business/multivariable calc question
help needed asap!!!!

I solved and got a max of (8/5,8) at 64/5

Answers

Answer 1

Answers:

There is a  max   value of   81/8   located at (x,y) =   (9/8, 9)  

=============================================================

Explanation:

Solve the second equation for y

8x+y = 18

y = 18-8x

Plug this into the first equation

f(x,y) = x*y

g(x) = x*(18-8x)

g(x) = 18x-8x^2

This graphs out a parabola that opens downward, and has a max point at the vertex.

If you apply the derivative to this, you get g ' (x) = 18 - 16x

Set this equal to zero and solve for x

g ' (x) = 0

18 - 16x = 0

18 = 16x

16x = 18

x = 18/16

x = 9/8

Use this x value to find y

y = 18 - 8x

y = 18 - 8(9/8)

y = 18 - 9

y = 9

So the max is x*y = (9/8)*9 = 81/8

Or we could say

g(x) = 18x-8x^2

g(9/8) = 18(9/8)-8(9/8)^2

g(9/8) = 81/8

----------------

To summarize,

There is a  max   value of   81/8   located at (x,y) =   (9/8, 9)  

When saying "max value of something", we're basically talking about the largest f(x,y) value. Which in this case is the largest x*y value based on the fact that 8x+y = 18.

A practical real world example of a problem like this would be if you wanted to max out a certain rectangular area based on constraints of how much building material you have for the fence.


Related Questions

True or false?
A function assigns each value of the independent variable to exactly one
value of the dependent variable.
A. True
B. False
SUB

Answers

Answer:

This statement would be true.

Step-by-step explanation:

Yep this a true statement

Factor 64a^3 -8b^3 Explain all steps.

Answers

Answer:

[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]

Step-by-step explanation:

factor out the 8

then you have the sum/difference of cubes..

look that up SOAP: same opposite, always a plus

[tex]64a^3 -8b^3\\8(8a^3 -b^3)[/tex]

[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]

44y + 321x = 0 biết x=30000

Answers

Answer:

y= -240750/11

Step-by-step explanation:

44y + 321. 30000 = 0

44y = - 963000

y= -240750/11

Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 2.1yd : 1.4yd

Answers

9514 1404 393

Answer:

  3/2

Step-by-step explanation:

Multiplying numerator and denominator by 10 will convert the ratio to a ratio of whole numbers. Then dividing by the common factor of 7 will reduce it to simplest form.

  [tex]\dfrac{2.1\text{ yd}}{1.4\text{ yd}}=\dfrac{2.1\times10}{1.4\times10}=\dfrac{21}{14}=\dfrac{3\times7}{2\times7}=\boxed{\dfrac{3}{2}}[/tex]

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is four
times the measure of the first angle. The third angle is 10 more than the second. Let , y, and z represent the measures of
the first, second, and third angles, respectively. Find the measures of the three angles.

Answers

9514 1404 393

Answer:

 (36°, 67°, 77°)

Step-by-step explanation:

The problem statement lets us write the equations ...

  x + y + z = 180 . . . . sum of angles in a triangle

  y + z = 4x . . . . . 2nd and 3rd total 4 times the first

  z = y +10 . . . . . . 3rd is 10 more than 2nd

__

Substituting for z in the second equation, we have ...

  y +(y +10) = 4x

  y +5 = 2x . . . . . . divide by 2

  y = 2x -5 . . . . . . rearranged

  z = 2x +5 . . . . . . substitute for y in the last equation

Now, we can write the first equation entirely in terms of x:

  x +(2x -5) +(2x +5) = 180

  5x = 180

  x = 36

  y = 2(36) -5 = 67

  z = 67 +10 = 77

The three angles are (x, y, z) = (36°, 67°, 77°).

help???

if abc =70 is what is adc ​

Answers

Answer:

I belive it is 46

Step-by-step explanation:

PLEASE HELP

Solve the equation for y. Identify the slope and y-intercept then graph the equation.

2y-3x=10

Y=
M=
B=

Please Include a picture of the graph and show your work if you can

Answers

Hey there! I'm happy to help!

Here is our equation.

