How would you find the width of a golden rectangle if your givin the length?

Answers

Answer 1

A golden rectangle is a rectangle whose length and width follow the golden ratio (about 1:1.618).

Given the length, you would divide by 1.618 to find the width.

Edit: The exact value is [tex] \frac{ 1+\sqrt{5} }{2} [/tex], but 1.618 should suffice.

Related Questions

please please please someone help me no one on this site will help me. i so confused. please help.

PLEASE SOMEONE HELP ME!!!!! ILL GIVE BRAINLIEST
1. A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y = –0.04x2 + 8.3x + 4.3, where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground. How far horizontally from its starting point will the rocket land?
A. 208.02 m
B. 416.30 m
C. 0.52 m
D. 208.19 m

2. A catapult launches a boulder with an upward velocity of 184 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h= -16t^2 + 184t + 20. How long does it take the boulder to reach its maximum height? What is the boulder's maximum height.
A. Reaches a maximum height of 11.6 feet after 5.75 seconded.
B. Reaches a maximum height of 549 feet after 11.5 seconds.
C. Reaches a maximum height of 549 feet after 5.75 seconds.
D. Reaches a maximum height of 23.2 feet after 11.6 seconds.

3. A ball is thrown into the air with an upward velocity of 32 ft/s. Its height (h) in feet after t seconds is given by the function h= -16t^2 + 32t + 6. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Round to the nearest hundredth, if necessary.
A. Reaches a maximum height of 22 feet after 1.00 second.
B. Reaches a maximum height of 22 feet after 2.00 seconds.
C. Reaches a maximum height of 44 feet after 2.17 seconds.
D. Reaches a maximum height of 11 feet after 2.17 seconds.

Answers

Problem One
The rocket will hit ground level when y = 0. The plan is is to set y =0 and solve the quadratic. Be careful how you go about to this. It is an odd way to represent this kind of problem. The question does say that y defines how far off the ground the rocket is at the beginning. Therefore the height of the building does not matter (or shouldn't). All that matters is that y is ground level when y = 0.

a = - 0.04
b = 8.3
c = 4.3

[tex]\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a} [/tex]
[tex]\text{x = }\dfrac{ -8.3 \pm \sqrt{8.3^{2} - 4*(-0.04)*(4.3) } }{2(-0.04)}[/tex]

From here you should be able to calculate the answer. One of them is -0.52 which is not the one you use. Minus heights do not matter in these problems yet. The other root is your answer.

Problem Two

Problem two is the usual way to express what happens to a projectile in the air. It again is going to be solved by the quadratic equation.

There are two ways to do this problem. If you know physics, you can solve it using the projectile formulas. If you don't , then you can use the trick in the previous problem. You can calculate how long it takes to hit the ground (h will then be zero).

This problem is rather nasty for someone who has not taken physics. There is another trick. You have to divide the time you get from the previous step by 2. When you solve the quadratic for h = 0, you get 11.6 seconds. But that is the time it takes to hit the ground. Half time is when the boulder will be at it's highest point. t = 11.6 / 2 = 5.8 (which your answers record as 5.75).

h = 0

a= -16

b = 184

c = 20

[tex]\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a} [/tex]

[tex]\text{x = }\dfrac{ -184 \pm \sqrt{184^{2} - 4*(-16)*(20) } }{2*(-16)} [/tex]

The answer from this equation is t = 11.6

The time you want is t = 5.75. You can calculate the maximum height by putting 5.75 in for t.

Problem 3

Problem 3 is done exactly the same way as problem two. You just have different numbers. When h = 0 the time taken to reach zero = 2.17 seconds. Therefore the time you want to put into the original equation for the maximum height is 1/2 of 2.17 seconds. From there you can find the maximum height.

Note: there is a lot of math in here. I have gotten you past the physics. I have also alluded to the answers. I think you should be able to carry out the rest.

A game involves rolling a fair six-sided die. If the number facing upward on the die is a whole number multiple of three, the player wins an amount equal to the number on the die times $20. If the number is not a multiple of three, the player gets nothing. What is the expected value of a player's winnings on each roll?

Answers

i would say about $10 about 1/6th the time

Answer:

$30

Step-by-step explanation:

To find the expected value, first we find the outcomes for the sample space.

Rolling a 6-sided die, we have

1, 2, 3, 4, 5, 6

There are 2 values that are whole number multiples of 3: 3 and 6.

There is a 1/6 chance of rolling a 3 and a 1/6 chance of rolling a 6.

There is a 1/6 chance of rolling a 1, 1/6 chance of rolling a 2, 1/6 chance of rolling a 4, and 1/6 chance of rolling a 5.

Next we multiply the value won or lost by each probability.

If the player rolls a 3, they win 3(20) = 60. Multiplying it by its probability, we have

1/6(60) = 60/6 = 10

If the player rolls a 6, they win 6(20) = 120. Multiplying it by its probability, we have

1/6(120) = 120/6 = 20.

If the player rolls a 1, 2, 4 or 5, they win nothing. 0 times all of these will be 0.

Lastly, we add together these products:

10+20+0+0+0+0 = 30

(evaluating expressions) what is the value of the expression 2½x + 3⅔y if x = 4 and y = 3? * 21

Answers

2 1/2 (4) + 3 2/3 (3)
10 + 11 = 21

Which of the following are exterior angles ? Check all that Apply NEED ASAP

Answers

Answer:

∠2 , ∠3 , ∠5 ,∠6 are exterior angles

Step-by-step explanation:

Given : Figure.

To find : Which of the following are exterior angles.

Solution : We have given a figure with angle 1 ,2, 3,4,5,6.

Exterior angle : An angle which lies outside the closed figure.

We can see ∠1 and ∠4 area lies in closed figure.

But all other angle ∠2 , ∠3 , ∠5 ,∠6 are lies outside so, these are the exterior angles.

Therefore, ∠2 , ∠3 , ∠5 ,∠6 are exterior angles

Answer:

5. 6. and 2

Step-by-step explanation:

All exterior ANGLES that are still connected to the triangle. 3 Is not an angle on Triangle 1. It is its own triangle, as well as a point.

. Convert 5π/3 to degrees

Answers

[tex] \pi [/tex] radians is equal to 180 degrees.

Convert [tex] \pi [/tex] to 180 to get the following fraction:

[tex] \frac{5 * 180}{3} [/tex]

Multiply 5 and 180 together to get the following fraction:

[tex] \frac{900}{3} [/tex]

Simplify the fraction.

[tex] \frac{900}{3} [/tex] = 300

The answer is 300 degrees.

π radians = 180 degrees

so 5π / 3 radians = 180 / π * 5 π / 3 = 900 / 3 = 300 degrees Answer

The angle of elevation from point A to the top of a cliff is 38 degrees. If point A is 80 feet from the base of the cliff, how high is the cliff?
A.
60.50 ft.
B.
62.50 ft.
C.
63.50 ft.
D.
61.50 ft.

Answers

tan 38 = h/80
h = 80 tan 38 = 62.50 ft

Its B

Jenna uses 18 inches if ribbon for each box she wraps how many yds of ribbon does she need to wrap 4 boxes

Answers

She needs 2 yards of ribbon to wrap 4 boxes.

if she uses 18 inches for each box then for 4 boxes she will use 18+18+18+18 or 18×4=72 inches.
since 1 yard is 36 inches she will need 72/36=2 yards.

if you like my answer please rate as brainliest! thx

Reduce the fraction to lowest terms. 38x^2yz^2/ -19 yz^2z^3

Answers

Hope this is helpful.

Six years ago annabelle was twice as old as jason was. now, annabelle is four years older than jason. how old is jason now?

Answers

The present age of Jason is given as 10 years.

How to solve a linear equation?

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

The given problem can be solved as follows,

Suppose the age of Jason 6 years ago was x.

Then, the age of Annabelle 6 years ago was 2x.

Their present ages are x + 6 and 2x + 6 years respectively.

As per the question, the following equation can be formed as follows,

2x + 6 = x + 6 + 4

=> 2x - x = 10 - 6

=> x = 4

Thus the present age of Jason is 4 + 6 = 10 years.

Hence, the age of Jason now is 10 years.

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Using the rate of $8 for every 2 pounds of rice, how much would a 1/2 pound of rice cost

Answers

2/½=4
8/4=2
It would be 2$

2 pound = $8

1 pound = $8 ÷ 2 = $4

1/2 pound = $4 ÷ 2 = $2

Answer: $2

Anyone know the answer?

Answers

the answer is c because k and m are the same so l and n are also the same

What is the surface area of this square pyramid?

Round your answer to the nearest tenth.

Answers

The question is to find the surface area of the square pyramid:

This pyramid encloses a volume V, so it has five surfaces, namely:

*One square base.
*four triangular surfaces.

