Determine the dimensions of the rectangle of largest area that can be inscribed in a semicircle of radius 4

Answers

Answer 1

Answer:

The length and width that maximize the area are:

W = 2*√8

L = 2*√8

Step-by-step explanation:

We want to find the largest area of a rectangle inscribed in a semicircle of radius 4.

Remember that the area of a rectangle of length L  and width W, is:

A = L*W

You can see the image below to see how i will define the length and the width:

L = 2*x'

W = 2*y'

Where we have the relation:

4 = √(x'^2 + y'^2)

16 = x'^2 + y'^2

Now we can isolate one of the variables, for example, x'

16 - y'^2 = x^'2

√(16 - y'^2) = x'

Then we can write:

W = 2*y'

L = 2*√(16 - y'^2)

Then the area equation is:

A = 2*y'*2*√(16 - y'^2)

A = 4*y'*√(16 - y'^2)

If A > 1, like in our case, maximizing A is the same as maximizing A^2

Then if que square both sides:

A^2 = (4*y'*√(16 - y'^2))^2

      = 16*(y'^2)*(16 - y'^2)

      = 16*(y'^2)*16 - 16*y'^4

      = 256*(y'^2) - 16*y'^4

Now we can define:

u = y'^2

then the equation that we want to maximize is:

f(u) = 256*u - 16*u^2

to find the maximum, we need to evaluate in the zero of the derivative:

f'(u) = 256 - 2*16*u = 0

      u = -256/(-2*16) = 8

Then we have:

u = y'^2 = 8

solving for y'

y' = √8

And we know that:

x' = √(16 - y'^2) = √(16 - (√8)^2) = √8

And the dimensions was:

W = 2*y' = 2*√8

L = 2*y' = 2*√8

These are the dimensions that maximize the area.

Determine The Dimensions Of The Rectangle Of Largest Area That Can Be Inscribed In A Semicircle Of Radius

Related Questions

the diagram below shows a square inside a regular hexagon. The apothem of the hexagon is 18.11 units. To the nearest square unit, what is the area of the shaded region.

A. 1027 square units
B. 1087 square units
C. 862 square units
D. 1948 square units

Answers

the answer is 862sq units probably

x y
10 27
11 a
12 11

In order for the data in the table to represent a linear function with a rate of change of -8, what must be the value of a?

a = 2
a = 3
a = 19
a = 35​

Answers

Answer:

a = 19

Step-by-step explanation:

If the rate of change is -8, subtract 8 from your y value of 27. And if 19 is correct, you should be able to subtract 8, and get 11 as the next number in the function, which you do, so 19 is the value of a.

Please help, it is a graph question

Answers

Answer:

[tex]y = \frac{1}{2} x + \frac{1}{2} [/tex]

Step-by-step explanation:

choose 2 points to find slope

(1,1) (-3,-1)

[tex]m = \frac{ - 1 - 1}{ - 3 - 1} = \frac{1}{2} [/tex]

y-y1 = m(x-x1)

y-1 = 1/2( x-1)

y = 1/2x + 1/2

guessing

y= 1/2x + 1/2

did y2 - y1/ x2-x1

which gave

-3

-6

also it passed through the y axis at +1/2

álgebra 1 solve -2 + 11(17y + 15)

Answers

Answer:   187y + 163

Work Shown:

-2 + 11(17y + 15)

-2 + 11(17y) + 11(15) .... distributive property

-2 + 187y + 165

187y + (-2+165)

187y + 163

Factor 60 − 36w, to identify the equivalent expressions.

Answers

Step-by-step explanation:

60-36w6(10-6w)

hope it helps

stay safe healthy and happy..

Answer:

all of the answers are correct

Step-by-step explanation:

Evaluate x^-2 for x = -3 plsss i really need help on this thank you

Answers

Answer: -1/9

Step-by-step explanation:

Answer:

- 1/9 OR -0.111....

Step-by-step explanation:

Make x= -3

-3^-2= -1/9

Consider the line y=7x-8.

Find the equation of the line that is parallel to this line and passes through the point (6, – 4).
Find the equation of the line that is perpendicular to this line and passes through the point (6, - 4).