[tex]2y-3x=10[/tex]

Let's add 3x to both sides.

[tex]2y=3x+10[/tex]

Divide both sides by 2.

[tex]y=\frac{3}{2}x+5[/tex]

Here is slope intercept form.

[tex]y=mx+b\\m=slope\\b=y-intercept[/tex]

So, we can just find those two things in the equation, and here are our answers.

[tex]y=\frac{3}{2}x+5\\m=\frac{3}{2}\\b=5[/tex]

The graph is down below. If our y-intercept is 5, then one of our points is (0,5). You can then plug a random x-value into the formula to find another point and then draw the line going through the two points.

[tex]y=\frac{3}{2}(2)+5\\y=3+5\\y=8\\(2,8)[/tex]

Have a wonderful day and keep on learning! :D

Use the substitution methed to solve the system of equations. Choose the correct ordered pair.
2y+5x=13
2y+3x=5

Answers

Solve both equations for 2y :

2y + 5x = 13   ==>   2y = 13 - 5x

2y + 3x = 5   ==>   2y = 5 - 3x

Solve for x :

13 - 5x = 5 - 3x

8 = 2x

x = 4

Solve for y :

2y = 13 - 5×4

2y = -7

y = -7/2

As an ordered pair, the solution is then the point (x, y) = (4, -7/2).

Please help do in an hour

Answers

Answer:

-4

Step-by-step explanation:

a1 = -8

an = an-1 +2

a2 = a1+2 = -8+2 = -6

a3 = a2+2 = -6+2 = -4

solve the following inequality -1≤d+2/5≤6∕5

Answers

Answer:

-7/5≤d≤4∕5

Step-by-step explanation:

-1≤d+2/5≤6∕5

Subtract 2/5 from all parts

-1-2/5≤d+2/5-2/5≤6∕5-2/5

-5/5-2/5≤d+≤4∕5

-7/5≤d≤4∕5

What is the volume of the following rectangular prism?

Answers

Answer:

44/3

Step-by-step explanation:

V=L*W*H

WH=22/3

V=2*(22/3)

I need help ASAP please

Answers

Answer:

5:10

6 (-2,0)

7 (-5,6)

8 (5,3)

9 No, ab=8 CD=6

Step-by-step explanation:

please Help with my area math question. ​ I don't remember how to do it. multiply or add? and what is the answer to this?

Answers

Answer:

100 inches^3

Step-by-step explanation:

The volume of the back rectangle is

V = l*w*h

V = 8*5*1 = 40 inches ^3

The volume of the front rectangle is

V = 6*2*5 = 60 inches^3

Add the volumes

40+60 = 100 inches^3

50T Q12 A man wants to buy bags of gravel to cover his driveway. He decides to work out the area of his driveway. 1 bag of gravel covers 14m2 3m Sketch of driveway Not to scale 3m 8m 6m What is the area of his driveway? How many bags of gravel must he buy?​

Answers

Answer:

hi amki nai patajjdkfkejd

Below is a geometric sequence. 3, 9, 27, 51, ... (b) what is the common raters if the geometric sequence?​

Answers

They multiply by three each time

3*3=9, 9*3=27, etc etc

2. In a 100m race, Luke was 2m ahead of Azam. Chandra was 3m behind Luke, Maggie was 7m ahead of Chandra. Luke was 5m behind Darren. Who was in the first place?​

Answers

Answer:

luke won

Step-by-step explanation:

he is 2 meters ahead of azam witch is in 2dn place

Maggie is the winner. She was the most ahead

Find the first five terms of the sequence..

Answers

Answer:

The Next fiver tems are - 2, -2,-8,-12,-16

Step-by-step explanation:

Answer:

2,-6,2,-6,2

Step-by-step explanation:

a1 = 2

an = -an-1 -4

Let n =2

a2 = -a1 -4 = -2-4 = -6

Let n=3

a3 = -a2 -4 = - (-6) -4 = +6 -4 = 2

Let n = 4

a4 = -a3 -4 = -2 -4 = -6

Let n=5

a5 = -a4 -4 = -(-6) -4 = +6-4 = 2

At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .50. Find the probability that in a sample of 14 customers, at least 7 will order a nonalcoholic beverage

Answers

For each customer, there are only two possible outcomes. Either they will order an alcoholic beverage, or they will not. The probability of a customer ordering an alcoholic beverage is independent of any other customer, which means that the binomial probability distribution is used to solve this question..

