The sum of two numbers is 38 and the difference is 10 what are the numbers

g A window is being built and the bottom is a rectangle and the top is a semi-circle. If there is 12 meters of framing materials

photoshop1234 [79]

Answer:

Semicircle of radius of 1.6803 meters

Rectangle of dimensions 3.3606m x 1.6803m

Step-by-step explanation:

Let the radius of the semicircle on the top=r

Let the height of the rectangle =h

Since the semicircle is on top of the window, the width of the rectangular portion =Diameter of the Semicircle =2r

The Perimeter of the Window

=Length of the three sides on the rectangular portion + circumference of the semicircle

$=h+h+2r+\pi r=2h+2r+\pi r=12$

The area of the window is what we want to maximize.

Area of the Window=Area of Rectangle+Area of Semicircle

$=2hr+\frac{\pi r^2}{2}$

We are trying to Maximize A subject to $2h+2r+\pi r=12$

$2h+2r+\pi r=12\\h=6-r-\frac{\pi r}{2}$

The first and second derivatives are,

Area, A(r) $=2r(6-r-\frac{\pi r}{2})+\frac{\pi r^2}{2}}=12r-2r^2-\frac{\pi r^2}{2}$

Taking the first and second derivatives

$A'\left( r \right) = 12 - r\left( {4 + \pi } \right)\\A''\left( r \right) = - 4 - \pi$

From the two derivatives above, we see that the only critical point of r

$A'\left( r \right) = 12 - r\left( {4 + \pi } \right)=0$

$r = \frac{{12}}{{4 + \pi }} = 1.6803$

Since the second derivative is a negative constant, the maximum area must occur at this point.

$h=6-1.6803-\frac{\pi X1.6803}{2}=1.6803$

So, for the maximum area the semicircle on top must have a radius of 1.6803 meters and the rectangle must have the dimensions 3.3606m x 1.6803m ( Recall, The other dimension of the window = 2r)

5 0

3 years ago

70% of days in june were sunny how many days were sunny

goblinko [34]

There are 30 days in June. So 30 days represent 100% of the days:

30 = 100% & x = 70%

so 100x= 2100

x= 21 Days

I hope this helps you! =^-^=

6 0

2 years ago

3x + 11 - 2y + 4x - 6 + 5y <br><br> please solve!!! just simplify by combining like terms

rusak2 [61]

the answer to your question is
7y+7x+5

6 0

3 years ago

Read 2 more answers

The perimeter of a square is 12p +4. One side of the square equals? Explain your answer.

Hoochie [10]

We know that a square, by definition, has four congruent sides.

So, simply divide the perimeter by 4, and you will get the expression equivalent to each side: 12p+4/4

3p+1 is equal to one side of the square

3 0

2 years ago

ANSWER THREE THROUGH FIVE , ILL GIVE YOU BRAINLIST!!!

Ray Of Light [21]

Answer:

Step-by-step explanation:

3) diameter of penny = 19 mm

r = 19/2 = 9.5 mm

Area of penny = πr²

= 3.14 * 9.5 * 9.5

= 283.385

= 283.39 mm²

Diameter of nickel = 21 mm

r = 21/2 = 10.5 mm

Area of nickel = πr²

= 3.14 * 10.5 *10.5

= 346.185

= 346.19 mm²

346.19 - 283.39 = 62.8 mm²

Area of Canadian nickel is greater than Canadian penny by 32.6 mm²

4) r = 12 mm

Area of circle = πr²

= 3.14 * 12 * 12

= 452.16 mm²

5) r = 20 cm

Area of circle = πr²

= 3.14 * 20 * 20

= 1256 cm²

6 0

3 years ago