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3 years ago

What is the slope of a line that is parallel to the x-axis?

Mathematics

1 answer:

JulijaS [17]3 years ago

3 0

The gradient of x axis is zero. As such, the gradient of the line parallel to x-axis can only be zero

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The teacher writes 10/12 on the board. He asks students to write the fraction in simplest form. Who writes the correct answer?

Sindrei [870]

In simplest form it is 5/6

6 0

3 years ago

Read 2 more answers

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: <em>derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus</em>

3 0

3 years ago

HELP PLEASE!!!!!!!!!!!!

Bogdan [553]

Answer:

See the explanation.

Step-by-step explanation:

We are given the function f(x) = x² + 2x - 5

Zeros :

If f(x) = 0 i.e. x² + 2x - 5 = 0

The left hand side can not be factorized. Hence, use Sridhar Acharya formula and

$x= \frac{-2+\sqrt{2^{2}-4\times(-5)\times1 } }{2}$ and

$x= \frac{-2-\sqrt{2^{2}-4\times(-5)\times1 } }{2}$

⇒ x = -3.45 and 1.45

Y- intercept :

Putting x = 0, we get, f(x) = - 5, Hence, y-intercept is -5.

Maximum point :

Not defined

Minimum point:

The equation can be expressed as (x + 1)² = (y + 5)

This is an equation of parabola having the vertex at (-1,-5) and axis parallel to + y-axis

Therefore, the minimum point is (-1,-5)

Domain :

x can be any real number

Range:

f(x) ≥ - 6

Interval of increase:

Since this is a parabola having the vertex at (-1,-5) and axis parallel to + y-axis.

Therefore, interval of increase is +∞ > x > -1

Interval of decrease:

-∞ < x < -1

End behavior :

$f(x) = x^{2} +2x-5 =x^{2} (1+\frac{2}{x} -\frac{5}{x^{2} } )$

So, as x tends to +∞ , then f(x) tends to +∞

And as x tends to -∞, then f(x) tends to +∞. (Answer)

7 0

2 years ago

. The psychology club is having a self-proclaimed psychic come to their campus fund-raising event to demonstrate his abilities.

ElenaW [278]

Answer:

the club looses 12.50$

Step-by-step explanation:

125 tickets * 1.50$ per ticket

125 * 1.50 = 187.5 earned

200$ fee for psychic - 187.5$ earned

200 - 187.5 = 12.5

the club will lose 12.50$

(this psychic seems like a bit of a scam lol)

3 0

3 years ago

Find the equation of the line that is parallel to x=6y-5 and that passes through (5,-3). express answer in standard form

Anestetic [448]

Answer:

Final answer is $x-6y=23$

Step-by-step explanation:

We need to find the equation of the line that is parallel to x=6y-5 and that passes through (5,-3).

So first we need to find the slope of given line.

rewirite x=6y-5 in y=mx+b form

x+5=6y

$\frac{1}{6}x+\frac{5}{6}=y$

Compare given equation with y=mx+b

we get: m=1/6

We know that parallel equations has equal slope.

Then slope of required line m=1/6

Now plug the given point (5,-3) and slope m=1/6 into point slope formula:

$y-y_1=m\left(x-x_1\right)$

$y-(-3)=\frac{1}{6}\left(x-5\right)$

$y+3=\frac{1}{6}x-\frac{5}{6}$

$y=\frac{1}{6}x-\frac{5}{6}-3$

$y=\frac{1}{6}x-\frac{23}{6}$

Now we need to rewrite that equation in standard form. Ax+By=C.

6y=x-23

x-23=6y

x-6y=23

Hence final answer is $x-6y=23$

6 0

3 years ago