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .50

This means that [tex]p = 0.5[/tex]

Sample of 14 customers

This means that [tex]n = 14[/tex]

Probability that at least 7 will order a nonalcoholic beverage

This is:

[tex]P(X \geq 7) = 1 - P(X < 7)[/tex]

In which

[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)[/tex]

Then

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{14,0}.(0.5)^{0}.(0.5)^{14} = 0.0001[/tex]

[tex]P(X = 1) = C_{14,1}.(0.5)^{1}.(0.5)^{13} = 0.0009[/tex]

[tex]P(X = 2) = C_{14,2}.(0.5)^{2}.(0.5)^{12} = 0.0056[/tex]

[tex]P(X = 3) = C_{14,3}.(0.5)^{3}.(0.5)^{11} = 0.0222[/tex]

[tex]P(X = 4) = C_{14,4}.(0.5)^{4}.(0.5)^{10} = 0.0611[/tex]

[tex]P(X = 5) = C_{14,5}.(0.5)^{5}.(0.5)^{9} = 0.1222[/tex]

[tex]P(X = 6) = C_{14,6}.(0.5)^{6}.(0.5)^{8} = 0.1833[/tex]

So

[tex]P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0001 + 0.0009 + 0.0056 + 0.0222 + 0.0611 + 0.1222 + 0.1833 = 0.3954[/tex]

[tex]P(X \geq 7) = 1 - P(X < 7) = 1 - 0.3954 = 0.6046[/tex]

0.6046 = 60.46% probability that at least 7 will order a nonalcoholic beverage.

For more on the binomial distribution, you can check https://brainly.com/question/15557838

are ratios 2:3 and 8:12 equalvelent to eachother

Answers

Answer:

2:3 is equal to 8:12

Step-by-step explanation:

2:3

To get the first number to 8

8/2 = 4

Multiply by all terms 4

2*3 : 3*4

8:12

2:3 is equal to 8:12

8:12 = 8/12

= 2/3

= 2:3

Therefore 2:3 and 8:12 are equalent to each other.

Answered by Gauthmath must click thanks and mark brainliest

find the measure of a

Answers

Answer:

Hello,

answer D 48°

Step-by-step explanation:

In the right triangle down, a+42°=90° ==> a=90°-42°=48°

Express the prime number 19 as the difference of two squares? 19 =​

Answers

Answer:

The two squares are 81 and 100, and their difference is 19

Step-by-step explanation:

Hey there!

Let's take out the square of 1st ten natural numbers to find out the exact answer.

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

Now; You can take any of these numbers and subtract from their squares.

So, let's check 6² and 5²

36-25 = 11 which is not equal to 19

Again check for 10²-9²

100 - 81 = 19 (True value)

Therefore, 19 can be expressed as the difference of square of 10 and 9.

Hope it helps!

Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ? f (x) = x3 – 2x2 – 3x + 6, f (x)= x3 – 2x2 + 3x + 6, f (x) = x3 + 2x2 – 3x + 6, f (x) = x3 + 2x2 – 3x – 6

Answers

To solve this question, we use the factor theorem, and using it, the polynomial function is:

[tex]f(x) = x^3 - 2x^2 - 3x + 6[/tex]

------------------------------

The factor theorem means that if k is a root of f(x), f(k) = 0.

