What is the decay factor of the exponential function
represented by the table?

Answer:

[tex]y = \tan(x + \frac{x^2}{2})[/tex]

Step-by-step explanation:

Poorly formatted question; The complete question requires that we prove that [tex]y=\tan(x+\frac{x\²}{2})[/tex]

When

[tex]\frac{dy}{dx} =1+xy\²+x+y\²[/tex] and [tex]y(0)=0[/tex]  

We have:

[tex]\frac{dy}{dx} =1+xy\²+x+y\²[/tex]

Rewrite as:

[tex]\frac{dy}{dx} =1+x+xy\²+y\²[/tex]

Factorize

[tex]\frac{dy}{dx} = (1+x)+y\²(x+1)[/tex]

Rewrite as:

[tex]\frac{dy}{dx} = (1+x)+y\²(1+x)[/tex]

Factor out 1 + x

[tex]\frac{dy}{dx} = (1+y\²)(1+x)[/tex]

Multiply both sides by [tex]\frac{dx}{1 + y^2}[/tex]

[tex]\frac{dy}{1+y\²} = (1+x)dx[/tex]

Integrate both sides

[tex]\int \frac{dy}{1+y\²} = \int (1+x)dx[/tex]

Rewrite as:

[tex]\int \frac{1}{1+y\²} dy = \int (1+x)dx[/tex]

Integrate the left-hand side

[tex]\int \frac{1}{1+y\²} dy = \tan^{-1}y[/tex]

Integrate the right-hand side

[tex]\tan^{-1}y = x + \frac{x^2}{2} + c[/tex]

[tex]y(0)=0[/tex] implies that: [tex](x,y) = (0,0)[/tex]

So:

[tex]\tan^{-1}y = x + \frac{x^2}{2} + c[/tex] becomes

[tex]\tan^{-1}(0) = 0 + \frac{0^2}{2} + c[/tex]

This gives:

[tex]0 = 0 +0 + c[/tex]

[tex]0 =c[/tex]

[tex]c = 0[/tex]

The equation [tex]\tan^{-1}y = x + \frac{x^2}{2} + c[/tex] becomes

[tex]\tan^{-1}y = x + \frac{x^2}{2} + 0[/tex]

[tex]\tan^{-1}y = x + \frac{x^2}{2}[/tex]

Take tan of both sides

[tex]y = \tan(x + \frac{x^2}{2})[/tex] --- Proved

Answer:

f(x) and g(x) are closed under multiplication because when multiplied, the result remains a polynomial.

Step-by-step explanation:

First, to be closed means that once an operation has commenced, the result is a polynomial, just like the two original ones.

When polynomials are multiplied, exponents simply add together, and constants are multiplied. A polynomial is a finite sum of terms in which all variables have whole numbered exponents.

In this scenario, when we multiply polynomials, exponents are solely added together, and one whole number plus another is still a whole number. Similarly, constants multiplied by constants stay as constants, and constants multiplied by variables keeps it in polynomial form. (e.g. 3 * x² makes it 3x², and 3x² is fine in a polynomial).

Therefore, given these facts, f(x) and g(x) are closed under multiplication because when multiplied, the result remains a polynomial.

Answer:

D: (4, 6)

Step-by-step explanation:

undefined slope is when the line is vertical

so we are given a point (4, -1)

the best point that will make the slope undefined is D because it will make a vertical slope

1, 2, 3, 4, 5, 6, 7, 8, i don't know, and i haven't ate, 9, 10, 11, 12, this really sucks cuz ur on ur own :(

Answer:

C

Step-by-step explanation:

The length of each side of the square is (3x-2) units

The dimensions of the rectangle are (5x + 4y) and (5x -4y) units

From the question, we are to factor out the given expression for the area of the square

The expression is

9x² − 12x + 4

Factoring

9x² − 12x + 4

9x² −6x -6x + 4

3x(3x -2) -2(3x-2)

(3x -2)(3x -2)

Hence, the length of each side of the square is (3x-2) units

Part B:

The given expression is

25x² − 16y²

Factoring

25x² − 16y²

By difference of two squares, we get

(5x + 4y)(5x -4y)

Hence, the dimensions of the rectangle are (5x + 4y) and (5x -4y) units

Learn more on Factoring an expression here: https://brainly.com/question/11660720

#SPJ1

Answer:â

Step-by-step explanation:

f(x)+g(x)=3x^2-14-12x+4=3x^2-12x-10

Answer:

12

Step-by-step explanation:

The expression 3c + 24 represents the amount of cookies you sell and the expression 5c represents the amount of cookies your sister sells. If we want to find when they become equal, we must set them equal to each other:

3c + 24 = 5c

24 = 2c

12 = c

Therefore, the answer is 12.

