Does anyone know the answer to number 4?

The directional derivative of [tex]f[/tex] at the given point in the direction indicated is [tex]\frac{5}{2}[/tex].

The directional derivative is represented by the following formula:

[tex]\nabla_{\vec v} f = \nabla f (r_{o}, s_{o})\cdot \vec v[/tex]   (1)

Where:

The gradient of [tex]f[/tex] is calculated below:

[tex]\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{\partial f}{\partial r}(r_{o},s_{o}) \\\frac{\partial f}{\partial s}(r_{o},s_{o}) \end{array}\right][/tex]   (2)

Where [tex]\frac{\partial f}{\partial r}[/tex] and [tex]\frac{\partial f}{\partial s}[/tex] are the partial derivatives with respect to [tex]r[/tex] and [tex]s[/tex], respectively.

If we know that [tex](r_{o}, s_{o}) = (1, 3)[/tex], then the gradient is:

[tex]\nabla f(r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{s}{1+r^{2}\cdot s^{2}} \\\frac{r}{1+r^{2}\cdot s^{2}}\end{array}\right][/tex]

[tex]\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{1+1^{2}\cdot 3^{2}} \\\frac{1}{1+1^{2}\cdot 3^{2}} \end{array}\right][/tex]

[tex]\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right][/tex]

If we know that [tex]\vec v = 5\,\hat{i} + 10\,\hat{j}[/tex], then the directional derivative is:

[tex]\nabla_{\vec v} f = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right] \cdot \left[\begin{array}{cc}5\\10\end{array}\right][/tex]

[tex]\nabla _{\vec v} f (r_{o}, s_{o}) = \frac{5}{2}[/tex]

The directional derivative of [tex]f[/tex] at the given point in the direction indicated is [tex]\frac{5}{2}[/tex]. [tex]\blacksquare[/tex]

To learn more on directional derivative, we kindly invite to check this verified question: https://brainly.com/question/9964491

Answer:

4 hours

Step-by-step explanation:

I hope this helps :)

Answer:

The answer is 1456

Step-by-step explanation:

Ok so what you have to do is take the 18 and the two 12s and you have to multiply then you have to square it and now i wasted your time and this is payback for deleting my post so no i cant help u with that

Answer:

45

Step-by-step explanation:

A right angle is ALWAYS equal to 90 degrees. If it is divided equally to two angles then both will be 45 degrees.

90/2=45.

Answer:

Complementary(word) 45(number)

Step-by-step explanation:

If any two angles were to make up a 90° angle (aka right angle), they would be complementary because complementary angles add up to a 90° angle.

90/2 = 45°

Where 2 represents the two angles that make up 90°

And 90 meaning the total of the right angle.

Answer: Start with the midpoint, G(10,8), and move your pencil point 4 units to the left and  1 unit up to reach the endpoint M(6,9).  To find the other end point, start with the midpoint G(10,8) again, but now move your pencil point 4 units to the right and 1 unit down.  Result:  N(14,7).

Check:  find the mean of the 2 x-coordinates:  Does (6+14)/2 = 10, the x-coordinate of the midpoint?  YES.  Does (9+7)/2 = 8, the y-coord. of the midpoint?  YES.

The desired other end point is therefore N(14,7).

Explanation:  the standard coordinate plane, what is the midpoint of a line segment that goes from the point (3, 5) to the point (7, 9)?. Possible Answers: (–2, –2). (7, 5).

Answer:

y=6x+8

Step-by-step explanation:

Since the lines are parallel, the slopes are the same. Once you have y=6x+b, you plug in (0,8) as the y-intercept and find that b=8.

Answer:

3 books for 10$

Step-by-step explanation:

Answer:

3 books for $10

Step-by-step explanation:

Answer:

  see attached

Step-by-step explanation:

Matrix addition, subtraction, and multiplication by a scalar are all done term by term. For example, the (1,1) term of the difference is the difference of (1,1) terms of matrices E and F.

The difference is ...

  [tex]\left[\begin{array}{cc}6-(-1)&-2-5\\9-10&4-7\end{array}\right] =\boxed{\left[\begin{array}{cc}7&-7\\-1&-3\end{array}\right] }[/tex]  

__

If you have trouble doing these operations in your head, a calculator or spreadsheet can help.

Step-by-step explanation:

Given: Two congruent sides, (DE and EF). Anlge. E is 36.

Let angle F be x°.

According to the base isoceles triangle theroem,

Since Angle F is opposite from DE and Angle D is opposite from EF, and DE=EF.

Angle D = Angle F.

