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]
1.)
a^2b^3
---------- <-----write in expanded form.
cd
2.)what is the exact solution to the equation 4^5x=3^x-2
Please show all work I've been struggling to understand these questions!!!! thank you so much <3
Answer:
1. Expanded form of [tex]a^{2} . b^{3}[/tex] = (a.a).(b.b.b)
2.Exact solution x = -0.376
Step-by-step explanation:
Solution:
First we have to write the Expanded Form of [tex]a^{2} . b^{3}[/tex], Let's do it.
1) [tex]a^{2} . b^{3}[/tex] = (a.a).(b.b.b)
Hence,
Expanded form of [tex]a^{2} . b^{3}[/tex] = (a.a).(b.b.b)
2) [tex]4^{5x} = 3^{x-2}[/tex]
Now, we have to find out the exact solution of the above equation:
In order to equate the exponents, we need to make sure the bases are same. Or we simply can use logarithm to solve the above equation.
So,
We are using logarithm to solve this equation.
Let's break this down:
[tex]4^{5x} = 3^{x-2}[/tex]
Taking log on both sides.
log[tex]4^{5x}[/tex] = log[tex]3^{x-2}[/tex]
[tex]5xlog(4)[/tex] = [tex](x-2)log(3)[/tex]
Dividing both sides by log(4)
[tex]5x[/tex] = (x-2) [tex]\frac{log(3)}{log(4)}[/tex]
value of log(3) = 0.4771
value of log(4) = 0.6020
[tex]5x[/tex] = (x-2) [tex]\frac{log(0.4771)}{log(0.6020)}[/tex] =
5x = (x-2)0.792
5x = 0.792x - 1.584
by rearranging the equation, we get:
0.792x - 5x = 1.584
x(0.792 - 5) = 1.584
x(-4.208) = 1.584
x = -1.584/4.208
x = -0.376
Exact solution x = -0.376
(Pic provided)
243 is equivalent to...
0 35
94
28
3
Help I’m timed :(
Answer:
The answer is 3⁵
Step-by-step explanation:
3×3×3×3×3
9×9×3
81×3
243
Consider f(x)=7x^2+8/x−6. Complete the following statements.
As x→∞, f(x)→
As x→−∞, f(x)→
As x→6+, f(x)→
As x→6−, f(x)→
Answer:
A
Step-by-step explanation:
Iwis
which terms are like terms in the expression 5x + 9 + (-7x)
Answer:
5x and -7x
Step-by-step explanation:
they both end in the variable "x"
What is the decimal multiplier to increase by 99%?
Answer:
1.99
Example:
Increase 10 by 99%. 99% of 10 is 9.9 so increased value would be 10 + 9.9 = 19.9
10 x 1.99 = 19.9 ... same answer
Step-by-step explanation:
Answer:
It is 1.99
Step-by-step explanation:
Hope this helped have an amazing day/month/year!
6x+4 divided by 2=8
You don’t have to explain... just answer
(2+6 +8+54 +...);S 12
Sunflower we haved renewed your helper thank you with working with our business
Answer: wdym? do u need any help
Step-by-step explanation:
Find ULE in the triangle
Factor 64x2 – 80xy + 25y2 using the binomial theorem.
The binomial that was expanded is .
The exponent on the factored expression is .
Answer:
Step-by-step explanation:
HELP PLEASE SUE TODAY
A coin contains 9 grams of nickel and 16 grams of Copper, for a total of 25 grams. What percentage of the metal is copper?
Answer:
The copper percentage = 64%
Step-by-step explanation:
Given
Nickle quantity = 9 grams of nickelCopper quantity = 16 grams of nickelTotal quantity = 25 gramsThe percentage of copper metal can be determined using the formula
Copper percentage = [Copper quantity / Total quantity] × 100
= [16 / 25] × 100
= 0.64 × 100
= 64%
Therefore, the copper percentage = 64%
will give branliest
Simplify the follow expression
3x + 8y + 13x
Answer:
16x+8y
Step-by-step explanation:
Let's simplify step-by-step.
3x+8y+13x
Combine Like Terms:
=3x+8y+13x
=(3x+13x)+(8y)
=16x+8y
find the slope please
The slope of the line is 2.
The slope is going up from left to right, so it'll be positive to start with. From there you have to do rise over run. That is pretty much how many units up and in towards the slope do you have to go until you find 2 points that are in the center of the line. In this case, the rise over run is 2/1 which equals 2.
May I have brainliest please? :)
Which math expression means "the difference of 40 and 12"?
