Find the partial derivatives of the following functions
a) z = 8x^2 − 4xy + 5y^2
b) z = 5xe^y
c) z = 3xln(y)

Answer:

2x+16

Step-by-step explanation:

PEMDAS

Answer:

b

Step-by-step explanation:

sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{s\sqrt{3} }{2s}[/tex] ( cancel s on numerator/ denominator ), then

sinA = [tex]\frac{\sqrt{3} }{2}[/tex] → b

Answer:

4

Step-by-step explanation:

Factorizing we get the answer 4

Answer:

On the way out the train traveled at about 40 mph, while on the return it did so at 20 mph.

Step-by-step explanation:

Since an empty freight train traveled 60 miles from an auto assembly plant to an oil refinery, and there, its tank cars were filled with petroleum products, and it returned on the same route to the plant, and the total travel time for the train was 4.5 hours, if the train traveled 20 mph slower with the tank cars full, to determine how fast did the train travel in each direction the following calculation must be performed:

60/20 = 3

60/40 = 1.5

60/20 = 3

3 + 1.5 = 4.5

Therefore, on the way out the train traveled at about 40 mph, while on the return it did so at 20 mph.

Answer:

400

Step-by-step explanation:

First, the firm produces 100 sets its first year. This means that our equation starts at 100. Next, the total number of calculator sets in 5 years is 4500. With y₁ representing the amount of calculator sets produced during year 1, y₂ representing the amount of sets during year 2, and so on, we can say that

y₁+y₂+y₃+y₄+y₅ = 4500

100 + y₂+y₃+y₄+y₅ = 4500

Next, we are given that the production increases uniformly by an amount each year. Representing that amount as a, we can say that

y₁+a = y₂

y₂+a = y₃

y₁+a+a = y₃

y₁+ 2 * a = y₃

and so on, so we have

100 + y₂+y₃+y₄+y₅ = 4500

100 + (100+a) + (100+2a) + (100+3a) + (100+4a) = 4500

500 + 10a = 4500

subtract 500 from both sides to isolate the a and its coefficient

4000 = 10a

divide both sides by 15 to isolate a

a = 400

Answer:

hello the answer is .04/0.04

Answer:

.04 is four hundredths

Step-by-step explanation:

I hope this helps

Answer:

C

Step-by-step explanation:

3.8 is the answer

68.4÷18=3.8

Answer:

no

Step-by-step explanation:

Substitute the point into the equation and see if it is true

34 = 2(7) +8

34 = 14+8

34 = 22

Since this is not true, the point does not satisfy the equation

Answer:

No

Step-by-step explanation:

because 7 is X and 34 is Y

So its 2 *7 +8=22

so no

Answer:

Step-by-step explanation:

There are 3 zero's but we see the polynomial is of degree 4.

It means it has 2 same zero's. We can verify it is -2. Since -2 is doubled, it reflects the local minimum and it is on the x-axis.

In reality we need to consider the other two zero's.

It is obvious the negative interval is between -1/3 and 6 since the polynomial is of even degree and has positive leading coefficient.

Correct choice is c.

The graph is attached to confirm the theory.

Answer:

2 elephants have short tusks.

Step-by-step explanation:

Long tusks: 4/5

Short tusks: 1/5

1/5 = x/10

x = 2

Answer:-

5

The highest degree included in the polynomial is known as degree of polynomial

[tex]\sf \checkmark[/tex] Polynomial with degree 1=monomial

[tex]\sf \checkmark[/tex] Polynomial with degree 2 =binomial

[tex]\sf \checkmark[/tex] Polynomial with degree 3=Trinomial

Answer: hello from the question the volume of tank = 6000 gallons while the value in the Torricelli's equation = 5000 hence I resolved your question using the Torricelli's law equation

answer:

1) a) -180  gallons/minute ,

  b)  -160 gallons/minute

  c)  -120 gallons/minute

  d) 0

2) The water is flowing out fastest when t = 5 min

3) The water is flowing out slowest after t = 20 mins

Step-by-step explanation:

Volume of tank = 5000 gallons

Time to drain = 50 minutes

Volume of water remaining after t minutes by Torricelli's law

V = 5000 ( 1 - [tex]\frac{1}{50}t[/tex] )^2 ----- ( 1 )

1) Determine the rate at which water is draining from the tank

First step : differentiate equation 1 using the chain rule to determine the rate at which water is draining from the tank

V' = [tex]-10000[ ( 1 - \frac{1}{50}t ) (\frac{1}{50}) ][/tex]

a) After t = 5minutes

V' = - 10000[ ( 1 - 0.1 ) * ( 0.02 ) ]

