Answer:
A. x
C. x – 5
D. x + 2
Step-by-step explanation:
From the question above, we are asked to find the factors of an algebraic expression that is given as:
x³ - 3x² - 10x
We would use the step of factorisation
Step 1
x(x² - 3x- 10)
The first factor of the algebraic expression has been obtained = x
Step 2
We factorise x² - 3x - 10
x² +2x - 5x - 10
(x²+2x) - (5x - 10)
x(x + 2) -5(x + 2)
(x + 2)(x - 5)
Step 3
x³ - 3x² - 10x
x(x² - 3x- 10)
(x)(x + 2)(x - 5)
Therefore, the factors of the algebraic expression are:
(x), (x + 2), (x - 5)
500 (the current collection) + 10 (the weekly addition) x 20 (weeks to add)
500 + 10*20 (Multiplication comes before addition)
500+200
700
<h3>
Answer: 65</h3>
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Explanation:
We'll need to compute the difference quotient. In this case, we need to find what is equal to. It's called a difference quotient because there's a subtraction in the numerator (aka "difference") and we're dividing to form the quotient.
The idea is that as h approaches 0, then that expression I wrote will approach the derivative we're after. Keep in mind that h will technically never get to 0 itself. It only gets closer and closer.
Anyways, let's compute first
Then we'll subtract off g(t)
A very important thing to notice: the terms that don't have any 'h's in them have been canceled out (eg: 5t^2 combined with -5t^2 added to 0). Why is this important? It's because we need to factor 'h' out and we'll have a pair of 'h's cancel like so
The left hand side cannot have h = 0, or else we have a division by zero error. But if we approached 0 (not actually getting there), then the expression 5h+10t+5 will approach 5(0)+10t+5 = 10t+5
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In short: The derivative of is
In terms of symbols,
Later on in calculus, you'll learn a shortcut so you won't have to compute the difference quotient every time you need a derivative. Refer to the power rule for more information.
After we find the derivative, it's as straight forward as plugging in t = 6 to compute g ' (6)
Side note: This tells us that the slope of the tangent line is m = 65 when t = 6. In other words, this line is tangent to g(t) when t = 6, and this particular tangent line has slope m = 65.