Calculus

7.5

Well, darling, 15 times 18 is 270. Easy peasy lemon squeezy. Now go impress someone with your newfound math skills.

you first need another equation with y in it. you cannot simply solve 1+y, unless you wish to say 1 + y = 0 therefore y = -1

Those terms are both used to describe different kinds of infinite series. As it turns out, somewhat counter-intuitively, you can add up an infinitely long series of numbers and sometimes get a finite sum. And example of this is the sum of one over n2 where n stands for the counting numbers from 1 to infinity. It converges to a finite sum, and is therefore a convergent series. The sum of one over n is a divergent series, because the sum is infinity.

First, I'll assume that you mean the radius of the circle is 6.8 yards.

The area of a circle is found using the formula (pi)r2

Note: the radius of a circle is half its diameter.

Substituting yields (3.14)(6.82) = (3.14)(46.24)

= 145.1936

Remember to round to the correct number of significant figures - in this case 2.

Your final answer will be 150 yd2

Let's create a happy little math problem here. If we take the year 1642 and subtract 1564 from it, we find that it's 78 years. That's a whole lifetime of opportunities to paint some beautiful landscapes and happy little trees.

3xy

x² + x³ = x² + x³. This expression is already as simplified as it can be.

21

0 - There are no 0s in pi

1 - 2nd digit

2 - 7th digit

3 - 1st digit

4 - 3rd digit

5 - 5th digit

6 - 8th digit

7 - 14th digit

8 - 12th digit

9 - 6th digit

Well, darling, the antiderivative of 70x is 35x^2 + C, where C is the constant of integration. It's as simple as that, honey. Just integrate like there's no tomorrow and don't forget that little "+ C" at the end.

Factor: x3 - 12x2 + 35x

1. Factor out a x: x(x2 - 12x + 35).

2. Factor x2 - 12x + 35 which is (x-5)(x-7).

3. Answer: x(x-5)(x-7).

5

Limit of Linearity is the concentration at which the calibration curve departs from linearity by a specified amount. A deviation of approximately 5% is usually considered the upper limit. Common at higher concentrations.

You simply write that as -6x. You can't calculate the actual value, unless you happen to know the value of "x".

Oh, my friend, let's imagine a peaceful scene with elephants wandering in a lush green forest. To answer your question, an average adult elephant weighs around 12,000 pounds. So, to reach one million pounds, we would need approximately 83 elephants. Isn't nature just amazing?

It is a very broad question. Generally, 'congruence' means 'agreeing'. Example: Many believe that congruence of religious affiliation increases the stability of a marriage. In other words, if you and your spouse are of the same religion, then your marriage will probably last longer.

I assume, however, that you mean congruence, in the mathematical sense: figures (such as triangles) are congruent if all their parts (angles and sides) are equal; one may be over-laid on the other, and they will look alike.

The importance of that and all mathematical concepts in your daily life will depend very much on what sort of daily life you have. Thousands of generations have survived without ever knowing anything about congruence; perhaps you prefer a primitive life, as a woodcutter in the forest, perhaps, or pumping petrol at the nearest full-serve petrol station, where no one will reduce your pay for not knowing anything about congruent triangles.

However, if you walk over a highway bridge, designed by an engineer, or ride in a car or train or aeroplane or seek surgery at the nearest hospital or even walk into such a building as an hospital or hotel or school or public building: you may then have reason to be glad that somebody knows about congruent triangles, so that the building may not collapse over your head or the bridge may not collapse under your feet or so that the miracle medical machine they use on you at the hospital may not fry you to a crisp or make you glow in the dark. But perhaps you are able to lead your entire life without ever doing any of these things.

Now, without congruent triangles, there would be almost no geometry or trigonometry; without geometry and trigonometry, there would be almost no calculus or differential equations or statistics or physics or any form of advanced science or engineering or medicine or economics. Even if you don't want to spend the time in school or make your living in any of these fields, you may well be glad that other people do and are paid for their knowledge.

Can you survive without knowing the concepts of mathematics, including that of congruence of figures? Of course, you can, and many people do. Is your life affected by the existence of these concepts and by people who understand them? You would have to be a hermit in the wood or in the desert, for them not to affect you.

Oh, dude, you're hitting me with some math lingo. So, like, 3 over x is just 3 divided by x. It's like saying you have 3 pieces of candy and you wanna share them with x friends. So, technically correct, but like, who really wants to share candy anyway, am I right?

0

To solve the equation 5m + 3 = 3m + 9, you need to isolate the variable m. Start by subtracting 3m from both sides to get 2m + 3 = 9. Then, subtract 3 from both sides to get 2m = 6. Finally, divide by 2 to find m = 3.

Well, isn't that a happy little math problem! When you have 3 times a number and you divide that by the same number, you're left with just 3. It's like painting a beautiful landscape with just three simple colors - simple and harmonious.

Well, darling, when you divide y by y squared, you're basically dividing y by y multiplied by y. So, the answer is 1 over y. Simple math, really. But hey, at least you're not dividing by zero and causing a mathematical apocalypse.

One possible list of words that add up to 100 based on the numerical values of their letters in the English alphabet could be: "fourteen" (86) + "eight" (49) + "six" (52) + "two" (58) + "zero" (64) = 100. Each letter is assigned a numerical value based on its position in the alphabet (A=1, B=2, ..., Z=26), and the sum of these values for each word is calculated to reach a total of 100.

Oh, what a delightful question! Counting a mole of rice would take quite a long time, my friend. You see, a mole is a very large number, approximately 6.022 x 10^23, so counting each individual grain of rice would take you far longer than a lifetime. But don't worry, just imagine the beautiful painting you could create while pondering such a lovely thought!