1. Surface area of the square base:

All four sides are equal, so:

As = LxL = (8.4yd)(8.4yd) = 70.56[tex]yd^2[/tex]

2. Area of triangular surfaces:

Given that the angle β=60°, we have four equilateral triangles which have three equal sides each, therefore:

At = [tex] 4(\frac{base.height}{2}) [/tex] = [tex]2L.Ap[/tex]

Now we need to calculate the apothem Ap.

Using trigonometry, we can calculate Ap using the sine function:

sinβ = [tex] \frac{opposite}{hypotenuse} [/tex] = [tex] \frac{Ap}{a} [/tex]

Given that the triangles are equilateral, then a = L

∴ Ap = (a)(sinβ) = 8.4sin(60°) = (8.4)([tex] \frac{ \sqrt{3} }{2} [/tex]) = 7.275yd

So:

[tex]At = 2(8.4)(7.275) = 122.22 yd^{2}[/tex]

Therefore, the surface area of the pyramid is:

A = As + At = 70.56 + 122.22 = 192.78 [tex] yd^{2} [/tex]

The answer is 192.8 yd²

Hi, I don't feel very confident about my work in this calculus problem and I would appreciate it if anyone else could note any corrections or ways to improve my answers. My problem is split into parts A, B, C, and D and my work is in green. Thank you!

Answers

You're pretty close. It's all in the details.

A. Correct.

B. Correct.

C. Sign error in the boxed answer. -(-0.5) = 0.5
The graph shows c ≈ 1.855. If a is more than that and decreasing, area is increasing. The sign of dA/dt will be positive. (Compare to D)

D. Units are not shown. Numerical value is correct.

ms blankenship had 80 dollars to purchase school supplies for her class.she bought 32 glue sticks and 32 boxes of crayons.each glue stick cost 1.40 and each box of crayons vost 0.59 .how much money did ms blankenship have left after these purchases

Answers

Together 32 glue sticks cost $44.80.
Together 32 box of crayons cost $ 18.88.

$44.80 + $18.88 = $63.68
$80 - $63.68 = $16.32

So Ms. Blankenship had $16.32 left after buying school supplies.

Hope this Helps!!

On a recent trip, sarah's car traveled 20 mph faster on the first 110 miles than it did on the remaining 80 miles. the total time for the trip was 4 hr. find the speed of sarah's car on the first part of the trip.

Answers

Let x mph be the speed for the 110 miles trip. Then for 80 miles,
Speed = (x-20) mph

Time, t = Distance/Speed
On 110 miles, t1 = 110/x hrs
On 80 miles, t2 = 80/(x-20) hrs

Total time = 4 hrs = t1+t2 = 110/x + 80/(x-20)

Solving for x;
4 = [110(x-20) + 80(x)]/x(x-20)
4(x)(x-20) = 110x -2200 + 80x
4x^2 - 80x = 110x - 2200 + 80x
4x^2 -80x -110x - 80x +2200 = 0
4x^2 -270x +2200 = 0
Solving the quadratic equation;
x = [-(-270)+/- Sqrt ((-270)^2 -4(4)(2200)]/2*4 = 33.75+/- 24.27 = 9.48 mph or 58.02 mph

Ignore the value smaller than 20 as this would yield a negative value of second speed which is not practical.

Therefore, speed in the first 110 miles is 58.02 mph

WILL MARK BRAINLIEST! PLEASE HELP
In triangle PQR, mP= 43, PQ=7.5 and PR= 8.4. What is mR to the nearest degree?
A. 64
B. 52
C. 41
D. 60

In triangle ABC mA=43, mB=62 and BC=22 in. What is AB to the nearest tenth of an inch?
A. 28.5
B. 15.6
C. 14.1
D.31.2

thank you.

Answers

Part 1) In triangle PQR, mP= 43, PQ=7.5 and PR= 8.4. What is mR to the nearest degree?

we know that
the law of cosines establishes that
c²=a²+b²-2*a*b*cos C

in this problem

c=QR
a=PQ=7.5
b=PR=8.4
C=angle P=43°
c²=a²+b²-2*a*b*cos C----> c²=7.5²+8.4²-2*7.5*8.4*cos 43°
c²=34.66--------> c=5.89
QR=5.9

applying the law of sines
7.5/sin R=5.9/sin 43-----> 7.5*sin 43=5.9*sin R---> sin R=7.5*sin 43/5.9
sin R=0.8669---------> R=arc sin (0.8669)----> R=60.11°----> R=60°

the answer Part 1) is the option
D. 60

Part 2) In triangle ABC mA=43, mB=62 and BC=22 in. What is AB to the nearest tenth of an inch?

we know that
∠C=180-(62+43)-----> ∠C=75°

Applying the law of sines
22/sin 43=AB/sin 75------> AB=22*sin 75/ sin 43-----> AB=31.16 in
AB=31.2 in

the answer Part 2) is
D.31.2

The angle of elevation from a boat to the top of a lighthouse is 22°. The lighthouse is 32 meters tall.

