15 will be considered "difficult." However, the ascending difficulty resets from easy to hard on the grid-ins.
Hence, multiple choice questions are arranged in increasing difficulty (questions 1 and 2 will be the easiest, questions 14 and 15 will be the hardest), but the difficulty level resets for the grid-in section (meaning questions 16 and 17 will again be "easy" and questions 19 and 20 will be very difficult).
the answer is 4/.12
:)
Answer:
Hence, multiple choice questions are arranged in increasing difficulty (questions 1 and 2 will be the easiest, questions 14 and 15 will be the hardest), but the difficulty level resets for the grid-in section (meaning questions 16 and 17 will again be "easy" and questions 19 and 20 will be very difficult).
What is the question??
Jeffrey is 5 years older than his brother. If j represents Jeffrey’s age, the expression j−5 can be used to find his brother’s age. If Jeffrey is 23, how old is his brother?
If j=23 and j-5 is how old Jeffery's brother is then Jeffrey's brother is 17 years old.
So j=17
48 is 16 2/3% of what number?
Answer:
288
Step-by-step explanation:
I hope this helps <3
n − 32 5 = 10 help plz
Answer:
n=335
Step-by-step explanation:
Answer:
Step-by-step explanation:
Here you go mate
Step 1
n − 325 = 10 equation
Step 2
n − 325 = 10 simplify by adding 325 to both sides
Answer
n=335
Find the missing values of the variables. The diagram is not to scale. Show steps
Step-by-step explanation:
i assume this is the question you asked me to look at.
Well, angle 116° and y are supplementary angles
therefore,116°+y=180°
y=180°-116°=64°
Now to find x
x+y+125+72=360°
x+64+125+72=360
x+261=360
x=360-261=99°
The measure of x° is 99° and the measure of y° is 64°.
What is quadrilateral?
A quadrilateral is a polygon with four sides four angles and four vertices. Whenever we name a quadrilateral, we need to keep in mind the order of the vertices.
From the given figure,
116°+y°=180° (Sum of adjacent angles is 180°)
y°=180°-116°
y°=64°
Sum of interior angles of quadrilateral is 360°.
Here, x°+y°+72°+125°=360°
x°+64°+72°+125°=360°
x°+261°=360°
x°=99°
Therefore, the measure of x° is 99° and the measure of y° is 64°.
Learn more about the quadrilaterals here:
https://brainly.com/question/29934440.
#SPJ2
What equation is a proportion?
7/9 = 21=28
1/3 = 1/4
5/8 = 20/32
3/4 = 6/9
Answer:
5/8=20/32
Step-by-step explanation:
Which pair of expressions is equivalent? 2(x + 5) and 2x + 10 B. 3x – 6 + 4x + 9 and 7x + 15 0. C. 4y - 2) and 4y - 2 0 D. 5y + 12 - 3y and 2y – 12
Answer:
A
Step-by-step explanation:
the equivalent pair of expression are 2(x+5)and 2x+10
Part A : At Mountain Park Middle school, there are 250 seventh-grade students who are not in advanced math. Let a represent the number of seventh-grade students who are not in advanced math?
Part B: How many students are NOT in advanced math?
Answer:
hard to explain
Step-by-step explanation:
Answer:I think 80 at bottom like
Step-by-step explanation:
Is 9/16 a terminating or repeating decimal plz ASAP brainley
Answer:
terminating.
Step-by-step explanation:
9/16 converted to a decimal is .5625 which is terminating
three blocks are placed together as shown below. 3.8cm 8.7cm 9.4cm
5(-6 + 4)=..................
Answer:
-10
Step-by-step explanation:
5(-6 + 4)
=-30+20
=-10
Answer:
-10 or just 10 in general
Step-by-step explanation:
Solve the inequality.
X + 25 < 33
O A. x< 58
B. x < 8
C. X> 58
O
D. X > 8
Answer:
x < 8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
x + 25 < 33
Step 2: Solve for x
Subtract 25 on both sides: x < 8Here we see that any value x smaller than 8 would work as a solution to the inequality.
Find the value of x.
4x + 5
2x + 21, smby help me wit dis pls
Answer: x = 8
Step-by-step explanation:
4x + 5 = 2x + 21
4x + 5 - 2x = -2x + 2x +21 (Subtract 2x from both sides)
2x + 5 = 21
2x + 5 - 5 = 21 - 5 (Subtract 5 from both sides)
2x = 16
2x/2 = 16/2 (Divide both sides by 2)
x = 8
Let f(x) = 16 – x^2 , g(x) = 4 – x. Find (fg)(x) and its domain
Directions: Convert the following equations from standard form to slope-intercept form.
