What equation has steeper slope? <br><br> A y = x + 1<br><br> B y = 2x + 6

EXAMPLE 5 If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (1, 2, 0) in the

solong [7]

Answer:

<h2>a) f = sin(yz)i + xzcos(yz)j + xycos(yz)k</h2><h2>b) -2</h2>

Step-by-step explanation:

Given f(x, y, z) = x sin(yz), the formula for calculating the gradient of the function is expressed as ∇f(x, y, z) = fx(x, y, z)i+ fy(x, y, z)j+fz(x, y, z)k where;

fx, fy and fz are the differential of the functions with respect to x, y and z respectively.

a) ∇f(x, y, z) = sin(yz)i + xzcos(yz)j + xycos(yz)k

The gradient of f = sin(yz)i + xzcos(yz)j + xycos(yz)k

b) Directional derivative of f at (1,2,0) in the direction of v = i + 4j − k is expressed as ∇f(1, 2, 0)*v

∇f(1, 2, 0) = sin(2(0))i +1*0cos(2*0)j + 1*2cos(2*0)k

∇f(1, 2, 0) = sin0i +0cos(0)j + 2cos(0)k

∇f(1, 2, 0) = 0i +0j + 2k

Given v = i + 4j − k

∇f(1, 2, 0)*v (note that this is the dot product of the two vectors)

∇f(1, 2, 0)*v = (0i +0j + 2k)*(i + 4j − k )

Given i.i = j.j = k.k =1 and i.j=j.i=j.k=k.j=i.k = 0

∇f(1, 2, 0)*v = 0(i.i)+4*0(j.j)+2(-1)k.k

∇f(1, 2, 0)*v = 0(1)+0(1)-2(1)

∇f(1, 2, 0)*v =0+0-2

∇f(1, 2, 0)*v= -2

Hence, the directional derivative of f at (1, 2, 0) in the direction of v = i + 4j − k is -2

7 0

3 years ago

• What is the solution to 5x+ 20 = 7(x+2)?

o-na [289]

For this case we must find the solution of the following equation:

$5x + 20 = 7 (x + 2)$

Applying distributive property on the right side of the equation we have:

$5x + 20 = 7x + 14$

Subtracting 7x from both sides of the equation:

$5x-7x + 20 = 14\\-2x + 20 = 14$

Subtracting 20 from both sides of the equation:

$-2x = 14-20$

Different signs are subtracted and the major sign is placed.

$-2x = -6$

Dividing between -2 on both sides of the equation:

$x = \frac {-6} {- 2}\\x = 3$

Thus, the solution of the equation is $x = 3$

Answer:

$x = 3$

6 0

4 years ago

the temperature at the south pole was -39degree f at 8am. at 3pm it was 10degree f, by how many degrees did the temperature rise

natita [175]

Answer:

Step-by-step explanation: start at -39 degrees. You need to find how many degrees is between -39 and 10 degrees.

+39+10= 49 degrees risen

6 0

3 years ago

PLS HELP ME ASAP WITH THIS WHOLE PAGE! THANK YOU SOO MUCH!!

Doss [256]

1a) The function has arrows on both ends and no place in the middle where it is not defined. Its domain is ...
All Reals

1b) The function gives no output values below -3, but it gives output values of -3 and all above that. Its range is ...
y ≥ -3

1c) For values of x less than -1, the function's output is 1. This matches g(x) and s(x). At x=0, the function's output is -3, which only matches g(x). The appropriate choice is ...
g(x)

2b) The function is only defined for 0 ≤ x < 8. This is its domain.

3) A definition might be ...
$y=\left\{ \begin{array}{rcl}x+1 & \mbox{for} & -4\le x \le 1\\-x & \mbox{for} & 1 < x \le 3 \end{array}$

6 0

3 years ago

Which value of x is in the domain of f(x) = square root of x-5

Gelneren [198K]

The answer is A. x= 5

3 0

3 years ago

What equation has steeper slope? A y = x + 1 B y = 2x + 6