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

Let ε = {5,6,7,8,9}, A = {x | x >7} and B = {5,6} Find

1. P(A’)

2. P(A) U P(B)

3. P(A) ∩ P(B)

4. P(A ∩ B)

Answers

Answer:

A={x| x>7} = 8,9

B= {5,6}

1,

2,{5,6,8,9}

3,{}

4{}


Which models best illustrates the inequality and its graph?
t< 55

a.) t is at least 55

b.) t is less than 55

c.) t is 55 or more

d.) t is at most 55

Answers

Answer:

B

Step-by-step explanation:

Open circle means the number is not included.

Hope this helps <3

I really need help anyone know which option is correct.?

Answers

Answer:

B, [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

This problem is essentially asking one to envision a line passing through the set of points on the coordinate plane, then to find the constant of proportionality of that line. The constant of proportionally, also known as the rate of change, or the slope, is a number that can be used to describe the range that happens between points on a line. The following formula can be used to find the slope of a line passing through a set of points.

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where the points ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are points on the line.

As one can see, on the given coordinate plane, the points ([tex]2,-1[/tex]), and ([tex]4,-2[/tex]) are on the coordinate plane. Substitute these points into the formula to find the slope of the line, then simplify to evaluate the equation and find the slope,

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

([tex]2,-1[/tex]),  ([tex]4,-2[/tex])

[tex]=\frac{-2-(-1)}{(4)-(2)}[/tex]

[tex]=\frac{-2+1}{4-2}\\\\=\frac{-1}{2}\\\\=-\frac{1}{2}[/tex]

What is the slope of the line through (3,2) and (-3,4)

Answers

Answer:

-1/3

Step-by-step explanation:

slope = m = rise/run = (difference in y)/(difference in x)

m = (4 - 2/(-3 - 3)

m = 2/(-6)

m = -1/3

The following relation is a function (10,12),(5,3),(15,10),(5,6),(1,0) true false

Answers

Answer:

True

Step-by-step explanation:

Lydia runs an experiment to determine if a coin

Answers

Not sure what your asking please provide more information

Q: Marci wants to prove that the diagonals of
a rectangle are congruent. Which of these
procedures would be best for Marci to use
to write a correct proof?

a) She should use the fact that the
diagonals of a square are perpendicular
and then use the triangle-angle-sum
theorem.

b) She should use the fact that the
opposite sides of a parallelogram are
congruent and then use the
Pythagorean theorem.

c) She should use the fact that the
opposite angles of a parallelogram are
congruent and then use triangle
similarity relationships.

d) She should use the fact that the
diagonals of a parallelogram bisect the
angles of the parallelogram and then
use triangle congruence relationships.

Answers

Answer: Option B

She should use the fact that the

opposite sides of a parallelogram are

congruent and then use the

Pythagorean theorem.

We cannot use the diagonals of square property because this is a rectangle, opposite angles will also not work, and we cannot use the diagonal property because thats what we have to prove.

Must click thanks and mark brainliest

Write the area A of an equilateral triangle as a function of the length s of its sides.

STEP 1: Find the base of the equilateral triangle in terms of s.

STEP 2: The height of an equilateral triangle can be found via the Pythagorean theorem. Use this information to find h in terms of s.

Answers

Write the area A of an equilateral triangle as a function of the length s of its sides. Draw the triangle; label each side "2s". Draw the altitute; it will bisect the base into s and s. ... Therefore, the area is equal to the measure of the bisected side times the measure of the altitude, quantity divided by 2.

HOPE SO IT HELPS YOU

Answer:

Step-by-step explanation:

Part A

Each side including     the base is s.

Part B

Use 1/2 the base to find the height. The height meets the base at 90 degrees which gives you the right to use c^2 = b^2 + a^2

The hypotenuse is s

The base is 1/2s

h^2 = s^2 - (1/2s)^2

h^2 = s^2 - 1/4 s^2

h^2 = 3s^2/4

h = sqrt(3)/2 *s

Area = 1/2 * s * sqrt(3)/2 s

Area = 1/4 * s^2 * sqrt(3)

5. Which expression is a simplified form of (3x2 + 2x - 4) + (-7x2 + 6x - 2)?
a 10x2 + 8x - 6
b. -4x2 + 8x - 2
C.-4x2 + 8x + 2
d. -4x2 + 8x - 6

Answers

Answer:

d. -4x² + 8x - 6

Step-by-step explanation:

(3x² + 2x - 4) + (-7x² + 6x - 2)

3x² + 2x - 4 - 7x² + 6x - 2

3x² - 7x² + 2x + 6x - 4 - 2

-4x² + 8x - 6

HELP!!!!!!!!!!!!!!!!!!!

