What does it mean to be an independent student? A. You must pick your own study topics and research them. B. You can set your own deadlines, within a fixed time frame. C. You are responsible for your own study schedule and organization. D. You are expected to work without extra help from a teacher or tutor.

Let [tex]f^{-1}(x)[/tex] be the inverse of

[tex]f(x) = 3 \log_3 (x + 3) + 1[/tex]

Then by definition of inverse function,

[tex]f\left( f^{-1}(x) \right) = 3 \log_3 \left(f^{-1}(x) + 3\right) + 1 = x[/tex]

Solve for the inverse :

[tex]3 \log_3 \left(f^{-1}(x) + 3\right) + 1 = x[/tex]

[tex]3 \log_3 \left(f^{-1}(x) + 3\right) = x - 1[/tex]

[tex]\log_3 \left(f^{-1}(x) + 3\right) = \dfrac{x - 1}3[/tex]

[tex]3^{\log_3 \left(f^{-1}(x) + 3\right)} = 3^{\frac{x-1}3}[/tex]

[tex]f^{-1}(x) + 3 = 3^{\frac{x-1}3}[/tex]

[tex]f^{-1}(x) = 3^{\frac{x-1}3} - 3[/tex]

(a) If there is a scalar function f(x, y) such that ∇ f(x, y) = x² i + y² j, then

∂f/∂x = x²

∂f/∂y = y²

Integrating both of these equations with respect to x and y (respectively) gives

f(x, y) = 1/3 x³ + g(y)

f(x, y) = 1/3 y³ + h(x)

Differentiating with respect to the other variable gives

∂f/∂y = g'(y) = y²

∂f/∂x = h'(x) = x²

so it follows that

f(x, y) = 1/3 x³ + 1/3 y³ + C

for some constant C.

(b) By the gradient theorem,

[tex]\displaystyle \int_C \nabla f \cdot d\vec r = f(0,0) - f(-1,2) = \boxed{-\dfrac73}[/tex]

Recall that

(x + y)² = x² + 2xy + y²

Then if x + y = √7 and x² + y² = 6, we have

(√7)² = 6 + 2xy   ⇒   2xy = 1

We also have

(x - y)² = x² - 2xy + y²

so that

(x - y)² = 6 - 1   ⇒   (x - y)² = 5

which means x - y has two possible values, √5 or -√5.

Answer:

No. they have a difference in value

the first ans is 6 while the second gives 9.56

Answer:

Explained below :)

(I tried my best, sorry if it doesn't make sense.)

Step-by-step explanation:

Example: 1/4 - 1/8= ?

1: Find the common denominator (bottom number)

2: If the common denominator is 8 then you multiply 1/4 by 2/2 to get the denominator of 8. If you needed then you can multiply the other fraction to get the same denominator.

3: Once you get multiply that then you get 2/8 -1/8.

4: Subtract the numerator (top number) 1

5: Keep the numerator (8)

6: Your answer would be 1/8

I can’t help because I can’t see the coordinate plane.

Answer:

25

Step-by-step explanation:

what is 4.5 18% of

100 / 18 = 5.56

4.5 x 5.55... = 25

Answer:

6:4:3

Step-by-step explanation:

Use 7 to simplify

Answer:

This is false.

Step-by-step explanation:

The easiest thing to do is notice that 8 goes into 16 whilst 9 doesn't so that shows 9/16 would not be the unit rate.

The ratio 5/8 to 10/9 has a unit rate of 9/16 is false.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given are two ratios 5/8 and 10/9.

The unit rate of (5/8) is (5/8)/(8/8) = 5/8 = 0.625 similary the unit rate of the ratio 10/9 is 1.11.

Now, the unit rate of 9/16 is 0.5625 which is not in the range of two ratio's unit rates.

learn more about the unitary method here :

https://brainly.com/question/28276953

#SPJ5

Answer:

1/2

Step-by-step explanation:

5 / 10 = 1/2

Answer:

5"

root4square+3square=root25

=5

Answer:

517 minutes

Step-by-step explanation:

Hope this helps:))

Answer:

517 mins

Step-by-step explanation:

1hour=60min

8hour=480min

37min is the same because it is already in minutes

480+37=517mins

Answer:

In "The Lottery Ticket", Chekhov develops the theme that the love of money can destroy one's satisfaction.

67-32x= 54-34

Subtract 54-34

you would get 20

67-32x= 20 (subtract 67 from both sides of the equation )

-67            -67

-32x/-32=  -47/-32     (Divide -32  on the both sides )

You get a decimal :

x= 1.46875    

Round this answer:

x= 1.5

Answer:

x = 47/32 or 1.46875 ( 1.5 rounded)

Step-by-step explanation:

1) Simplify 54 - 34 to 20.