Answers

Answer:

a). y = 7x - 46      b). y = -1/7x - 22/7

Step-by-step explanation:

a). y = 7x + b

-4 = 7(6) + b

-4 = 42 + b

-46 = b

y = 7x - 46

b). y = -1/7x + b

-4 = -1/7(6) + b

-4 = -6/7 + b

-22/7 = b

y = -1/7x - 22/7

Directions: Solve for the missing proportion in each of the following problems.
9. 12/n = 20/25
10. 5/8 = n/24
11. 2/3 = 16/n
12. 12/14 = n/21
13. n/10 = 6/15
14. 12/3 = 10/n
15. 5/n = 10/16
16. 12/8 = 4/n

Answers

Answer:

Step-by-step explanation:

9) 12/n=20/25

simplify 20/25=4/5

12/n=4/5

cross product

n*4=12*5

4n=60

n=60/4

n=15

The missing proportion in each of the following problems shown below:

What is equation?

Statement of equality between two expressions consisting of variables and/or numbers

9) 12/n=20/25

12/n=4/5

n*4=12*5

4n=60

n=60/4

n=15

10) 5/8=n/24

   8n= 5*24

   8n= 120

    n= 120/8

    n=15

11) 2/3= 16/n

   2n=48

   n=24

12) 12/14= n/21

     n=18

13) n/10 = 6/15

    n=4

14)  12/3 = 10/n

     n= 2.5

15) 5/n = 10/16

       n=8

16) 12/8 = 4/n

     n=8/3

Learn more about equation here:

https://brainly.com/question/10413253

#SPJ2

At the beginning of the chemistry experiment, Lisa measured the temperature of a liquid to be -5°C. During the experiment, she measured the liquid 3 times and the results showed, its dropped 9°C, rose 25°C, and drop 15°C. What was the liquid temperature at the end of the experiment?

Answers

Answer:

-4°C

Step-by-step explanation:

At the beginning of the chemistry experiment the temperature of the liquid was -5°C and it dropped 9°C so you do:

-5°C - 9°C = -14°C

The answer is -14°C for the first part of the question because when you are subtracting a positive number from a negative number you have to add the two numbers together but your answer will always be a negative number.

Then you add 25°C to -14°C:

-14°C + 25°C = 11

Because when adding a negative number to a positive number that is bigger than the negative number you have to subtract but your answer will always be a positive number, however if the positive number is smaller than the negative number your answer will be a negative number.

Then you subtract 11°C from 15°C:

11°C - 15°C = -4°C

Because when you subtract a number that is bigger than the first number you get a negative number.

Find value of x.
A. 110
B. 47
C. 68
D. 112

Answers

Answer:

B

Step-by-step explanation:

The sum of the inner angles of a quadrilateral is 360 degrees

135 + 110 + 68 + x = 360

313 + x = 360

x = 47 degrees

Answer:

47

Step-by-step explanation:

whole thing is 360 degrees

68 + 110 + 135 = 313

360 - 313 = 47

x looks small too (if you had to guess in a multiple choice question)

If the 5th term in a geometric sequence is 162, and the common ratio is 3. What is the first term in the sequence?

Answers

Answer:

2

Step-by-step explanation:

a2 = a1×3

a3 = a2×3 = a1×3×3

=>

an = an-1 × 3 =

[tex]a1 \times {3}^{n - 1} [/tex]

a5 = 162 = a1×3⁴ = a1×81

a1 = 162/81 = 2

What value of g makes the equation true?

Answers

Answer:

[tex](x + 7)(x - 4) \\ = { \tt{ {x}^{2} + 7x - 4x - 28 }} \\ = { \tt{ {x}^{2} + 3x - 28 }} \\ { \boxed{ \bf{g \: is \: 3}}}[/tex]

Answer:

g=3

Step-by-step explanation:

Hi there!

To find the value of g, we can expand the two binomials using the distributive property:

[tex](x+7)(x-4)\\= x(x-4)+7(x-4)\\= x^2-4x+7x-28\\= x^2+3x-28[/tex]

Therefore, the value of g that makes the equation true is 3.

I hope this helps!

Suppose that the scores on a statewide standardized test are normally distributed with a mean of 64 and a standard deviation of 2. Estimate the percentage of scores that were (a) between 60 and 68.

