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3 years ago

A theorem is proved using a geometric proof. True or False?

1 answer:

6 0

A theorem is defined as an existing fact that was proved to be correct through experimentation or mathematical reasoning. In this case, we can say that a theorem can be proven by geometric proof as it is required for people to consider it as a fact. Answer is true.

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What are you required to do when you buy in bulk to save money??

beks73 [17]

Spend more money on a bigger product

8 0

2 years ago

Read 2 more answers

SAFE 42s + 32s + s - 42s

Marrrta [24]

75 S is the answer :)

5 0

2 years ago

PLEASE HELP ASAP WILL MARK BRAINLIEST Solve the quadratic equation 18x^2 -153x -172 =0

Vika [28.1K]

Answer:

The answer is : x = 9.505 and x = -1.005

Step-by-step explanation:

To solve the quadratic equation use the formula :

$x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

Where a is the coefficient of x² , b is the coefficient of x and c is the numerical term

∵ a = 18 , b = -153 and c = -172

∴ $x=\frac{-(-153)+\sqrt{(-153)^{2}-4(18)(-172) } }{2(18)}$

$x = \frac{18+\sqrt{35793} }{36} &x=\frac{18-\sqrt{35793} }{36}$

∴ x = 9.505 and x = -1.005

8 0

2 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

Ms. Ramirez has a class of 15 students. She can spend $18 on each student to buy math supplies for the year. She first buys all

Aloiza [94]

Answer:7.775

Step-by-step explanation:

So u do 130.05 ÷18 =7.225

Now u do 15 - 7.225 = 7.775

7.775 is the money she can still spend for them.

Also u could do 15 x 18 = 270

270 ÷ 2 = 135

8 0

3 years ago