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3 years ago

Show all your work for 3 4 and 5, please

Mathematics

2 answers:

drek231 [11]3 years ago

7 0

Answer:

I can't see the picture so I can't sovle it

Step-by-step explanation:

klio [65]3 years ago

4 0

3. 1/15

explanation:
-3/5 and -2/3 need the same denominator so multiply them so that they equal the same. so multiply -3/5 by 3 and then -2/3 by 5. so that equals: -9/15 -(-10/15). The minis a negative cancels out and it becomes plus. so -9 plus 10 is 1 and 15 stays the same. so 1/15.

4. -5.2

explanation:
a negative (-2.5) subtracted by a technically smaller negative (-5.2) will equal a positive number

5.B

i just used a calculator tbh

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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

I need help please with this

lord [1]

Answer:

no.

Step-by-step explanation:

nigerians are cool

6 0

3 years ago

The circulation of a newsletter decreased from 5300 to 3630. Find the percent of decrease in circulation to the nearest percent.

Rainbow [258]

((3,630−5,300)÷5,300)×100=−31.5%

8 0

3 years ago

What is the surface area of the cylinder with height 7 cm and radius 5 cm? Round

nalin [4]

Answer:

376.991 cm²

Step-by-step explanation:

$SA_{cylinder} = 2\pi r^{2} + 2\pi rh$

Surface Area = 2π(5²) + 2π(5)(7)

= 50π + 70π

= 120π

= 376.9911184... ≈ 376.991

<h2>Derive Surface Area of A Cylinder</h2>

If you take a look at a net of a cylinder, you can see it is composed of two circles(bases) and a rectangular strip with the length of the diameter of the circle

The formula for the area of a circle = πr², and since there are 2, it is 2πr²

The formula for circumference of a circle = 2πr, and since we are multiplying that by the height by the height of the cylinder, it is 2πrh

∴ 2πr² + 2πrh

5 0

3 years ago

Luca made a scale drawing of the auditorium. in real life, the stage is 45 feet long. it is 18

ollegr [7]

Answer:

30:1

Step-by-step explanation:

45*12 = 540

540/18 = 30

8 0

2 years ago