• Just a math question I thought of?

    Best answer:   Three points on the curve y = sinx: A (a, sin a), B (b, sin b), C (c, sin c) where 0 ≤ a < b < c ≤ 2π Triangle ABC has base |AC| = √((a − c)² + (sin a − sin c)²) Line AC has slope = (sin a − sin c) / (a − c) Equation of line AC: y − sin a = (sin a − sin c) / (a − c) (x − a) (a − c) (y − sin a) = (sin a −... show more
    Best answer:  
    Three points on the curve y = sinx:
    A (a, sin a), B (b, sin b), C (c, sin c)
    where 0 ≤ a < b < c ≤ 2π

    Triangle ABC has base |AC| = √((a − c)² + (sin a − sin c)²)

    Line AC has slope = (sin a − sin c) / (a − c)
    Equation of line AC:
    y − sin a = (sin a − sin c) / (a − c) (x − a)
    (a − c) (y − sin a) = (sin a − sin c) (x − a)
    (sin a − sin c) (x − a) + (c − a) (y − sin a) = 0

    Triangle ABC has height = distance from B to line AC
    = |(sin a − sin c) (b − a) + (c − a) (sin b − sin a)| / √((sin a − sin c)² + (a − c)²)
    = |(b−c) sin a + (c−a) sin b + (a−b) sin c| / √((sin a − sin c)² + (a − c)²)

    Area (ABC)
    = 1/2 * √((a − c)² + (sin a − sin c)²) * |(b−c) sin a + (c−a) sin b + (a−b) sin c| / √((sin a − sin c)² + (a − c)²)
    = 1/2 * |(b−c) sin a + (c−a) sin b + (a−b) sin c|

    Using WolframAlpha, we find area is maximized when:

    a = 0
    b = 1.72545
    c = 5.32211
    Maximum area = 3.33656

    http://www.wolframalpha.com/input/?i=max...

    Here is a diagram showing the triangle with maximum area:
    https://www.desmos.com/calculator/di4j6s...
    You can move the points around on the curve.
    The area is shown on the second line.
    6 answers · 1 day ago
  • Please demonstrate how to solve this problem step by step using PEMDAS 3-5*(-1)/(1-3*(-1)) Thank you.?

    Best answer: 3-5*(-1)/(1-3*(-1))
    3 + 5/(1+3)
    3 + 5/4
    12/4 + 5/4
    17/4
    Best answer: 3-5*(-1)/(1-3*(-1))
    3 + 5/(1+3)
    3 + 5/4
    12/4 + 5/4
    17/4
    6 answers · 14 hours ago
  • How do you simplify?

    Best answer: sec²(x)/(sec²(x)-1) = sec²(x)/tan²(x)
    = (1/cos²(x)) / (sin²(x)/cos²(x))
    = 1/sin²(x)
    = csc²(x)
    Best answer: sec²(x)/(sec²(x)-1) = sec²(x)/tan²(x)
    = (1/cos²(x)) / (sin²(x)/cos²(x))
    = 1/sin²(x)
    = csc²(x)
    10 answers · 2 days ago
  • How do you solve this math question?

    John rides his bike one-third of the way from his house to school where he meets his friend, Joe. After he rides another mile John is halfway to school. How far is the school from Joe’s house?
    John rides his bike one-third of the way from his house to school where he meets his friend, Joe. After he rides another mile John is halfway to school. How far is the school from Joe’s house?
    14 answers · 17 hours ago
  • Could someone explain what type of Algebra this is: 16x^2 - 80x + 100?

    Best answer: This is what is known as a Quadratic expression.
    16x² - 80x + 100 = 0 would be a Quadratic Equation.
    Best answer: This is what is known as a Quadratic expression.
    16x² - 80x + 100 = 0 would be a Quadratic Equation.
    5 answers · 22 hours ago
  • I do not understand where the negative in -sqrt x ^ 6 comes from?
  • Find the x of (x-6)^2?

    Best answer:   This is a badly worded question. Are you looking for a root? Or are you looking for the "x" term in the expansion of (x − 6)²? To find root, set expression = 0 and solve for x: (x − 6)² = 0 x − 6 = 0 x = 6 To find the "x" term in the expansion of (x − 6)², use binomial... show more
    Best answer:  
    This is a badly worded question.

    Are you looking for a root? Or are you looking for the "x" term in the expansion of (x − 6)²?

