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3 years ago

Slope intercept form of y+3= 1/2(x-2)?

Mathematics

1 answer:

WITCHER [35]3 years ago

8 0

The slope intercept form looks like y=mx+b (m-slope, b is the y intercept)

y+3=1/2(x-2)
y=(1/2)x-(2/2)-3

y=(1/2)x-4

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A rectangle has a length of 3x-5 and a width of 2x+9.

Montano1993 [528]

Step-by-step explanation:

l = 3x - 5

w = 2x + 9

perimeter = 2l + 2w = 2(3x - 5) + 2(2x + 9) =

= 6x - 10 + 4x + 18 = 10x + 8

area = l×w = (3x - 5)(2x + 9) = 6x² + 27x - 10x - 45 =

= 6x² + 17x - 45

8 0

2 years ago

Decide whether the change is an increase or a decrease, and find the percent change. Original number = 35; New number = 16.... P

Elodia [21]

Answer: 60 decrease or 150 decrease

Step-by-step explanation:

3 0

3 years ago

6 yd 3 yd 8 yd equal what?

Kamila [148]

Hello!

Answer:

17 yards

Step-by-step explanation:

Hope this helps have a wonderful day! :3

7 0

2 years ago

Read 2 more answers

if log 2 = ( 0.3010 ), Log 3 = ( 0.4771 ) and Log 5 = ( 0.6990 ) then find the value of the following: Log 24... The answer is (

tekilochka [14]

Answer: 1. 3801

Step-by-step explanation:

Log 24 = Log(8x3)

From the laws of Logarithm

Log ( a xb) = Log a + Log b

so, Log (8x3) = Log8 + Log 3

Also Log 8 can be written as Log $2^{3}$ since $2^{3}$ is still 8 , so the expression becomes

Log $2^{3}$ + Log 3

⇒ 3 Log 2 + Log 3

since the value of Log 2 and Log 3 has been given , substitute into the expression , we have

3 (0.3010) + 0.4771

= 0.903 + 0.4771

= 1.3801

4 0

2 years ago

Hello again! This is another Calculus question to be explained.

podryga [215]

Answer:

See explanation.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Functions

Function Notation

Exponential Property [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Property [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

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:

We are given the following and are trying to find the second derivative at x = 2:

$\displaystyle f(2) = 2$

$\displaystyle \frac{dy}{dx} = 6\sqrt{x^2 + 3y^2}$

We can differentiate the 1st derivative to obtain the 2nd derivative. Let's start by rewriting the 1st derivative:

$\displaystyle \frac{dy}{dx} = 6(x^2 + 3y^2)^\big{\frac{1}{2}}$

When we differentiate this, we must follow the Chain Rule: $\displaystyle \frac{d^2y}{dx^2} = \frac{d}{dx} \Big[ 6(x^2 + 3y^2)^\big{\frac{1}{2}} \Big] \cdot \frac{d}{dx} \Big[ (x^2 + 3y^2) \Big]$

Use the Basic Power Rule:

$\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} (2x + 6yy')$

We know that y' is the notation for the 1st derivative. Substitute in the 1st derivative equation:

$\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 6y(6\sqrt{x^2 + 3y^2}) \big]$

Simplifying it, we have:

$\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]$

We can rewrite the 2nd derivative using exponential rules:

$\displaystyle \frac{d^2y}{dx^2} = \frac{3\big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]}{\sqrt{x^2 + 3y^2}}$

To evaluate the 2nd derivative at x = 2, simply substitute in x = 2 and the value f(2) = 2 into it:

$\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = \frac{3\big[ 2(2) + 36(2)\sqrt{2^2 + 3(2)^2} \big]}{\sqrt{2^2 + 3(2)^2}}$

When we evaluate this using order of operations, we should obtain our answer:

$\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = 219$

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

Unit: Differentiation

5 0

2 years ago