Write an equation for the translation of "left 7 units Y=|x|

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

The Ohio Department of Agriculture tested 203 fuel samples across the state in 1999 for accuracy of the reported octane level. F

OlgaM077 [116]

Answer:

The Sample size is 1918.89035

Step-by-step explanation:

Consider the provided information.

It is given that 14 out of 105 samples failed.

Therefore p = 14/105 = 0.13 3... and q=1-0.133=0.867

Samples would be needed to create a 99 percent confidence interval.

Subtract the confidence level from 1, then divide by two.

$\frac{(1 -0.99)}{2}=0.005$

By standard normal table z=2.5758≈2.58

Calculate the sample size as:

$n=\frac{z^2pq}{e^2}$

Where, e is the margin of error,

Substitute the respective values.

$n=\frac{(2.58)^2(0.133)(0.867)}{(0.02)^2}=1918.89$

Hence, the Sample size is 1918.89035

4 0

3 years ago

12. A carpenter made two tables. The first table is 4 feet

Arte-miy333 [17]

Answer:

a. True

b. True

c. False

d. False

Step-by-step explanation:

First Table

Length=10 feet, Width=4 feet

Area =10 X 4=40 Square Feet

Second Table

The second table is half as long as the first table.

Length =0.5 X 10 =5 feet

Area=5 X Width= 5w

The area of the second table is one fourth the area of the first table.

Area of Second Table = $\frac{1}{4}$ X Area of first table

5w= $\frac{1}{4}$ X 40

5w=10

Width of the Second table, w=2 feet

The following are true.

(a)The width of the second table is 2 feet.

(b) The area of the second table is 10 square feet.

6 0

3 years ago

A math teacher graded 45 problems in 3/5 of an hour. At that rate, how many problems can she grade in one hour

dolphi86 [110]

Answer:

75

Step-by-step explanation:

45*1/3=15

15*5=75

6 0

3 years ago

Read 2 more answers

What is the prime factorization of 2,800

11111nata11111 [884]

$2800|2\\1400|2\\.\ 700|2\\.\ 350|2\\.\ 175|5\\.\ \ 35|5\\.\ \ \ 7|7\\.\ \ \ 1|\\\\\boxed{2800=2\times2\times2\times2\times5\times5\times7=2^4\times5^2\times7}$

4 0

3 years ago

Read 2 more answers