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What is the integral of f divided by the quantity f plus b times f plus c with respect to x where f is a function of x and b and c are constants?
∫ f(x)/[(f(x) + b)(f(x) + c)] dx = [b/(b - c)] ∫ 1/(f(x) + b) dx - [c/(b - c)] ∫ 1/(f(x) + c) dx b ≠c
What is x in y equals mx plus b?
The x in y=mx+b is the independent variable. You could solve for x, making this a function of y, with simple algebra. y = mx + b y - b = mx (y-b)/m = x
Solve for x and y. ax plus by equals a-b bx-ay equals a plus b plus b?
Your two equations are: AX + BY = A - B BX - AY = A + B + B Because you have four variables (A, B, X, Y), you cannot solve for numerical values for X and Y. There are a total of four answers to this question, solving each equation for X and Y independently. First equation: X = (A - B - BY)/A Y= (A - B - AX)/B Second equation: X = (A +2B +AY)/B Y = (BX - A - 2B)/A
Factoring x cubed?
b represents a number ^ represents raised to a power (x - b)(x^2+ bx +b^2) For example: (X^3 - 27) (x - 3)(x^2 + 3x + 3^2) = (x - 3)(x^2 + 3x + 9)
How do you Solve the formula y equals mx plus b for M?
the answer is: (y-b)/x = m y = mx + b y - b = mx (y-b)/x = m
What does x-a plus x-a plus b equal?
(x - a) + (x - a) + (b) = 2 (x - a) + (b) = x - a + x - a + b = 2x - 2a + b
What are the index?
X^â x X^b= x^â+b x^a divided by x^b = x^a+b (x^a)^b=x^ab x^0=1 x^-a=1/x^a
What are index laws?
X^â x X^b= x^â+b x^a divided by x^b = x^a+b (x^a)^b=x^ab x^0=1 x^-a=1/x^a
What are the index laws?
X^â x X^b= x^â+b x^a divided by x^b = x^a+b (x^a)^b=x^ab x^0=1 x^-a=1/x^a
What is the index of a x a x b x b x b?
a2b3
What are the laws for dividing and multiplying exponents?
x^a / x^b = x^(a-b)andx^a * x^b = x^(a+b)
How do you convert a interval notation into a inequality?
[a, b] : a ≤ x ≤ b [a, b) : a ≤ x < b (a, b] : a < x ≤ b (a, b) : a < x < b
What is the least common multiple for x plus 1 and x?
It must be x*(x+1). To see this, suppose that there existed a smaller common multiple formed by taking a*x and b*(x+1), where a =/= b since multiplying by the same number won't give you a common multiple. Then we have a*x < x*(x+1) => a < (x+1) b*(x+1) < x*(x+1) => b < x => a*b < x*(x+1). Also, a*x = b*(x+1) => x = b/(a-b) & (x+1) = a/(a-b). Therefore x*(x+1) = a*b/(a-b)^2 < x*(x+1)/(a-b)^2 => (a-b)^2 < 1 => (a-b) < 1. The problem here is that this requires that a=b, which cannot be. Therefore, x*(x+1) is the smallest common multiple of both x and (x+1)
How do you differentiate exponential function?
The derivative of e^u(x) with respect to x: [du/dx]*[e^u(x)]For a general exponential: b^x, can be rewritten as b^x = e^(x*ln(b))So derivative of b^x = derivative of e^u(x), where u(x) = x*ln(b).Derivative of x*ln(b) = ln(b). {remember b is just a constant, so ln(b) is a constant}So derivative of b^x = ln(b)*e^(x*ln(b))= ln(b) * b^x(from above)
How do you do exponential functions?
The derivative of e^u(x) with respect to x: [du/dx]*[e^u(x)]For a general exponential: b^x, can be rewritten as b^x = e^(x*ln(b))So derivative of b^x = derivative of e^u(x), where u(x) = x*ln(b).Derivative of x*ln(b) = ln(b). {remember b is just a constant, so ln(b) is a constant}So derivative of b^x = ln(b)*e^(x*ln(b))= ln(b) * b^x(from above)
What is the greatest common factor of 16B3 and 24B4?
16B3 = 2 x 2 x 2 x 2 x B x B x B24B4 = 2 x 2 x 2 x 3 x B x B x B x BGreatest Common Factor = 2 x 2 x 2 x 2 x B x B x B = 8B3
What the LCM of 63 and 76?
Factor them. 2 x 2 x b x b = 4b2 2 x 3 x b x b x b = 6b3 Combine the factors, eliminating duplicates. 2 x 2 x 3 x b x b x b = 12b3, the LCM
