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Mathematical Analysis
Mathematical analysis is, simply put, the study of limits and how they can be manipulated. Starting with an exhaustive study of sets, mathematical analysis then continues on to the rigorous development of calculus, differential equations, model theory, and topology. Topics including real and complex analysis, differential equations and vector calculus can be discussed in this category.
2,575 Questions
To find how fast the angle of elevation is changing as the observer approaches the wall, we can use the relationship between the height of the picture, the distance from the observer to the wall, and the angle of elevation. The angle can be represented using the tangent function: (\tan(\theta) = \frac{h}{d}), where (h) is the height of the picture (40 cm), and (d) is the horizontal distance from the observer to the wall. As the observer approaches the wall at a rate of 40 cm/sec, we can differentiate the tangent function to find the rate of change of the angle (\frac{d\theta}{dt}) in terms of (d) and the height (h). The exact rate will depend on the initial distance (d) at which the observer starts.
What are other names for subtraction?
Other names for subtraction include "minus," "take away," "difference," and "decrease." These terms all refer to the operation of finding the result when one quantity is removed from another. Subtraction is the inverse operation of addition, and it is denoted by the "-" symbol.
To solve this problem, we can use the concept of man-days. If 6 tractors take 8 days to collect the harvest, they complete the work in 6 x 8 = 48 man-days. Therefore, for 18 tractors to do the same work, they would take 48 man-days / 18 tractors = 2.67 days. So, it would take approximately 2.67 days for 18 tractors to collect the harvest.
How many times does 16 go into 52?
Well, isn't that a happy little math problem! If you take 52 and divide it by 16, you'll find that it goes in 3 times with a remainder of 4. Remember, there are no mistakes in math, just happy little accidents!
Application of mensuration in day to day life?
Mensuration, the branch of mathematics dealing with the measurement of geometric figures, is applied in various aspects of daily life. For example, when cooking or baking, understanding measurements like volume and area is crucial for following recipes accurately. In construction, mensuration is used to calculate dimensions for building materials and estimate costs. Additionally, in fields like agriculture and landscaping, mensuration helps in determining the area of land for planting or designing outdoor spaces.
First assuming the log base is '10' ; as per calculaotrs.
Then
log(10) x = y
Then its inverse is
x = 10^(y)
Hence it follows
Inverseof log(10) -0.123 = 10^(-0.123) = 1/10^(0.123) = 1/1.327394458... = 0.753355563....
NB Logs of different bases , like 'e/ln' will give different answers.
Why is division by zero is undefined or not allowed?
Any non-zero number divided by zero is infinity (positive or negative), but your calculator may give an error. Try it with a very small number such as 0.000001, as you make it smaller the result will become larger. The reason is that for a given number, you can put 0 into it as many times as you want - an infinite amount.
However, this will give us many problems with division. For any other number, division has very useful properties. If we have some unknown number called 'x', and we have an equation that says: x/3 = 5/3, then we can deduce that x=5. Another example: x/4 = 7/4. We can deduce that x=7. But when we allow division by zero, this property is lost: 3/0 = infinity = 4/0, but 3 is not equal to 4. We also lose many other useful properties if we allow division by zero. However, we do almost allow division by zero. This is done by taking what is known as a limit as the divisor, x, tends to zero (we write x→0), and this is an integral part of calculus.
0/0 is a special case of division by zero. Notice that for any non-zero number, let's call it 'y', we get y/y = 1. But we say that 0/0 is undefined, or indeterminate. We can still take limits when something looks like it might be equal to 0/0. For example, the limit of sine(x)/x as x→0. We know that sine(x) = 0 when x=0, but it can be proven that sine(x)/x →1 as x→0. But we can also prove that x2/x → 0 as x→0. So the result is different depending of different situations.
To solve the equation 3x = 42, you need to isolate the variable x. To do this, divide both sides of the equation by 3. This gives you x = 14, as 42 divided by 3 equals 14. Therefore, the solution to the equation 3x = 42 is x = 14.
To convert kiloliters (kl) to liters (l), you need to multiply the number of kiloliters by 1000. This is because there are 1000 liters in one kiloliter. So, the formula for converting kl to l is: liters = kiloliters x 1000. For example, if you have 2 kl, the conversion would be 2 kl x 1000 = 2000 l.
What does the math symbol W mean?
It stands for a Whole number
+++ And in science, it is the international abbreviation for the Watt, the unit of power.
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W is NOT the symbol for whole numbers. The set of natural numbers is denoted by N, the set of all integers by Z. Never W. W can also denote the fourth dimension in space, but usually it would appear in lower case.
Note that the subtraction of a negative number is the equivalent of the addition of a positive number, therefore the equation x - -4 = 12 can be converted to
x + 4 = 12 subtract 4 from both sides and you get
x = 8
How many thousands in 1 million?
Oh, dude, seriously? There are a thousand thousands in a million. So, like, if you're counting in thousands, you'd be like, "1, 2, 3... up to 1,000, then start over again." It's like counting sheep, but way more zeros.
If 4 people can paint fences in 5 hours how many hours will it take for 8 people to paint fences?
If 4 people can paint fences in 5 hours, this means that the rate of painting is 1 fence per person every 5 hours. Therefore, 4 people can paint 4 fences in 5 hours. To find out how many hours it will take for 8 people to paint the same number of fences, we can use the concept of inverse variation. Since the number of people has doubled (from 4 to 8), the number of hours needed will be halved. So, it will take 2.5 hours for 8 people to paint the same number of fences.
What is 2 units to the right of 0?
Ah, what a happy little question we have here! If we start at 0 on a number line and move 2 units to the right, we end up at the number 2. Just imagine a little bird flying from 0 to 2, spreading joy along the way. Remember, mistakes are just happy accidents, so keep painting your beautiful math masterpiece!
Oh, what a lovely question! You can create 6 combinations by repeating the same number 4 times. It's like painting a beautiful pattern with numbers - 1111, 2222, 3333, 4444, 5555, and 6666. Each combination is unique and special in its own way, just like every brushstroke on a canvas.
One fifth of five is equal to one. This can be calculated by dividing five by five, which equals one. In mathematical terms, one fifth of a number is found by multiplying the number by 1/5. Therefore, one fifth of five is equal to one.
To find what times 9 equals 15, you would divide 15 by 9. The result is approximately 1.6667. So, 1.6667 times 9 equals 15.
36 cm is the perimeter of the rectangle.
Since it is the perimeter, there will be two long sides and two short sides. , making the four sides.
This can be algebraically expressed as
P = 2(l + s)
P = 2l + 2s
Substituting
P = 36 sm
s = 4 cm ( assumed).
36 cm = 2l + 2(4cm)
36 cm = 2l + 8 cm
2l = 36 cm - 8cm ( Note the change of sign , when 'crossing the '=' sign
2l = 28 cm
Divide both sides by '2'
l = 14 cm ( is the length).
How many lines of symmetry does a water melon have?
It depends on the shape of the water melon, round, oval, etc.
If it was oval there would probably only be 2 lines of symmetry - top to bottom and left to right. You can't go diagonal because it wouldn't be even. A circle has an infinite number of lines of symmetry. Any chord of the circle that passes through its center will be line of symmetry. And there are an infinite number of lines that can be drawn through the center of the circle. So if the water melon was a circle it would have an infinite amount of symmetry lines.
Hope it helps!! :)
How do you write 2.5 crore in figures?
To write 2.5 crore in figures, you would write it as 25,000,000. In the Indian numbering system, one crore is equal to ten million. Therefore, 2.5 crore is equivalent to 25 million.
