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3 years ago

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Mathematics

1 answer:

Setler79 [48]3 years ago

8 0

Answer:

g(x) = 5x + 2.

r(x) = x

b(x) = 1/2 x³

k(x) = - 3 x + 1

Step-by-step explanation:

The function notation ⇒ it is the form to write the function, It is meant to be a precise way of giving information about the function, like f(x) , v(x) and so on.

Given the following:

g(x) = 5x + 2.

y = 1 x

h = x²

r(x) = x

f/x = x⁵ - 3

b(x) = 1/2 x³

p/x = -7x

k(x) = - 3 x + 1

y = mx + b

fx = -x³ + 4

So, in the given options the following are in function notations:

g(x) = 5x + 2.

r(x) = x

b(x) = 1/2 x³

k(x) = - 3 x + 1

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Two ladders are leaning against a building, forming two similar triangles as shown below. The top of the longer ladder is 28 fee

postnew [5]

Answer:

The length of the longer ladder is 35 ft

Step-by-step explanation:

Please check the attachment for a diagrammatic representation of the problem

We want to calculate the length of the longer ladder ;

We make reference to the diagram

Since the two right triangles formed are similar. the ratios of their sides are equal;

Thus;

20/15 = 28/x + 15

20(x + 15) = 15(28)

20x + 300 = 420

20x = 420-300

20x = 120

x = 120/20

x = 6

So we want to calculate the hypotenuse of a right triangle with other sides 28ft and 21 ft

To do this, we use the Pythagoras’ theorem which states that square of the hypotenuse equals the sum of the squares of the two other sides

Let the hypotenuse be marked x

x^2 = 28^2 + 21^2

x^2 = 1,225

x = √1225

x = 35 ft

7 0

2 years ago

Solve If QR = 6x + 1, PR = 14x - 13, and PQ = 5x - 2, find PR

solong [7]

Answer:

P____Q____R

PR= PQ+ QR

(14x-13) = (5x-2)+(6x+1)

14x-13= 11x – 1

14x – 11x = 13–1

3x = 12

x= 12/ 3

x= 4

PR= 14x – 13 = 14 (4) – 13 = 18 – 13= 5

If you want (PQ , QR ) this is the solution

PQ =5x-2=5(4)-2=20-2=18

QR =6x+1=6(4)+1=24+1=25

I hope I helped you^_^

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3 years ago

A small pouch contains 8 black marbles, 5 white marbles, and 12 red marbles. What is the probability of picking a red then a bla

Alina [70]

Answer:

8/600

Step-by-step explanation:

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3 years ago

Convert 1000100 two to base sixteen

Shalnov [3]

Answer:

(44)₁₆

Step-by-step explanation:

to convert it into hexa decimal we have select four pair of binary digit

(1000100)₂→(?)₁₆

100 0100

to solve this we have to no the decimal conversion of

0100 which is '4'

so,

conversion of (1000100)₂→(44)₁₆

4 0

3 years ago

Differentiate the function. y = (3x - 1)^5(4-x^4)^5

TiliK225 [7]

Answer:

$\displaystyle y' = -5(3x-1)^4(4 - x^4)^4(15x^4 - 4x^3 - 12)$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Distributive Property

Algebra I

Terms/Coefficients
Factoring

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

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

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

Step-by-step explanation:

Step 1: Define

Identify

y = (3x - 1)⁵(4 - x⁴)⁵

Step 2: Differentiate

Product Rule: $\displaystyle y' = \frac{d}{dx}[(3x - 1)^5](4 - x^4)^5 + (3x - 1)^5\frac{d}{dx}[(4 - x^4)^5]$
Chain Rule [Basic Power Rule]: $\displaystyle y' =[5(3x - 1)^{5-1} \cdot \frac{d}{dx}[3x - 1]](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^{5-1} \cdot \frac{d}{dx}[(4 - x^4)]]$
Simplify: $\displaystyle y' =[5(3x - 1)^4 \cdot \frac{d}{dx}[3x - 1]](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^4 \cdot \frac{d}{dx}[(4 - x^4)]]$
Basic Power Rule: $\displaystyle y' =[5(3x - 1)^4 \cdot 3x^{1 - 1}](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^4 \cdot -4x^{4-1}]$
Simplify: $\displaystyle y' =[5(3x - 1)^4 \cdot 3](4 - x^4)^5 + (3x - 1)^5[5(4 - x^4)^4 \cdot -4x^3]$
Multiply: $\displaystyle y' = 15(3x - 1)^4(4 - x^4)^5 - 20x^3(3x - 1)^5(4 - x^4)^4$
Factor: $\displaystyle y' = 5(3x-1)^4(4 - x^4)^4\bigg[ 3(4 - x^4) - 4x^3(3x - 1) \bigg]$
[Distributive Property] Distribute 3: $\displaystyle y' = 5(3x-1)^4(4 - x^4)^4\bigg[ 12 - 3x^4 - 4x^3(3x - 1) \bigg]$
[Distributive Property] Distribute -4x³: $\displaystyle y' = 5(3x-1)^4(4 - x^4)^4\bigg[ 12 - 3x^4 - 12x^4 + 4x^3 \bigg]$
[Brackets] Combine like terms: $\displaystyle y' = 5(3x-1)^4(4 - x^4)^4(-15x^4 + 4x^3 + 12)$
Factor: $\displaystyle y' = -5(3x-1)^4(4 - x^4)^4(15x^4 - 4x^3 - 12)$

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

Unit: Derivatives

Book: College Calculus 10e

6 0

3 years ago