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4 years ago

What dimensions would maximize the area of a rectangle with a perimeter of 40 centimeters

1 answer:

3 0

Hi,
For all rectangle having a perimeter constant, the square have the maximum area.
So the rectangle is a square of 10 cm of side.
On other method:
Let assume x le length of the rectangle,(40-2*x)/2=20-x is the width
area=y=x*(20-x)
y=20x-x²
a)
y'=20-2x=0==>x=10 and y=10
b) y=-(x²-2*10*x+100)+100y=100-(x-10)² is maximum if x=10.

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Find two consecutive positive intergers such that the square of the smaller interger is nineteen more than five times the larger

Naddika [18.5K]

Answer:

8 and 9

Step-by-step explanation:

Let the two consecutive integers be x - 1 and x

Smaller = x-1

Largere = x

If the square of the smaller integer is nineteen more than five times the larger integer, then;

(x-1)² = 19 + 5x

Expand

x²-2x+1= 19+5x

x²-2x-5x+1-19 -0

x²-7x-18 =0

Factorize

x²-9x+2x-18 =0

x(x-9)+2(x-9) = 0

(x+2) = 0 and x - 9 = 0

x = -2 and 9

SInce x cannot be negative;

x = 9

Smaller number = 9-1

Smaller number = 8

Hence the two consecutive integers are 8 and 9

6 0

3 years ago

Elle wanted to order candy online. Company A is offering 2 1/2 pounds of chocolate for $32.50, while Company B is offering 2 3/4

podryga [215]

To determine price per lb, divide dollar amount by lbs.
- Company A sells 2 1/2lbs (2.5lbs) for $32.50
So, Company A's price / lb = ($32.50/2.5lbs) = $13.00/lb

- Company B sells 2 3/4lbs (2.75lbs) for $35.00
And, Company B's price / lb = ($35.00/2.75lbs) = $12.73/lb

Therefore, Company B is offering the lowest price/lb at $12.73/lb.

5 0

4 years ago

Can someone please tell me what is the solution

vovangra [49]

Answer:

$\frac{1}{4} \tan {}^{4}(x) + c$

8 0

3 years ago

The expression wA - 36 is equivalent to

lions [1.4K]

Answer:

4. (w² + 6)(w² - 6)

Step-by-step explanation:

w^4 - 36

(w² + 6)(w² - 6)

8 0

3 years ago

What is the answer??

denis-greek [22]

Answer:

10a²+5ab+2b²

Step-by-step explanation:

Start by combining like terms aka the ones that match:

Step 1: (4a²-5ab-6b²) + (10ab+6a²+8b²)

Step 2: (10a²-5ab-6b²) + (10ab+8b²)

Step 3: (10a²+5ab-6b²+8b²)

Final answer: 10a²+5ab+2b²

In step 1, I added the 4 and 6. In step 2, I added -5 and 10. In step 3, I added -6 and 8. For each I attached the proper ending (a², ab, and b²).

I hope this clears some confusion!

3 0

3 years ago