What is the distance from the boat to the base of the lighthouse?

Enter your answer as a decimal. Round only your final answer to the nearest tenth.

Answers

look at this like a right triangle with a height of 32 M and the angle at the base of 22 degrees
The distance from the boat to the lighthouse would be the base of the triangle

to find the base given the height and angle given the formula is

x = height / tan(angle)

x = 32 / tan(22)

x = 79.2 Meters

Maria is ordering copy paper for her office. The office is low on white paper and on blue paper. She will pay $3.50 per realm of white paper and $3.75 per realm of blue paper. If the purchase order is for $36.00 and she ordered 10 realms of paper, how many realms of white paper will she receive

Answers

You have:

x: the number of reams of white paper purchased
y:the number of reams of blue paper purchased

Then, you have the following system of equations:

x+y=10
3.50x+3.75y=36

When you solve the system shown above, you obtain:

x=6
y=4

The answer is: 6 reams of white paper

Let a = reams of white pape b = reams of blue paper

1>>> a+b=10
2>>> 3.50a+3.75b=36

a=6
b=4
There will be 6 realms of white paper that Maria will receive

What is the length of AB?

Answers

The radius of the circle is given to be r = 14.5

Let the center be O. So OB is the radius = 14.5

We can draw a triangle as shown in the image below. We have a right angled triangle. We know the hypotenuse and the base, we need to find the perpendicular side. This can be done using the Pythagorean theorem.

So, we can write:

[tex](14.5)^{2}=10^{2}+OA^{2} \\ \\ OA^{2}=110.25 \\ \\ OA=10.5 [/tex]

Thus, the measure of OA = 10.5

OB = OA + AB

14.5 = 10.5 + AB
⇒
AB = 4

r = 14.5

form a right triangle with the 10 as 1st side and r as the hypotenuse.
get the length of the other side using pythagorean.

c = sqrt(14.5^2 - 10^2) = 10.5

The length from the center to point A = c = 10.5
AB = r - c = 14.5 - 10.5 = 4

length AB = 4

I WILL MARK BRAINLIEST

Answers

Hello!

You can use the Pythagorean Theorem

[tex]a^{2} + b^{2} = c^{2} [/tex]

c is the hypotenuse which is the side across the right angle
a and b are the other sides

Put in the values you know

[tex] a^{2} + 5^{2} = 12^{2} [/tex]

Square the numbers

[tex]a^{2} + 25 = 144[/tex]

Subtract 25 from both sides

[tex] a^{2} = 119[/tex]

Take the square root of both sides

a = 10.9

The answer is D) 10.9 centimeters

Hope this helps!

5.0/5

prestonshelton

Expert

1.1K answers

231K people helped

Hello!

You can use the Pythagorean Theorem

c is the hypotenuse which is the side across the right angle

a and b are the other sides

Put in the values you know

Square the numbers

Subtract 25 from both sides

Take the square root of both sides

a = 10.9

The answer is D) 10.9 centimeters

Hope this helps!

Mr bartley is taking the theater club on a field trip he wrote the the folowing function for the school treasure 52(25+2)

Answers

The answer would be 1,404

Answer:

The answer is 1,404

Step-by-step explanation:

To do this operation, you should be aware of the order of operations. PEMDAS is a good way to remember the order of operations:

1. Parenthesis

2. Exponents

3. Multiplication

4. Division

5. Addition

6. Substraction

Therefore, the first thing we have to do is the parenthesis.

(25+2) = 27

And now, we can do the multiplication

52*27 = 1,404.

what is the value of this expression 3*[(7+8)*2+6] A.64 B.87 C.96 D.108

Answers

D. 108
thats the answer

[tex]3((7+8)*2+6)[/tex]
[tex]=3*36[/tex]
[tex]=108[/tex]
Hope this helps :)

what is 4.6 repeating as a fraction???
please help!! :'(

Answers

Your answer would be 4 2/3.

Let

x=4.66¯6

Then 10x=46.66¯6

So 10x−x=46.66¯6
4.66¯6.−−−−−−−− subtract
9x=42

Divide both sides by 9

x=429=423

The volume of a right rectangular prism is 573.3 cm³. The length of the right rectangular prism is 7.35 cm and the height is 16.25 cm. What is the width of the right rectangular prism? Enter your answer in the box.