Answer:

x=96

Step-by-step explanation:

We can solve by writing ratios

9 trousers             12 trousers

------------------- = ----------------------

72 dollars              x dollars

Using cross products

9x = 12 *72

9x =864

Divide by 9

9x/9 = 864/9

x=96

Answer:

Step-by-step explanation:

Answer:

72π (I think)

Step-by-step explanation:

Think of it in terms of the entire circle. A semi-circle is just half a circle, so the area of a semicircle will be half of the area of the entire circle. The radius of the semicircle is 6, so the radius of the whole circle is 12. Then, we can do [tex]\frac{pi*r^{2} }{2}[/tex] to get the area of the semicircle is 72π. I'm pretty sure that's right. Let me know if I made a mistake somewhere.

Answer: A,B

Step-by-step explanation: the numbers constantly add up only by 218 or 1240 , C and D would not be correct because the rate of change increases as will with the total sum after each period of time

also tiny hint, if you were to draw an X,Y axis graph, A and B would be a straight line while C and D are curved up-wards

Answer:

A

Step-by-step explanation:

A zero in a polynomial function is what the variable is equal to to make the function equal to 0. In the graph, there is only one point that is on the x, 0. Meaning there is only one zero.

Answer:

No, because you can't have a negative number of owls.

The correct answer is C

Answer:

Answer:

-3 maybe, sorry if wrong im doing a pretest on this on edge

Step-by-step explanation:

Answer:

540 g flour

4 tsp baking powder

8 tbsps sugar

520 mL milk

4 eggs

8 tbsps oil

Step-by-step explanation:

Multiply each ingredient by 4!

Because the initial recipie provides the amounts for 6, simply divide 24/6 and you'll find that you only need 4x the original recipie.

135g*4 = 540

1 tsp*4 = 4 etc!

Answer:

[D] [tex]\displaystyle \lim_{h \to 0} \frac{[5(x + h)^2 - 2(x + h)] - (5x^2 - 2x)}{h}[/tex]

General Formulas and Concepts:

Calculus

Limits

Derivatives

Definition of a Derivative: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle f(x) = 5x^2 - 2x[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e

Answer:

25%

Step-by-step explanation:

400/100•300/x=0.75

1.00-0.75= 0.25

25%

Answer:

25 percent of discount

Step-by-step explanation:

[tex]original_price=400\\final_price=300\\discount=100\\\\\frac{400*percent}{100}=100 =>percent=\frac{100^2}{400}=25[/tex]

Answer:

5:15 or can be simplified to 1:3

Step-by-step explanation:

There are 5 boys out of 15 total students in glee club.

(x + 3)(x − 2) in standard form

x2+x-6

Answer:

the answer is D :))) hope you pass this

Answer:

  No

Step-by-step explanation:

The only arithmetic sequence of side lengths that will form a right triangle is (3, 4, 5) or some multiple of that, such as (9, 12, 15).

Sides of length 10, 11, 12 cannot form a right triangle.

Answer:

First one is 120, second is 185

Step-by-step explanation:

So basically it is literally just segmenting the object into rectnagles and squares.

From there, we can subtract and use different side lengths to find the width and length of the segmented pieces.

Hope this makes sense!

Answer:

x=10 y=90 z=20

Step-by-step explanation:

Answer:

multiply

Step-by-step explanation:

Answer:If terms have the same base a and same fractional exponent n/m, we can add them. The rule is given as:

Can/m + Dan/m = (C + D)an/m

Here’s an example of adding fractional exponents:

2x2/5 + 7x2/5 = 9x2/5

Step-by-step explanation: anyway, i hope that this answers your question. Have a good day!

Answer:

poi nts

Step-by-step explanation:

7

Answer:

1

Step-by-step explanation:

Add teh exponents.

9^c * 9^-c = 9^(c - c) = 9^0 = 1