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3 years ago

Draw a shape with 3 straight sides and 3 vertices

Mathematics

2 answers:

max2010maxim [7]3 years ago

7 0

The attached file shows a shape with 3 straight sides, and 3 vertices. This shape is also known as a triangle.

Luden [163]3 years ago

4 0

I can't draw it here but its a triangle

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Please help with the graph below!

sleet_krkn [62]

Answer:

definitely B

Step-by-step explanation:

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3 years ago

You are given the polar curve r = e^θ

galina1969 [7]

The tangent to $r(\theta)=e^\theta$ has slope $\frac{\mathrm dy}{\mathrm dx}$ , where

$\begin{cases}x(\theta)=r(\theta)\cos\theta\\y(\theta)=r(\theta)=\sin\theta\end{cases}$

By the chain rule, we have

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

and by the product rule,

$\dfrac{\mathrm dx}{\mathrm d\theta}=\dfrac{\mathrm dr}{\mathrm d\theta}\cos\theta-r(\theta)\sin\theta$

$\dfrac{\mathrm dy}{\mathrm d\theta}=\dfrac{\mathrm dr}{\mathrm d\theta}\sin\theta+r(\theta)\cos\theta$

so that with $\frac{\mathrm dr}{\mathrm d\theta}=e^\theta$ , we get

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}=-\dfrac{1+\sin(2\theta)}{\cos(2\theta)}$

The tangent line is horizontal when the slope is 0; this happens for

$-\dfrac{1+\sin(2\theta)}{\cos(2\theta)}=0\implies\sin(2\theta)=-1\implies2\theta=-\dfrac\pi2+2n\pi\implies\theta=-\dfrac\pi4+n\pi$

where $n$ is any integer. In the interval $0\le\theta\le2\pi$ , this happens for $n=1,2$ , or

$\theta=\dfrac{3\pi}4\text{ and }\theta=\dfrac{7\pi}4$

i.e at the points

$(r,\theta)=\left(e^{3\pi/4},\dfrac{3\pi}4\right)$

and

$(r,\theta)=\left(e^{7\pi/4},\dfrac{7\pi}4\right)$

8 0

3 years ago

What is the surface area of a sphere with a radius of 12 units?

seraphim [82]

Answer:

Step-by-step explanation:

The surface area (A) of a sphere is calculated as

A = 4πr² ← r is the radius, here r = 12, hence

A = 4π × 12²

= 4π × 144 = 576π units² → C

6 0

4 years ago

Is the opposite of the direction in which the hands of a clock move

Mnenie [13.5K]

Counter clockwise i assume

6 0

3 years ago

What is (4x+1)(4x+1)

aksik [14]

Answer:

(4x+1)^2

Step-by-step explanation:

Anything times itself is itself squared

5 0

3 years ago

Read 2 more answers