All categories

4 years ago

Please help me with this 20 points

Mathematics

2 answers:

Tema [17]4 years ago

5 0

Answer:

Step-by-step explanation:

MM AA TT H E I C S

Total = 11

2/11 × 1/11 × 4/10

= 4/605

JulsSmile [24]4 years ago

3 0

Answer:

A 4/605

Step-by-step explanation:

mathematics = 11 letters

P(m) = number of m's/total = 2/11

we replace it so we have mathematics = 11 letters

P(s) = number of s's/total = 1/11

not replacing it

we replace it so we have mathematic = 10 letters

P(vowel) = number of vowel/total = 4/10 = 2/5

P(m, replace,s, no replace, vowel) = 2/11* 1/11 * 2/5 = 4/605

You might be interested in

Can someone answer this pls

sineoko [7]

Answer:

(1,2,3)

Step-by-step explanation:

plugg in

3 0

3 years ago

If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (2, 4, 0) in the direction

valentina_108 [34]

Answer:

a) $\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$ .

b) $Du_{f}(2,4,0) = -\frac{8}{\sqrt{11}}$

Step-by-step explanation:

Given a function $f(x,y,z)$ , this function has the following gradient:

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

(a) find the gradient of f

We have that $f(x,y,z) = x\sin{yz}$ . So

$f_{x}(x,y,z) = \sin{yz}$

$f_{y}(x,y,z) = xz\cos{yz}$

$f_{z}(x,y,z) = xy \cos{yz}$ .

$\nabla f(x,y,z) = f_{x}(x,y,z)\mathbf{i} + f_{y}(x,y,z)\mathbf{j} + f_{z}(x,y,z)\mathbf{k}$ .

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

(b) find the directional derivative of f at (2, 4, 0) in the direction of v = i + 3j − k.

The directional derivate is the scalar product between the gradient at (2,4,0) and the unit vector of v.

We have that:

$\nabla f(x,y,z) = \sin{yz}\mathbf{i} + xz\cos{yz}\mathbf{j} + xy \cos{yz}\mathbf{k}$

$\nabla f(2,4,0) = \sin{0}\mathbf{i} + 0\cos{0}\mathbf{j} + 8 \cos{0}\mathbf{k}$ .

$\nabla f(2,4,0) = 0i+0j+8k=(0,0,8)$

The vector is $v = i + 3j - k = (1,3,-1)$

To use v as an unitary vector, we divide each component of v by the norm of v.

$|v| = \sqrt{1^{2} + 3^{2} + (-1)^{2}} = \sqrt{11}$

$v_{u} = (\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}})$

Now, we can calculate the scalar product that is the directional derivative.

$Du_{f}(2,4,0) = (0,0,8).(\frac{1}{\sqrt{11}}, \frac{3}{\sqrt{11}}, \frac{-1}{\sqrt{11}}) = -\frac{8}{\sqrt{11}}$

6 0

3 years ago

David invested 220 in a savings account that’s offers a 3% return on the investment the value of David’s investment will be at l

Levart [38]

Zzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

5 0

3 years ago

Read 2 more answers

Whai si (3x+5) (x-2)

Vika [28.1K]

The answer is 3x squared -11x-10

3 0

2 years ago

Which of the following are functions? x=-3 y=10 3x+2y=3

choli [55]

Y=10 and 3x+2y=3

X=-3 is NOT a function because it has multiple y values for one x value.

Y equals ten is a horizontal line, and passes the vertical line test, as does the third equation

7 0

3 years ago