So using transitive property, Angle D is x°. as well.

All angles in triangles add up to 180 so

[tex]36 + x + x + = 180[/tex]

[tex]36 + 2x = 180[/tex]

[tex]2x = 144[/tex]

[tex]x = 72[/tex]

So angle F is 72°.

Since DF is opposite from 36°, the shortest angle, DF is the shortest side.

Answer: 8 inches: 10 hours

Step-by-step explanation:

From the above question, we are informed that during the last snow storm, the snow accumulated at 4/5 inch per hour and that the snow continues at this rate for 10 hours.

The the ratio of the amount of snow in inches to the amount of time in hours first thus:

We have to calculate the amount of snow in inches first. This will be:

= 4/5 × 10

= 8 inches

Therefore, the the ratio of the amount of snow in inches to the amount of time in hours will be 8 inches for 10 hours

Answer:

its D

Step-by-step explanation:

The equivalent expression is  (1/6)³.

When a number is multiplied by itself a finite number of times, the number being multiplied is called the base number, and the number of times it is being multiplied is called the exponent.

Suppose a number is being multiplied by itself n number of times, then this expression is called the nth power of the given number.

An exponent is the number of times a given number is being multiplied by itself and power is the value of the product of the base number raised to an exponent.

Given:

[tex]6^{-3}[/tex]

now, applying exponents

[tex]a^{-m} = 1/ a^{m}[/tex]

Then after applying the above law we have

[tex]6^{-3}[/tex] = (1/6)³

Hence, the equivalent expression of [tex]6^{-3}[/tex] is (1/6)³.

Learn more about exponents and powers here:

https://brainly.com/question/15722035

#SPJ5

Answer:

21

Step-by-step explanation:

29 squared  then 20 squared

subtract them

then get the squared root

and then you have 21

Answer: 45?

Step-by-step explanation: because a perfect corner is 90 degrees so if you split that, you will get 45!

Answer:

720[tex]\sqrt{5x}[/tex]

Step-by-step explanation:

First you want to simplify both of them. To do this on 4[tex]\sqrt{30^{2} }[/tex] you can just cancel out the square and the square root to get 4 x 30 which is 120. Now you simplify 3[tex]\sqrt{20x}[/tex] you do this by splitting the radical into 2 radicals. So you want to take out a perfect square which in this case is [tex]\sqrt{4}[/tex] and you have [tex]\sqrt{5x}[/tex] left over. This brings us to 120 x 3 x 2 (2 is the square root of 4) [tex]\sqrt{5x}[/tex]. Now multiply 120 x 3 x 2 and get 720[tex]\sqrt{5x}[/tex].

Answer:

A 20 percent tip is basically multiplying the price by 0.2

Percent means out of a hundred.
20/100 is 0.2

We have to find 0.2 of 15.

We can multiply 15 by 0.2 to find 20 percent of 15 and you would get 3.

20 percent of 15 is 3 dollars thats your answer to A

Now the total price would just be the percentage you found in A and add it to the total breakfast.
3 + 15 = 18

Kieran spend 18 dollars for brekfast.

Answer:

x = 54°

Step-by-step explanation:

Since there are 180 degrees in a triangle, all you would do is add up the angles that you already have. In this case, you would do 64 + 62, which is 126. Then you would do 180 minus the sum of the other two degrees to find x. 180 - 126 = 54, so 54 is the value of x.

Hope this helps!!

By the concepts of the transversal line we obtain the measure of angle c is 21°.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

From the given diagram angle opposite to the 159° must also be 159° and it is the measure of angle b.

We know, The sum of pair of angles in a straight line is 180°.

Therefore, m∠C = 180° - 159°.

m∠C = 21°.

learn more about transversals here :

https://brainly.com/question/27643943

#SPJ2

Answer:

Step-by-step explanation:

25g + 35 = 260

25g = 225

g = 9 games

[tex]\longrightarrow[/tex]Let us write all expression in factorised form .

[tex]\leadsto[/tex] Common factors are 2,x,y,z and their product will give us highest common factor

[tex]\implies \sf 2\times x\times y \times z[/tex]

[tex]\implies \sf 2xyz[/tex]

Answer:

if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.

Step-by-step explanation:

The value of variable x is,

⇒ x = - 3/2

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

Two functions are;

⇒ f(x) = (2x+5)/8 and g(x) = 3x - 4.

