Let f be a function of two variables that has continuous partial derivatives and consider the points

A(8, 9),

B(10, 9),

C(8, 10),

and

D(11, 13).

The directional derivative of f at A in the direction of the vector AB is 9 and the directional derivative at A in the direction of

AC is 2. Find the directional derivative of f at A in the direction of the vector AD.

(Round your answer to two decimal places.)

Answer:

one solution: (2.5, 0)

Step-by-step explanation:

We are given the following system of equations:

y = 2x - 5

-8x - 4y = -20

Replacing the first equation into the second:

[tex]-8x - 4(2x - 5) = -20[/tex]

[tex]-8x -8x + 20 = -20[/tex]

[tex]-16x = -40[/tex]

[tex]16x = 40[/tex]

[tex]x = \frac{40}{16}[/tex]

[tex]x = 2.5[/tex]

y

[tex]y = 2x - 5 = 2(2.5) - 5 = 5 - 5 = 0[/tex]

Thus the system has one solution: (2.5,0).

Answer: 4166.67$

Step-by-step explanation:

1920 x 250 = amount

Amount = 120%

Cost price = 100%

1920 x 250= 120%

Cost price = 100%

Cross multiply and divide both side by 120

1920 x 250 x 100/120 = price

Exchange rate = cost in #/cost in $

= (1920 x 250 x 5/6)/(5000)

= (96 x 5/6) = 16 x 5= 80

Exchange rate then was 80 to 1$

The sales will be 400000/96 = 4166.67$

Answer:

1. $1:#80

2.$5000

Step-by-step explanation:

ok... lots of moving parts here ....

$5000 / 250 = $20 per lantern.

~~~~~~~~~~~~~~~~~~

x (1 + .2) = 1920

x = 1600

~~~~~~~~~~~~~~

$5000 : (1600*250)