Answers

The width of the right rectangular prism is 4.8. You multiply 7.35 by 16.25 and then you divide 573.3 by that answer. So, 573.3 ÷ 119.4375 = 4.8. Hope this helped

Answer:

4.8

Step-by-step explanation:

What is the area of a circle with a radius of 13 millimeters?
(Use 3.14 for Pi.)

Answers

Final answer:

The area of a circle with a radius of 13 millimeters is calculated using the formula πr², which equals 530.66 mm².

Explanation:

The area of a circle is calculated using the formula πr², where 'r' represents the radius of the circle and 'π' (Pi) is a mathematical constant approximately equal to 3.14. When you have a circle with a radius of 13 millimeters, you would substitute 13 into the formula in place of 'r'.

So, the calculation for this circle's area becomes π*(13)² = 3.14 * 169. When you calculate this, you get 530.66 mm². Therefore, the area of a circle with a radius of 13 millimeters is 530.66 mm².

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A mirror frame in the shape of an oval is shown below. The ends of the frame form semicircles:

An oval is formed by a rectangle with semicircles at each end. The length of the rectangle is 62 inches. The width of the rectangle is 27 inches.

Which of the following is the perimeter of the inner edge of the frame?

(π = 3.14)

146.78 inches

208.78 inches

293.56 inches

347.56 inches

Answers

To solve this problem you must apply the proccedure shown below:

1. You have that:

- An oval is formed by a rectangle with semicircles at each end.
- The length of the rectangle is 62 inches. The width of the rectangle is 27 inches.

2. Then, the perimeter is:

P=((3.14)(diameter)/2)(2)+(Lenght of the rectangle)(2)

P=((3.14)(27 inches)/2)(2)+(62 inches)(2)
P=208.78 in

Answer: P=208.78 in

i took the test on flvs its right

A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.1%, 3.2%). what is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?

Answers

Error = 1/2(Maximum range - Minimum range) = 1/2(3.2-1.1) = % = 0.0105

If p is the point estimator;

Then,
Minimum range = p - Error
Maximum range = p + Error

Solving one of the two expressions,
0.011 = p - 0.0105 => p = 0.011+0.0105 = 0.0215 = 2.15%

Answer:

Read more on Brainly.com - https://brainly.com/question/9975138#read more Error = 1/2(Maximum range - Minimum range) = 1/2(3.2-1.1) = % = 0.0105If p is the point estimator; Then, Minimum range = p - Error Maximum range = p + Error Solving one of the two expressions,0.011 = p - 0.0105 => p = 0.011+0.0105 = 0.0215 = 2.15%

Step-by-step explanation:

What formula would I use to find A?

Answers

For this case by cosine theorem, we can use the following formula to find the value of a:
a ^ 2 = (6.3) ^ 2 + (15.10) ^ 2 - 2 * (6.3) * (15.10) cos (70)
Clearing a we have:
a = root ((6.3) ^ 2 + (15.10) ^ 2 - 2 * (6.3) * (15.10) cos (70))
Answer:
A formula to find A is:
a = root ((6.3) ^ 2 + (15.10) ^ 2 - 2 * (6.3) * (15.10) cos (70))

If there is a ratio of 3 to 2, than how many are there in the first number if there is a total of 80?

Answers

Answer:

Step-by-step explanation:

The total number of "ratio units" is 3+2 = 5, so each stands for 80/5 = 16 items. Then 3 ratio units stand for 3×16 = 48 items.

3 : 2 = 48 : 32

The first number is 48.

Simplify the expression 1 + 2a - 3(4+5a) + 6(7-8a)

Answers

Answer:

31 - 61a

Step-by-step explanation:

We distribute, being especially careful with the negative signs:

1 + 2a - 3(4 + 5a) + 6(7 - 8a)

1 + 2a - 3 * 4 - 3 * 5a + 6 * 7 - 6 * 8a

1 + 2a - 12 - 15a + 42 - 48a

31 - 61a

The required simplified expression of the given expression is 31 - 61a.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

As mentioned in the quesiton, to simplify the expression 1 + 2a - 3(4+5a) + 6(7-8a),
⇒ 1 + 2a - 3(4+5a) + 6(7-8a),
⇒ 1 + 2a - 12 - 15a + 42 - 48a

Adding alike terms,
⇒ 31 - 61a

Thus, the required simplified expression of the given expression is 31 - 61a.

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