Calculus

To factorize xy + 3x, we first need to factor out the common factor, which is x. This gives us x(y + 3). Therefore, the factorized form of xy + 3x is x(y + 3).

A real life application is a situation that you may have faced or could face in the near future, usually based on a skill learned from typical school subjects. It is used to help prepare students for such situations, or to demonstrate that something they are learning is relevant to their lives. For example, while reading a textbook on mathematics you may encounter a passage that describes a real-life application of one of the skills in the chapter.

Pie times x? Well, I hope you're hungry because that sounds delicious! But if you're talking math, then pie times x is just x times the numerical value of pi, which is approximately 3.14159. So, in a nutshell, pie times x is just a fancy way of saying "3.14159 times x."

1

1.5

The result would be 12a2b.

Well, isn't that a happy little question! The square root of 126 is approximately 11.22. Just imagine that number as a little tree in a beautiful meadow, reaching for the sky with its square root branches. Remember, there are no mistakes in math, just happy little miscalculations.

To simplify the expression sin(30°) cos(90°) sin(90°) cos(30°), we first evaluate the trigonometric functions at the given angles. sin(30°) = 1/2, cos(90°) = 0, sin(90°) = 1, and cos(30°) = √3/2. Substituting these values into the expression, we get (1/2) * 0 * 1 * (√3/2) = 0. Therefore, the final result of sin(30°) cos(90°) sin(90°) cos(30°) is 0.

(8 + y) / 4 = 8/4 + y/4 = 2 + y/4

Well, isn't that just a happy little question! You see, when it comes to balancing consumption of goods like x and y, we don't always need to assign specific numbers to utility. Instead, we can focus on understanding the preferences and satisfaction of the consumer to see how they make choices. It's all about finding harmony and balance in the choices we make, just like adding colors to create a beautiful painting.

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".