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2 years ago

Use the quadratic formula to solve for x. 4x2 +9x-1=0

Mathematics

1 answer:

insens350 [35]2 years ago

5 0

Answer:

$x=\frac{-9\pm\sqrt{65} }{8}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Standard Form: ax² + bx + c = 0
Quadratic Formula: $x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Step-by-step explanation:

Step 1: Define

4x² + 9x - 1 = 0

Step 2: Define variables

a = 4

b = 9

c = -1

Step 3: Find roots

Substitute: $x=\frac{-9\pm\sqrt{9^2-4(4)(-1)} }{2(4)}$
Exponents: $x=\frac{-9\pm\sqrt{81-4(4)(-1)} }{2(4)}$
Multiply: $x=\frac{-9\pm\sqrt{81-16} }{8}$
Subtract: $x=\frac{-9\pm\sqrt{65} }{8}$

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Basile [38]

The answer is 1 by multiplying by itself

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3 years ago

How to find the derivative of cos^2x? i seem to be confused.

slamgirl [31]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2927231

————————

You can actually use either the product rule or the chain rule for this one. Observe:

• Method I:

y = cos² x

y = cos x · cos x

Differentiate it by applying the product rule:

$\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x\cdot cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x)\cdot cos\,x+cos\,x\cdot \dfrac{d}{dx}(cos\,x)}$

The derivative of cos x is – sin x. So you have

$\mathsf{\dfrac{dy}{dx}=(-sin\,x)\cdot cos\,x+cos\,x\cdot (-sin\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=-sin\,x\cdot cos\,x-cos\,x\cdot sin\,x}$

$\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark$

—————

• Method II:

You can also treat y as a composite function:

$\left\{\!
\begin{array}{l}
\mathsf{y=u^2}\\\\
\mathsf{u=cos\,x}
\end{array}
\right.$

and then, differentiate y by applying the chain rule:

$\mathsf{\dfrac{dy}{dx}=\dfrac{dy}{du}\cdot \dfrac{du}{dx}}\\\\\\
\mathsf{\dfrac{dy}{dx}=\dfrac{d}{du}(u^2)\cdot \dfrac{d}{dx}(cos\,x)}$

For that first derivative with respect to u, just use the power rule, then you have

$\mathsf{\dfrac{dy}{dx}=2u^{2-1}\cdot \dfrac{d}{dx}(cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=2u\cdot (-sin\,x)\qquad\quad (but~~u=cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=2\,cos\,x\cdot (-sin\,x)}$

and then you get the same answer:

$\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark$

I hope this helps. =)

Tags: derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus

3 0

3 years ago

Answer fast please!

zepelin [54]

I believe it's A but it's not exactly clear

6 0

3 years ago

Read 2 more answers

Jan age is 3 less than the twice triss agethe sum of thier ages is 30

tresset_1 [31]

Jan is 19, Triss is 11.

3 0

2 years ago

Please help me with my homework I don't understand it

Damm [24]

Answer:

Part A:

0.1111111111111 = 1/9

Part B:

Step-by-step explanation:

Part A:

When I put 0.111111111 into my calculator I get a conversion of 1/9.

Part B:

The fraction 1/9 means that for every 9 kids he surveyed, 1 of them replied "yes."

So covert 1/9 into x/27

27/9 = 3 which means 9 goes into 27, 3 times.

Multiply 1 by 3.

1 x 3 = 3

Put into fraction form

3/27

This means 3 students out of 27 answered "yes."

6 0

3 years ago

Use the quadratic formula to solve for x. 4x2 +9x-1=0​

Use the quadratic formula to solve for x. 4x2 +9x-1=0