F1 = Ferris wheel one

F2= Ferris wheel two

F1, \(\displaystyle h=-12\cos\frac{\pi}{10}t+12.5\)

F2, \(\displaystyle h=-12\cos\frac{\pi}{30}t+15\)

Now from these two equations, I want to know when F2+F1= 27.5m i.e I want to find the times when the combined height of each Ferris wheels seat adds up to 27.5m.

How would I go about doing this?]]>

and i know the radius of the inside circel, how can i calculate the outside radius]]>

An airplane flies 470 miles from point $A$ to point $B$ with a bearing of 25 degrees. It then flies from 250 miles from point $B$ to point $C$ with a bearing of 40 degrees. Find the distance and the bearing from A to point C.

Work

I understand that I need to use law of cosines for the side $b$ which is opposite of the angle $B$. But I have a hard time with find what is the angle $B$ is. I forgot many things from geometry. How to...

Bearings-Finding the angle of B as well as the finding the bearing from point A to Point C.]]>

We have a rectangle inside a semicircle with radius $1$ :

From the midpoint of the one side we draw a line to the opposite vertices and one line to the opposite edge.

Are the acute angles of the right triangles all equal to $45^{\circ}$ ?

All four triangles are similar, aren't they? We have that the hypotenuse of each right triangle is equal to $1$, since it is equal to the radius of...

Acute angle of right triangles]]>

Moreover, the company uses a hexagonal-shaped plastic box to pack 24 chocolate bars together as shown in the figure below.

What is the...

Find the volume of the hexagonal-shaped plastic box]]>

x = -5 + 8t, y = 1 + 10t, z = 9 + 8t ; -2x + 8y + 8z = 10]]>

Determine the general solutions cos(2x+20)=-cos(x-11)]]>

An equation of a line perpendicular to the line represented by the equation y= -1/2x-5 and passing through (6, -4) is

1) y= -1/2x + 4

2) y= -1/2x - 1

3) y= 2x + 14

4) y= 2x - 16

I know it's not 1 or 2 because perpendicular lines have to be negative reciprocals. What I don't know is how to figure out whether the answer is 3 or 4.]]>

Triangle ABC has a perimeter of 16cm.

Triangle DEF has side of 6cm, 8cm and 10cm.

What is the scale factor of triangle ABC to triangle DEF?

A. 1/2

B. 1/3

C. 2/3

D. 3/2

E. 2/1

I concluded the answer is D. Am I correct?]]>

is it just plug and play??

find factors of -48

$-1(48)=-48$

$-2(24)=-48$

$-3(16)=-48$

$-4(12)=-48$

$-6(8)=-48$

check sums for positive number

$-1+48=47$

$-2+24=22$

$-3+16=13$

$-4+12=8$

$-6+8=2$

it looks like

Number 8 asks about what is the area of the quadrilateral.

Number 9 asks about what number is below the number 25.

Those are questions for Elementary School Math Olympiads in my country but both of us were having a hard time figuring them out.

For question no. 9, if only that number 9 is located right above number 13 it would be easy to solve. However, we don't know whether the placement of 9 above is intentional or not. Can someone help us...

[ASK] Geometry and Series]]>

This seems to be rather common GRE Exam Question

Which appears to harder that what it is

It looks like a similar triagle solution

$\dfrac{800}{7000}=\dfrac{x}{1400}$]]>

I am writing a piece of software where the user can select a polygon of 3, 4, 5, 6 or 8 sides. All of the polygon points are equidistant from the x, y point. In other words, if you drew a circle where the center was the x, y point, all of the points of the polygon would line on the circle.

That means, obviously, that the distance of each polygon point is equal to the imaginary circle's radius.

Given that information, what are the...

Finding 2D Polygon Coordinates from a point]]>

I made a large circular tortilla.

Ate half of it. Then decided to put the rest into the fridge on a smaller plate.I raised the knife to cut the remaining semi-circle in two, and then went : "Hmmmmmmmm...".

Anyway, it's in the fridge now with an approximate solution, but I'm wondering if anyone knows the mathematical one?

I'm wondering if there are 3 different optimal solutions:

1) In which the straight-line cut necessarily is from the center of the original circle to...

