Find a POSITIVE and NEGATIVE co-terminal angle for<br> -19(pie)/8

Write the expanded form of the decimal 0.082¯ using powers of 10

Softa [21]

Answer:

0.082 = 8.2× 10^-2

Step-by-step explanation:

Given the decimal number 0.082, the expanded form using the power of 10 can be gotten by writing the decimal number in standard format(writing as a multiple of 10).

To do that we will shift the decimal point to the front up to the front of digit 8. This shows that the decimal point will be shifted 2times to the front. Since of is shifted 2times to the front, our power of 10 will be -2.

0.082 = 8.2× 10^-2

This gives the required answer.

Note that, the power of 10 is positive when decimals are shifted to the back and negative when shifted to the front(in this case).

3 0

3 years ago

Find the directional derivative of f at the given point in the direction indicated by the angle θ.

anygoal [31]

Answer:

Directional derivative = 1/√2

Step-by-step explanation:

We are given f(x, y) = y cos(xy)

Now, we know that;

∇f(x, y) = ycos xy

Thus, applying that to the question, we have;

∇f(x, y) = [-y² sin xy, cos (xy) - xy sin xy]

At coordinates (0,1),we now have;

∇f(0, 1) = [-1²•sin0, (cos 0) - 0]

∇f(0, 1) = [0, 1]

Now, unit vector indicated by the angle θ is given as; u = [cos θ, sin θ]

From the question, since θ = π/4, thus

u = [cos π/4, sin π/4]

Cos π/4 in surd form is; 1/√2

Also, sin π/4 in surd form is; 1/√2

So, u = [1/√2, 1/√2]

Directional derivative = [∇f(0, 1)] • u

= [0, 1] × [1/√2, 1/√2] = 0 + 1/√2 = 1/√2

4 0

3 years ago

4 7/12 + 2 1/12 what is the estimate answer

Pani-rosa [81]

$4 \frac{7}{12} = \frac{12*4+7}{12} = \frac{55}{12} \\ \\ 2 \frac{1}{12} = \frac{2*12+1}{12} = \frac{25}{12} \\ \\ \frac{55}{12} + \frac{25}{12} = \frac{80}{12} \\ \\ \frac{80 :4}{4:4} = \frac{20}{3}$