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2 years ago

Which of the following is true?

Mathematics

1 answer:

marin [14]2 years ago

7 0

Step-by-step explanation:

0 is neither a rational number nor an irrational number

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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

Solve 3b - 8 = 7b - 2 -4b

lutik1710 [3]

Answer:

Step-by-step explanation:

Start by combing the terms on the right. 3b - 8 = 3b - 2 because 7b - 4b is going to equal 3b

You are now officially stuck. The moment you try and put the 3b's on the same side of the equation, they will cancel out. There is no unique solution.

6 0

3 years ago

Which of the following is a solution of the inequality 0.75n + 1.5 < 59.25

mojhsa [17]

Answer:

b.77

Step-by-step explanation:

0.75n + 1.5 < 59.25

0.75n < 59.25 - 1.5

0.75n < 57.75

n < 57.75 / 0.75

n < 77

5 0

3 years ago

Median and range of 11,17,19,6,17

Alexxandr [17]

6,11,17,17,19
median is 17
11+17+19+6+17=70
70/5=14
mean is 14
19-6=13
13 is range

6 0

2 years ago

Jill had 2 apples. Addy gave Jill 5 more apples. How many apples does Jill have altogether? Mark, you brainlieest if correct!

Sidana [21]

Answer:

its 7 apples

Step-by-step explanation:

Brainliest pls

6 0

3 years ago

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