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Mademuasel [1]
3 years ago
15

Two functions are shown below.

Mathematics
1 answer:
frozen [14]3 years ago
5 0

Answer:

x = 6

Step-by-step explanation:

As the function f(x) is an exponencial function, it will grow faster than g(x), that is a linear function.

For small values of x, we have that f(x) < g(x). For example:

f(1) = 1/2 * 2 = 1

g(1) = 5*1 + 2 = 7

f(2) = 1/2 * 4 = 2

g(2) = 5*2 + 4 = 14

So we just need to check some integer values and see when f(x) will be bigger than g(x). It will not be a big value, as the exponencial function grows very fast.

For x = 5, we have:

f(5) = 1/2 * 32 = 16

g(5) = 5*5 + 4 = 29

For x = 6, we have:

f(6) = 1/2 * 64 = 32

g(6) = 5*6 + 4 = 34

For x = 7, we have:

f(7) = 1/2 * 128 = 64

g(7) = 5*7 + 4 = 39

So the largest integer value of x for f(x) ≤ g(x) is x = 6.

Another way to solve this is by plotting both equations, and then checking where they cross, that is, where f(x) = g(x).

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I need some one to help me!! <br><br> Is (7, 0) a solution to the equation y = x − 7?
Marianna [84]

Answer:

Yes

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

Coordinates (x, y)

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

Point (7, 0)

Equation y = x - 7

<u>Step 2: Find</u>

  1. Substitute in point [Equation]:                                                                         0 = 7 - 7
  2. Subtract:                                                                                                            0 = 0

Since 0 = 0 is true, then it would be a solution to the equation.

3 0
3 years ago
Consider the differential equation
Gennadij [26K]

The first solution is quadratic, so its derivative y' on the left side is linear. But the right side would be a polynomial of degree greater than 1, so this is not the correct choice.

The third solution has a similar issue. The derivative of √(x² + 1) will be another expression involving √(x² + 1) on the left side, yet on the right we have y² = x² + 1, so that the entire right side is a polynomial. But polynomials are free of rational powers, so this solution can't work.

This leaves us with the second choice. Recall that

1 + tan²(x) = sec²(x)

and the derivative of tangent,

(tan(x))' = sec²(x)

Also notice that the ODE contains 1 + y². Now, if y = tan(x³/3 + 2), then

y' = sec²(x³/3 + 2) • x²

and substituting y and y' into the ODE gives

sec²(x³/3 + 2) • x² = x² (1 + tan²(x³/3 + 2))

x² sec²(x³/3 + 2) = x² sec²(x³/3 + 2)

which is an identity.

So the solution is y = tan(x³/3 + 2).

4 0
2 years ago
Read 2 more answers
8(-9-5x)+4b X=9 B=-9
True [87]
-468
Explanation: Substitute in the numbers for the variables presented. I’ve shown it step-by-step in the photo below.

6 0
3 years ago
Workout the problem and explain it in paragraph form
Anna71 [15]
He answer of this question is 17
3 0
3 years ago
Read 2 more answers
Convert (-2/sqrt[3] , 2) to polar coordinates
anyanavicka [17]
If you have these conditions:

1. (r ,theta) where r > 0 
<span>2. (r, theta) where r < 0
</span>
The solution would be:

<span>r = sqrt(x^2 + y^2) 

t = arctan(y/x) 


r = sqrt(12 + 4) = sqrt(16) = +/- 4 

t = arctan(2 / -2sqrt(3)) = arctan(-1 / sqrt(3)) = 5pi/6 , 11pi/6 


1) 
r > 0 
(4 , 11pi/6) 

2) 
r < 0 
(-4 , 5pi/6)
</span>

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
5 0
3 years ago
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