Answers

Answer:

1. 22+b

2. 7x

3. 6+t

4. Z(4+6)

5. -10+4a

6. N(8+-2)

7. X^2/2

4/5(m^2)

HOPE THIS HELPS

- Todo ❤️

Step-by-step explanation:

1.) b + 21

2.) x × 7 or 7x

3.) t + 6

4.) 4 + 6z

5.) -10+4a

6.) 8 +(-2n)

7.) (1/2)×n³

8.) (4/5)×m²

Must click thanks and mark brainliest

Kristian and Stephanie share money in the ratio 3 :2 Kristian receives $72 How much will Stephanie receive​

Answers

Answer:

48

Step-by-step explanation:

Kristian : Stephanie

3                 2

Kristian receives 72

72/3 = 24

Multiply each side by 24

Kristian : Stephanie

3*24                 2*24

72                        48

A baby can crawl ¾ foot in ¼ minute. How far does the baby get per minute?

Answers

Answer:

3 ft per minute

Step-by-step explanation:

Take the distance and divide by the time

3/4 ft ÷ 1/4 minute

Copy dot flip

3/4 * 4/1

Rewriting

3/1 * 4/4

3/1 *1

3 ft per minute

find the missing side

Answers

13.9. Use pythagoras theorem to find it. Square root of 12*2 + 7*2 = square root of 193 = 13.89 ~ 13.9

Answer:

[tex]\boxed{x=13.89\:km}[/tex]

Step-by-step explanation:

Pythagorean theorem

[tex]x^2=(12^2)+(7^2)[/tex]

[tex]x^2=144+49[/tex]

[tex]x^2=193[/tex]

[tex]x=\sqrt{193}[/tex]

[tex]\boxed{x=13.89\:km}[/tex]

What is the range of function represented by the graph below?

Answers

Answer:

y ≥ 0

Step-by-step explanation:

The range of the function is the output values.

The y value goes from 0 to infinity

y ≥ 0

Can sone One help me please, Thanks a lot

Answers

I don’t really understand what you mean where is the question?

Answer:m

       

Step-by-step explanation:m

For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 8 N acts on a certain object, the acceleration of the object is 4 m/s?. If the acceleration of the object becomes 3 m/s?, what is the force?

Answers

Here Mass is constant

F1=8Na_1=4m/s^2a_2=3m/s^2F_2=?

Using Newtons s law

[tex]\\ \sf \longmapsto F=ma[/tex]

[tex]\\ \sf \longmapsto \dfrac{F}{a}=m[/tex]

[tex]\\ \sf \longmapsto \dfrac{F_1}{a_1}=\dfrac{F_2}{a_2}[/tex]

[tex]\\ \sf \longmapsto \dfrac{8}{4}=\dfrac{F_2}{3}[/tex]

[tex]\\ \sf \longmapsto F_2=\dfrac{24}{4}[/tex]

[tex]\\ \sf \longmapsto F_2=6N[/tex]

Answer:

F = 6N

Step-by-step explanation:

Equation

F = ka

F - force

k - constant of proportionality

a - acceleration

Step 1 - find k  

8N=k*4m/s^2

k=2

Step 2 - find F

F=2*3m/s^s

F=6

PLEASE HELPP!!!!
Find the area.

A.530in²
B. 779in²
C.390in²
D.1060in²

Answers

Answer:

530in²

Step-by-step explanation:

Area of triangle(a)=1/2bh=1/2*40*26.5=530

whats the volume the triangular prism?​

Answers

Answer:

the volume is 1000 cm^3

Step-by-step explanation:

first we need to find where is the base, and height, for this case, the trian is the base, not the rectangle, so it maybe eas if you draw a upright angle os the shape, with the triangle facing down.

As show you need to have bare and height for the volume of the prism, which we already know the height is 25 (h=25) so now we need to find the base.

for the base, since it’s a triangle, which has the area formal of 1/2(bh), so now just plot the number in, 1/2x10x8= 40 cm^2

now using the volume of prism formal; V = bh = 40 x 25 = 1000 cm^3

Which of the following are good ideas to use when gathering your resources?
Check all that apply.
O A. Form an equation:
B. Draw a diagram.
C. List potential formulas.
D. Guess at the solution and see if you are close.
E. Organize into a table.
F. Write down the facts.