Answer:C
Step-by-step explanation:This is because c has subtract sign and you are trying to find the difference and difference you need to subtract.And you need to find the difference of 40 and 12 so u write 40- 12 which is choice c.
Hope it helps and it does please give Brainliest .Thanks ;)
please please please please
PLEASE HELP I WILL GIVE BRAINLIEST!!!
1 - A graph of an equation in two variables or a function is a representation of an infinite number of solutions to the equation or function.
2 - A system of equations may not have an exact solution that meets the conditions of a real-world solution.
it would be so amazing if you could help, im legit so confused :(
Answer:
1- 1+2+3+4+5 = 15
Step-by-step explanation:
Geometry question
What is the formula to find the surface area of a pyramid with a triangle base?
Answer:
Step-by-step explanation:
12pl+B where p represents the perimeter of the base, l the slant height and B the area of the base.
3.7(-4x - 3)
(1 Point)
28x - 21
-28x - 21
-4x + 21
Answer:
-28x - 21
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyStep-by-step explanation:
Step 1: Define
7(-4x - 3)
Step 2: Simplify
Distribute 3.7: 7(-4x) + 7(-3)Multiply: -28x - 21A company rents out 18 food booths and 21 game booths at the county fair. The fee for a food booth is $150 plus $8 per day. The fee for a game booth is $65 plus $6 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount, in dollars, that the company is paid.
Answer:
the expression is 21+18d
Step-by-step explanation:
Answer:
The answer is t(2844 + 1491) or t(4335)
Step-by-step explanation:
18 x 150 = 2700
18 x 8 = 144
2700 + 144 = $2844
21 x 65 = 1365
21 x 6 = 126
126 + 1365 = 1491
t = ? <--- t stays the same
1491 + 2844 = 4335
t(4225)
Shane made a scale drawing of a house and its lot. The scale he used was 1 inch : 3 feet. In
the drawing, the backyard is 11 inches wide. What is the width of the actual yard?
Answer:
33
Step-by-step explanation:
Please help solve this. (Answer is not 80)
Answer:
70
Step-by-step explanation:
triangle is 180deg in total thus,
Evaluate the expression 2 + 23 × 5 - 3.
20
39
37
47
The expression after evaluating results in the number 114.
What is BODMAS Rule?BODMAS rule is the rule used when solving expressions involving more than one operations.
It is the abbreviation of Brackets, Order, Division, Multiplication, Addition, Subtraction, which is the order of the operations to be done.
The expression given is,
2 + 23 × 5 - 3
We have to evaluate the expression in the order of BODMAS.
There are no brackets and orders and division.
Start with the multiplication.
2 + 23 × 5 - 3 = 2 + 115 - 3
Next do the addition.
2 + 115 - 3 = 117 - 3
= 114
Hence the value of the expression given is 114.
To learn more about BODMAS Rule, click :
https://brainly.com/question/16738857
#SPJ2
Find the value of x.
Answer: [tex]x = 2\sqrt{15}[/tex]
Step-by-step explanation:
[tex]\dfrac{15}{x}=\dfrac{x}{4} \\\\ x \times x = 15 \times 4\\x^{2} =60\\x=\sqrt{60} =2\sqrt{15}[/tex]
In the balance scale/equation analogy, what should you write in the blank on the right side of the equation in order to balance the scale for the following equation? 2(x + 1) = 2x + ______
(x + 1)
4
x
2
Answer:
Option D: 2 is the correct answer.
Step-by-step explanation:
Given equation is:
2(x + 1) = 2x + ______
For balancing the equation, the variables and constants must be same on both sides of the equation.
Simplifying 2(x+1) gives us 2x+2
As 2x is already there, we will add 2 with it in the equation.
Hence,
Option D: 2 is the correct answer.
Find the slope of the two points (-7, 8) and (4, -3).
Answer:
y = (15/24)x + 6
Step-by-step explanation:
Helppp (20 points )pleaeeee
Answer:
LxWxH= 920
Step-by-step explanation:
hope this helps!
pls help asap no trolls
Answer:
yes
Step-by-step explanation:
This is because the sum of 2 sides of a triangle has to be greater than the side that was not used
find the slope please
Answer:
11) 1/3
12) 5/3
13) -3/5
14) 4/3
15) -3/5
16) 2/4
Step-by-step explanation:
Sandy has 15 roses, 3 daisies, and 12 tulips. She wants to arrange all the flowers in bouquets. Each bouquet has the same number of flowers and the same type of flower. What is the greatest number of flowers that could be in a bouquet? The greatest number of flowers that could be in a bouquet is flowers.
Answer:
3 bouqetes 5 roses 4 tulips
Step-by-step explanation:
