• If pi is really a constant as my teacher claims, then how come big circles have greater area than small ones?

    Best answer: If A is the area of the circle, then: A = pi × r². (i.e. the area is = pi times the radius and times the radius again)
    Bigger circle will have a bigger radius, and thus bigger area, but the value of pi doesn't change.
    Best answer: If A is the area of the circle, then: A = pi × r². (i.e. the area is = pi times the radius and times the radius again)
    Bigger circle will have a bigger radius, and thus bigger area, but the value of pi doesn't change.
    10 answers · 12 hours ago
  • If two thirds of a sum of money has been spent, leaving £24, how much money was there originally?

    How do I work out finding the original quantity involving a fraction and an amount of money left, like this?
    How do I work out finding the original quantity involving a fraction and an amount of money left, like this?
    8 answers · 2 days ago
  • This probability question has me stumped. Can anyone help?
  • How many quarts are there in 1 cup?

    16 answers · 5 days ago
  • Rewrite as a power (-8)(-8)?

    8 answers · 2 days ago
  • Are negative numbers just more scientific fraud like global warming or evolution?

    It seems there is no concrete reality to them and can't be proved. You can't have 'negative' anything. You can owe someone money or such things, but that is just a different classification of an actual number. I think it might just be maintained to keep maths teachers in jobs.
    It seems there is no concrete reality to them and can't be proved. You can't have 'negative' anything. You can owe someone money or such things, but that is just a different classification of an actual number. I think it might just be maintained to keep maths teachers in jobs.
    10 answers · 3 days ago
  • What is -2 doubled?

    Best answer: Minus four. (-2 x 2)
    Peace.
    Best answer: Minus four. (-2 x 2)
    Peace.
    5 answers · 1 day ago
  • Help. The answer is 10 hp.?

    Best answer: A city of 25,000 uses 15 gallons of water per day per capita. If it is required to raise this water 150 feet, what is the number of horsepower required? 25000 users x 15 gallons / per user = 375000 gal density of fresh water at 20C = 0.998 g/cm³ = 998 kg/m³ = 8.33 lb/gal = 62.1 lb/ft³ 375000 gal x 8.33... show more
    Best answer: A city of 25,000 uses 15 gallons of water per day per capita. If it is required to raise this water 150 feet, what is the number of horsepower required?

    25000 users x 15 gallons / per user = 375000 gal

    density of fresh water at 20C = 0.998 g/cm³
    = 998 kg/m³ = 8.33 lb/gal = 62.1 lb/ft³

    375000 gal x 8.33 lb/gal = 3120000 lb
    work = f-d = 3120000 lb x 150 ft = 468000000 ftlb
    and there are 24•60 min in a day, so the power is
    Power = 468000000/24•60 ftlb/min

    1 HP = 33,000 ft lbf/min

    power in HP = 468000000/24•60• 33000 = 9.86 HP
    4 answers · 2 hours ago
  • 6 7/8 divided by (3 3/4) =?

    5 answers · 8 hours ago
  • An open box with a rectangular base is to be constructed from a rectangular piece of cardboard 18 in wide and 22 in long by...?

    Best answer: Starting with a piece of cardboard that is 18" by 22", we have a starting length and width. If we cut out x" by x" squares from the corners, the length and widths each gets reduced by 2x (since there is a left and right side and a top and bottom side), so the new lengths and widths become: (18... show more
    Best answer: Starting with a piece of cardboard that is 18" by 22", we have a starting length and width.

    If we cut out x" by x" squares from the corners, the length and widths each gets reduced by 2x (since there is a left and right side and a top and bottom side), so the new lengths and widths become:

    (18 - 2x) and (22 - 2x)

    with the height of the box being x

    The volume in terms of x is then:

    V(x) = lwh
    V(x) = (18 - 2x)(22 - 2x)x

    Simplify and put into standard form:

    V(x) = (396 - 36x - 44x + 4x²)x
    V(x) = (396 - 80x + 4x²)x
    V(x) = (4x² - 80x + 396)x
    V(x) = 4x³ - 80x² + 396x

    That's your function for volume in terms of x.

    For the domain of x, it cannot be zero otherwise you don't have a box.
    it can't be half of the smallest dimension since you will no longer have length.

    so the domain is:

    0 < x < 9

    So you can graph the function in this domain using whatever method you know of.