Answers

Answer:

Organize into a table for good gatherings.

Find the length of the third side. If necessary, round to the nearest tenth.
16
12
Answer:
Submit Answer
PLS HELP ASAP

Answers

Answer:

I think 16.

Step-by-step explanation:

because 12 is impossible and last answer is 16.

Answer:

the third side will be √500

Step-by-step explanation:

[tex]\sf{}[/tex]

using PGT

(16)²+(12)²=H²

=> 256+144 = H²

=> 500 = H ²

=> √500 = H

How much would $500 invested at 9% interest compounded annually be
worth after 4 years? Round your answer to the nearest cent.

Answers

Answer:

I think 705.79 if I did it right

Step-by-step explanation:

500(1+.09/1)^4 = 705.79

4x+3=x+9

What is the number?

X=?

Answers

Answer:x=3

Step-by-step explanation:

4x+3=x+9

4x-x=(-3)+9

3x=6

x=6:3

x=2

Instead of using the values {1,2,3,4,5,6}
on dice, suppose a pair of dice have the
following: {1,2,2,3,3,4} on one die and
{1,3,4,5,6,8} on the other. Find the
probability of rolling a sum of 2 with
these dice. Be sure to reduce.
[?]

Answers

Answer:

1/36

Step-by-step explanation:

it is the exact same as if both your dice had the numbers {1,2,3,4,5,6}

you said the SUM of the dice that is indicates the answer of the addition of two (or for that matter more) numbers,... the only numbers that would sum 2 is 1+1,... and because you only have two ones (one per die) the answer is the same as if they where die with normal numbers,...

The probability of rolling a sum of 2 with these dice is 1/36.

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

We are given that;

Pair of dice have= {1,2,2,3,3,4}

Now,

The probability of rolling a sum of 2 with two dice is the same as the probability of rolling snake eyes, since the only way to get a sum of 2 is if both dice show a 11. The probability of rolling a 1 on a single die is 1/6, so the probability of rolling a 1 on both dice is (1/6) × (1/6) = 1/3612.

However, in this case, the dice are not standard six-sided dice, but have different numbers on their faces. The first die has {1,2,2,3,3,4} and the second die has {1,3,4,5,6,8}. The probability of rolling a 1 on the first die is still 1/6, but the probability of rolling a 1 on the second die is also 1/6. Therefore, the probability of rolling a sum of 2 with these dice is still (1/6) × (1/6) = 1/36.

This probability cannot be reduced any further, since 1 and 36 have no common factors other than 1.

Therefore, the probability will be 1/36.

Learn more about probability here;

https://brainly.com/question/9326835

#SPJ7

Jol 28, 3:44:44 AM
Solve the equation for all values of x.
(x2 – 16)(x2 + 49) = 0
Answer:
Submit Answer

Answers

Answer:

x = 4, -4, 7i, -7i

Step-by-step explanation:

(x^2 – 16)(x^2 + 49) = 0

x^2 – 16 = 0 or x^2 + 49 = 0

x^2 = 16 or x^2 = -49  

x = ± 4 or x^2 = ±7√-1  =±7i

Use the graph that shows the solution to f(x) = g(x).

f(x) = 1+2x/x

g(x) = 2+x

What is the solution to f(x) = g(x)?

Select each correct answer:

X = -2

X = -1

X = 1

X = 2

Answers

Answer:

B and C

Step-by-step explanation:

The equation intersects each other at x=-1 and x=1

Diana and Dulce were selling tickets for their upcoming
softball game. Dulce sold 20% more than Diana. If they
sold 55 tickets total, how many tickets did each of them
sell?

Answers

Answer:

Diana sold 25 tickets and Dulce sold 30 tickets

Step-by-step explanation:

Let us assume that Diana sold x number of tickets, dulce sold 20% more x or 1.2x. ATQ, x+1.2x=55. x=25. So Diana sold 25 tickets and Dulce sold 30 tickets

The radius of a circle is 3 cm. Find its area in terms of pi

Answers

Answer:

A = 9 pi cm^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2 where r is the radius

r=3

A = pi (3)^2

A = 9 pi cm^2

Area of circle = πr²

Area = π3²

Area = 9π

There area in terms of pie is 9πcm²

Must click thanks and mark brainliest

What is the missing reason in the proof? Given: ∠ABC is a right angle, ∠D B C is a straight angle Prove: ∠ABC ≅ ∠A B D A horizontal line has points D, B, C. A line extends vertically from point B to point A. Angle A B C is a right angle. definition of angle bisector segment addition property definition of congruent angles transitive property

Answers

Answer:

Definition of Congruent angles.

