If 7% of a number equals 9, find 70% of that number.

I assume the given plane has equation

x + 3y + 4z = d

for some constant d ≠ 0.

You want to maximize the function V(x, y, z) = xyz subject to the above constraint. The Lagrangian would be

L(x, y, z, λ) = xyz - λ (x + 3y + 4z - d)

Find its critical points:

∂L/∂x = yz - λ = 0

∂L/∂y = xz - 3λ = 0

∂L/∂z = xy - 4λ = 0

∂L/∂λ = x + 3y + 4z - d = 0

The first three equations tell you that λ = yz = xz/3 = xy/4. Then, for instance,

yz = xz/3   →   3yz - xz = z (3y - x) = 0   →   z = 0   or   3y - x = 0

If z = 0, we get zero volume which is not useful. So 3y = x. Similarly, you would find x = 4z and 3y = 4z, so a critical point occurs when x = 3y = 4z.

In the fourth equation, we get upon substituting

x + 3y + 4z = 3x = d   →   x = d/3, y = d/9, z = d/12

Then the largest volume of this box would be

V(d/3, d/9, d/12) = d ³ / 324

Answer:

false

Step-by-step explanation:

Answer:

false they are called addend s

Answer:

6/6

Step-by-step explanation:

Answer: slope = (6,6)

Step-by-step explanation:

Answer:

[tex]x \ge 0[/tex]  

[tex]y \ge 0[/tex]

[tex]x + y \le 9[/tex]

[tex]8 - x \ge 0[/tex]

[tex]3 - y \ge 0[/tex]

[tex](8 - x) + (3 - y) \le 6[/tex]

Step-by-step explanation:

Given

x = Cars from Baltimore to Trenton

y = Cars from Baltimore to Philadelphia

Required

Write out 6 inequalities

First, 0 or more cars must be shipped to both locations

So:

[tex]x \ge 0[/tex]

[tex]y \ge 0[/tex]

Considering the warehouse in Baltimore.

(1) The warehouse can not ship more than the number of car it has (9).

So:

[tex]x + y \le 9[/tex]

Considering the warehouse in New York.

(1) After shipping cars to Trenton and Philadelphia, the warehouse will have 0 or more cars.

So:

[tex]8 - x \ge 0[/tex] --- To Trenton

[tex]3 - y \ge 0[/tex] --- To Philadelphia

(2) The warehouse cannot send out more than 6.

So:

[tex](8 - x) + (3 - y) \le 6[/tex]

So, the inequalities are:

[tex]x \ge 0[/tex]

[tex]y \ge 0[/tex]

[tex]x + y \le 9[/tex]

[tex]8 - x \ge 0[/tex]

[tex]3 - y \ge 0[/tex]

[tex](8 - x) + (3 - y) \le 6[/tex]

Answer:

If Jenny gives her brother 28 marbles, they will have 59 marbles each.

Step-by-step explanation:

The key to finding this answer is a mean, or average. Find it for the number of marbles:

[tex]\text{Mean}=\frac{87+31}{2}= \frac{118}{2}=59 \text{ marbles}[/tex]

So, on average, each one should have 59 marbles.

Finally, to find out how many marbles Jenny should give to her brother, subtract the average (59 marbles) from her count:

[tex]87-59=28 \text{ marbles}[/tex]

This means Jenny would give up 28 of her marbles to her brother.

Answer/Step-by-step explanation:

There are actually two methods that can be used to calculate AC (x):

1. Using Pythagorean Theorem

2. Using Trigonometric Function

1. Using Pythagorean Theorem, we have:

x = √(15² + 20²)

x = √625

x = 25 units

2. Using Trigonometric Function:

Reference angle = 37°

Adjacent = 20

Opposite = 15

Hypotenuse = x

Apply SOH:

Sin 37 = Opp/Hyp

Sin 37 = 15/x

x × Sin 37 = 15

x = 15/sin 37

x = 24.9246021 ≈ 25 units (nearest whole number)

Answer:

3 times the difference of a number and 4 equals 12.

Step-by-step explanation:

Answer:

Hey mate.....

Step-by-step explanation:

This is ur answer.....

The first six multiples of 18 are :-

Hope it helps!

mark me brainliest plz....

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Answer:

x=6

Step-by-step explanation:

7x+5+13x-8+11x-3=180

31x-6=180

31x=186

x=186÷31

x=6

I wrote the wrong answer so I erased it

Answer: 1224 miles

Step-by-step explanation:

Given

the average speed of a person is 51 mph

If speed is increased to 72 mph, he would have reached 7 hr earlier

Suppose d and t be the distance and time taken

[tex]\Rightarrow t_1=\dfrac{d}{51}[/tex]

If the speed is 72 mph

[tex]\Rightarrow t_2=\dfrac{d}{72}[/tex]

Also, [tex]t_1-t_2=7[/tex]

[tex]\Rightarrow \dfrac{d}{51}-\dfrac{d}{72}=7\\\\\Rightarrow \dfrac{1}{51}-\dfrac{1}{72}=\dfrac{7}{d}\\\\\Rightarrow \dfrac{24-17}{1224}=\dfrac{7}{d}\\\\\Rightarrow \dfrac{7}{1224}=\dfrac{7}{d}\\\\\Rightarrow d=1224\ miles[/tex]

Answer:

 1/a = xy/(y-x)

Step-by-step explanation:

Simplify the reciprocal:

 1/a = 1/(1/x -1/y) = 1/((y-x)/(xy))

 1/a = xy/(y-x)

Answer:

140

Step-by-step explanation:

First we would find the unit rate of students per seventh. So we would do 40 divided by 2 which gives us 20. So per 1/7 we have 20 students. Which we can then say 7 x 20 = 140. So in total there are 140 students

Hope this helped

Answer:

x= 230

Step-by-step explanation:

since a circle is 360 degrees

x + 130 = 360

x= 360 -130

x=230

Answer:

8^(3n+1) = 80/5

8^(3n+1) = 16

(2^3)^(3n+1) = 2^4

2^(3*(3n+1) = 2^4

Having same power so;

9n+3 = 4

9n = 4-3

9n = 1

n = 1/9

Answer:x= 9

Step-by-step explanation:

-4(x+5) = 16

-4*x= -4x -4*5= -20

16 - -20= 36

-4x/-4= x 36/-4=9

Answer:

it takes his dad 3 hours

Step-by-step explanation:

4.5-1.5 =3

Answer:

A (50)

Step-by-step explanation:

Mean is the total numbers added up divided by the # of numbers.

