MATHEMATICS COLLEGE

Although still a sophomore at college, John O'Hagan's son Billy-Sean has already created several commercial video games and is currently working on his most ambitious project to date: a game called K that purports to be a "simulation of the world." John O'Hagan has decided to set aside some office space for Billy-Sean against the northern wall in the headquarters penthouse. The construction of the partition will cost $8 per foot for the south wall and $12 per foot for the east and west walls.What are the dimensions of the office space with the largest area that can be provided for Billy-Sean with a budget of $432?south wall length ft -east and west wall length -What is its area?

Answers

Answer 1

Answer:

Answer:

27 feet for the south wall and 18 feet for the east/west walls

Maximum area= $486\ ft^2$

Step-by-step explanation:

Optimization

This is a simple case where an objective function must be minimized or maximized, given some restrictions coming in the form of equations.

The first derivative method will be used to find the values of the parameters that control the objective function and the maximum value of that function.

The office space for Billy-Sean will have the form of a rectangle of dimensions x and y, being x the number of feet for the south wall and y the number of feet for the west wall. The total cost of the space is

C=8x+12y

The budget to build the office space is $432, thus

$8x+12y=432$

Solving for y

$\displaystyle y=(432-8x)/(12)$

The area of the office space is

$A=xy$

Replacing the value found above

$\displaystyle A=x\cdot (432-8x)/(12)$

Operating

$\displaystyle A= (432x-8x^2)/(12)$

This is the objective function and must be maximized. Taking its first derivative and equating to 0:

$\displaystyle A'= (432-16x)/(12)=0$

Operating

$432-16x=0$

Solving

$x=432/16=27$

$x=27\ feet$

Calculating y

$\displaystyle y=(432-8\cdot 27)/(12)$

$y=18\ feet$

Compute the second derivative to ensure it's a maximum

$\displaystyle A'= (-16x)/(12)$

Since it's negative for x positive, the values found are a maximum for the area of the office space, which area is

$A=xy=27\ ft\cdot 18\ ft\n\n\boxed{A=486\ ft^2}$

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Simplify –2x 3 y × xy 2 . A. –3x 4y 3 B. –12x 4y 3 C. –2x 3y 4
Basic kinematics. Please help! Will give brainliest! Show all work!

Which statement about the data in the table shown is true?x –2 –1 0 1
y –3 –1 1 3
A. The data do not represent a function.
B. The data represent a nonlinear function.
C. The data represent a quadratic function.
D. The data represent a linear function

Answers

Answer:

i would say B.. sorry of its not the right one..

Step-by-step explanation:

Answer:

Step-by-step explanation:

What is the greatest common factor of 8x and 40y?

8
8xy
320
320xy

Answers

The greatest common factor of 8x and 40y is 8.

What are Factors?

Factors of a number or an algebraic expression are the numbers or expressions which divides the given number evenly.

For example, 10 = 2 × 5

So we can say that 2 and 5 are factors of 10.

Greatest common factor of two or more numbers is the factor which is the greatest among all the common factors of both the numbers.

8x can be prime factorized as,

8x = 2 × 2 × 2 × x

Similarly, 40y can be prime factorized as,

40y = 2 × 2 × 2 × 5 × y

Greatest common factor of both the numbers is the product of the common prime factors of both.

Greatest common factor = 2 × 2 × 2 = 8, which is common to both.

Hence 8 is the greatest common factor of 8x and 40y.

Learn more about Greatest Common Factors here :

brainly.com/question/11221202

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Answer:

Hope this helps!

How many integers between 160 and 279 inclusive, are divisible by 7?

Answers

Answer:

Step-by-step explanation:

We can put this as an AP (arithmetic progression).

The first number, after 160, that is divisible by 7 is:

161

The last number before 279 that is divisible by 7 is:

273

We can use the formula:

$t_n=a+(n-1)d$

Where

tn is the nth term [here we take the last one, 273

a is the first term [161]

d is the common difference [7]

and n is the number of terms, we are trying to find this.

Substituting we get:

$t_n=a+(n-1)d\n273=161+(n-1)(7)\n273=161+7n-7\n273=154+7n\n7n=119\nn=17$

Hence, there are 17 integers

Use a table to multiply (–5a)(2a – 1). A) –15a B) 5a2 + 10a C) –10a2 – 5a D) –10a2 + 5a

Answers

Answer:

-10a² + 5a

Step-by-step explanation:

Given the expression (–5a)(2a – 1)

Open the bracket

(–5a)(2a – 1)

= -5a(2a) -5a(-1)

= -10a² + 5a

hence the equivalent expression is -10a² + 5a

Laquita divides 3 pizzas equally among her 5 children how much pizza does each child receive

Answers

Answer:

0.6

Step-by-step explanation:

each child gets just over half a pizza

Answer:

About 4

Step-by-step explanation:

Depends how many slices each pizza is but based on the average 8 slice pizza, 8 slices each pizza 3 pizzas 8*3= 24 slices

24/5= about 4 slices per child with 4 slices left

Use the distance formula to find the distance between (−8, 2.5) and (0, −4.5).d = StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
1. Substitute coordinates: d = StartRoot (negative 8 minus 0) squared + (2.5 minus (negative 4.5)) squared EndRoot
2. Simplify parentheses: d = StartRoot (negative 8) squared + (7) squared EndRoot
3. Evaluate powers: d = StartRoot 64 + 49 EndRoot
4. Simplify.
What is the distance between (–8, 2.5) and (0, –4.5)? Round to the nearest hundredth.

d ≈

Answers

The distance between points (- 8, 2.5) and (0, - 4.5) is,

⇒ d = 10.67

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

Two points are,

⇒ (- 8, 2.5) and (0, - 4.5)

Hence, The distance between (- 8, 2.5) and (0, - 4.5) is,

d = √ (- 8 - 0)² + (2.5 + 4.5)²

d = √ 64 + 7²

d = √64 + 49

d = √114

d = 10.67

Thus, The distance between points (- 8, 2.5) and (0, - 4.5) is,

⇒ d = 10.67

Learn more about the coordinate visit: