Calculus

Well, sweetheart, the integral of dV/V is simply ln|V| + C, where C is the constant of integration. So, in other words, the integral of dV/V is the natural logarithm of the absolute value of V, plus some boring constant. Math can be a real snoozefest, but hey, at least now you know the answer!

The given equation is in the form y = mx + b, where m is the gradient or slope of the line. By comparing the equation y = -4x + 3 to the standard form, we see that the gradient is -4. Therefore, the gradient of the line y = -4x + 3 is -4.

The expression "negative x plus 3x" can be simplified by combining like terms. Negative x can be written as -1x, so the expression becomes -1x + 3x. When you combine -1x and 3x, you get 2x. Therefore, the simplified expression is 2x.

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Oh, dude, like, totally! So, a term in math is like a single mathematical expression, right? And 3x is totally just one term because it's like, one number (3) multiplied by a variable (x). So, yeah, 3x totally qualifies as a term in math lingo.

x2 + 9x2 = 10x2

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."

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The alfebgraic result is 12a^(2)b

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.

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

One plus y is simply "one plus y." That's the answer, honey. You can't simplify it further without knowing the value of y. So, go ahead and plug in a number for y if you want an actual sum.

A convergent series is a series whose terms approach a finite limit as the number of terms approaches infinity. In other words, the sum of the terms in a convergent series approaches a finite value. On the other hand, a divergent series is a series whose terms do not approach a finite limit as the number of terms approaches infinity. The sum of the terms in a divergent series does not converge to a finite value.

Oh, dude, you just need to use the formula for the area of a circle, which is πr^2. So, if the radius is 6.8 yards, you just plug that into the formula and calculate it. Like, it's not rocket science, just some simple math.

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.

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