There are 6 numbers.

51 + 60 + 80 + 32 + 47 + 30 = 300

300/6 = 50

Therefore, the answer is A.

Answer:

A

Step-by-step explanation:

Because to find the mean you add up all the numbers.

51+60+80+32+47+30=300

Then your suppose to divide by the sum.

300/6=50

Answer:

G

f is 6/8=3/4 = 75%

h is 9/12=3/4 = 75%

I is 3/4 = 75%

so the answer is G

Answer:

3.75%

Step-by-step explanation:

Total interest (4 years) - $3000

Annual interest (1 year) - $3000 ÷ 4 = $750

Annual interest rate (1 year) - [tex]\frac{750}{20 000}[/tex] × 100% = 3.75%

Checking:

Interest after 1 year - [tex]\frac{3.75}{100}[/tex] × $20,000 = $750

Interest after 4 years - $750 × 4 = $3000 (Correct)

Answer:

The interest rate was 3.75%.

Step-by-step explanation:

Attention: I am assuming simple interest here since I am not told otherwise.

Knowing Lebrun's interest was a total of $3000 on the $20000 loan, we can safely assume that it was a $750 interest flat fee paid on top of the loan amount dividing the $3000 by the four years it took for them to return the loan.

Dividing the amount of interest, in dollars, by the total amount of the loan and multiplying by 100, you will get the interest rate on the loan:

[tex]\frac{750}{20000}=\frac{75}{2000}=\frac{15}{400}=\frac{3}{80}\\\\\frac{3}{80}*100=\frac{3}{8}*10=\frac{30}{8}=3\frac{3}{4} =3.75\%[/tex]

Answer:

2

Step-by-step explanation:

(1/64)^-(1/6) = 64^(1/6) = 2

Answer:

8

Step by Step Explanation

Answer and Step-by-step explanation:

To find Z, we have to use the trigonometric function of Sine.

The Sine trig function looks like this:

sin(Angle) = [tex]= \frac{opposite.side}{hypotenuse}[/tex]

Plug in the values and solve for z.

[tex]sin(30) = \frac{4}{z} \\\\\\\\\\z = \frac{4}{sin(30)}[/tex]

Plug into a calculator and solve.

We get z to be 8.

#teamtrees #PAW (Plant And Water)

Answer:

05(9)+20

Step-by-step explanation:

becasue i know and this was the only way to allow me to give you the answer

Answer:

x+y≤15

Step-by-step explanation:

We need to write an inequality that represents the sum of x and y is at most 15. At most in inequality is defined as less than or equal to i.e. ≤.

Sum of x and y means x+y

The inequality becomes,

x+y≤15

Hence, the correct option is (b).

The inequality which represents the sum of x and y is at most 15 is; Choice (b) x+y_<15

According to question;

In essence, the sum of x and y is either equal to or lesser than 15.

Therefore, the inequality is Choice B; x+y_<15

Read more;

https://brainly.com/question/23382973

Answer:

1/5+8/10=1

Step-by-step explanation:

1/5 = 2/10

9514 1404 393

Answer:

  (a, b) = (√2/2, √2/2) . . . . . choice C in each case

Step-by-step explanation:

The points on a unit circle will not have coordinate values greater than 1 (eliminates √2). The coordinates will only be 0 or 1 if the point is on one of the axes. The coordinates (a, b) of the point at 45° are ...

  (cos(45°), sin(45°)) = (a, b) = (√2/2, √2/2)

The coordinate of point (a, b) is (√2/2, √2/2)

Note that the points on a unit circle will not have coordinate values greater than 1.

The coordinates will only be 0 or 1 if the point is on one of the axes. The coordinates (a, b) of the point at 45° is given according to the coordinate point (cos45, sin45)

a = cos45 = √2/2

b = sin45 = √2/2

Hence the coordinate of point (a, b) is (√2/2, √2/2)

Learn more on unit circle here: https://brainly.com/question/23989157

Answer:

lol

Step-by-step explanation:

Answer:

one there is no milk in the fridge but you already poured the cereal

Answer:

B

Step-by-step explanation:

Answer:

The ratio of a 45-45-90 traingle is 1:1:[tex]\sqrt{2}[/tex].

Answer:

69.72 inches.

Step-by-step explanation:

The best point estimate for the average height if males in the United States is...

For large samples, as we have here, the best point estimate is the sample mean. In this question, the sample mean is of 69.72 inches, so the answer is 69.72 inches.

Answer:

slope of AB = -1/2

slope of CD = -2

No.

Step-by-step explanation:

slope of AB = (5-7)/(6-2) = -2/4=-1/2

slope of CD = (-6-2)/(4-0) = -8/4 =-2

for being two opposite sides of parallelogram, their slopes should be equal. But there slopes aren't equal

Answer:

It definitely is linear, and it is a straight line

Step-by-step explanation:

Try using desmos, it may help

Answer:

A) it is linear and it is a straight line

Step-by-step explanation:

it is a linear equation. It will be straight

y=mx+b is linear