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]
The y intercept is at the point '?'
The roots are x = ? and x = ?
The turning point is at ( ? , ? )
Answer:
See below.
Step-by-step explanation:
The y-intercept is the point where the line passes the y-axis. In this instance, that is at the point (0, 3).
The roots are the x-intercepts are the points where the line crosses the x-axis. In this instance, the roots are x = -3 and x = -1.
The turning point is the vertex of the equation. In this instance, the vertex is on the point (-2, -1).
Solve for x
4^x/9^x=½
Answer:
x = 0.85476
Step-by-step explanation:
4ˣ/9ˣ=½
9ˣ / 4ˣ = 2
(9/4)ˣ = 2
2.25ˣ = 2 .... aⁿ = x logₐx = n
log₂.₂₅2 = x
x = 0.85476
y
is inversely proportional to
x
.
When
y
=
4
,
x
=
16
Work out
y
when
x
=
8
Answer:
y inversely proportional to 1/x
y=4, x=16
4=k/16
k=64
find y when x=8
y=64/8
y=8
Mr. and Mrs. Phillips are going to build a new home with a foundation that is in the shape of a square. The house will cover 222 square yards. Find the length of the side of the house to the nearest tenth of a yard.
Answer:
the answer is 14.9 yd
Step-by-step explanation:
• The average cow drinks 168 quarts of water each day. Given that there
are 4 quarts to one gallon, how many gallons of water does the average
cow drink?
Lena purchased a prepaid phone card for $20. Long distance calls cost 14 cents a minute using this card.
Lena used her card only once to make a long distance call. If the remaining credit on her card is S18.04, how
many minutes did her call last?
|minutes
?
Answer:
havenche ai polld pener es quanto
Step-by-step explanation:
Please help me answer this !!
Explain your answer !!!
I will give brainlst
Any amount of rotation will not change the angle between the two spokes. This is because each piece of the wheel moves in unison as the rotation is applied. Nothing changes about the wheel. Imagine instead of rotating the wheel, we instead rotated the camera that is capturing the wheel (or the person looking at the wheel rotates their head). This is a good way to see how the wheel itself isn't changing at all, but instead rather just the look of it is changing.
72 = –6(y + 37)
plz help
Answer:
-49
Step-by-step explanation:
you can first divide both sides by -6
so
-12 = y+37
so y = -12-37 = -49
What is the least common denominator of 1/4 and 7/9
Answer: It is 36
Step-by-step explanation:
simplify −k−(−8k+7) to create an equivalent expression
Answer:
7k - 7
Step-by-step explanation:
-k - (-8k + 7)
= -k + 8k - 7
= 8k - k - 7
= 7k - 7
Billy purchased four more oranges than apples. Apples cost 30 cents each and oranges cost 50 cents each. Billy
spent a total of $3.60. Write an equation, to find how many apples, a, he purchased.
Answer:
0.30a + 0.50 (4+a) = 3.60
Step-by-step explanation:
find the measure of the angle
Answer:
2 = 74
1 = 106
Step-by-step explanation:
none
In 1850, there were 564 textile mills in New England states with a total of 61,893 workers. The average wmployment per textile mill was ?
Answer Choices
109
110
108
111
. Which expression is equivalent to 14-9?
math
Answer:
5
Step-by-step explanation:
Find the slope intercept equation of the line
Answer:
Step-by-step explanation:
slope-intercept formula looks like [y=mx + b]
use two points to find the slope.. or look at the graph carefully to see it there are easy points to count from.... hmmm
yes.. this is very easy to just count.. no math needed :P
the slope is posive. b/c the graph looks like you are walking up hill.. and it's rise over run is 2/1 .. so the slope is 2
then by looking at the graph I can also see that when x = 0 the line pass exactly thur +1.. sooo that tells me all I need to know for the sloop-intercept formula
y= 2x+1 :) see?
Camille bought a set of kitchen chairs discounted 25% off of the original price of $170. What was the sale price of the set of chairs?
Answer:
127.5
Step-by-step explanation:
0.25*170 then take away from 170
$127.5 was the sale price of the set of kitchen chairs.
Given:
Camille bought a set of kitchen chairs at discounted 25% off of the original price.
The original price of a set of kitchen chairs = $170
To find:
The sale price of the set of kitchen chairs.
Solution:
The original price of a set of kitchen chairs = O.P = $170
The percent of discount on the set of kitchen chairs = d% = 25%
The discount price on the set of kitchen chair= D
[tex]d\%=\frac{D}{O.P}\times 100\\25\%=\frac{D}{\$170}\times 100\\D=\frac{25\times \$170}{100}=\$42.5[/tex]
The sales price of a set of kitchen chairs = S.P
[tex]S.P=O.P-D\\=\$170-\$42.5=\$127.5[/tex]
$127.5 was the sale price of the set of kitchen chairs.
Learn more about the discount price here:
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Which graph represents y = √ X
Explanation:
[tex]\displaystyle [9, 3] → 3 = \sqrt{9} \\ [4, 2] → 2 = \sqrt{4} \\ [1, 1] → 1 = \sqrt{1} \\ [0, 0] → 0 = \sqrt{0}[/tex]
**In this case, we want NON-NEGATIVE terms.
I am joyous to assist you at any time.
Emily is entering a bicycle race for charity. Her mother pledges $0.60 for every 0.75 mile she bikes. If Emily bikes 21 miles, how much will her mother donate?
Her mother will donate $
Solve the system by substitution.
y = -2x+ 28
y = 5x
Answer:
-2x+8=5x
8=7x
x=7/8
y=5x
y=5×7/8
y=35/8
the local water slides have 70 employees, of which 10% are temporary. how many temporary employees are there?
