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3 years ago

Fill in the blank with the correct term or number to complete the sentence.

Mathematics

1 answer:

Furkat [3]3 years ago

4 0

Mentally, they are numbers in which you can do mental math with since they are whole numbers

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Consider F and C below. F(x, y, z) = y2 sin(z) i + 2xy sin(z) j + xy2 cos(z) k C: r(t) = t2 i + sin(t) j + t k, 0 ≤ t ≤ π (a) Fi

Liono4ka [1.6K]

Answer:

a) $f (x,y,z)= xy^2\sin(z)$

b) $\int_C F \cdot dr =0$

Step-by-step explanation:

Recall that given a function f(x,y,z) then $\nabla f = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})$ . To find f, we will assume it exists and then we will find its form by integration.

First assume that F = $\nabla f$ . This implies that

$\frac{\partial f}{\partial x} = y^2\sin(z)$ if we integrate with respect to x we get that

$f(x,y,z) = xy^2\sin(z) + g(y,z)$ for some function g(y,z). If we take the derivative of this equation with respect to y, we get

$\frac{\partial f}{\partial y} = 2xy\sin(z) + \frac{\partial g}{\partial y}$

This must be equal to the second component of F. Then

$2xy\sin(z) + \frac{\partial g}{\partial y}=2xy\sin(z)$

This implies that $\frac{\partial g}{\partial y}=0$ , which means that g depends on z only. So $f(x,y,z) = xy^2\sin(z) + g(z)$

Taking the derivative with respect to z and making it equal to the third component of F, we get

$xy^2\cos(z)+\frac{dg}{dz} = xy^2\cos(z)$

which implies that $\frac{dg}{dz}=0$ which means that g(z) = K, where K is a constant. So

$f (x,y,z)= xy^2\sin(z)$

b) To evaluate $\int_C F \cdot dr$ we can evaluate it by using f. We can calculate the value of f at the initial and final point of C and the subtract them as follows.

$\int_C F \cdot dr = f(r(\pi))-f(r(0))$

Recall that $r(\pi) = (\pi^2, 0, \pi)$ so $f(r(\pi)) = \pi^2\cdot 0 \cdot \sin(\pi) = 0$

Also $r(0) = (0, 0, 0)$ so $f(r(0)) = 0^2\cdot 0 \cdot \sin(0) = 0$

So $\int_C F \cdot dr =0$

5 0

2 years ago

How many ways can you arange the letters in the word cube

Margarita [4]

You could four times because there are four letters in the word cube, so there are only four possible ways you could spell it.

Hope this helps:)
Plz rate branliest

3 0

2 years ago

3. Graph y=-4x² – 2 and its inverse. (1 point)

madam [21]

Function and its inverse was graphed.

<u>Step-by-step explanation:</u>

y = -4x²- 2

To find the inverse function of y = -4x²- 2 we have to transform the formula to calculate x in terms of y.

y = -4x²- 2

-4x² = y - 2

x = √(y-2) / -4

Now we can change the letters to follow the convention that x is the independent variable and y is the function's value:

y = √(x-2) / -4

Now we have to draw the graph as,

It was side by side that is LHS is the function and the RHS is its inverse.

6 0

3 years ago

The opposite inverse of -1/9 is

melomori [17]

Answer:

1/-9

Step-by-step explanation:

hope it helps... ✌️✌️✌️✌️

Byeeee..

7 0

2 years ago

What is the missing number in this pattern?<br> 0, 2, 6, ----, 30, 62

mario62 [17]

Answer:

Step-by-step explanation:

so the pattern is they add 2 then they add 4 then they add 8 then the add 16 basically they are double the number being added each number so the missing number is 14

5 0

2 years ago

Read 2 more answers