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3 years ago

Find the perimeter of this shape

Mathematics

1 answer:

telo118 [61]3 years ago

7 0

To find the circumference of a semi-circle, it would be 1/2<span> π × d. So, pi (3.14) times the diameter, 5 would be 15.7, but then we would need to multiply it by 1/2 to get the circumference for half the circle, and that will get you 7.85. Now you can add all the lengths now. 7.85 + 7 + 5 + 7 = 26.85. Hope this helps! Let me know if you still don't get it. <3</span>

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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

I need help please. Which graph shows y=⌊x⌋+2?

slavikrds [6]

Answer: Top right graph.

Step-by-step explanation:

The function ⌊x⌋ rounds the value x to the lower whole number.

for example:

⌊1.5⌋ = 1

⌊1.923⌋ = 1

⌊2.0⌋ = 2

then, the graph of ⌊x⌋ will be a black dot in the each whole number, and a horizontal segment to the right that ends with a white dot in the next whole number. Right above the white dot, we have another black dot, and it repeats.

if we have ⌊x⌋ + 2, we move te previous graph 2 units upwards, then the correct option is the top right graph.

You can check some points if you like:

f(0) = ⌊0⌋ + 2 = 2

f(0.5) = ⌊0.5⌋ + 2 = 2

f(1) = ⌊1⌋ + 2 = 3

So in x = 0 we have a black dot in y = 2, and in x = 1 we have a white dot in y = 2 and a black dot in y = 3.

5 0

3 years ago

Michael Phelps consumes 15,000 calories per day, swimming the butterfly stroke burns 1200 calories per hour. Michael can swim an

Evgen [1.6K]

To calculate this we should firstly calculate that how many laps can he do in an hour. So assuming that he does all the laps at the same rate he must do 120 laps in an hour.

Now because he burns 1200 calories per hour we can see how many number of hours it would take him to burn 15000 calories. So it would take him around 15000 / 1200 = 12.5 hours. So now we will multiply 12.5 by 120 laps as that is the number laps he can do in an hour. So that is around 1500 laps a day.

4 0

3 years ago

In a class there are 40 students 30 are boys and what is the percentage of girls ....

Artyom0805 [142]

Answer:

25%

Step-by-step explanation:

Total= 40 students

boys +girls= 40

30 +girls= 40

number of girls

= 40 -30

= 10

Percentage of girls

$= \frac{10}{40} \times 100\% \\ = 25\%$

Alternatively,

percentage of girls

= 100% -(percentage of boys)

$= 100\% - ( \frac{30}{40} \times 100\%) \\ = 100\% - 75\% \\ = 25\%$

6 0

3 years ago

: Naveen has a bag that contains 6 blue marbles, 3 green marbles, and 1 red marble. He will draw one marble randomly from the ba

loris [4]

Answer:

If Naveen wants to make sure that drawing a red marble is equally likely as drawing a different color marble, then he could add ***8 red marbles to the bag***

Step-by-step explanation:

The bag that contains 6 blue marbles, 3 green marbles, and 1 red marble.

Naveen wants to make sure that drawing a red marble is equally likely as drawing a different color marble, then he could add what?

Current total number of marbles = 10

Probability of drawing a red marble = (1/10)

Probability of drawing marble of other colour = (9/10)

And we want the the probability of drawing a red marble and one of the other marble to be the same.

This means we have to add a number of red marbles.

Let the number of red marbles to be added be n.

After adding n red marbles, the probability of drawing a red marble = (n+1)/(10+n)

Probability of drawing one of the other marbles = 9/(10+n)

And the probabilities are equal

(n+1)/(10+n) = 9/(10+n)

n+1 = 9

n = 9 - 1 = 8

This makes the number of red marbles 9 and total number of marbles 18.

The probability of drawing a red marble becomes (9/18) = 0.5

Probability of drawing a marble of other colour = (9/18) = 0.5 also.

4 0

3 years ago