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3 years ago

Which function increases the fastest?

Mathematics

1 answer:

Lapatulllka [165]3 years ago

8 0

Considering we are looking for an increasing function, all negative xs are incorrect, which only leaves A and C left

Because C is a logarithmic function this means it will increase exponentially faster than a standard function like A

So the answer is C

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For a-b, reduce to the least non-negative residue

Olenka [21]

Answer:

a. 6

b. 9

Step-by-step explanation:

a. The product modulo 7 can be found from the product of the individual numbers modulo 7:

(88·95·36·702) mod 7 = (88 mod 7)·(95 mod 7)·(36 mod 7)·(703 mod 7) mod 7

= (4·4·1·3) mod 7 = 48 mod 7 = 6

b. Powers of 4 mod 11 repeat with period 5:

4 mod 11 = 4

4^2 mod 11 = 5

4^3 mod 11 = 9

4^4 mod 11 = 3

4^5 mod 11 = 1

So, 4^83 mod 11 = 4^3 mod 11 = 9

3 0

4 years ago

Find the % of change in the cost of gasoline from 1970 with $1.25 and 2010 with $2.75

sashaice [31]

The rate of change is 110 percent.

3 0

4 years ago

(4 - x ≤ -1) ∩ (2 + 3x ≥ 17)

DaniilM [7]

Step-by-step answer:

Given:

two inequalities:

4-x <= -1 ........................(1)

2+3x >= 17......................(2)

Required: find the solution of the intersection of inequalities.

Solution:

Solution to (1):

4-x <= -1 transpose

4+1 <=x simplify

5 <= x rewrite

x >= 5

Solution to (2)

2+3x >= 17

3x >= 17-2

3x >= 15

x >= 5

The intersection of the two solutions x>=5 and x>=5 is therefore x>=5

Check:

x=4, => 4-4 = 0 >1 so not a solution

x=4, => 2+3(4) = 14 < 17 so not a solution

x=5, => 4-5 = -1 so a solution

x=5, => 2+3(5) = 17, so a solution.

similarly for 6, 7, ....

3 0

3 years ago

Pete is choosing his clothes for the day. His bottoms will be either cargo shorts(C) or jeans (J). His top will be T shirt (T),

Sauron [17]

The question is incomplete. Here is the complete question.

Pete is choosing his clothes for the day. His bottoms will be either cago shorts (C) or jeans (J). His top will be T-shirt (T), sweatshirt (S) or long sleeved shirt (L).

Which is a complete list of the possilbe outfits he can choose from?

CT, CS, CL, JT, JS, JL

CJ, CT, CS, CL

CJT, CJS, CJL

CT, TC, JS, SJ, CL, LC

Answer: CT, CS, CL, JT, JS, JL

Step-by-step explanation: The Fundamental Counting Principle is a method of determining a number of ways independents events can occur, i.e., it states that if there are t ways of doing something and w ways of doing another, then there are t x w ways of doing both things.

For example:

Peter has 2 choices of bottom and 3 choices of top. So, according to the principle, he will have 2 x 3 choices of clothing.

And the choices are:

shorts and t-shirt = CT

shorts and sweatshirt = CS

shorts and long sleeved = CL

jeans and T-short = JT

jeans and sweatshirt = JS

jeans and long sleeved = JL

The order he chooses doesn't matter.

So, the right alternative is CT, CS, CL, JT, JS, JL.

7 0

3 years ago

\int\limits^0_∞ cos{x} \, dx

JulijaS [17]

Answer:

$\displaystyle \int\limits^0_\infty {cos(x)} \, dx = sin(\infty)$

General Formulas and Concepts:

Pre-Calculus

Unit Circle
Trig Graphs

Calculus

Limits
Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$
Integrals
Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$
Trig Integration
Improper Integrals

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^0_\infty {cos(x)} \, dx$

Step 2: Integrate

[Improper Integral] Rewrite: $\displaystyle \lim_{a \to \infty} \int\limits^0_a {cos(x)} \, dx$
[Integral] Trig Integration: $\displaystyle \lim_{a \to \infty} sin(x) \bigg| \limits^0_a$
[Integral] Evaluate [Integration Rule - FTC 1]: $\displaystyle \lim_{a \to \infty} sin(0) - sin(a)$
Evaluate trig: $\displaystyle \lim_{a \to \infty} -sin(a)$
Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle -sin(\infty)$

Since we are dealing with infinity of functions, we can do a numerous amount of things:

Since -sin(x) is a shift from the parent graph sin(x), we can say that -sin(∞) = sin(∞) since sin(x) is an oscillating graph. The values of -sin(x) already have values in sin(x).
Since sin(x) is an oscillating graph, we can also say that the integral actually equates to undefined, since it will never reach 1 certain value.

∴ $\displaystyle \int\limits^0_\infty {cos(x)} \, dx = sin(\infty) \ or \ \text{unde}\text{fined}$

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

Unit: Improper Integrals

Book: College Calculus 10e

7 0

3 years ago

Which function increases the fastest?​

Which function increases the fastest?