WORTH 20 POINTS ✨HELPPP PLEASEEE

The curve

kherson [118]

Answer:

Point N(4, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Coordinates (x, y)
Functions
Function Notation
Terms/Coefficients
Anything to the 0th power is 1
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

$\displaystyle y = \sqrt{x - 3}$

$\displaystyle y' = \frac{1}{2}$

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = (x - 3)^{\frac{1}{2}}$
Chain Rule: $\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3]$
Basic Power Rule: $\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)$
Simplify: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1$
Multiply: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}$
[Derivative] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}$
[Derivative] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = \frac{1}{2\sqrt{x - 3}}$

Step 3: Solve

Find coordinates

x-coordinate

Substitute in y' [Derivative]: $\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply 2 on both sides: $\displaystyle 1 = \frac{1}{\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply √(x - 3) on both sides: $\displaystyle \sqrt{x - 3} = 1$
[Equality Property] Square both sides: $\displaystyle x - 3 = 1$
[Addition Property of Equality] Add 3 on both sides: $\displaystyle x = 4$

y-coordinate

Substitute in x [Function]: $\displaystyle y = \sqrt{4 - 3}$
[√Radical] Subtract: $\displaystyle y = \sqrt{1}$
[√Radical] Evaluate: $\displaystyle y = 1$

∴ Coordinates of Point N is (4, 1).

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

Unit: Derivatives

Book: College Calculus 10e

4 0

3 years ago

Nico can do 42 push-ups in 3 minutes.

Alchen [17]

Step-by-step explanation:

Hey there!

It is said we need to find the unit rate.

What we can do is apply Unitary Method.

3 minutes = 42 push ups

1 minute = $\sf{\bf{\dfrac{42}{3}}}$

So, 12 push ups per minute is the unit rate.

In 5 minutes, he will do 12×5 = 60 push ups!

Hope it helps :)

4 0

3 years ago

Will Mark Brainliest!!! Which statement represents the simplified form of the given equation and correctly describes the solutio

Iteru [2.4K]

The statement $14 \neq 15$ no solutions represents the simplified form of the given equation 6x + 14 = 3(2x + 5). Hence Option A is correct

Solution:

Given, equation is 6x + 14 = 3(2x + 5).

We have to find the correct options that represents the simplified form of the given equation and correctly describes the solution.

So, now let us simplify the given equation

⇒6x + 14 = 3(2x + 5) ⇒ 6x + 14 = 6x + 15 ⇒ 6x – 6x + 14 = 15 ⇒ 14 ≠ 15

As L.H.S not equals with R.H.S, no value of x can satisfy the equation and there will be no solution for given equation.

Hence, option A is correct.

4 0

3 years ago

Which is an estimate of square root of 15 to one decimal place?

Wewaii [24]

3.9 is the estimated square root of 15 to one decimal place

8 0

3 years ago

Read 2 more answers

How many kilometers did they drive per hour

Elza [17]

The distance from San Francisco to New York is 4140 km. Since the question asks how long it took the Humphrey family in km/hr (kilometers per hour), you would just divide 4140km by 6.
Why? Because it took them 6 hours to make a trip of 4140 km. Dividing 4140 by 6 gives you the distance they traveled per hour.

690 km/hr

3 0

4 years ago