    To find the maximum volume, we can solve for the zero of the first derivative and throw out any value of x that is outside of this domain:

    V(x) = 4x³ - 80x² + 396x
    V'(x) = 12x² - 160x + 396
    0 = 12x² - 160x + 396

    Divide both sides by 2:

    0 = 6x² - 80x + 198

    Using quadratic equation:

    x = [ -b ± √(b² - 4ac)] / (2a)
    x = [ -(-80) ± √((-80)² - 4(6)(198))] / (2 * 6)
    x = [ 80 ± √(6400 - 4752)] / 12
    x = [ 80 ± √(1648)] / 12
    x = [ 80 ± √(16 * 103)] / 12
    x = [ 80 ± 4√(103)] / 12

    factor out a 4 and cancel out:

    x = [ 20 ± √(103)] / 3

    Using 10.15 as an approximation for √103, we get:

    x = (20 + 10.15) / 3 and (20 - 10.15) / 3
    x = 30.15 / 3 and 9.85 / 3
    x = 10.05 and 3.283

    We said that x had to be less than 9, so we can throw out the one answer, leaving this as the only value:

    x = (20 - √103) / 3 inches
    5 answers · 2 days ago
  • How many zeros are between 1 through 1,000?

    Best answer: You said 1 *through* 1000, so I'm going to assume 1000 is included. If not, just subtract 3 from the final answer. Also, I assume you want to know how many times the *digit* zero appears in all the numbers 1 through 1000. Let's focus on each place value separately as we count the digits. Exactly one-tenth... show more
    Best answer: You said 1 *through* 1000, so I'm going to assume 1000 is included. If not, just subtract 3 from the final answer. Also, I assume you want to know how many times the *digit* zero appears in all the numbers 1 through 1000.

    Let's focus on each place value separately as we count the digits.

    Exactly one-tenth of the numbers will have a zero in the ones place.
    1000/10 = 100 zeros in the ones place

    For the tens place, it's almost the same thing, except we can exclude the numbers 1 to 9 which don't have a leading zero.
    100 - 9 = 91 zeros in the tens place

    For the hundreds place, we would exclude 1 to 99, so that leaves only 1 number (namely 1000) which has a zero in the hundreds place.
    100 - 99 = 1 zero in the hundreds place

    Obviously no numbers have a 0 in the thousands place.

    Adding that up:
    100 + 91 + 1
    = 192

    Answer:
    192 zeros (assuming 1000 is included).
    14 answers · 1 week ago
  • Can someone explain why a=8 . I don´t get it at all .?

    Can someone explain why a=8 . I don´t get it at all .?

    Best answer: h(-4) = -8 -8 = a / (-4 - b) -8 * (-4 - b) = a 32 + 8b = a h(x) = (32 + 8b) / (x - b) MN is the line x = -3. So we know that h(-2) = 8, because if we draw a line that passes through (-4 , -8) and (-3 , 0), then it must also pass through (-2 , 8) 8 = (32 + 8b) / (-2 - b) 8 * (-2 - b) = 32 + 8b -2 - b = 4 + b -2... show more
    Best answer: h(-4) = -8

    -8 = a / (-4 - b)
    -8 * (-4 - b) = a
    32 + 8b = a

    h(x) = (32 + 8b) / (x - b)

    MN is the line x = -3. So we know that h(-2) = 8, because if we draw a line that passes through (-4 , -8) and (-3 , 0), then it must also pass through (-2 , 8)

    8 = (32 + 8b) / (-2 - b)
    8 * (-2 - b) = 32 + 8b
    -2 - b = 4 + b
    -2 - 4 = b + b
    -6 = 2b
    -3 = b

    32 + 8b = a
    a = 32 - 24
    a = 8
    6 answers · 2 days ago
  • PLEASE EXPLAIN: what is the limit of (3cos(x)) / x, as x --> + infinity?

    Best answer: cos(x) is bounded between -1 and 1

    3 * cos(x) is therefore bounded between -3 and 3

    So your limit is bound between some real number divided by infinity. We'll call this real number R

    R / (-inf) < L < R / inf
    -R/inf < L < R/inf
    0 < L < 0

    So the limit is 0
    Best answer: cos(x) is bounded between -1 and 1

    3 * cos(x) is therefore bounded between -3 and 3

    So your limit is bound between some real number divided by infinity. We'll call this real number R

    R / (-inf) < L < R / inf
    -R/inf < L < R/inf
    0 < L < 0

    So the limit is 0
    8 answers · 4 days ago