67 - 32x = 20.

2) Subtract 67 from both sides.

-32x = 20 - 67.

3) Simplify 20 - 67 to -47.

-32x = -47.

4) Divide both sides by -32.

x = -47/-32.

5)  Two negatives make a positive.

x = 47/32

The approximate population in 2016 is 91, 604 population

The exponential equation representing the statement is [tex]P=P_0e^t[/tex]

Substituting into the formula will give:

If by 2012 the population had increased to 81,000, then:

81000 =  56000e^12k

81000/56000 = e^12k

1.4464 = e^12k

ln1.4464 = 12k

0.3691 = 12k

k = 0.3690/12

k = 0.03076

Get the prediction of the population in 2016.

[tex]P = 56000e^{16(0.03076)}\\P=56000e^{0.49213}\\P = 56000(1.6357)\\P = 91,603.70[/tex]

Hence the approximate population in 2016 is 91, 604 population

Learn more on exponential function here:https://brainly.com/question/2456547

Answer:

i think the answer to this question is positive correlation

Step-by-step explanation:

this image below may help u

Answer:

12 + 0.40L = 14.75 + 0.25L

Answer:

Step-by-step explanation:

Total = t

Square feet = f

t = 5.6f + 150

you didnt say how many square feet the customer wanted, but just plug it in for f and t is the answer

Answer:

375.30

Step-by-step explanation:

it's 375.302 but simplified to 375.30

Answer:

8 • 54=8 • 50 + 8 • 4

Option C is the right answer

Step-by-step explanation:

Answer:

C I think, sorry if I'm wrong

Answer:

y= 10x² + 7x + 2.8

Step-by-step explanation:

because the 10x was used twice then the it went to the line of 7x and went down to 2.8 then for the second time it went to 10x

Answer:

-10x^2+7x+4 Would be the correct option

Please thank my question. :)

Answer:

Option B is correct.

add 4 times the second equation to 3 times the first equation

Step-by-step explanation:

Answer:

B) add 4 times the second equation to 3 times the first equation

Step-by-step explanation:

So you have these two equations:

2x - 4y = 6

-3x + 3y = 12

In order "to solve this system of equations by elimination" we want to make BOTH of the equations have a term (in this case the y term) and have the same coefficient (that's the number right next to the y) If they are the exactly same number, even the same sign in front, then we would subtract the equations. If they have the same coefficient but different signs, then we would add the equations. This will eliminate the y term completely. So in order to make them have the same coefficient. We'll multiply the first equation by 3 and the second equation by 4

3(2x - 4y = 6)

4(-3x + 3y = 12) multiplying all the way across the equation (distributing)

We'll get

6x -12y = 18

-12x + 12y = 48 Then you are actually adding from the top, down and get one equation from adding the two existing ones together.

-6x = 66 And then you are able to solve it by dividing both sides by -6 to get

x = -11

You can then use either equation and x = -11 to find y. Your solution is the x, y pair. You can check it by putting the x and y into both equations and finding it makes a true statement in both.

Answer:

[tex]\sqrt{18a}[/tex]

Step-by-step explanation:

To insert the factor, you must first find its squared value, in this case, 3's squared number is 9 so.....[tex]3=\sqrt{9}[/tex]

Now with square roots, they multiply like any other number

so you end up with[tex]\sqrt{9}*\sqrt{2a} \\\sqrt{9*2a}\\\\\sqrt{18a} <------ ANSWER[/tex]

Please leave a thanks!!!

Answer:

The letter C

Step-by-step explanation:

North china plain runs along near the northern east border. It's territory has a noticeable river going through it, and is close to the Gulf of Jilin. A is most likely not correct, since North china plane doesn't go up that high the Yellow river. So it is safe to assume the answer is most likely C

Answer:

Simple Interest: A=P(1+rt)

A=15000(1+(0.1*4.2))

A=$21,300

Compound Interest:A=P(1+r/n)^nt

A=15000(1+0.1/4.2)^1*4.2

A=$64,500

Step-by-step explanation:

Answer:

5 x + 25 ≤ 20

Step-by-step explanation:

Simplify 5  +  5  (  x  +  4  ) .

5  + 5 x  +  20  ≤  20

Add  5  and 20 .

Answer:

Please send a picture or explain properly

Answer: B)1/4

Step-by-step explanation: If you divide a pizza into 4 pieces, each person will get a fourth of the pizza.