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ANEK [815]
3 years ago
15

Bob's bill for dinner at surefire steak house was $45. In addition he piad 5°\° of the bill in tax and he left a tip for 15°\° o

f the bill how much did Bob spend for tax and tip combined how much did Bob spend in all?
Mathematics
1 answer:
Anuta_ua [19.1K]3 years ago
5 0

Answer:

$54

Step-by-step explanation:

First

45 times .05= 2.25

Second

45 plus 2.25

Third

45 times .15= 6.75

Fourth

45+2.25+6.75

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Find the slope of the line (-3,-2) (1,6)
nlexa [21]

Answer:

slope = 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (- 3, - 2) and (x₂, y₂ ) = (1, 6)

m = \frac{6-(-2)}{1-(-3)} = \frac{6+2}{1+3} = \frac{8}{4} = 2

5 0
3 years ago
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
3 years ago
Can someone check my answers to see if they are correct please? They are on the 2nd page. Thank you!
soldier1979 [14.2K]

Answer:

Yes, all your answers are correct.

They are correctly matched with their reasons.

3 0
2 years ago
Kevin weighed his baggage before going on a trip. In what unit did the measuring scale show the weight of his baggage? What is t
seropon [69]

Step-by-step explanation:

the answer is lbs i think

4 0
2 years ago
Which statements about opposites are true? 39 POINTS!
kramer
It only the last one.

Hope this helps :)
4 0
3 years ago
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