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3 years ago

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Please help me solve it

1 answer:

Vilka [71]3 years ago

3 0

Step-by-step explanation:

D

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If -y-2x^3=Y^2 then find D^2y/dx^2 at the point (-1,-2) in simplest form

algol13

Answer:

$\frac{d^2y}{dx^2} = \frac{-4}{3}$

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

<u>Algebra I</u>

Factoring

<u>Calculus</u>

Implicit Differentiation

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

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

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

Quotient Rule: $\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

<u>Step 1: Define</u>

-y - 2x³ = y²

Rate of change of tangent line at point (-1, -2)

<u>Step 2: Differentiate Pt. 1</u>

<em>Find 1st Derivative</em>

Implicit Differentiation [Basic Power Rule]: $-y'-6x^2=2yy'$
[Algebra] Isolate <em>y'</em> terms: $-6x^2=2yy'+y'$
[Algebra] Factor <em>y'</em>: $-6x^2=y'(2y+1)$
[Algebra] Isolate <em>y'</em>: $\frac{-6x^2}{(2y+1)}=y'$
[Algebra] Rewrite: $y' = \frac{-6x^2}{(2y+1)}$

<u>Step 3: Differentiate Pt. 2</u>

<em>Find 2nd Derivative</em>

Differentiate [Quotient Rule/Basic Power Rule]: $y'' = \frac{-12x(2y+1)+6x^2(2y')}{(2y+1)^2}$
[Derivative] Simplify: $y'' = \frac{-24xy-12x+12x^2y'}{(2y+1)^2}$
[Derivative] Back-Substitute <em>y'</em>: $y'' = \frac{-24xy-12x+12x^2(\frac{-6x^2}{2y+1} )}{(2y+1)^2}$
[Derivative] Simplify: $y'' = \frac{-24xy-12x-\frac{72x^4}{2y+1} }{(2y+1)^2}$

<u>Step 4: Find Slope at Given Point</u>

[Algebra] Substitute in <em>x</em> and <em>y</em>: $y''(-1,-2) = \frac{-24(-1)(-2)-12(-1)-\frac{72(-1)^4}{2(-2)+1} }{(2(-2)+1)^2}$
[Pre-Algebra] Exponents: $y''(-1,-2) = \frac{-24(-1)(-2)-12(-1)-\frac{72(1)}{2(-2)+1} }{(2(-2)+1)^2}$
[Pre-Algebra] Multiply: $y''(-1,-2) = \frac{-48+12-\frac{72}{-4+1} }{(-4+1)^2}$
[Pre-Algebra] Add: $y''(-1,-2) = \frac{-36-\frac{72}{-3} }{(-3)^2}$
[Pre-Algebra] Exponents: $y''(-1,-2) = \frac{-36-\frac{72}{-3} }{9}$
[Pre-Algebra] Divide: $y''(-1,-2) = \frac{-36+24 }{9}$
[Pre-Algebra] Add: $y''(-1,-2) = \frac{-12}{9}$
[Pre-Algebra] Simplify: $y''(-1,-2) = \frac{-4}{3}$

6 0

3 years ago

A product code consists of four letters followed by five digits. Only the letters X, Y, and Z can be used ( and any of the digit

Morgarella [4.7K]

Answer:

$\frac{49}{81}$ , 60.494%

Step-by-step explanation:

I am going to try to tackle this. I might miss a step as I am currently taking discrete mathematics.

We want to find all the possibilities with 1y, 2ys, 3ys, and 4ys, out of all total possibilities.

_ _ _ _ _ _ _ _ _

For the letters, in each spot, we have 3 choices. For the numbers, we have 10 choices in each spot

so

3*3*3*3 * 10*10*10*10*10

= 81*100000

= 8100000

The number of Y's will never affect the number of permutations of the numbers.

So:

For 1 y, we have

Y _ _ _ * 10*10*10*10*10

But we also have

_ Y _ _

_ _ Y _

and

_ _ _ Y

So we can multiply the number we get in one calculation by 4

4 *

Y _ _ _ * 10*10*10*10*10

2*2*2 * 10*10*10*10*10

= 800000 * 4 = 3200000

For 2 y's, we have

YY _ _

_ YY _

__ YY

3*

YY 2*2 * 10^5

4 * 100000

400000 * 3 = 1200000

For 3 y's, we have

YYY _

_ YYY

2 *

YYY 2 * 10^5

200000 * 2

= 400000

For 4 y's, we have

YYYY * 10^5

100000

Now we can add them all up and divide it by our original number 8100000

$\frac{100000 + 400000 + 1200000 + 3200000}{8100000} = \frac{49}{81}$

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3 years ago

How to do a multi step problem

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Luke and Matthew ran a lemonade stand on Saturday. They agreed that Matthew would get 60%, percent of the profit because the lem

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4 years ago