   = -180  gallons/minute

b) After t = 10 minutes

V' = - 10000[ ( 1 - 0.2 ) * ( 0.02 ) ]

   = - 160 gallons/minute

c) After t = 20 minutes

V' = - 10000 [ ( 1 - 0.4 ) * ( 0.02 ) ]

   = -120 gallons/minute

d) After t = 50 minutes

V' = - 10000 [ ( 1 - 1 ) * ( 0.02 ) ]

   = 0 gallons/minute

2) The water is flowing out fastest when t = 5 min

3) The water is flowing out slowest after t = 20 mins  because no water flows out after 50 minutes

Answer:

Male & action movie among a group of total 479

Step-by-step explanation:

We only choose male from action movie category so:

p = 105/ 479 = 0.22

The probability that a randomly chosen person from this group is male and attended an action movie will be 0.22. Then the correct option is C.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

This table shows how many male and female students attended two different movies.

                   Action      Drama          Total

Mala             105            124              229

Female         99             151               250

Total            204           275              479

Then the probability that a randomly chosen person from this group is male and attended an action movie will be

Favorable event = 105

Total event = 479

Then the probability will be

P = 105 / 479

P = 0.219

P ≈ 0.22

Then the correct option is C.

More about the probability link is given below.

https://brainly.com/question/795909

#SPJ2

[tex]3x=x+10[/tex]

We tripple something and get 10 more than something.

Put the x-es on the left and non x-es to the right,

[tex]2x=10[/tex]

Divide both sides by 2,

[tex]x=5[/tex]

Et Viòla.

Hope this helps :)

When a number is tripled, its value increases by 10 then the original number is 5.

Let's call the original number "x". According to the problem, when this number is tripled, its value increases by 10. Mathematically, we can represent this as an equation:

3x = x + 10

Now, we can solve for "x" step by step:

1. Subtract "x" from both sides of the equation:

  3x - x = 10

2. Simplify the left side:

  2x = 10

3. Divide both sides by 2 to solve for "x":

  x = 10 / 2

  x = 5

So, the original number "x" is 5.

In other words, if you take a number, triple it (multiply by 3), and then increase the result by 10, you would end up with the value 5. This can be verified by checking:

3 * 5 = 15

15 + 10 = 25

The equation 3x = x + 10 represents the relationship between the original number and its tripled value with an increase of 10. Solving this equation helps us find the original value that satisfies the given condition.

To know more about Equation here

https://brainly.com/question/17387622

#SPJ3

Answer:

2. Not Divisible

3. Divisible

4. Divisible

5. Divisible

6. Not Divisible

7. Divisible

Step-by-step explanation:

Question 2. Is 629,257 divisible by 5?

- Numbers that are divisible by 5 should end with either 5 or 0.

- The ending term of [629,257] is 7, which is neither 5 nor 0. Therefore, it is not divisible.

Question 3. Is 3,791,916 divisible by 2?

- Numbers that are divisible by 2 should end with an even number or 0, which include 0, 2, 4, 6, 8.

- The ending term of [3,791,916] is 6, which is an even number. Therefore, it is divisible.

Question 4. Is 63,726,125 divisible by 5?

- Numbers that are divisible by 5 should end with either 5 or 0.

- The ending term of [63,726,125] is 5. Therefore, it is divisible.

Question 5. Is 486,342 divisible by 3?

- In numbers that are divisible by 3, the sum of all digits is a multiple of 3.

- The sum of all digits of [486,342] is [4 + 8 + 6 + 3 + 4 + 2 = 27].

- 27 / 3 = 9

- Since the sum of all digits is divisible by 3, then 486,342 is divisible by 3.

Question 6. Is 474,493 divisible by 10?

- Numbers that are divisible by 10 should end with 0.

- The ending term of [474,493] is 3, which is not 0. Therefore, it is not divisible.

Question 7. Is 53,017,587 divisible by 9?

- In numbers that are divisible by 9, the sum of all digits is a multiple of 9.

- The sum of all digits of [53,017,587] is [5 + 3 + 0 + 1 + 7 + 5 + 8 + 7 = 36].

- 36 / 9 = 4

- Since the sum of all digits is divisible by 9, then 53,017,587 is divisible by 9.

