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If we were to graph the number it would be:
y = x
If we were to graph the square it would be:
y = x²
The difference would be:
f(x) = x - x²
You want to maximize this difference, so take the derivative:
f'(x) = 1 - 2x
Then set it to zero:
0 = 1 - 2x
Add 2x to both sides:
2x = 1
Divide both sides by 2:
x = ½
Answer: ½ is the number that most exceeds its square.
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What number most exceeds its square?
If we were to graph the number it would be: y = x If we were to graph the square it would be: y = x² The difference would be: f(x) = x - x² You want to maximize this difference, so take the derivative: f'(x) = 1 - 2x Then set it to zero: 0 = 1 - 2x Add 2x to both sides: 2x = 1 Divide both sides by 2: x = ½ Answer: ½ is the number that most exceeds its square.
Three times the square of a certain positive number exceeds six times the number by nine Find the number?
The problem can be written as3x2 = 6x + 9x is the number we want to findSolution:x2 = 2x + 3x2 - 2x - 3 = 0(x-3)(x+1) = 0x = -1, 3
How do you figure out a number is a square number?
If the square root is an integer, it's a square number.
Is the square root of a positive number an irrational number?
Sometimes the square root of a positive number can be irrational, as in the square root of 2 (which is a non-perfect square number), but sometimes it is a rational number, as in the square root of 25 (which is a perfect square number).
The square of 9 more than a number is equal to 9 more than the square of the number?
The square of 9 more than a number is equal to nine more than the square of a number. What is the number?
What is the first prime number whose square exceeds 1000?
31 squared = 961. 32 squared = 1,024. The first prime number that is greater than 32 is 37. Therefore, 37 is the first prime number whose square exceeds 1,000.
What type of number has an odd amount of factors?
A square number.
What do you call a number that has an odd amount of factors?
A square number
If you have a circle and a square what is the maximum number of points of intersection that the shapes can share?
If the circle is inside the square, four.
Which country covers more than 6.5 million square miles?
Russia just barely exceeds that number, and it's the only one.
What number most exceeds its square?
If we were to graph the number it would be: y = x If we were to graph the square it would be: y = x² The difference would be: f(x) = x - x² You want to maximize this difference, so take the derivative: f'(x) = 1 - 2x Then set it to zero: 0 = 1 - 2x Add 2x to both sides: 2x = 1 Divide both sides by 2: x = ½ Answer: ½ is the number that most exceeds its square.
What do you call a number with a odd amount of factors?
A perfect square
What is the maximum number of points of intersection between a circle and a square that lie in the same plane?
8
How many number of factors do square roots have?
There's no set amount.
What is a number that is the rsult of a number multiplied by itself that also has an odd amount of factors?
A perfect square
A number exceeds its square root by 56.what is number?
"7" is the number because its square root is "49" & 49+7=56
Wild crickets living in a field have a population density of 2 4 crickets m2 if the fields area is 250m2 what is the aproximite size of the cricket population why would the population density of?
TANK 1 With 200 crickets occupying an area of 0.80 square meters, that gives a population density of . . 200 crickets -------------------------- = ? crickets / square meter 0.80 square meters Is that amount < or = or > the maximum of 210 crickets / square meter?. = = = = = = = = = = = = = = = = = = = = = = = = = TANK 2 With 150 crickets occupying an area of 0.80 square meters, that gives a population density of . . 150 crickets --------------------------- = ? crickets / square meter 0.80 square meters Is that amount < or = or > the maximum of 210 crickets / square meter?. = = = = = = = = = = = = = = = = = = = = = = = = = TANK 3 With 315 crickets occupying an area of 1.5 square meters, that gives a population density of . . 315 crickets ------------------------- = ? crickets / square meter 1.5 square meters Is that amount < or = or > the maximum of 210 crickets / square meter?. = = = = = = = = = = = = = = = = = = = = = = = For PROBLEM #1, when you move crickets from tank to tank, remember to change the value of the numerators in the fractions above. EXAMPLE If you remove 10 crickets from tank 2 and put them in tank 3, then decrease tank 2's numerator from 150 to 140 and increase tank 3's numerator from 315 to 325. For PROBLEM #2, we need to rearrange the formula from above (number of crickets) -------------------------- = population density . . . . (area) Multiply both sides of the equal sign by (area). (area)(number of crickets) ----------------------------------- = (area)(population density) . . . . . . . (area) Notice how the (area) on the left side cancels out? (number of crickets) = (area)(population density) (number of crickets) = (250 square meters)(2.4 crickets / square meter) (number of crickets) = ?
