Pls help me.........

Find the first partial derivatives of the function f(x,y,z)=4xsin(y−z)

Amanda [17]

Answer:

$f_x(x,y,z)=4\sin (y-z)$

$f_x(x,y,z)=4x\cos (y-z)$

$f_z(x,y,z)=-4x\cos (y-z)$

Step-by-step explanation:

The given function is

$f(x,y,z)=4x\sin (y-z)$

We need to find first partial derivatives of the function.

Differentiate partially w.r.t. x and y, z are constants.

$f_x(x,y,z)=4(1)\sin (y-z)$

$f_x(x,y,z)=4\sin (y-z)$

Differentiate partially w.r.t. y and x, z are constants.

$f_y(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial y}(y-z)$

$f_y(x,y,z)=4x\cos (y-z)$

Differentiate partially w.r.t. z and x, y are constants.

$f_z(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial z}(y-z)$

$f_z(x,y,z)=4x\cos (y-z)(-1)$

$f_z(x,y,z)=-4x\cos (y-z)$

Therefore, the first partial derivatives of the function are $f_x(x,y,z)=4\sin (y-z), f_x(x,y,z)=4x\cos (y-z)\text{ and }f_z(x,y,z)=-4x\cos (y-z)$ .

4 0

3 years ago

Kenzie makes quilts from blue and purple pieces of fabric. The diagram shows the ratio of blue pieces to

REY [17]

The purple pieces are 35 and total pieces is 32 if the Kenzie makes quilts from blue and purple pieces of fabric.

<h3>What is the ratio?</h3>

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

The question is incomplete.

The complete question is in the picture, please refer to the picture.

Total number of pieces = 3+5 = 8

So, the purple pieces = 5(5/8) = 35

Total pieces = 20/(5/8) = 4×8 = 32

Thus, the purple pieces are 35 and total pieces is 32 if the Kenzie makes quilts from blue and purple pieces of fabric.

Learn more about the ratio here:

brainly.com/question/13419413

#SPJ1

3 0

2 years ago

Material for a dress costs £5.50 per metre.<br> find the cost of 10cm and 70cm

Zielflug [23.3K]

Answer:

<em>The cost of 10 cm and 70 cm are £0.55 and £3.85 respectively.</em>

Step-by-step explanation:

Material for a dress costs £5.50 per meter.

We know that, <u>1 meter = 100 cm</u>.

Suppose, the cost of 10 cm material is $x$ and the cost of 70 cm material is $y$

Now, <u>according to the ratio of "cost" to the "length of material"</u> , we will get.......

$\frac{x}{10} =\frac{5.50}{100}\\ \\ 100x=10*5.50=55\\ \\ x=\frac{55}{100}=0.55$

and

$\frac{y}{70} =\frac{5.50}{100}\\ \\ 100y=70*5.50=385\\ \\ x=\frac{385}{100}=3.85$

So, the cost of 10 cm material is £0.55 and the cost of 70 cm material is £3.85

5 0

3 years ago

The resting heart rate of an adult is usually about 60 beats per minute. Use your completed table to find approximately how many

Dvinal [7]

60x=1,000,000
----- ---------------
60 60
X=16,666 2/3 or
X=16,666.6667 it would take approximately 16,667 minutes for the average resting heart to beat 1,000,000 times.

3 0

3 years ago

PLEASE HELP FAST THANKS :)

Paladinen [302]

Answer:

x, y = 0.10

Step-by-step explanation:

5 0

3 years ago