    To find root, set expression = 0 and solve for x:

    (x − 6)² = 0
    x − 6 = 0
    x = 6

    To find the "x" term in the expansion of (x − 6)², use binomial expansion:

    "x" term of (x − 6)²
    = C(2,1) (x)¹ (−6)¹
    = 2 (x) (−6)
    = −12x
    5 answers · 1 day ago
  • Area of a triangle??? Heron’s formula???? what is the area of a triangular lot with sides of lengths 118, 152, and 201 ft?

    Best answer: Heron's formula:

    S = (A + B + C)/2

    A = √[S(S - A)(S - B)(S - C)]

    For a triangle with sides 118, 152, and 201 ft:

    S = (118 + 152 + 210)/2 = 235.5

    A = √[235.5 * (235.5 - 118) * (235.5 - 152) * (235.5 - 210)]
    A = √[235.5 * 117.5 * 83.5 * 34.5]
    A = √79,713,953.4375

    A = 8,928.3 ft²
    Best answer: Heron's formula:

    S = (A + B + C)/2

    A = √[S(S - A)(S - B)(S - C)]

    For a triangle with sides 118, 152, and 201 ft:

    S = (118 + 152 + 210)/2 = 235.5

    A = √[235.5 * (235.5 - 118) * (235.5 - 152) * (235.5 - 210)]
    A = √[235.5 * 117.5 * 83.5 * 34.5]
    A = √79,713,953.4375

    A = 8,928.3 ft²
    6 answers · 2 days ago
  • When you perform the following operations, how many significant figures should your answer have? (2.000 cm3 x 15.6 g /cm3) + 1.000 kg?

    Best answer: The simple rule of taking the least of all the numbers does not apply when you have addition or subtraction.

    2x15.6 = 31.2 g, to 3 places
    adding 1000 g, to 4 places gives you 1031.2 g to 4 places, as 1000 g is only good to 4 places. so the answer is 1031 g
    Best answer: The simple rule of taking the least of all the numbers does not apply when you have addition or subtraction.

    2x15.6 = 31.2 g, to 3 places
    adding 1000 g, to 4 places gives you 1031.2 g to 4 places, as 1000 g is only good to 4 places. so the answer is 1031 g
    5 answers · 2 days ago
  • How are the equations y=mx=b and y=kx alike?

    Best answer: Assuming that y = mx + b

    The equations are both in slope intercept form.
    Best answer: Assuming that y = mx + b

    The equations are both in slope intercept form.
    5 answers · 2 days ago
  • Math question help?

    x² + 1 = 5
    x² + 1 = 5
    14 answers · 2 days ago
  • Math order of operations?

    I have an equation -x^2 + 8 Let s assume x is 4 Is the answer going to be 8 or 24?
    I have an equation -x^2 + 8 Let s assume x is 4 Is the answer going to be 8 or 24?
    10 answers · 14 hours ago
  • Is 4 5/8 inches the same as 4.6 inches?

    I am very confused with fractions. I'm trying to buy an item online and i want to know its dimensions. So is 4 5/8 inches over 4.5 inches?
    I am very confused with fractions. I'm trying to buy an item online and i want to know its dimensions. So is 4 5/8 inches over 4.5 inches?
    13 answers · 1 day ago
  • Is it cheating to use a math calculator in class when allowed to?

    I consider people who use a calculator to add and subtract problems to be too easy and I consider it cheating because I think people should know how to do math by hand. If you are in a Math class when you are allowed to use a calculator, isn’t this cheating? Why would some Math classes allow you to use a calculator... show more
    I consider people who use a calculator to add and subtract problems to be too easy and I consider it cheating because I think people should know how to do math by hand. If you are in a Math class when you are allowed to use a calculator, isn’t this cheating? Why would some Math classes allow you to use a calculator but others won’t allow you? Isn’t it cheating in general to do math problems by a calculator because you know you are going to be 100 percent right and not have a challenge to do problems by hand with using scratch paper?
    15 answers · 2 days ago
  • Which would you, personally, consider to be easier? Geometry or Algebra?

    From what I've heard, Geometry is more of a logic based part of mathematics whereas Algebra is more solid and factual. I'm not entirely sure if that's true, but I would like to hear your opinions. What do you find easier to do?
    From what I've heard, Geometry is more of a logic based part of mathematics whereas Algebra is more solid and factual. I'm not entirely sure if that's true, but I would like to hear your opinions. What do you find easier to do?
    8 answers · 3 hours ago
  • How much is 1/3 from $4,000?

    10 answers · 15 hours ago
  • What is 80,000 a year , monthly ?

    11 answers · 2 days ago