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Simora [160]
3 years ago
9

Do ya'll the answer to this problem well its not really a problem you have to write the equation.

Mathematics
1 answer:
AleksandrR [38]3 years ago
5 0

Z Z Z Z Z Z Z Z Z Z  Z Z Z  Z Z Z Z Z Z  Z Z  Z Z Z Z  Z Z Z  Z Z Z  Z

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A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimen
Vikki [24]

Answer:

bottom side (a) = 3.36 ft

lateral side (b) = 4.68 ft

Step-by-step explanation:

We have to maximize the area of the window, subject to a constraint in the perimeter of the window.

If we defined a as the bottom side, and b as the lateral side, we have the area defined as:

A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}

The restriction is that the perimeter have to be 12 ft at most:

P=(a+2b)+\dfrac{\pi a}{2}=2b+a+(\dfrac{\pi}{2}) a=2b+(1+\dfrac{\pi}{2})a=12

We can express b in function of a as:

2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a

Then, the area become:

A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2

To maximize the area, we derive and equal to zero:

\dfrac{dA}{da}=6-2\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right )a=0\\\\\\6-(1-\pi/4)a=0\\\\a=\dfrac{6}{(1+\pi/4)}\approx6/1.78\approx 3.36

Then, b is:

b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a\\\\\\b=6-0.393*3.36=6-1.32\\\\b=4.68

3 0
3 years ago
I need help for this question please!!!!
Arisa [49]

Answer:

a. 35 degrees

b. 145 degrees

Step-by-step explanation:

a. Since the two base angles of this triangle are congruent, we can conclude that the triangle is <em>isosceles, </em>which means that the two base angles and sides are congruent.

Now, knowing that information, we can subtract 110 from 180 (the sum of all interior angles in a triangle) and we get 70. But this isn't our answer. This is the sum of both base angles. Since the base angles are congruent, we can divide the 70 by 2 to get the measure of ONE base angle, which is 35 degrees.

b. There are two approaches to solve this problem. I have worked both out.

1) We can use the Exterior Angle Theorem, which states that the sum of the interior angles is equal to the exterior angle. We can add 110 to 35, so we get 145 degrees as the measure of <1.

2) The second approach is supplementary angles. Since we see that one of the base angles and <1 is on the same line, we can subtract 35 from 180 to find the measure of <1 to get 145 degrees.

Either way you use, you get the correct answer. Hope this helped!

6 0
3 years ago
Avery has 2 blue marbles. One sixth of Avery's marbles are blue. How many marbles does Avery have?
dedylja [7]
Avery has 12 marbles total. 2 x 6 = 12
5 0
3 years ago
Plzzzzz help meee plz due today soon
katovenus [111]

Answer:

a

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Use the points (2, 14) and (10, 22) to write the equation of the line of best fit shown
luda_lava [24]

Answer:

The equation of the line best fit is y = x + 12

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

  • m is the slope of the line
  • b is the y-intercept

The rule of the slope is m = \frac{y2-y1}{x2-x1} , where

  • (x1, y1) and (x2, y2) are two points on the line

∵ The line passes through points (2, 14) and (10, 22)

∴ x1 = 2 and y1 = 14

∴ x2 = 10 and y2 = 22

→ Substitute them in the rule of the slope above to find it

∵ m = \frac{22-14}{10-2}=\frac{8}{8}=1

∴ m = 1

→ Substitute it in the form of the equation above

∴ y = (1)x + b

∴ y = x + b

→ To find b substitute x by 2 and y by 14 in the equation

∵ 14 = 2 + b

→ Subtract 2 from both sides

∴ 14 - 2 = 2 - 2 + b

∴ 12 = b

→ Substitute it in the equation

∴ y = x + 12

∴ The equation of the line best fit is y = x + 12

8 0
3 years ago
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