The smallest circle that two parts of a semi-circle can fit into?]]>

Answer:-

How to answer this question using geometry or calculus or by using both techniques.]]>

totally lost and confused with this question:

A machine is subject to two vibrations at the same time.

one vibration has the form: 2cosωt and the other vibration has the form: 3 cos(ωt+0.785). (0.785 is actually expressed as pi/4)

determine the resulting vibration and express it in the general form of: n cos(ωt±α)]]>

a. \(\displaystyle x^2+y^2-3x-6y=0\)

b. \(\displaystyle x^2+y^2-12x-6y=0\)

c. \(\displaystyle x^2+y^2+6x+12y-108=0\)

d. \(\displaystyle x^2+y^2+12x+6y-72=0\)

e. \(\displaystyle x^2+y^2-6x-12y+36=0\)

Since the center (a, b) lays in the line y = 2x then b = 2a.

\(\displaystyle (x-a)^2+(y-b)^2=r^2\)

\(\displaystyle (0-a)^2+(6-b)^2=r^2\)...

[ASK] Equation of a Circle in the First Quadrant]]>

a. (3, -4)

b. (6, -4)

c. (6, -8)

d. (-6, -4)

e. (-6, -8)

I already eliminated option c and e since based on the coefficient of y in the equation, the ordinate of the center must be -4. However, I don't know how to determine the abscissa since we need to determine the value of p first, in which we need to substitute the value of x and y while the only info I have is y = 0. How should...

[ASK] A Circle Which Touches the X-Axis at 1 Point]]>

All I knew is that \(\displaystyle sin(\beta+\gamma)=sin(180°-\alpha)=sin\alpha\), but I think it doesn't help in this case.]]>

Need help finding Diagonals of a Rhombus]]>

There are about 167 marbles in a jar.

Volume of sphere (marbles) = (4/3)πr^3

r = (4/3)π(0.25)^3

volume of sphere/marble = 0.0654 inches

Volume of cylinder (glass) = v=πr^2h

v=π(1.625)^2*2.80

volume of cylinder/glass = 23.23 inches

It is a given that the glass is 74% filled and 26% empty due to space in between the marbles.

Number of marbles = (jar volume * 0.74)/volume of one marble

= (23.23*0.74)/0.0654

= 262 marbles

Math says that there is 262 marbles...

How many marbles are in a jar?]]>

Surface of Angular Land]]>

A. 3 cm

B. 4 cm

C. 5 cm

D. 6 cm

It was a question for a 9th grader and the book hasn't covered trigonometry by name yet (As in, they don't know about the term sine, cosine, and tangent, but the books do explain the length ratio of triangle which has 45°-90°-45° angle or 30°-60°-90° angle. How to do it and explain it to them?]]>

I stumbled with a striking claim in https://www.cut-the-knot.org/do_you_know/GoldenRatioInYinYang.shtml

Sorry, I couldn't paste the pic. The question is if there is an algebraical or trig proof for this claim, as the angle seems to be just 45º. Then, is there an EXACT proof for this claim?]]>

Ok this is considered a "hard" GRE geometry question... notice there are no dimensions

How would you solve this in the fewest steps?]]>

I have this quote:

"The extractor of the 0.1L unit has a volume of 100mL and an internal height/diameter relationship of 19 (H

Sorry to sound so silly, but can someone please help me work with this equation?

I would like a cylinder that would hold approximately 5.0L.

What should the Height and Diameter be?

Cheers

Nelg]]>

The students are required to show their work how to solve this problem.]]>

Check if two points are symmetrics/asymmetric]]>

Could anyone help me understand the steps on the below questions?

A cone has a total surface area of 300π cm² and a radius of 10 cm. What is its slant height?

A cone has a slant height of 20 cm and a curved surface area of 330 cm2. What is the circumference of its base?

I'd really like to know what steps I need to take to get to the answer on these.

Thank you in advance ]]>

What I got is \(\displaystyle 4a=–4\pm3r\sqrt2\) and \(\displaystyle b=4\pm r\sqrt2\). Dunno how to continue from here.]]>

]]>

in order to find cos(x)

i tried to slove for sin(x) using sin

btw i used the (a+b)

if anyone could help me...

solving trig equation cos(x)=sin(x) + 1/√3]]>

I need to find the angle of the parable tangent derived from the theoretical arc traced by a foot during a step and the ground (see attached). The arc comprises of a persons step height and step length and I need to find the angle of the arc it creates. No other research regarding this angle has manual calculated it.

