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3 years ago

7

tapes-R-US is having a sale on hq tape players. the regular price is 60 dollars.the discount is 18 dollars. what percent discoun

t is this?

1 answer:

Vitek1552 [10]3 years ago

5 0

60 - 18 = 42
42/60 x 100 - 70%

To check this do 0.7 x 60 (which gets you 18, so it is right)

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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.

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

So

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

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

Plz help, I promise I will give brainliest

Vadim26 [7]

Answer:

Graph shifts five units down.

Step-by-step explanation:

6 0

2 years ago

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What are the x- and y-intercepts of the graph of 3x+6y=12?

Dafna1 [17]

Answer:

X-int.: (4,0)

Y-int.: (0,2)

Step-by-step explanation:

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2 years ago

If f (x) = 8(5x-2) find f -1 (x).

saw5 [17]

Step-by-step explanation:

f(x)=8(5x-2)

interchanging the role of x&y

x=8(5y-2)

x=40y-16
x+16=401y
y=(x+16)/40

f-1(x)=(x+16)/10

<h3>stay safe healthy and happy.</h3>

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3 years ago

Need help ASAP! (Geometry 1)

melisa1 [442]

Answer:

The Length of third side is 52 units.

Step-by-step explanation:

Given:

Length of First side = 48

Length of second side = 20

Also given the angle between them is 90°.

Hence we can say figure shown is a right angled triangle.

For finding the third side we can use Pythagoras theorem which states that;

"If a triangle is right angled then, the Square of the hypotenuse is equal to sum of the square of the other two sides."

$Third \ side ^2=First \ side^2+Second \ side^2$

Hence substituting the values we get;

$Third\ side^2= 48^2+20^2 = 2304+400 =2704$

Now taking Square root on both side we get;

$\sqrt{Third \ side^2} = \sqrt{2704}\\ Third \ side = 52 \ units$

Hence Length of Third side is 52 units.

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3 years ago