Answer:

a) 2.06

b) variance = 270.90 , std = 275.14

Step-by-step explanation:

a) Determine Expected rate of return

attached below is the calculated table for the solution provided

∴ Expected rate of return = ∑ Xp(x) = -6.46 + 3.84 + 4.68 = 2.06

b) Determine the variance and standard deviation

Variance ( Vx ) = E(x)^2 - [ Expected rate of return ]^2

                         = 275.14 - ( 2.06 )^2 ≈ 270.90

standard deviation = √ variance = √270.90 = 16.459

note : E(x)^2 = ∑ x^2 p(x) = 275.14

Answer:

Oh no I am sorry! If you want answers to be done the real way let me know

Answer:I'm so sorry for you but congrats you did get the answer right it's just the test I guess

Step-by-step explanation:

Answer:

There are 666 numbers multiple of 3 in the interval.

Step-by-step explanation:

Multiples of 3:

A number is a multiple of 3 if the sum of it's digits is a multiple of 3.

Range [2,2000]:

First multiple of 3 in the interval: 3

Last: 1998

How many:

[tex]1 + \frac{1998 - 3}{3} = 1 + 665 = 666[/tex]

There are 666 numbers multiple of 3 in the interval.

Lets do

[tex]\\ \sf\longmapsto K=\dfrac{AB}{A+B}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{K}=\dfrac{A+B}{AB}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{K}=\dfrac{1}{A}+\dfrac{1}{B}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{B}=\dfrac{1}{K}-\dfrac{1}{A}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{B}=\dfrac{K-A}{AK}[/tex]

[tex]\\ \sf\longmapsto B=\dfrac{AK}{K-A}[/tex]

Without knowing what Juan's exact steps were, it's hard to say what he did wrong. The least you could say is that his solution is simply not correct.

4 sin²(θ) - 1 = 0

==>   sin²(θ) = 1/4

==>   sin(θ) = ±1/√2

==>   θ = π/4, 3π/4, 5π/4, 7π/4

9514 1404 393

Answer:

  none

Step-by-step explanation:

No work is required to maintain an object at a constant speed with no change in direction. Work is only done when an object is accelerated, or moved some distance in the direction of the net force applied.

you would do no work

Answer:

= 6 ways = Required number of ways = (120×6)=720

Answer:

$14.40

Step-by-step explanation:

my way of doing things:

15/100=0.15=1%of total amount

0.15 x 6=0.9= the 6% which is the tax

0.15 x 10 = 1.5=the coupon

Take the coupon amount $1.50 minus the tax amount $0.90 =$0.60. Because the coupon amount is greater than the tax the 60 cents gets taken away from the original 15 dollars leaving Mr. Longely only having to pay $14.40.

Answer:

[tex]\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}[/tex]

Step-by-step explanation:

Given

The above table

Required

The discrete probability distribution

The probability of each is calculated as:

[tex]Pr = \frac{Frequency}{Total}[/tex]

Where:

[tex]Total = 2140+ 2853 + 4734 + 4880 + 10715[/tex]

[tex]Total = 25322[/tex]

So, we have:

[tex]P(1) = \frac{2140}{25322} = 0.0845[/tex]

[tex]P(2) = \frac{2853}{25322} = 0.1127[/tex]

[tex]P(3) = \frac{4734}{25322} = 0.1870[/tex]

[tex]P(4) = \frac{4880}{25322} = 0.1927[/tex]

[tex]P(5) = \frac{10715}{25322} = 0.4231[/tex]

So, the discrete probability distribution is:

[tex]\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}[/tex]

To convert [tex]24.123[/tex] in base 8, also notated with [tex]24.123_8[/tex] into base 10 simply multiply each digit with 8 to the power of its position relative to the decimal point.

So,

[tex]24.123_8=2\cdot8^1+4\cdot8^0+1\cdot8^{-1}+2\cdot8^{-2}+3\cdot8^{-3}=20.162109375_{10}[/tex]

Hope this helps :)

Answer:

56.5

I think this is right

Answer:

20 percent

Step-by-step explanation:

Each year is 10 percent so 10x2 or 10+10 will equal 20

Answer:

Hello,

I have reply too quick in comments (sorry)

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}log_x (27)+log_y (4)=5\\log_x (27)-log_y (4)=1\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}2*log_x (27)=6\\2*log_y (4)=4\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}log_x (27)=3\\log_y (4)=2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x^{log_x (27)}=x^3\\y^{log_y (4)}=y^2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}27=x^3\\4=y^2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x=3\\y=2\\\end{array}\right.\\\\[/tex]

Answer:

87, which is positive

Step-by-step explanation:

-8 --95

Subtracting a negative is like adding

-8 +95

87