(10 points)
14. 4x + y = -1
15. 5x - 2y = 14
16. 10x - 2y = -6
17. 8x + y = 12
18. 6x - 10y = 20
FinWhat is the perimeter of the triangle in the graph? Round your answer to the nearest tenth if necessary. (1 point) 8.9 8.0 12.9 8.5d the missing y-coordinate that makes the two triangles congruent. Triangle ABC: A(8,4), B(2,6), C(5, 0) Triangle MNO: M(7,4), N(1,2), O(4, y)
Answer:
man did you ever find out the answer bc I'm dying I cannot fail this test-
Answer:
12.9
Step-by-step explanation:
it is common sense
also i just took test
Please I need help like now
Answer:
it's is d
Step-by-step explanation:
seening this info
for every 2/3 of cold water there is 1/2 of vegetable Oil
to make this answer complte if if we add a another cup of water the amount that is requared and since were adding 1/2 of oil which is 2/3 of water need adding 2/3+2/3=4/3
Hence 4/3 or D is right
Eidoskaijsizjzkxkxdkjajjsjeksjsii
Answer:
Yes, Yes, No, Yes
Step-by-step explanation:
whats the value of v 69 = 7v – 6
Answer:
75/7
Step-by-step explanation:
69=7v-6 rewrite as 69+6=7v
75 = 7v
75/7 = v
halp
A 43-foot ladder is leaning against a building and forms a 29.37° angle with the ground. How far away from the building is the base of the ladder? Round your answer to the nearest hundredth.
21.09 feet
24.20 feet
37.47 feet
49.34 feet
Answer:
37.46
Step-by-step explanation:
I think not sure tho
4) Which formulas can be used to find the area of a parallelogram and a
square? There are two possible answers. Check one.
10 pa
O A = b x h
A = 2L + 2W
A = L + L + W + W
A = bh
Answer:
O A = Bx H and A = L + L + W + W.
Step-by-step explanation:
Find the measure of angle b (15
Answer:
Angle b is 15 measure the scale
You are running a concession stand at a basketball game. You are selling hot dogs and
sodas.Each hot dog costs $1.50 and each soda costs $ 0.50. At the end of the night, you made a total of
$78.50. You sold a total of 87 hot dogs and sodas combined. You musſt report the number of hot dogs
sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?
Answer: 52
Step-by-step explanation: Friend me and yes that is right!
please help i m clusless
Answer:
-25+? = -5
cross -5 over and it the negative sign would turn to postive sign
-25+(5)=?
Therefore answer = 20
To confirm this answer
-25+20= -5
Factor the expression using the GCF. 44-11 I NEED HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
11(4-1)
Step-by-step explanation:
11 is the greatist common factor of 44 and 11 so you factor an 11 out of both terms
44/11=4
11/11=4
Therefore the answer is 11(4-1)
The population of a certain community is known to increase at a rate proportional to the number of people present at time t. If the population has doubled in 5 years, how long will it take to triple?
Answer:
[tex]t=7.85 years[/tex]
Step-by-step explanation:
We can write this rate as an ordinary differential equation.
[tex]\frac{dP}{dt}=aP[/tex]
Where a is proportional constant, P the population variable, and t the time.
[tex]\frac{dP}{P}=adt[/tex]
Integrating each side of the equation.
[tex]\int \frac{dP}{P}=\int adt[/tex]
[tex]ln(P)=at+c[/tex]
[tex]P=e^{at+c}[/tex]
[tex]P=e^{c}e^{at}=Ce^{at}[/tex]
To find C we need to use the initial condiction, it means evaluae P at t=0.
[tex]P_{0}=Ce^{0}=C[/tex]
[tex]P=P_{0}e^{at}[/tex]
Now, we use the sentence the population has doubled in 5 years.
[tex]2P_{0}=P_{0}e^{a5}[/tex]
We can find "a" in this condition.
[tex]2=e^{a5}[/tex]
[tex]ln(2)=a5[/tex]
[tex]a=\frac{ln(2)}{5}[/tex]
[tex]a=0.14[/tex]
Finally, let's find how long will it take to triple.
[tex]3P_{0}=P_{0}e^{0.14t}[/tex]
[tex]3=e^{0.14t}[/tex]
[tex]t=\frac{ln(3)}{0.14}[/tex]
[tex]t=7.85 years[/tex]
I hope it helps you!
help me , my project is do soon .
Answer:
whats the question
Step-by-step explanation: