Answers
[tex]~~~\dfrac{d}{dx} f(x) \\ \\=\dfrac{d}{dx} \left(x^3 \cdot \log_6 x \right)\\\\=x^3\dfrac{d}{dx} \left(\log_6 x\right) + \log_6 (x)\dfrac d{dx} x^3 \\\\=x^3 \cdot \dfrac 1{x \ln 6} + \log _6 (x) \cdot 3x^2\\\\=\dfrac{x^2}{\ln 6} + \log_6(x) \cdot 3x^2\\\\\\=x^2 \left(\dfrac 1{\ln 6} + 3\log_6 x \right)[/tex]
[tex]\text{The derivative is now in a form of}~ x^A (B + C \log_D (x))[/tex]
Related Questions
If 15 percent of cars are blue and an observer's observation is 80 percent accurate, what is the probability that a car is, in fact, blue when the witness reports it as blue
Answers
The probability that a car is blue is the likelihood of the car being blue
The probability that a car is, in fact, blue when the witness reports it as blue is 12%
How to determine the probability?The given parameters are:
P(Blue) = 15%
P(Accurate) = 80%
The probability that a car is blue, and the observation is accurate is calculated as:
P(Blue and Accurate) = P(Blue) * P(Accurate)
This gives
P(Blue and Accurate) = 15% * 80%
Evaluate the product
P(Blue and Accurate) = 12%
Hence, the probability that a car is, in fact, blue when the witness reports it as blue is 12%
Read more about probability at:
https://brainly.com/question/25870256
Two students determined the value of this expression.
-2.5(1.4+3.1) + 6.9(-4.3)
These are the steps each student used.
Student P
Step 1: -3.5 + 7.75 + 6.9(-4.3)
Step 2: -3.5 + 7.75 - 29.67
Step 3: 7.75 - 3.5 - 29.6
Step 4: -25.42
Student Q
Step 1: -3.5 - 7.75 + 6.9(-4.3)
Step 2: -3.5 - 7.75 - 29.67
Step 3: -(3.5 - 7.75 - 29.67)
Step 4: -(-33.92)
Step 5: 33.92
Analyze the steps and describe any errors made by Student P and Student Q.
Answers
Let's solve
[tex]\\ \rm\rightarrowtail -2.5(1.4+3.1)+6.9(-4.3)[/tex]
[tex]\\ \rm\rightarrowtail -3.5-7.75-29.67[/tex]
[tex]\\ \rm\rightarrowtail -11.25-29.67[/tex]
[tex]\\ \rm\rightarrowtail -40.92[/tex]
Both did error in signs
Answer:
Given expression:
-2.5(1.4+3.1) + 6.9(-4.3)
Student P
Step 1: -3.5 + 7.75 + 6.9(-4.3)
Step 2: -3.5 + 7.75 - 29.67
Step 3: 7.75 - 3.5 - 29.67
Step 4: -25.42
Student P made an error in step 1. When expanding the first part of the expression, they forgot the negative sign when multiplying -2.5 by 3.1.
So Step 1 should be: -3.5 - 7.75 + 6.9(-4.3).
This error then impacted all following steps and gave an incorrect final solution.
Student Q
Step 1: -3.5 - 7.75 + 6.9(-4.3)
Step 2: -3.5 - 7.75 - 29.67
Step 3: -(3.5 - 7.75 - 29.67)
Step 4: -(-33.92)
Step 5: 33.92
Student Q made an error in step 3. When placing the numbers in parentheses and placing a negative sign outside the parentheses, they should have changed the two negative signs inside the parentheses to positives.
So Step 3 should be: -(3.5 + 7.75 + 29.67).
This error then impacted all following steps and gave an incorrect final solution.
Correct steps and solution
Step 1: -3.5 - 7.75 + 6.9(-4.3)
Step 2: -3.5 - 7.75 - 29.67
Step 3: -(3.5 + 7.75 + 29.67)
Step 4: -(40.92)
Step 5: -40.92
x – 5 ÷ 3 + b
6b + 15b ÷ 3
c - 2c × 4
PLEASE ANSWER ITS CONFUSING
Answers
Hey there!
Basically for all of your equations/questions you have to COMBINE the LIKE TERMS (if they are any in the particular equation you have)
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
QUESTION/EQUATION #1
x - 5 ÷ 3 + b
We pretty much CANNOT do anything to this equation because it doesn’t have that many like terms.
So, thus your answer will most likely be/
[b + x - 5 ÷ 3]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
QUESTION/EQUATION #2
6b + 15b ÷ 3
= 21b ÷ 3
= 7b
Thus, your answer is: [7b]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
QUESTION/EQUATION #3
c - 2c × 4
REWRITE
= 1c - 2c × 4
COMBINE the LIKE TERMS
= 1c - 7
= -7c
Thus, your answer is: [-7c]
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
After 2 years, a certain car is worth $16600. When it is 9 years old, the same car is then worth
$9950.
Find the equation of the line in this situation.
Identify the slope for this situation and interpret it.
Identify the y - intercept for this situation and interpret it.
Identify the x - intercept for this situation and interpret it.
Answers
The linear function that describes the situation is:
y = -950x + 18500.
The slope of -950 means that the price of the car decays $950 per year.The y-intercept of 18500 means that the initial value of the car is of $18,500.The x-intercept of 19.47 means that the value of car is of $0 after 19.47 years.What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem, in 7 years, the price of the car decays by $6,650, hence the slope is given by:
m = -6650/7 = -950.
The slope of -950 means that the price of the car decays $950 per year.
Then, the equation is:
y = -950x + b.
After 2 years, a certain car is worth $16600, hence when x = 2, y = 16600, and:
16600 = -950(2) + b
b = 18500.
The equation is:
y = -950x + 18500.
The y-intercept of 18500 means that the initial value of the car is of $18,500.
The x-intercept is found when y = 0, hence:
-950x + 18500 = 0.
x = 18500/950
x = 19.47.
The x-intercept of 19.47 means that the value of car is of $0 after 19.47 years.
More can be learned about linear functions at https://brainly.com/question/24808124
-77x - 78x = -155x
-66y - (-66y) = -66y + 66y = 0
264 - (-666) = 264 + 666 = 930
This leaves us with -155x = 930. Dividing by -155 on both sides, we find:
x = -6
Substitute x = -6 into one of the two original equations, solve for y, and then state the full solution to the system of equations.
Answers
Answer:
I don't understand
Step-by-step explanation:
You answer it.
Given that a= 6 cm and b = 5 cm, work out the area of the triangle.
Answers
Answer:
15cm²
Step-by-step explanation:
Area of a triangle: 1/2*b*h
a = height (6cm)
b = base (5cm)
A = 1/2* b * h
A = 1/2 * 5 * 6
A = 1/2 * 30
A = 15cm² <== final answer
Hope this helps!
helpppppppppppppppppppppppppp walk me thru
Answers
Answer:
i think its a trapazoid
Step-by-step explanation:
i need help please its due today
Answers
Chapter 1 Test
What is the simplified form of the expression 3 + 8x - 2y - x + 1 + 4y? Enter your answers in the boxes.
X +
ly+
Answers
Answer:
7x+4+2y is your answer
Carlos is saving for a new bike. he is paid $6.60 an hour and works 10 hours per week at his after-school job. If he saves 75% of the money he earns, how much does he save each week?
Answers
Answer:
16.50 per week
Step-by-step explanation:
6.60 times 10 equals 66 minus 75% equals 16.50
a thousand dollars is left in a bank savings account drawing 7% interest, compounded quarterly for 10 years. what is the balance at the end of that time
Answers
Work Shown:
A = P*(1+r/n)^(n*t)
A = 1000*(1+0.07/4)^(4*10)
A = 2001.59734318603
A = 2001.60
This assumes that you do not withdraw any of the money over the course of the 10 years. Also, the interest rate must stay the same at 7%.
Can you be serious and more understanding about the home work
Answers
Answer:
yes
Step-by-step explanation:
is there a specific question?
Answer: All children should be doing homework. But the amount and quality should change." His basic prescription.
Step-by-step explanation:
Read the sentence. Patriots, people who supported freedom from England, were especially angry when British soldiers overtook their homes. What type of phrase is people who supported freedom from England?
Appositive
Fragment
Participial
Prepositional
Answers
Answer: Fragment.
Step-by-step explanation:
A Fragment phrase can be defined as a sentence that resembles a sentence but lacks delivering a complete idea. This sentence serves as a dependent clause in a sentence.
The given sentence is an example of a fragment phrase or sentence. Though the phrase appears to be a sentence but it lacks complete idea because we don't know about which 'people' is it talking about.
three subtracted from five times a number is -39. what number is?
A) Translate the statement above into an equation that you can solve to answer this question, Do not solve it yet. Use x as your variable.
The equation is _____
B) Solve your equation in part {A} for x
.Answer x=
Answers
Answer:
A) 5x - 3= -39
B) 5x = -39 + 3
5x = -36
x = -36/ 5
x= -7.2
A painter bought 14 gallons of paint just enough to cover 2 room
Answers
7
Step-by-step explanation:
[tex]Based\ on\ the\ given\ conditions,\ formulate:[/tex]
[tex]14\div 2[/tex]
[tex]\frac{14}{2}[/tex]
Creoss out the common factor
[tex]7[/tex]
I hope this helps you
:)
write a quadratic function f whose only zero is 11
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Here's the solution ~
To write a quadrilatic function, we have to use its roots, like we have to subtract the roots from x and multiply them ~ then we will get our required function !
Since our only root is 11 here, we have to do t double
[tex]\qquad \sf \dashrightarrow \:(x - 11)(x - 11)[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 11x - 11x + 121 [/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 22x + 121[/tex]
That's our required function ~ I hope you understood the whole thing !
Which of the following equations are true for the number 5? (Select all that apply)
a 4 ÷ ⬜ = 4/5
b ⬜ ÷ 1/5 = 25
c 1/5 = ⬜ ÷ 5
d 4 ÷ ⬜ = 1/5
Answers
Answer:
A. True
B. True
C. False
D. False
A passport consists of 2 letters followed by 2 digits. How many different passports can be formed?
Answers
67,600 different passwords can be formed.
26 x 26 x 10 x 10 = 67,600 (26 letters in the alphabet and 10 from 0-9)
Does anyone know the answers? Need help!!
Answers
Answer:
nice handwriting
Step-by-step explanation:
A recipe calls for 4 cups of pecans for every 5 cups of walnuts. How many cups of pecans should be added to 8 cups of walnuts?
A. 1.6 cups
B. 2.5 cups
C. 6.4 cups
D. 10 cups
Answers
If you should feed 1½ lbs of hay per 100 lbs of your horse’s body weight, how much should you feed a 1100 lb horse?
A. 23lbs
B. 16.5lbs
C. 13.6lbs
D. 7.5lbs
Answers
I think it's 16.5lbs I'm sorry if I'm wrong I don't know for sure
These numbers are common multiples of ________.
15, 30, 45, 60
A) 2 and 3
B) 3 and 5
C) 4 and 5
D) 3 and 4
Answers
.
Answer:
The answer is B.
Step-by-step explanation:
15÷3=5 15÷5=3
30÷3=10 30÷5=6
45÷3=15 45÷5=9
60÷3=20 60÷5=12
A High School’s football Stadium holds a total of 7,000 fans. A survey shows that of the total number of fans, 68% root for the home team. How many fans attending a football game are rooting for the home team?
A. 4,760
B.2,240
C. 47,600
D. 5,512
Answers
Answer:
the answer is; 68% of 7000 which gives 4760 football fans rooting for the home team
The average daily rainfall in Seattle for the month of June has a mean absolute deviation of 1.3 inches. What conclusion can you make about the average daily rainfall in Seattle for the month of June?
Answers
Using the mean absolute deviation, it can be concluded that the daily rainfall volume differs from the mean by an average of 1.3 inches.