Answers

Answer:

95. 45%

Step-by-step explanation:

Given :

Mean score, = 64

Standard deviation = 2

Score between 60 and 68

P(Z < (x - mean) / standard deviation)

P(Z < (60 - 64) / 2) = P(Z < - 2) = 0.02275 (Z probability calculator)

P(Z < (68 - 64) / 2) = P(Z < 2) = 0.97725 (Z probability calculator)

P( score between 60 and 68)

P(Z < 2) - P(Z < - 2)

0.97725 - 0.02275 = 0.9545

Score between 60 and 68 = 0.9545 = 0.9545 * 100% = 95.45%

the 28th term of an ap is -5,find the common difference if the first term is 31​

Answers

Answer:

The common difference is -4/3.

Step-by-step explanation:

Recall that the direct formula for an arithmetic sequence is given by:

[tex]\displaystyle x_n=a+d(n-1)[/tex]

Where n is the nth term, a is the initial term, and d is the common difference.

We are given that the first term a is 31.

We also know that the 28th term is -5. Hence, x₂₈ = -5. Substitute:

[tex]\displaystyle x_{28}=-5=(31)+d(28-1)[/tex]

Solve for d. Simplify:

[tex]-5=31+27d[/tex]

Thus:

[tex]\displaystyle 27d=-36[/tex]

Divide both sides by 27. Hence, the common difference is:

[tex]\displaystyle d=-\frac{36}{27}=-\frac{4}{3}[/tex]

Answer:

-4/3

Step-by-step explanation:

This question is equivalent to:

Find the slope of a line going through points (28,-5) and (1,31).

*Arithmetic sequences are linear. The common difference is the slope.

Any ways to find the slope line the points up and subtract vertically. Then put 2nd difference over 1st difference.

(28,-5)

(1,31)

---------subtracting

27, -36

So the slope or the common difference of this line or arithmetic sequence is -36/27. This reduces to -4/3.

A rectangular prism and a pyramid have congruent bases and equal altitudes.Wha is the retio between the volume of the pyramid to the volume of the rectangular prism.What is the answer

Answers

Answer:

The required ratio is 1 : 3.

Step-by-step explanation:

Let the length is L, width is W and the height is H.

Volume of the prism is

V = LW H

Volume of the pyramid

V' = 1/3 L W H

Ratio of volume of pyramid to the prism is

[tex]\frac{V'}{V} = \frac{1}{3}[/tex]

The
hypothesis
represents the statistical claim that the company's
tablet computers have an average recharge time of
less than 3 hours.

Answers

Answer:

Alternative

Step-by-step explanation:

Answer:

U=3 , U<3 , alternative

Step-by-step explanation:

Question
The quotient of a number and 5 has a result of 2. What is the number?

Answers

Answer:

10.

Step-by-step explanation:

Answer:

The number is 10.

Step-by-step explanation:

x/5 = 2

Multiply both sides by 5.

5 * x/5 = 5 * 2

x = 10

Answer: The number is 10.

Where do the light-dependent reactions of photosynthesis occur in a plant cell? Choose 1 answer:
A) Chloroplast; stroma
B) Mitochondrion: thylakoid membrane
C) Chloroplast; thylakoid membrane
D) Chloroplast: outer membrane​

Answers

Answer:

C) Chloroplast; thylakoid membrane

Step-by-step explanation:

The question is a biological science question

The light-dependent reactions also known as the light reactions take place at the location site of the chlorophyll of the plant cell, within the chloroplast thylakoid membrane, and involves the energizing of the electrons within the pigment molecules, the electrons are then transferred through a transport chain within the thylakoid membrane

The dark reactions take place inside the stroma

Therefore, the correct option is chloroplast; thylakoid membrane

Select all of the equations below that are equivalent to:

w + 13 = –8

Answers

Answer:

w= -21

Step-by-step explanation:

Please help me .. I really need help with this ASAP ​

Answers

Given:

Number of flower pots = 6

To find:

The number of ways of the gardener to arrange the flower pots.

Solution:

Number of ways to arrange n items is n!.