$5,000:#400,000

c

~~~~~~~~~~~

sales back to the us at $1:#96

1920*250 = 480000

#480000/#96=$5000

Answer:

160000

Step-by-step explanation:

Let ratio be 3x,5x,4x

Sum of ratios 3x+5x+4x=12x

Share of Kofi:-

(3/12)x480000=120000

Share of Kojo:-

(5/12)x480000=200000

Share of Ama:-

(4/12)x480000=160000

Answer:

[tex]\sqrt[6]{2\\}[/tex]

Step-by-step explanation:

Rewriting

2 ^1/2 ÷ 2 ^ 1/3

We know a^ b ÷ a^c = a^ (b-c)

2 ^ (1/2 -1/3)

Getting a common denominator

2^ ( 3/6 - 2/6)

2^ 1/6

[tex]\sqrt[6]{2\\}[/tex]

Answer:

[tex]\sqrt[6]{2}[/tex]

Step-by-step explanation:

We can start by writing the expression as one power of two, and then comparing it to the options. The square root of two is the same and [tex]2^{\frac{1}{2} }[/tex] and the cube root of two is the same as [tex]2^{\frac{1}{3} }[/tex]. Therefore, we can rewrite the expression:

[tex]\frac{2^{\frac{1}{2} }}{2^{\frac{1}{3} }}[/tex]

Now, to write them as one power of two, we can use the quotient rule which states, [tex]\frac{x^m}{x^n} = x^{m-n}[/tex]:

[tex]2^{\frac{1}{2} -\frac{1}{3}}[/tex]

We just need to subtract 1/3 from 1/2 to get:

[tex]2^{\frac{1}{6} }[/tex]

This is the same as the 6th root of 2, which is the second option.

9514 1404 393

Answer:

  149.04°

Step-by-step explanation:

You must consider the signs of the components of the vector. The value -5+3i will be in the 2nd quadrant of the complex plane.

When you use the single-argument arctan function, it will tell you the angle is -30.96°, a 4th-quadrant angle. (arctan( ) is only capable of giving you 1st- or 4th-quadrant angles.)

You find the 2nd-quadrant angle by adding 180° to this value:

  -30.96° +180° = 149.04° = arg(-5+3i)

__

The attachments show the calculation using a suitable calculator (1st) and a spreadsheet (2nd). The spreadsheet function ATAN2(x,y) gives the 4-quadrant angle in radians, considering the signs of the two arguments. Here, we converted it to degrees. The calculator can be set to either degrees or radians.

Answer:

10x^2 - 3x -18

Step-by-step explanation:

if you meant (2x-3)(5x+6), you just multiply out

Answer:

Step-by-step explanation:

Use FOIL method

(2x - 3)(5x + 6) = 2x*5x + 2x*6 + (-3)*5x  + (-3) *6

                        = 10x² + 12x - 15x  - 18 {Combine like terms}

                        = 10x² - 3x - 18

Like terms are terms that have same variable with same power.

Answer:

C

Step-by-step explanation:

17.156 is the irrational number as it is terminating(means it ends)

Rest all are irrational

Answer: 100.5

Step-by-step explanation:

multiply 3.14 by 2 to the 2nd power by 8. so first 2 to the second power is 4. Then 4x8 is 32. Final step is to multiply 3.14 by 32 to get 100.48. Then you gotta round to get 100.5.

Answer:

f(x) = 4*e^(0.05*x)

Step-by-step explanation:

We want to find the equation for the graph.

The first thing we can see, is that, as the value of x increases, also does the value of y.

So f(x) increases as x increases.

Then we can discard the options with negative exponents, as those decrease when x increases.

Then the remaining options are:

f(x) = 4*e^(0.05*x)

f(x) = 4*e^(0.5*x)

In the graph, we can see that:

f(5) ≈ 5

So let's check that with the two remaining options:

For the first one we have:

f(5) = 4*e^(0.05*5) = 5.13

While for the second option we have:

f(5) = 4*e^(0.5*5) = 48.73

Then the correct option is the first one:

f(x) = 4*e^(0.05*x)

Answer:

Answer:

6 digits.

Step-by-step explanation:

The repeating numbers after the decimal is 571428.

Answer:

[tex]Area = 0.25 \ m^2[/tex]

Step-by-step explanation:

Force = 1500N , Pressure = 6000

[tex]Pressure = \frac{Force}{Area }[/tex]

[tex]6000 = \frac{1500}{Area }[/tex]

[tex]6000 \times Area = 1500\\\\Area = \frac{1500}{6000} \\\\Area = \frac{1}{4} = 0.25 \ m^2[/tex]

Answer:

Leo stop at 1339. 3 feet tall and Leo almost reach the top of the building

Answer:

A    2:1

B    1:2

Step-by-step explanation:

If there is 24 students and 8 are girls, then 24 - 8 tells you how many are boys.

24 - 8 =  16.

There are 16 boys.

If there is 16 boys and 8 girls, the ratio would be 2 : 1 or 2/1 or 2 because 16  and 8 have a common factor of 8, so both sides can be divided by 8.

Hence the 8 : 2.

Ratios are commonly expressed with a colon, so that is going to be the symbol I'm using to differenciate the numbers.

We can just reverse the ratio since the original was boys to girls, but it is now girls to boys.

1:2

Answer:

52

Step-by-step explanation:

k(x) = 5x - 6

(k + k)(4) =

First find k(4) = 5(4)+6 = 20+6 = 26

(k + k)(4) = 26+26 = 52

Answer: A. A random sample

Step-by-step explanation:

