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2 years ago

In ΔABC, the measure of ∠C=90°, the measure of ∠A=78°, and BC = 6.6 feet. Find the length of CA to the nearest tenth of a foot.

Mathematics

1 answer:

Vanyuwa [196]2 years ago

3 0

Answer:

1.4 feet

Step-by-step explanation:

I got it right on delta

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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

In at least 4 complete sentences explain what a reciprocal is in relation to fraction? and how you would find the reciprocal of

sveta [45]

To find the reciprocal of a fraction, you switch the numerator and denominator, for example the reciprocal of 2/5 is 5/2. With our mixed number, we convert to an improper fraction, 17/3Then we find the reciprocal, which is 3/17. I hope this helps!

3 0

2 years ago

Can someone help with this?

valina [46]

Answer:

(a) is 8 x 7 x 3 = 168

(b) is 8 x 7 = 56

(b2) is weird I don't know what it's asking

7 0

2 years ago

For the function g(x) = x – 2x^2, find g (–3) + 13

svp [43]

Answer:

Step-by-step explanation:

g(x) = x - 2x²

To find g( - 3) + 13 substitute the value of x that's - 3 into g(x) and add 13 to it

We have

g( - 3) + 13 = - 3 - 2(-3)² + 13

= -- 3 - 2(9) + 13

= 3 - 18 + 13

We have the final answer as

Hope this helps you

8 0

3 years ago

The shortest side of a right triangle measures 13 m. the lengths of the other two sides are consecutive integers. Find the lengt

mariarad [96]

So, the shortest side is 13, the other two fellows are two consecutive values.... ok... let's say the other leg is "a", a consecutive value to that will be a+1, so the hypotenuse is "a + 1" then

check the picture below

and surely you'd know what "a" is

6 0

3 years ago