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the number of observations.The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.In this problem, the mean absolute deviation is of 1.3 inches, hence, it can be concluded that the daily rainfall volume differs from the mean by an average of 1.3 inches.
More can be learned about the mean absolute deviation at https://brainly.com/question/3250070
Answer:
Step-by-step explanation:
This recipe makes three portions of soup.
Navina follows this recipe but only wants to make enough for one portion of soup.
How much of each ingredient does she need?
Recipe: Serves 3
180 g onions
120 g carrots
3 tablespoons of oil
600 g tomatoes
1.2 litres vegetable stock
Answers
Answer:
Step-by-step explanation:
To get one portion of soup, each ingredient should be divided by 3
Quantity of onion required= 180 ÷ 3 = 60 g
Quantity of carrots required = 120 ÷ 3 = 60 g
Oil = 3 ÷ 3 = 1 table spoon
Quantity of tomatoes required = 600 ÷ 3 = 300 g
Vegetable stock = 1.2 ÷ 3 = 0.4 litres
If z7=4-3i, thenz7 is
Select one:
O-7
O 7
O 5
O -5
Answers
By using Euler's notation, we will see that:
z^7 = 78,125*e^(-i*4.48)
How to get z^7?
We know that:
z = 4 - 3i
Remember that for a complex number:
w = a + bi
In Euler's notation, we can write this as:
w = √(a^2 + b^2)*e^(i*Atan(b/a))
Then, for z, we will get:
z = √(4^2 + (-3)^2)*e^(i*Atan(-3/4))
z = 5*e^(-i*0.64)
Now, if we apply an exponent of 7 to this number, we will get:
z^7 = ( 5*e^(-i*0.64))^7
z^7 = 5^7*e^(-i*7*0.64) = 78,125*e^(-i*4.48)
If you want to learn more about complex numbers, you can read:
https://brainly.com/question/10662770
Simplify (X-2)(x+3)(2x+1)
Answers
Answer:
Step-by-step explanation:
Use FOIL method.
(x -2)(x+3) = x*x + x*3 + (-2)*x + (-2)*3
= x² + 3x - 2x -6 {Combinelike terms}
= x² + x - 6
(x² + x -6)*(2x + 1) = x²*2x + x²*1 + x*2x +x*1 + (-6)*2x + (-6)*1
= 2x³ + x² + 2x² + x -12x - 6
= 2x³ + 3x² - 11x - 6
mitchell has a small bag with 12 m& ms
Answers
Answer:
You may want to add more context to this question.
Step-by-step explanation:
Which transformation would create an image and a pre image that are similar figures?
Answers
The transformation which would create an image and pre image that are similar figures is dilation.
What is Similarity Transformation?Similarity transformations are transformations where there occurs a dilation with one or more transformations like rotation, reflection or translation.
This is called so because the triangles so formed will be similar figures.
Transformation of geometrical figures or points is the manipulation of a given figure to some other way.
Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.
When the pre image is reflected, rotated or translated, it is not affecting the shape and the size. So the image and the pre image will be congruent.
Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.
Dilation enlarges or reduces the size, so they are similar figures.
Hence dilation is the similar transformation.
Learn more about Similarity Transformations here :
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George wanted to measure the angle of a water slide at the lake. He used a sheet of folded paper that formed a 20° angle. He measured and found that three of the folded paper angles would fit in the angle made by the slide and the ground.
Which of the following was the angle of the water slide?
Answers
The angle of the water slide is 60 degrees.
The equation that models his work is 3 × 20 = 60 degrees.
How to find the sum of angles of a figure/object?
He wants to measure the angle of a water slide at the lake.
He used a sheet of folded paper that formed 20 degrees to measure the angle of the the water slide at the lake.
He noticed three folded paper angle fits in the angle made by the slide and the ground.
Since each angle is equals to 20 degrees, and the three fits into the angle made by the slide and the ground, the angle of the water slide is as follows:
20 × 3 = 60 degrees
learn more on angles here: https://brainly.com/question/16746032