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2 years ago

the proper scientific notation for 676,000,000,000 is a. .676 × 1012 b. 6.76 × 1011 c. 67.6 × 1010 d. 676 × 109

Mathematics

1 answer:

Iteru [2.4K]2 years ago

8 0

The answer is either c of d but if I had to pick one I would say C.

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The cone shown has a volume of 48 pi cubic inches. what is the radius of the cone?

Basile [38]

Answer:

r = 4 inches

Step-by-step explanation:

$V=\frac{\pi*r^{2}*h}{3}\\ \\48*\pi*3=\pi*r^{2}*9\\\\\\r^{2}=\frac{48*\pi*3}{\pi*9}\\ \\r^{2}=\frac{48}{3}\\ \\\\r^{2}=16\\ \\r=4~inches$

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3 years ago

PLEASE ANSWER QUICK 15 POINTS

Licemer1 [7]

The answer to this problem would be D since you cannot solve for .33, or put into a fraction.

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2 years ago

How many different lines pass through a 3x3-point grid if a line only needs two points?

lions [1.4K]

Answer:

How many different lines pass through a 3x3-point grid if a line only needs two points?

Step-by-step explanation:

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7 0

2 years ago

Read 2 more answers

Use the Chain Rule (Calculus 2)

atroni [7]

1. By the chain rule,

$\dfrac{\mathrm dz}{\mathrm dt}=\dfrac{\partial z}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial z}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}$

I'm going to switch up the notation to save space, so for example, $z_x$ is shorthand for $\frac{\partial z}{\partial x}$ .

$z_t=z_xx_t+z_yy_t$

We have

$x=e^{-t}\implies x_t=-e^{-t}$

$y=e^t\implies y_t=e^t$

$z=\tan(xy)\implies\begin{cases}z_x=y\sec^2(xy)=e^t\sec^2(1)\\z_y=x\sec^2(xy)=e^{-t}\sec^2(1)\end{cases}$

$\implies z_t=e^t\sec^2(1)(-e^{-t})+e^{-t}\sec^2(1)e^t=0$

Similarly,

$w_t=w_xx_t+w_yy_t+w_zz_t$

where

$x=\cosh^2t\implies x_t=2\cosh t\sinh t$

$y=\sinh^2t\implies y_t=2\cosh t\sinh t$

$z=t\implies z_t=1$

To capture all the partial derivatives of $w$ , compute its gradient:

$\nabla w=\langle w_x,w_y,w_z\rangle=\dfrac{\langle1,-1,1\rangle}{\sqrt{1-(x-y+z)^2}}}=\dfrac{\langle1,-1,1\rangle}{\sqrt{-2t-t^2}}$

$\implies w_t=\dfrac1{\sqrt{-2t-t^2}}$

2. The problem is asking for $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$ . But $z$ is already a function of $x,y$ , so the chain rule isn't needed here. I suspect it's supposed to say "find $\frac{\partial z}{\partial s}$ and $\frac{\partial z}{\partial t}$ " instead.

If that's the case, then

$z_s=z_xx_s+z_yy_s$

$z_t=z_xx_t+z_yy_t$

as the hint suggests. We have

$z=\sin x\cos y\implies\begin{cases}z_x=\cos x\cos y=\cos(s+t)\cos(s^2t)\\z_y=-\sin x\sin y=-\sin(s+t)\sin(s^2t)\end{cases}$

$x=s+t\implies x_s=x_t=1$

$y=s^2t\implies\begin{cases}y_s=2st\\y_t=s^2\end{cases}$

Putting everything together, we get

$z_s=\cos(s+t)\cos(s^2t)-2st\sin(s+t)\sin(s^2t)$

$z_t=\cos(s+t)\cos(s^2t)-s^2\sin(s+t)\sin(s^2t)$

8 0

2 years ago

Whats this answer i need it fast uwu

IrinaVladis [17]

Find slope (y2-y1)/(x2-x1)
Pick points: (1,10) , (2,8)
(8-10)/(2-1) = -2/1 = -2
Y = -2x + b
10 = -2 + b, b = 12
It would be the first response
12 = initial while -2 is rate of change

3 0

2 years ago