So, the number of ways to arrange 6 pots is:

[tex]6!=6\times 5\times 4\times 3\times 2\times 1[/tex]

[tex]6!=720[/tex]

Therefore, there are total 720 ways of the gardener to arrange the flowerpots.


Can someone help solve the problems 2-4

Answers

Answer:

1234567891011121314151617181920

Step-by-step explanation:

you just count

Determine the measure of the interior angle at vertex C. PLEASE HELP ASAP

Answers

Answer:

B.  120°

Step-by-step explanation:

Sum of the measures of the interior angle of a polygon with n sides:

(n - 2)180

We have a pentagon, a 5-sided polygon, so n = 5.

We first find the sum of the measures of the angles of any pentagon.

(5 - 2)180 = 3(180) = 540

From the figure, we add the measures of the 5 angles and set the sum equal to 540°.

3x + 4x + 4x + 4x + 3x = 540°

18x = 540°

Divide both sides by 18.

x = 30°

The angle at vertex C measures 4x.

4x = 4 * 30° = 120°

Answer: B.  120°

Dose 4(x+1)= 3x+4 have a solution

Answers

Answer:

x = 0

Step-by-step explanation:

First, multiply 4 by x+1

4x + 4 = 3x + 4

Subtract 3x on both sides

x + 4 = 4

Subtract 4 from both sides

x =

this is x = 0, since x = nothing.

Answer:

x=0

Step-by-step explanation:

4(x+1)= 3x+4

Distribute

4x+4 = 3x+4

Subtract 3x from each side

4x-3x+4 =3x-3x+4

x+4 = 4

Subtract 4 from each side

x+4-4 = 4-4

x=0

What is the degree & leading coefficient?

h(t) = 0.2t^3 - 4t^2 +20t

Answers

Answer:

degree=3

coefficient=0.2

Can someone please be generous & help I’ve been struggling all night

Answers

Answer:

Slope-intercept

y = 3/4(x) - 7

Point slope

y -5= 3/4(x - 16)

Step-by-step explanation:

In slope-intercept

We have the general slope intercept as;

y = mx + b

where m is the slope and b is the y-intercept

in this case, m = 3/4 and b = -7

So we have;

y = 3/4(x) - 7

In point-slope

we have the general form as;

y-y1 = m(x-x1)

So what we have is as follows;

y -5= 3/4(x - 16)

Where we have (x1,y1) = (16,5)

At a school concert the total value of tickets sold was $4452. Student tickets sold for $8 and adult tickets sold for $12. The number of adult tickets sold was 7 less than 4 times the number of student tickets. Find the number of student tickets sold.

Answers

Answer:

there is 81 student and 317 adults adults :) got u

Step-by-step explanation:

4452 = 8n + (4n-7)12

4452 = 8n + 48n - 84

4536 = 56n

81 = n

can anyone help with integers?

Fill in the blanks.

6) 83 + 17 = 17 +

7) |46| – |50| =

8) 42 – 2 + (18 – 10) =

9) 18 – (3 – 1) =

10) 8 - 0 =

Answers

Answer:

a) 83,b) -4,c) 48,d) 16,e) 8

What's 70 x4 I just wanna see if it’s really going to help me

Answers

Step-by-step explanation:

70

*4

___

280.......ans

Kiera is reading a book that has 120 pages. She wants to know whether 'e' is the most commonly used letter in the book. Write down examples for each of the six steps for Kiera to follow.. What other factors could Kiera consider? Write down some problems Kiera might have in collecting her data. Plz help

Answers

Answer and explanation:

Keira could get or look up an electronic copy of the book online. Once she has an electronic copy(pdf for instance) of the book, she can count number of e's in her book using the PDF reader or any software extension(good number of tools online) that would do just that.

Factors for Keira to consider:

How many lines and words are there on average per page; how many words are there per line?

How many e's are there manually counting for at least 5 pages.

Problems Keira might have in collecting data:

If book is physical and not an electronic copy, Keira may have to go through a tedious task of counting manually. She could make a rough estimation based on a few pages counted but she would need more accurate figures which requires the tedious task of counting e 's manually

I swear imma fail this class

Answers

Answer:

use mathpapa If that helps, it a math calculator

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