Since everyone is equally as likely yo be selected for this sample, is has to be random because there won't be any interference to the probability of your chances of being selected in the population

I hope this helps!

Answer:

3,090 diamonds

Step-by-step explanation:

To get 10 shards, you need to spend 30 diamonds.

First thing we need to find, how many rounds you need to play to get 1,024 shards if in each round you win 10 shards?

1,024/10 = 102,4

But you can not play 102.4 rounds, you only can play whole numbers, so we need to round it to the next whole number (not the previous one, because in that case, we would get less than 1,024 shards)

Then you need to play 103 rounds.

And each round costs 30 diamonds, then the total number of diamonds that you need is:

103*30 diamonds = 3,090 diamonds

Answer:

I don't want to be silly here, but....

if x > 9 and < 13...

there is only one answer that is >9 and < 13

that is answer "A" (11)

Step-by-step explanation:

Answer:

A. 11

Step-by-step explanation:

Hi there!

We're given the trapezoid EBFD, with bases (the parallel sides) EB and DF, which equal 9 and 13 respectively

AC is a segment that belongs to EBFD, and has the measure of x

AC is a midsegment, which is a segment that connects the midpoints of 2 sides

the midpoint divides a segment to create create two congruent segments

In this example, point A is a midpoint, as it divides ED into the congruent segments EA and AD (you can tell they are congruent by their markings)

C is also a midpoint, as it divides BF into the congruent segments BC and CF

line segment AC connects the points A and C together

anyway, the measure of a midsegment in a trapezoid is the average of the bases

in other words, the midsegment (AC, or x) is equal to (EB+DF)/2

since we know the measures of EB and DF, we can substitute them into the expression above to find x

x=(EB+DF)/2

x=(9+13)/2

add the numbers on the numerator

x=22/2

divide

x=11

So the answer is A

Hope this helps! :)

Answer:

C

Step-by-step explanation:

Given f(x) then f(x + a) is a horizontal translation of f(x)

• If a > 0 then a shift left of a units

• If a < 0 then a shift right of a units

The graph of g(x) is the graph of f(x) shifted 6 units left , then

g(x) = f(x + 6) → C

Answer:

First, remember that mathematics is a logical construct.

So, when something has no logical sense, it is undefined.

Now, let's think about a division by zero:

If you have $100, and you want to divide it between 0 people, how much gets each one of them?.

Naturally, there is no logical answer to this question, we can not know how much gets each one of these people because we have no people to divide that money.

Now, we can find another logical problem if we assume that the division is actually defined.

For example if 1 divided by zero is equal to a number A, we have:

1/0 = A

ok, if now multiply both sides by zero we get:

(1/0)*0 = A*0

1*(0/0) = A*0

1 = 0

So, 1/0 can be defined only if 1 = 0, again, a logical problem.

This is why the division by zero is not defined.

Answer:

so for this we do

39.42*1.08=42.5736

Hope This Helps!!!

Answer:

6

Step-by-step explanation:

6^2/(2m)

Let m = 3

6^2/(2*3)

6^2 / 6

36/6

6

Answer:

6

Step-by-step explanation:

(6)² / 2m

36 / 2 × (3 ) ( given :- m = 3)

36 / 6

6

Answer:

Ok, so im not 100% sure about this answer but i think its D:

Step-by-step explanation:

I think this is correct because i used desmos  and had plotted those answer and the only one that looks close enough to this answer was D.

I'll also put up the pictures so you can see what i mean.

I hope this help.

Answer:

$8.40

Step-by-step explanation:

The formula for calculating simple interest is

principal * interest rate * time .

Plugging 140 into the principal, or starting value, 3% as the interest rate, and 2 (years) for the time, we get 140*0.03*2 = 8.4, or $8.40 as our answer. Note that 3% turned into 0.03 as turning a percentage into a decimal requires us to divide the decimal by 100

The answer is C.

45^-3 can be transferred to the denominator, making the 45 in the denominator have a power to the 6th power.

Answer:

1,936 square units

Step-by-step explanation:

From the question, we have it that the original image was dilated by a factor of 1/4

what this mean is that the original image was reduced by up to a quarter size to get this new image

Now, to get the original image, we have to enlarge by a factor of 4

So, we simply have to multiply the side length of the new square by 4

We have that as;

11 * 4 = 44 units

Mathematically, the area of a square is the square of its side length

So, we have the area of the square as;

44 * 44 = 1,936 square units

Answer:

.y= 140 + 15x

Happy to help :)