I have contacted the researcher and he gave me the following formula:

Stride (step) angle tangent = 4*height...

Find the angle of the parable tangent derived from the theoretical arc traced by a foot]]>

ok this is what I posted on the

mathquiz community

it was done by simple observation

typos maybe,,,,]]>

I need help with this question

so if you can help me with the answer please please.

]]>

I think I can work out the pyramid's base area by deriving for the formula of equilateral triangle area. What I can't is determine the pyramid's height. All I knew is that is must be less than 4√3 cm. Anyone willing to help me?]]>

The question is in the image. Working out with every step would be much appreciated.]]>

A: 75.04

B: 66.9

C: 41.13

The first thing I need to do is move just lines A and C in towards each other .5 and recalculate all sides.

Then I need to inscribe the largest quadrilateral that will fit while having one side being no shorter than 7.5, with the entire quadrilateral maintaining a distance of 5 away from all three sides of the scalene triangle.

I need the new measurements for the scalene triangle and the quadrilateral.]]>

Real world trigonometry problem making furniture]]>

Borrowed from HiSet free practice test]]>

I'm trying to work out this question, and the answer I'm coming up with isn't right. Can anyone help me understand the calculation used to work this out?]]>

Here I got that triangle BCH and triangle EHD is similar with angle BCH = angle HDE = 45°, angle CHB = angle DHE = 112.5°, and angle CBH = angle DEH = 22.5°. The area of triangle BCH is ½ × CH × h, where h is the parallelogram's...

[ASK] Find the ratio of the area of triangle BCH and triangle EHD]]>

Could someone check that I'm right with this one, or put me right! I've worked the value out as

x=30 and y (2x) = 60. I've come to this as I think it's an isosceles triangle so the base angles would be equal. Am I right?

Thank you!

]]>

Attached is a picture of a circle.

The lower tangent line is y=0.5x. The center of the circle is M(4,7) while the point A is (3,6).

I found the equation of the circle, it is:

$(x-4)^{2}+(y-7)^{2}=20$

and I wish to find the dotted tangent line. I know that it is parallel to the lower one, therefore, the slope is the same. I can't find the tangent point.

Can you give me a hint please ?]]>

Hi

I need help with a problem on 'Nets'. I have attached an image , need help coming up with a 3D figure based on top, side and front views. The closest i could come to was a triangular prism but the front view does not seem to agree with the prism. Please help.

Thanks

Neha]]>

I'm trying to work out how I'd calculate the values in the below. Rather than just have the answer, I'd really like to understand how I'd calculate this. Thank you in advance!

]]>

Thank you for your help!]]>

In this diagram, x is the circumference of the circles, and the bit of the bottom circle which is drawn blue (the overlapping bit) is 1/6th of the whole circumference.

What I'm looking for is y, which is this:

Now, working out x is easy - it's 2 \pi r, thus the overlapping bit is 1/3 \pi r. But how do I proceed...

The height of a section of overlapping circles.]]>

Now, I am looking for two things:

A proof that each part of the circle which is in an intersection is 1/4 the size of the whole circle's circumference

The exact area of the non-shaded region.

Now, in my search to finding the answer to this, I stumbled upon this Circle-Circle Intersection -- from Wolfram...

Find the exact shaded area of the region in 4 overlapping circles]]>

I have no idea how to do it, all help will be appreciated.]]>

the answer for this is

2100 x 2 pie = 4200 pie radian

3 mins = 180 seconds

4200 / 180 = 73.3 rad/s

(ii) Determine the area and arc length of the minor sector shown here for the 120mm diameter circle.

minor section angle = pie / 3 x radians (this question is formatted as pie with a line under it then 3 under the line and radians next to it...

Angular Velocity]]>

In this question, I tried this:

sin^2(180-x) cosec(270+x) + cos^2(360-x) sec(180-x), where cosec(x) = 1/sin(x) and sec(x) = 1/cos(x)

-sin^2(180-x) = sin^2(x) and cos^2(x) = cos^2(x)

-The sin^2 and the 1/sin(x) cancle out along with the cos^2 and the 1/cos(x)

Therefore, I am left with sin(x)(270+x) + cos(x)(180-x)

This looks wrong. The answer on the answer sheet is -sec(x). I ask you for help please.]]>

(sinx+cosx)/(secx+cscx)= sinxcosx

if you could list out the steps it would be appreciated]]>

$$\theta=\tan^{-1}\sqrt{3}$$

rewrite

$$\tan(\theta)=\sqrt{3}$$

using $\displaystyle\tan\theta = \frac{\sin\theta}{\cos\theta}$ then if $\displaystyle\theta = \frac{\pi}{3}$

$$\displaystyle\frac{\sin\theta}{\cos\theta}

=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}

=\sqrt{3}$$

ok I think this is a little awkward since it is observing the unit circle to see what will work

so was wondering if there is a more proper way.]]>

$$\sin(4x)$$

use $\sin2a=2\sin a\cos a$ then

$$\sin4x=2\sin 2x\cos 2x$$

with $\cos(2x) = \cos^2(x)-\sin^2(x)$ replace again

$$\sin 4x=4\sin x\cos x+\cos^2(x)-sin^2(x)$$

ok not real sure if this is what they are asking for

and if I should go further with it even if the steps are ok]]>

A smaller (of course!) circle tangent to the above

circle and 2 sides of the square is inscribed in

one of the corners of the square.

What is the diameter of this circle?]]>

I need to find the length of a Chord of a circle given that I have the Arc length and Arc Height (that's all), no radius or anything else.

I suspect that I will need a radius to find this. Or am I missing a point here?

The below spreadsheet I found on the web proports to be able to do this but the answer is not correct. The edges of my material does not match up when I calculate the Chord length given...

Finding Chord length given arc length and arc height?]]>

I know if the...

Making a formula that finds the horizontal and vertical distance between two points that change with]]>

For example, I want to divide a circumference into 78 equal parts, and the circumference diameter is 1 meter!

Whats the length of each part? And how do you calculate it? (no compass please) Maths only please.]]>

\begin{align*}\displaystyle

\frac{\tan^2 t -1}{\sec^2 t}

&=\frac{\tan t-\cot t}{\tan t+\cot t}\\

\frac{\tan^2 t -1}{\tan^2 t+1}&=

\end{align*}

OK I continued but I could not derive an equal identity

I saw a solution to this on SYM but it was many steps and got very bloated

there must be some way to do this in like 3 steps?]]>

a) cos(sin

b) cos

(VERY HARD)]]>

[ASK] How to Read A'?]]>

I need help finding the area of triangle ABC.]]>

diagonal 2=37cm.

AB=25.5cm

S (AMC)= 306cm.

S (ABCD)=?]]>

Ok this should be just an observation solution ..

But isn't the equation for chord length

$$2r\sin{\frac{\theta}{2}}=

\textit{chord length}$$

Don't see any of the options

Derived from that..]]>

I am having problems trying to find the way of drawing a line which is tangent to a circle and intersects another circle making a 30º intersection.

Let´s say I have circle A with coordinates 479183.87, 4365099.87 (x1,y1) and a radius of 27780m. I have a second circle, B, with coordinates 488889.66, 4390316.69 (x2,y2) and a radius of 5294m. I would like to draw a line which joins both circle, being the line tangent to circle B and intersects circle A with...

Tangent line to circle making 30º with a second circle]]>

a) y\ge0

b) y<0

I'm not sure how to explain this in words.Thank You!]]>

The answer needs to be in rectangular and polar form.]]>

\frac{\cot {x}-1}{\cot{x}+1}&=\frac{1-\sin 2x}{\cos 2x}\\

\frac{\cos {x}-\sin x}{\cos{x}+\sin x}

\frac{\cos x-\sin x}{\cos x-\sin x}&= \\

\frac{\cos^2x-2\sin x\cos x+\cos^2 x}{\cos^2 x-\sin^2 x}

\end{align*}$

so far..]]>

(e^ix)-1=(2ie^(ix/2))x(sin (x/2))

Calculate this sum

Zn=1+e^(ix)+e^(2ix)+.....+e^((n-1)ix)

And deduce those values :

Xn=1+cos(x)+cos(2x)+.....+cos((n-1)x)

Yn=sin(x)+sin(2x)+.....+sin((n-1)x)]]>

An airplane flies at a fixed air speed which is unknown. There is a wind with unknown heading and unknown speed. The airplane has a known ground speed and direction. The airplane changes heading (with reference to ground), and now there is a different ground speed and direction. How to determine on basis of this information (two sets of ground speeds and directions) the wind strength and wind direction? The speed of the airplane with reference to...

Trigonometric riddle]]>

Two pulleys with radii r1 and r2 rotate at angular speeds of w1 and w2. if the pulleys are connected by a belt, show that r1/r2=w2/w1]]>

I have sin^n(x)/(sin^n(x)+cos^n(x))

The expression is the same with 1/(ctg^n(x)+1) and I have no idea how to get to this answer.

Can you help me?]]>

To better describe the problem I have uploaded here:

https://docs.google.com/document/d/13l9MZaSrdoh7oF7m75OB9jTRPnXlL_e7VXjUCFkqQBc/edit?usp=sharing

Feel free to ask any questions.

Any help is appreciated!]]>

1.What is the sum of the measures of the interior angles of a heptagon?

A. 1260∘

B. 2520∘

C. 900∘

D. 1800∘

my answer is C

5.If the sum of the interior angle measures of a polygon is 3600∘, how many sides does the polygon have?

A. 22 sides

B. 20 sides

C. 18 sides

D. 10 sides

MY ANSWER ?

3.What is the angle measure of each exterior angle of a regular octagon?

A. 45∘

B. 135∘

C. 360∘

D. 1080∘

MY ANSWER ?]]>

This is where I got so far. I can't figure out how to prove AH = DK in order to prove the HL property of congruency]]>

(2) Is there a pi in polygons entities (e.g square)? not or yes?

(3) If there is pi in some geometries and other not - What is the

(4) How cloud I know that are no hidden formula of pi in a square figure that the expression in formula, his value is: 0 in addition and 1 in multiplicatoin and etc]]>

Answer: 55 m.]]>

suppose, there is a new triangle that called AED.

alpha is a angle between LB to AD that is bisector of AED.

The triangles can be on any place in the plane.

What the value biggest angle (\(\displaystyle alpha\)) can be?]]>

Normally I consider myself quite adept in mathematics, but I simply lack the right idea and/or the mathematical creativity to solve this assignmenent:

"Prove that the Simpsons formula V = 1/6 * h * (Ab + 4Am + At) can be used to calculate the volume of a pyramid frustrum."

V = Volume of the pyramid frustrum

h = height of the pyramid frustrum

Ab = Area of the "bottom" of the pyramid frustrum

Am = Area of a horisontal slice of the pyramid...

Simpsons formula and the volume of a pyramid frustum]]>

12) area of full circle is πr²

area of sector is (120/360)(πr²) or 12π

13) same

area is (270/360)(πr²)

Am i correct?

]]>

14) area of sector is πr²/3 = 12π

length of chord. that triangle has two sides of 6 and angle of 120º

split the triangle in two right triangles with angle of 120/2 = 60 and hyp=6. other (longer) side is:

sin 60 = x/6

s = 6 sin 60 = 6(√3/2) = 3√3

third side is

s = 3 cos 60 = 3

area =(1/2)(3)(3√3) = 4.5√3, double for both triangles

subtract that from the sector to get (12π) – (9√3)

15) similar to above.

find the area of the 270º sector and add the area of the triangle...

Find the areas of segment in circle]]>

So far i have 270/360× (pi)r^ i dont know what to do next please help.]]>

Into 2, a triangle and a square, i know that the additional leg length to the triangle can be found by subtracting base 1 and base 2=4 so i have a triangle with a hypotenuse of 8 inches, 1 leg=4 and now i have to find the length of the other leg. The length of the other leg can be found by multiplying the length of the other leg by the square root of 3 to get (4×3squared)=6.9282 the area for that triangle would be 13.84. Now i have to find the...

Find the height and base of a trapezium]]>

]]>