Step-by-step explanation:

Given

See attachment

Required

Complete the proof at step 8

At step 8, we have:

[tex]\angle ABC \cong \angle ABD[/tex]

When the sign [tex]\cong[/tex] is used, it means congruence

In other words;

ABC and ABD are congruent

Hence, the missing statement at step 8 is: Definition of Congruent angles.

Answer:

ABC and ABD are congruent

Step-by-step explanation:

3x – (7x + 2) > 5x + 4

Answers

Answer:

x < -2/3

Step-by-step explanation:

3x – (7x + 2) > 5x + 4= 3x -7x - 2 > 5x + 4= -4x - 2 > 5x + 4= -4x -5x > 4 + 2 = -9x > 6= x < -2/3

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

I do not understand this question can someone help me with good explanation will give Brainliest

Answers

Answer:

60 (E)

Step-by-step explanation:

He plants seeds -> plants grow to 12 times the original weight of the seeds -> he sells 50 tonnes from the harvest -> remainder is used as the next batch of seeds

He harvested 120 tonnes this year which means the original weight of the seeds planted was 120÷12 = 10 tonnes. This means that last years harvest would be the 10 tonnes used as seeds plus the 50 tonnes that would have been sold immediately, 10+50 = 60 tonnes

Other Questions
herical piece of candy is suspended in flowing water. The candy has a density of 1950 kg/m3 and has a 1.0 cm diameter. The water velocity is 1.0 m/s, the water density is assumed to be 1000.0 kg/m3, and the water viscosity is 1.010-3 kg/m/s. The diffusion coefficient of the candy solute in water is 2.010-9 m2/s, and the solubility of the candy solute in water is 2.0 kg/m3. Calculate the mass tran DNA is referred to as a______, meaning that it hasstrands that are______together. II. Find the word which has a different sound in the underlined part. 1. A. Put B. Adult C. Junk D. Sun 2. A. Itchy B. Riding C. Sick D. Swimming 3. A. Chemical B. Children C. Headache D. Architect 4. A. Regularly B. Identify C. Really D. Healthy 5. A. Cycling B. Doctor C. Aerobics D. Calories please help! -10y= y+ 1 Which of the following isotopes would deflect the most in a mass spectrometer?a) Sr-84b) Sr-86c) Sr-87d) Sr-88 The bar graph shows the median income for families in the United States from 1993 through 2000. Which two consecutive years saw the largest increase in median income?A. 19941995B. 19971998C. 19981999D. 19992000 what was one advantage and one disadvantage of joint-stock companies? Please see picture for question. Which amendment expanded the right to vote to about half the population? FifteenthAfrican American men Nineteenthwomen Twenty-fourthno poll taxes Twenty-sixth18 years old Based on Emerson's evidence and your examples, do you agree or disagree withEmerson? PLEASE HELP!!! WILL MARK BRAINLIEST!!What role did economic issues play in the Founding Fathers decisions about how to structure the United States government, including what powers the government would hold over trade and commerce?Please give a detailed explanation preferably paraphrased thank you! help me please !! find the domain and range of the function represented by the graph. determine wether the domain is discrete or continuous. HELP PLSSSSSSSSS i really need it right now Kim just turned 10 years old her mother is four times older than Kim how old is Kims mother What are the three consequences of poverty to the community and why ? The solubility of gaseswhen the temperature isincreased.A. increasesB. decreasesC. does not change 24 cars pass through an intersection each minute while the traffic light is green. In addition, 6 cars pass through the intersectionwhile the light is yellow. If 84 cars pass throughthe intersection during one light cycle (one green light and one yellow light), how long was the green light? if cos7x-cos8x/1+2cos5x=cos(ax)-cos(bx),where a,b are positive integers, then a+b=??pls help! :( Why are there so many young people sick abroad? I can't understand the routine of the media playing a double role with the government. I can't believe in the free media. Which media is not the capital behind? What capital is not profit-seeking? The US government is doing evil and the media is exposing a tiny fraction of it. It's just a show for the American people. An epidemic, 700,000 dead, 40 million infected, the world of evil, which media dare to expose? To conjugate a verb in the future you remove the endings ar, -er, -ir and add the endings of the future. BRAINLY 10 POINTS