Here, The inverse of (fog)(x) is an identity function,

Hence, We get;

⇒ (f o g) (x) = f (g (x))

                 = f (3x- 4)

                 = [ 2 (3x - 4) + 5 ] / 8

                 = (6x - 8 + 5) / 8

                 = (6x - 3) / 8

Thus, The inverse of (fog)(x) is,

⇒ (f o g) (x) = (6x - 3) / 8

⇒ y = (6x - 3) / 8

Solve for x;

⇒ 8y = 6x - 3

⇒ 8y + 3 = 6x

⇒ x = (8y + 3) / 6

⇒ (f o g)⁻¹ (x) = (8x + 3) / 6

Here, The inverse of (fog)(x) is an identity function, \

Hence, We get;

⇒ (f o g)⁻¹ (x) = x

⇒ (8x + 3) / 6 = x

⇒ 8x + 3 = 6x

⇒ 8x - 6x = - 3

⇒ 2x = -3

⇒ x = - 3/2

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ2

Answer:

Directly proportional, 2:3

Step-by-step explanation:

Directly proprtional as when one increases, so does the other.

2:3 because for every 2 notes there are 3 backbeats.

The amount that Wyatt’s effective interest rate is greater than his nominal interest rate is given by: Option D: 0.71% points

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]

The final amount becomes:

[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]

It is provided that:

Nominal interest rate = 13.62% compounding quarterly.

usually, interest rates are given in annual terms.

Converting 13.62 in quarterly terms, we get:

R = [tex]13.62/4 = 3.405\%[/tex] (as there are 4 quarters annually)

This rate is quarterly and is compounding quarterly.

Since these two things matched (the rate is in quarter version and so as the compounding of interest), we can take:

Unit of time = quarter of an year

Getting effective interest means interest that the principal grows by in one year.

One year = 4 quarters = 4 times unit of time.

Thus, T = 4

Thus, compound interest would be:

[tex]CI = P(1 +\dfrac{R}{100})^T - P = P( (1+3.405/100)^4 - 1) \approx P(0.1433)[/tex]

Taking its percent compared to principal amount P:

[tex]\dfrac{P(0.1433)}{P} \times 100 = 14.33\%[/tex]

Thus, the effective interest rate is 14.33%

The difference between effective and nominal interest rate is:

14.33 - 13.62 = 0.71%

Thus, the amount that Wyatt’s effective interest rate is greater than his nominal interest rate is given by: Option D: 0.71% points

Learn more about compound interest here:

https://brainly.com/question/11897800

Answer:

option D

Step-by-step explanation:

Answer: $714

Step-by-step explanation:

Find the time distances between both of the times, one being 4 hours and one being 4 hours and 30 minutes. Now multiply 4x12 and 4.5x12. You get 48 and 54. Add these together and get 102. Now multiply 102 by the numbers of the week (7) and you get 714. With this knowledge you now know that is is $714

Answer:

2 cups of popcorn and 1/2 cups of cereal per cup

Step-by-step explanation:

khan told me

Answer:

The answer is D or 13/36

Step-by-step explanation:

Step-by-step explanation:

that is not clearly defined.

what does "bigger circle" mean ? bigger area or bigger radius or diameter ? or even bigger circumference ?

I assume we mean here that the area is 4 times bigger.

then the area of P is

A of P = 4×412 = 1648

the perimeter (= circumference) of a circle is

C = 2×pi×r

with r being the radius.

the area of a circle is

A = pi×r²

since we have the area of the circle, we have to calculate backwards to find r, so that we can calculate the circumference :

1648 = pi×r²

r² = 1648/pi

r = sqrt(1648/pi) = sqrt(16×103/pi) = 4×sqrt(103/pi) =

= 22.90359562...

the circumference of P

C = 2×pi×r = 143.9075355...

Answer:

y=5x

Step-by-step explanation:

please mark me as brainlest

Answer:

a) y = 5x

Step-by-step explanation:

Given :-

x : y = 1 : 5

Solving :-

x/y = 1/5

y = 5x

Solution :-

a) y = 5x

Answer:

y = [tex]-\frac{5}{12} x[/tex] Slope is [tex]-\frac{5}{12}[/tex]; y-intercept is [tex]-\frac{11}{12}[/tex].

Step-by-step explanation:

-5x - 12y = 11 Add 5x to each side.

-12y = 5x + 11 Divide each side by -12.

y = [tex]-\frac{5}{12} x + (-\frac{11}{12} )[/tex] Change the + to -.

y = [tex]-\frac{5}{12} x - \frac{11}{12}[/tex]

Slope intercept form is y = mx + b, so slope is [tex]-\frac{5}{12}[/tex]; y-intercept is [tex]-\frac{11}{12}.[/tex]

Answer:

d

Step-by-step explanation: