You have given an equal sided triangle with side length a. A straight line connects the center
of the bottom side to the border of the triangle with an angle of α. Derive an expression for
the enclosed area A(α) with respect to the angle (see drawing
Answers
Answer:
First case;
α < 90°
The area of the shaded triangle = 1/8·a²·sin(60)sin(α)csc(120 - α)
Second case;
α > 90°
The shaded area of the triangle = 1/8·a²·sin(60)sin(180 - α)csc(60 - α) + (a²·√3)/4
Step-by-step explanation:
First case;
α < 90°
The given parameters are;
The type of triangle = Equilateral triangle
The length of the sides of the triangle = a
The area of the triangle = 1/2×a×b×sinC
Where;
a and b are two legs (sides) of the triangle and C is the included angle
e/(sin(α)) = a/(2sin(120 - α)) = f/(sin60)
f = a·sin(60)/(2sin(120 - α))
The area of the triangle = 1/2 × a·sin(60)/(2sin(120 - α))×a/2 × sin(α)
By an online application, we have
1/2 × a·sin(60)/(2sin(120 - α))×a/2 × sin(α) = 1/8·a²·sin(60)sin(α)csc(120 - α)
The area of the triangle = 1/8·a²·sin(60)sin(α)csc(120 - α)
Second case;
α > 90°
The shaded area of the triangle = The area of the equilateral triangle - The unshaded area of the triangle
With an online tool, we have;
The shaded area of the triangle = (a²·√3)/4 - 1/8·a²·sin(60)sin(180 - α)csc(120 - (180 - α)
The shaded area of the triangle = 1/8·a²·sin(60)sin(180 - α)csc(60 - α) + (a²·√3)/4
Related Questions
Dexter is curious as to whether there is a relationship between a person’s height and thumb length. Fourteen of his classmates volunteered to be measured. He listed his data in a table.
Examine the data set and determine the relationship, if any, between height, h, and thumb length, t. Use your model to predict the thumb length of a person who is 174 cm tall.
Answers
The answer to this question is 7.404
Hey, if there is anyone that likes Miraculous ladybug as much as me, you can dial my number and i can pretend to be adrien, chat noir, alya, marinette, or ladybug. (I like acting out chat noir the best) 3856026122
Answers
Answer:
This is amazing and funny but I would rather not give a stranger my phone number but i would if I wasnt such protective
Step-by-step explanation:
Answer:
cool
Step -by-step explanation:
brain list me please
What is the percent increase 41,700 and 63,00
Answers
Answer:
51.0791%
Step-by-step explanation:
Calculate percentage change
from V1 = 41700 to V2 = 63000
(V2−V1)|V1|×100
=(63000−41700)|41700|×100
=2130041700×100
=0.510791×100
=51.0791%change
=51.0791%increase
Suppose that f(x)=3x+1....
Answers
Answer:
3
Step-by-step explanation:
f(x) = 3x+1
f(x+h) = 3(x+h)+1 = 3x+3h+1
f(x+h) - f(x)= 3x+3h+1-3x-1 = 3h
3h/h=3
An exterior angle of a triangle is 152°. If the non-adjacent angles are congruent, then what are the measures of all of the interior angles of the triangle?
a. 62°, 59°, 59°
b. 90°, 45°, 45°
c. 152°, 14°, 14°
d. 28°, 76°, 76°
Answers
9514 1404 393
Answer:
d. 28°, 76°, 76°
Step-by-step explanation:
The sum of the "non-adjacent" interior angles of the triangle is equal to the exterior angle, so is 152°. If those angles are congruent, each is half of 152°, or 76°. The remaining angle is the supplement to 152°, so is 180-152 = 28 degrees.
The interior angles are 28°, 76°, 76°.
you are playing a game you lose 4.8 points lose another 7.6 points and then win 2.5 points what is the overall change in your score?
Answers
Answer:
9.9
Step-by-step explanation:
Fists you have to choose a number, ex. 20. Then subtract 4.8 from 20 equalling 15.2, then subtract 7.2 from 15.2, which equals 7.6, then add 2.5 and get 10.1. When you have that final number you must subtract it from the starting number to find the change, 20 - 10.2 = 9.9
can you please help me with these two questions thank u
Answers
Answer:
the answer to question 1 is 24 and the answer to number 2 is 1
Answer:
frist one is 24. second is 1
Step-by-step explanation:
The last time Robert filled up his car with gas, he paid $24.50 for 7 gallons. This time, he needs 15 gallons. If the price is the same, how much will he pay?
Answers
Answer:
$52.50
Step-by-step explanation:
Set up the ratio:
[tex]\frac{24.50}{7}[/tex]
Simplify in order to find the cost per gallon.
The cost per gallon is $3.50 because 7 divided by 7 is one and 24.50 divided by seven is 3.5.
Now you have this left:
[tex]\frac{3.50}{1}[/tex]
Multiply the denominator by 15 since Robert needs 15 gallons.
Then, multiply the top by 15 because whatever you do to the denominator, you have to do to the top.
Now you have this left:
[tex]\frac{3.5}{1}[/tex] = [tex]\frac{52.50}{15}[/tex]
Therefore, Robert needs to pay $52.50 in order to recieve 15 gallons of gasoline.
please help me.
im dying
Answers
Answer:
19/37
Step-by-step explanation:
47/148 + 29/148 = 76/148 = 38/74 = 19/37
HELP PLS THIS IS A TEST QUESTION
Which linear inequality is represented by the graph?
y<1/2x+2
y>1/2x+2
y<1/3x+2
y>1/3x+2
Answers
Answer:
y<1/2+2
Step-by-step explanation:
Answer:
I think the answer is A because I learned about slope last year
PLEASE HELP ASAP
Write the slope-intercept form of an equation of the line that passes through the
given point and is perpendicular to the graph of the equation..
(-3, -2), y = x + 2 .
Answers
Answer:
y=-x-5
Step-by-step explanation:
) Al repartir laminas entre mis amigos, pude darle 5 a
cada uno y me sobran 2. Pero luego llegaron 2 amigos
más, por lo que las repartí de nuevo y pude darle
láminas a cada uno. ¿cuántos amigos había al principio y
cuántas láminas tenia?
Answers
Answer:
Había cinco amigos al principio y siete laminas en total. (Using google translate)
Step-by-step explanation:
pude darle 5 a cada = 5 amigos
5 a cada uno y me sobran 2 amigos más, por lo que las repartí de nuevo y pude darle = siete laminas
Draw a graph of the line that goes through the points (-4, 7) and (0, 3)
What is the y-intercept and slope of the line you've drawn?
Answers
Answer:
y = -x + 3
Step-by-step explanation:
Use this formula to get the slope [tex]\frac{y2 - y1}{x2 - x1}[/tex]
PLUG IN
[tex]\frac{3 - 7}{0 - -4} \\\\\frac{-4}{4} \\[/tex]
-4/4 = -1
The slope is -1
To find the y- intercept plug your slope and one of your points in this y=mx+b
We will use (0,3)
3 = -1(0) + b (b represents y-intercept)
3 = b
The equation would look like this
y = -x + 3
Hope this helps ya!!
ABC and DEF are similar. Find the missing side length.
Answers
Answer:
The missing side length is 5
Step-by-step explanation:
Basically 32 to 4 and 56 to 7 is 8 to 1, so you divide 40 by 8 to get the answer, 5
CAN SOMEONE PLEASE HELP! I WILL MARK BRIANLIEST
Answers
Answer:
yes is is proportional
x=ydivided by 3.5
Step-by-step explanation:
Answer: multiplying by 3.5
Step-by-step explanation: because if you divide 7 by 2 you will 3.5
Joe pays $25.10 for 2.5 pounds of wall-paper. What is the price, in dollars and cents, per pound of wall paper?
Answers
Answer:
10.04
Step-by-step explanation:
25.10/2.5=10.04
Answer:
10.04
Step-by-step explanation:
All you do is divide 25.10 by 2.5, the total($25.10) by the amount(2.5) then that is where
25.10 divided by 2.5 comes from, therefore your answer is 10.04
What is 45 percent of 37 A. 0.1665 B. 1.665 C. 16.65 or D 166.5
Answers
Answer:
The answer is C. 16.65 Hope that helps :)
45 percent of 37 is equal to 16.65. The correct answer is C) 16.65.
To find 45 percent of 37, we can multiply 37 by 0.45 since 45 percent is equivalent to 0.45 as a decimal.
37 * 0.45 = 16.65
Therefore, 45 percent of 37 is equal to 16.65.
The correct answer is C) 16.65.
The calculation represents taking 45 percent (or 0.45) of the value 37, resulting in the product 16.65. This means that if you were to take 45 percent of 37, you would obtain the value 16.65. It's essential to understand how to convert percentages to decimals to perform accurate calculations involving percentages.
Learn more about percentages here
https://brainly.com/question/29014288
#SPJ6
what would the value of X be on this one?
Answers
Answer:
i think it's 51 because if you add 106 and 23 together it's 129 then 180-129= 51
Step-by-step explanation:
Jim stands on a dock that is 3 3/4 feet above the lake. He dives down 12 1/2 feet below the dock. What is Jims vertical location relative to the lake surface?
Answers
Given:
Jim stands on a dock that is [tex]3\dfrac{3}{4}[/tex] feet above the lake. He dives down [tex]12\dfrac{1}{2}[/tex] feet below the dock.
To find:
The Jims vertical location relative to the lake surface.
Solution:
We have,
Vertical location of dock relative to the lake surface [tex]=3\dfrac{3}{4}[/tex] feet
He dives down [tex]12\dfrac{1}{2}[/tex] feet below the dock. So,
Vertical location relative to the lake surface [tex]=3\dfrac{3}{4}-12\dfrac{1}{2}[/tex]
[tex]=\dfrac{3\times 4+3}{4}-\dfrac{12\times 2+1}{2}[/tex]
[tex]=\dfrac{12+3}{4}-\dfrac{24+1}{2}[/tex]
[tex]=\dfrac{15}{4}-\dfrac{25}{2}[/tex]
Taking LCM, we get
[tex]=\dfrac{15-50}{4}[/tex]
[tex]=\dfrac{-35}{4}[/tex]
[tex]=-8\dfrac{3}{4}[/tex]
Here, negative sign means Jim location is below the lake surface.
Therefore, Jim is [tex]8\dfrac{3}{4}[/tex] feet below the lake surface.
Answer:-8 3/4
Step-by-step explanation:
I just took the cahoot
(b) A solid metal cone has radius 1.65 cm and slant height 4.70 cm.
Calculate the volume of the cone.
Answers
Answer:
13.4
Step-by-step explanation:
πr2h
3
Answer:
12.5
Step-by-step explanation:
use pythag to find perpendicular height
then from that your answer should be 4.40cm
Select "Rational" or "Irrational" to classify each number
Answers
Answer:
rational
Step-by-step explanation:
I'm coochie man
A circular tablecloth is 6 feet in diameter. How many feet of ribbon would be required
to edge the circumference of this tablecloth? Use 3.14 as the value of pi. Round to
the nearest whole number.
Answers
Answer:
You'll need 18.85 feet of ribbon.
Step-by-step explanation:
The circumference is [tex]\pi d[/tex].
[tex]\pi * 6 = 18.85[/tex]
prove algebraically that n^2 -n is never an odd number when n>1
Answers
Answer:
See Below.
Step-by-step explanation:
We want to prove that:
[tex]n^2-n[/tex]
Is never an odd number when n>1.
We will have two cases. We can prove them for each case individually.
The Even Case: n is Even:
Let n be even. Then, we can rewrite n as:
[tex]n=2k[/tex]
Where k is any positive integer.
This is because twice of any integer is even, so n must be even.
Substitute this into our expression to acquire:
[tex]=(2k)^2-(2k)[/tex]
Square:
[tex]=4k^2-2k[/tex]
4 times anything is even. 2 times anything is also even. Therefore, our expression will stay even.
The Odd Case: n is Odd:
Let n be odd. Then we can rewrite n as:
[tex]n=2k-1[/tex]
Where k is any positive integer.
This is odd because twice of any number is even, but if subtracted by 1, it yields an odd number.
We will substitute this into our expression to acquire:
[tex]=(2k-1)^2-(2k-1)[/tex]
Square:
[tex]=(4k^2-4k+1)+(-2k+1)[/tex]
Simplify:
[tex]=4k^2-6k+2[/tex]
4 times anything is even. 6 times anything is even. And anything even added to 2 will still be even.
Therefore:
[tex]n^2-n[/tex]
Will never be an odd number when n>1.
The perimeter of an isosceles triangle is 15.6 cm. Find the lengths of its sides, if: The base is 3 cm smaller than a leg.
Answers
Answer:
The sides of the isosceles triangle are 3.2 cm, 6.2 cm and 6.2 cm
Step-by-step explanation:
The sides of an isosceles triangle are equal in length
Let the base be x cm
Since it is 3 cm smaller than a leg, the legs will be (x + 3) cm
To find the perimeter of a triangle, we add up the sides
x + x + 3 + x + 3 = 15.6
3x + 6 = 15.6
3x = 15.6 - 6
3x = 9.6
x = 9.6/3
x = 3.2 cm
So the base is 3 + 3.2 =6.2 cm
What is the measure of ∠ABD?
Answers
Answer:
m∠ABD = 114°
Step-by-step explanation:
Given measurements of interior angles are:
m∠D = 2n°
m∠C = 60°
m∠ABD = (4n+6)°
The measurement of exterior angle of a triangle is equal to the sum of two opposite interior angles.
This can be mathematically expressed as:
m∠ABD = m∠C+m∠D
Putting the respective values
[tex]4n+6 = 2n+60\\4n-2n+6 = 60\\2n+6 = 60\\2n = 60-6\\2n = 54\\\frac{2n}{2} = \frac{54}{2}\\n = 27[/tex]
Putting n=27 in (4n+6)°
[tex]=4(27) + 6\\= 108+6 = 114[/tex]
Hence,
m∠ABD = 114°
Solve the system of equations below.
y=3x
2x + y = 15
Answers
Answer:
x=3
Step-by-step explanation:
2x+(3x)=15
5x=15
x=3
solving for y:
3(3)=9
y=9
Answer:
(y,x) (9,3)
Step-by-step explanation
WHICH ONE DO I PICK?
Answers
Determine if the figure below has rotational symmetry, line symmetry or both and
describe the transformation that mas the figure onto itself. BE SPECIFIC. You must
name the center of rotation and degree of rotation if it has rotational symmetry or
lines of reflection if it has line symmetry
Answers
Answer:
A) Given that the figure is a rectangle, it has a rotational symmetry and by rotating the figure 180° about the center of the figure, the preimage and image will coincide
The figure also has a line symmetry for the vertical line x = 5, and a line symmetry for the horizontal line y = 5
Therefore the figure has both symmetry
B) The transformation that maps the figure unto itself are therefore;
1) Rotating the figure 180° about the point (5, 5) which is the center of the figure
2) Reflection of the figure across the line x = 5 and also reflection of the figure across the line y = 5
Step-by-step explanation:
Write an equation in slope-intercept form for a line with m = 3 and includes the
point (0, 2).
Answers
Answer:
y=3x+2
Step-by-step explanation:
dont put 0 because it dont make sense
if you put 0 n the equation, you will not will get the right equation
Find the slope of the line y
=2x + 3/7
Answers
Answer:2
Step-by-step explanation:
Number by x
Answer:
Below!
Step-by-step explanation:
The equation y = 2x + 3/7 is in slope-intercept form: y = mx + b, where m = slope and b = y-intercept.
Note that m is the coefficient of x, and b is the constant.
The coefficient of x is 2, and the constant is 3/7.
Hence, these are the answers.
[tex]\rule{350}{4}[/tex]
[tex]\frak{-Dream-}[/tex]