Answer:
7 employees
Step-by-step explanation:
Given that 10% are temporary .
So number of temporary employees will be 10% of 70 employees = 7employees ( Answer)
60 sixth grade students chose to watch a movie on the last day of school. This is 25% of the 6th-grade class. How many total students are in the 6th grade?
Answer:
240
Step-by-step explanation:
25% =1/4
if 1/4 of class is 60, the class have 60x4 students
Kenny drank 37 ounces of milk during the
day. How many cups of milk did he drink?
Answer:
4.625
Step-by-step explanation:
that is the answer
Solve for w. -34=-6+w/4
Answer:
w=−112
Step-by-step explanation:
-34=-6+w/4
Simplify both sides of the equation.
−34=−6+ w /4
−34=−6+ 1 /4 w
−34= 1 /4 w−6
Flip the equation.
1 4/ w−6=−34
Add 6 to both sides.
1 /4 w−6+6=−34+6
1 /4 w=−28
Multiply both sides by 4.
w=−112
Answer:
w = - 112
Step-by-step explanation:
-34=-6+w/4
1. Add 6 on both sides
-34 + 6 = -6 + 6 + w/4
-28 = w/4
2. Multiply 4 on both sides since it's the opposite of dividing
-28 * 4= w/4 * 4
- 112 = w
Hope this helped!
Amy plays a game with an ordinary, fair dice.
If she rolls: 1 she wins, 2 or 3 she loses, 4, 5 or 6 she rolls again.
When she has to roll again: if she rolls an even number she wins
if she rolls an odd number she loses.
a) Work out the probabilities that should be
First roll
Second roll
placed at P, Q, R and S on the tree diagram.
Give your answers as fractions in the form a/b
P
Q
2 or 3
P:
Q:
R:
S:
R
even
4, 5 or 6
(1)
(1)
b) Work out the probability that Amy will win
and the probability she will lose.
Give your answers as fractions in the form a/b
S
odd
P(win) =
P(lose) =
(2)
(2)
Answer:
Ok so I’m stuck with this question too But I got the top part.
p=1/6
q=2/6
r=3/6
s=3/6
A) The probabilities placed at P, Q, R and S on the tree diagram are;
P = 1/6; Q = 1/3; R = 1/4; S = 1/4
B) The probabilities of her winning or losing is;
Probability that she will win = 5/12
Probability that she will lose = 7/12
A) From the given tree diagram, we can see that;At point P; Only 1 is rolled.
Since there are 6 possible numbers, then Probability at P = 1/6
At point Q; either 2 or 3 can be rolled.
Since there are 6 possible numbers, then Probability at Q = 2/6 = 1/3
At point R; 4,5, or 6 can be rolled on first roll.
Thus, Probability on first roll = 3/6
At R on second roll if she gets even, probability on second roll = 3/6
At S on second roll if she gets odd, probability on second roll = 3/6
Thus;
Overall probability at R = 3/6 × 3/6 = 1/4
Overall probability at S = 3/6 × 3/6 = 1/4
B) Probability that she will win are the probabilities at P and R.Thus, probability that she will win = 1/6 + 1/4 = 5/12
Probability that she will lose are the probabilities at Q and S.
Probability that she will lose = 1/3 + 1/4 = 7/12
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Which expression is NOT equivalent to 24 + 6x?
A. 2(3x + 12)
B. 28 + 4x – 4 + 2x
C. 5x + 7 + x + 17
D. 3(8 + 3x)
Answer:
D
the answer is D because when you multiply 3(8 + 3x), it will give you 24+9x
3(8 + 3x) is not equivalent to 24 + 6x.
Option D expression is not equivalent to 24 + 6x.
What is an expression?An expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them.
According to the question
Expression is NOT equivalent to 24 + 6x
A . 2(3x + 12)
= 2(3x) + 2(12)
= 6x + 24
= 24 + 6x
B. 28 + 4x – 4 + 2x
= (28 - 4) + (4x + 2x)
= 24 + 6x
C. 5x + 7 + x + 17
= (5x + x) + (7 + 17)
= 6x + 24
= 24 + 6x
D. 3(8 + 3x)
= 3(8x) + 3(3x)
= 24 + 9x
Hence, Option D is not equivalent to 24 + 6x.
3(8 + 3x) is not equivalent to 24 + 6x.
Find out more information about expression here
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anyone ?mknwonthisssss
The area of the triangle below is 33.12 square inches what is the length of the base
Answer:12.72
Step-by-step explanation:
Help me please I'm bad at geometry
Clayton draws 3 pictures in 25 minutes. He drew 24 pictures this week. How many minutes did Clayton spend drawing the pictures?
NEED A ANSWER ASAP
Answer:
200 minutes
Step-by-step explanation:
24 / 3 = 8
25 * 8 = 200
200 minutes
The rate will be 8.33 minutes per picture. Then the number of minutes will be 200 minutes.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Clayton draws 3 pictures in 25 minutes. Then the rate is given as,
Rate = 25 / 3
Rate = 8.33 minutes per picture
He drew 24 pictures this week. Then the number of minutes is calculated as,
⇒ 24 x 8.33
⇒ 200 minutes
The rate will be 8.33 minutes per picture. Then the number of minutes will be 200 minutes.
More about the rate link is given below.
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pls help I will give brain list to first
Answer: y= 3
Step-by-step explanation:
Step 1: Add y to both sides.
y + 3 = −y + 9
+y +y
2y + 3 = 9
Step 2: Subtract 3 from both sides.
2y+3 = 9
-3 -3
2y = 6
Step 3: Divide both sides by 2.
2y = 6
2 = 2
y= 3