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Calculus
The branch of mathematics that deals with the study of continuously changing quantities, with the use of limits and the differentiation and integration of functions of one or more variables, is called Calculus. Calculus analyzes aspects of change in processes or systems that can be modeled by functions. The English physicist, Isaac Newton, and the German mathematician, G. W. Leibniz, working independently, developed calculus during the 17th century.
25,068 Questions
What can you infer when you end up with a solution of x equals 0?
You infer that the value of x, which satisfies the equations or inequalities, is zero!
How do you solve the inequality 12x plus 5 so that the variable Xis on the left side?
12x + 5 = y
Subtract 5 from both sides of the equation. Then divide both sides by 12. The 5 and 12 on the left cancel out, leaving only X.
x = (y - 5) / 12
Is this equation a quadriatic equation 3x³ plus 2x equals -3?
no
only equations with x2 and lower powers can be considered quadratic.
those with x3 cannot be considered quadratic, just as x2 cannot be considered linear
How many degrees is 0.875 turn?
That would be 7/8 (seven-eighths) of 360 degrees, which would be 315 degrees. Hope this helps!
How do you solve x plus y equal 79 and xy equals 1288?
If: x+y = 79 Then: y = 79-x
If: xy = 1288 Then: x(79-x) = 1288 and it follows that: 79x-x2-1288 = 0
Solving the above quadtratic equation gives x a value of 23 or 56
So the values are x = 23 and y = 56
Check: 23+56 = 79 and 23*56 = 1288
What does x equal if 3 equals 2x plus 5?
3 = 2x + 5
Subtract 5 from each side:
-2 = 2x
Divide each side by 2:
-1 = x
20 = -4f + 6 + 14
Subtract 20 from each side:
0 = -4f
Divide each side by 4:
f = 0
Six x squared plus twenty one x - forty five?
Assume the question refers to solving the quadratic equation 6x2 +21x - 45 = 0, then :-
This equation can be factored 6x2 + 21x - 45 = (6x - 9)(x + 5) = 0
This holds true when either 6x - 9 or x + 5 = 0
When 6x - 9 = 0 then x = 9/6 = 1.5 : When x + 5 = 0 then x = -5
How do you factor 12x2 plus 28x-17?
The trick with this kind of question is to find two terms that add up to the middle one (28x), and whose coefficients are equal multiples of the first and last term:
12x2 + 28x - 17
= 12x2 - 6x + 34x - 17
= 6x(2x - 1) + 17(2x - 1)
= (6x + 17)(2x - 1)
The only trick with this technique is that sometimes it's difficult to find those two middle terms (-6x and 34x in this case). If it takes too long to figure this out, you can actually break it down into ~another~ quadratic equation, which will usually be easier to factor, and give you those two values. Consider:
Let "a" and "b" be the unknown coefficients. We know:
b = 28 - a <-- we know this because they must add up to the middle term
12/a = b/17 <-- this must be true in order for us to end up with a common multiple.
∴ 12/a = (28 - a)/17
∴ 28a - a2 = 204
∴ a2 - 28a + 204 = 0
We can then solve for "a" by factoring this equation:
(a - 34)(a + 6) = 0
So our coefficients are the two possible values for "a", 34 and -6. We can then simply plug them in to the original equation and factor it out as shown above.
What is the answer to 5x plus 6 equals 1divided by 4 times 13x-11?
5x + 6 = 1 / 4(13x-11)
(5x+6)(4)(13x-11)= 1
4(65x2-55x+78x-66)=1
260x2 +92x-264-1=0
260x2+92x-263=0
Graph y = 260x2 +92x -263 and find its zero or use the quadratic formula
How do you foil 1 plus 2sinx plus sin2 x?
sin2(x) + 2 sin(x) + 1
It might be easier for you if you use 'S' temporarily to represent 'sin(x)', just long enough to look at it.
Then you have
S2 + 2S + 1
Can you 'foil' that ?
It's just the square of (S + 1). The factors are (S+1) and (S+1).
The original expression is the square of [sin(x) + 1].
Find the relative maximum of -x2 plus 6x-4?
f(x) = -x2 + 6x - 4
∴ f'(x) = -2x + 6
Solve for f'(x) = 0:
0 = -2x + 6
x = 3
So the peak occurs at the point where x = 3. Now you can calculate the value of f(3)
f(3) = -32 + 6(3) - 4
∴ f(3) = -9 + 18 - 4
∴ f(3) = 5
So the maximum value of that function is 5, and it occurs when x = 3.
To prove that it's a maximum, take the second derivative:
f'(x) = -2x + 6
∴ f''(x) = -2
Because it's negative, we know that this is the peak of the curve.
