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yuradex [85]
4 years ago
7

2 points) Suppose w=xy+yzw=xy+yz, where x=et, y=2+sin(t)x=et, y=2+sin⁡(t), and z=2+cos(3t)z=2+cos⁡(3t). A ) Use the chain rule t

o find dwdtdwdt as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite etet as x. dwdtdwdt = Note: You may want to use exp() for the exponential function. Your answer should be an expression in x, y, z, and t; e.g. "3x - 4y" B ) Use part A to evaluate dwdtdwdt when t=0t=0.
Mathematics
2 answers:
Olenka [21]4 years ago
6 0

Answer:

\frac{\partial w}{\partial t}  = y(e^t) +(x+z)*(cos(t))  - 3y*sin(3t)

Step-by-step explanation:

First, note that

\frac{\partial x}{\partial t}  = e^{t} \\\frac{\partial y}{\partial t}  = cos(t)\\

And using the chain rule in one variable

\frac{\partial z}{\partial t}  = -3sin(3t)

Now remember that the chain rule in several variables sates that

\frac{\partial w}{\partial t}  = \frac{\partial w}{\partial x} * \frac{\partial x}{\partial t} + \frac{\partial w}{\partial y} * \frac{\partial y}{\partial t} + \frac{\partial w}{\partial z} * \frac{\partial z}{\partial t}

Therefore the chain rule in several variables would look like this.

\frac{\partial w}{\partial t}  = y(e^t) +(x+z)*(cos(t))  - 3y*sin(3t)

skelet666 [1.2K]4 years ago
6 0

Answer:

At t = 0

dw/dt = x + y + z

Step-by-step explanation:

Since w is a function of x, y, z

dw/dt = w_x • x_t + w_y • y_t + w_z • z_t

Given w = xy + yz

w_x = y

w_y = x + z

w_z = y

Given

x = e^t

y = 2 + sin(t)

z = 2 + cos(3t)

x_t = e^t

y_t = cos(t)

z_t = -3sin(3t)

Using all these,

dw/dt = ye^t + (x + z)cos(t) - 3ysin(t)

At t = 0

dw/dt = y + x + z

dw/dt = x + y + z

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Convert them to comparable thingummys

convert to fraction

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30%=30/100=3/10

3/10 vvs 1/3
make bottom number 30

3/10 times 3/3=9/30

1/3 times 10/10=10/30
10/30>9/30


1/3 is bigger


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3 years ago
What is the equation of a line that contains the points (2,-2) and (0, -2)? y = 0
kvasek [131]
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In the year 2019, Lee County used approximately 55 million gallons of water. Historical trends show that each year the water dem
Harlamova29_29 [7]

Answer:

Approximately 62 gallons of water will be used by Lee County by the year 2025.

Step-by-step explanation:

The amount, in millions gallons of water, spent by Lee County, in t years after 2019, is given by the following equation:

P(t) = P(0)(1 + r)^{t}

In which P(0) is the amount spent on 2019 and r is the increse rate, as a decimal.

In the year 2019, Lee County used approximately 55 million gallons of water.

This means that P(0) = 55

Historical trends show that each year the water demand is increasing by a rate of approximately 2.1%.

This means that r = 0.021

So

P(t) = P(0)(1 + r)^{t}

P(t) = 55(1 + 0.021)^{t}

P(t) = 55(1.021)^{t}

Approximately how many million gallons of water will be used by Lee County by the year 2025?

2025 is 2025 - 2019 = 6 years after 2019. So this is P(6).

P(t) = 55(1.021)^{t}

P(6) = 55(1.021)^{6}

P(6) = 62.3

Rounded to the nearest millions

Approximately 62 gallons of water will be used by Lee County by the year 2025.

3 0
3 years ago
A cookie recipe states for every 3 cups of flour, 1.5 teaspoons of vanilla are
guapka [62]

Answer:

2.5 Teaspoons of vanilla are needed.

Step-by-step explanation:

If 3 cups of flour is 1.5 teaspoons of vanilla. 1.5 /3=.5 Meaning there is .5 teaspoons of vanilla per cup of flour.

If you have 5 cups of flour   5 x .5= 2.5 (teaspoons)

7 0
3 years ago
Someone help and solve for X
IgorC [24]

Step-by-step explanation:

since all angles add up to 180:

(8x-1)+(3x+4)+(3x+9)=180

add like terms:

14x+12=180

x=12

Hope that helps :)

7 0
3 years ago
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