Thus, applying the factor theorem for this question, we have to choose the function for which: [tex]f(2) = 0, f(\sqrt{3}) = 0, f(-\sqrt{3}) = 0[/tex]

------------------------------

Function 1:

[tex]f(x) = x^3 - 2x^2 - 3x + 6[/tex]

Testing the values:

[tex]f(2) = 2^3 - 2(2)^2 - 3(2) + 6 = 8 - 8 - 6 + 6 = 0[/tex]

[tex]f(\sqrt{3}) = \sqrt{3^3} - 2(\sqrt{3})^2 - 3\sqrt{3} + 6 = \sqrt{3^2\times3} - 6 - 3\sqrt{3} + 6 = 3\sqrt{3} - 3\sqrt{3} = 0[/tex]

[tex]f(-\sqrt{3}) = -\sqrt{3^3} - 2(-\sqrt{3})^2 - 3(-\sqrt{3}) + 6 = -\sqrt{3^2\times3} - 6 + 3\sqrt{3} + 6 = -3\sqrt{3} + 3\sqrt{3} = 0[/tex]

Thus, since all three conditions are satisfied, [tex]f(x) = x^3 - 2x^2 - 3x + 6[/tex] is the polynomial function.

A similar question is given at https://brainly.com/question/11378552

Álgebra 2 need help

Answers

Answer:

first term = -1/5

I cant see part b (sorry its too blurry)

thirteenth term = -0.2

part d: -19a/95a -0.2a

Step-by-step explanation:

socratic

I purchased a new Apple iPad on Amazon for $249.00. The tax rate is 8.625%. What is the total purchase price of the iPad?

Answers

Answer:

270.47625

Step-by-step explanation:

249 is the original price

(249/100) · 8.625 = 21.47625 the tax total

249 + 21.47625 = 270.47625

Fill in the blank by performing the indicated elementary row operation(s).
6
1
5
-6R2+R
1
-5
0
Answer 7 Points
Keybo
<
Prev

Answers

In this question, we are given a matrix, and we have to perform the given operation.

The matrix is:

[tex]\left[\begin{array}{ccc}6&-1&|5\\1&-5&|0\end{array}\right][/tex]

The following operation is given:

[tex]R_1 \rightarrow -6R_2 + R_1[/tex]

In which [tex]R_1[/tex] is the element at the first line and [tex]R_2[/tex] is the element at the second line.

Updating the first line:

[tex]R_{1,1} = -6*1 + 6 = 0[/tex]

[tex]R_{1,2} = -6*-5 - 1 = 30 - 1 = 29[/tex]

[tex]R_{1,3} = -6*0 + 5 = 5[/tex]

Thus, the filled matrix will be given by:

[tex]\left[\begin{array}{ccc}0&29&|5\\1&-5&|0\end{array}\right][/tex]

For another example where row operations are applied on a matrix, you can check https://brainly.com/question/18546657

solve the equation
0.09w+1.8

Answers

Step-by-step explanation:

0.09w + 1.8 = 0

0.09w = 0 - 1.8

0.09w = - 1.8

0.09w ÷ 0.09 = - 1.8/ 0.09

w = - 20

please help me with geometry

Answers

Answer:

A. If the side lengths are the same, then a triangle is not scalene.

Step-by-step explanation:

A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.

Simply stated, any polygon with three (3) lengths of sides is a triangle.

In Geometry, a triangle is considered to be the most important shape.

Generally, there are three (3) main types of triangle based on the length of their sides and these include;

I. Equilateral triangle: it has all of its three (3) sides and interior angles equal.

II. Isosceles triangle: it has two (2) of its sides equal in length and two (2) equal angles.

III. Scalene triangle: it has all of its three (3) sides and interior angles different in length and size respectively.

This graph represents which expression?

Answers

Answer:

x >7

Step-by-step explanation:

There is an open circle at 7, which means it cannot equal 7.  The line goes to the right

x >7

What is the sum of the interior angles of a regular polygon with 5 sides?

A. 1260
B. 180
C. 360
D. 540

Answers

Answer:

540 is the ans

Step-by-step explanation:

this is the correct answer

180

Step-by-step explanation:

the measure of interior angles of polygon =180×(n-2)

Find the equation of a line that is perpendicular to x+y=8 and passes through the point (8, 10).

Answers

Answer:

Y = -x + 2

Step-by-step explanation:

y = -x + 8

y = 1x + b

10 = 8 + b

b = 2

Answer:

y-y1=m(x-x1)

y-10=8(x-8)

y-10=8x-64

y-10+64-8x

y+54-8x

y-8x+54

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