Answer:
y = 4x - 10
Step-by-step explanation:
This means that the slope of line q is also 4, and since it contains (5, 10), the slope intercept form is y = 4x - 10.
Answer:
Step-by-step explanation:
Let the three consecutive integers be x, x + 2 and x + 4
<u>So, the given condition is:</u>
x + x + 2 + x + 4 = 129
3x + 6 = 129
Subtract 6 to both sides
3x = 129 - 6
3x = 123
Divide 3 to both sides
x = 123/3
x = 41
<u>So, the integers are:</u>
x = 41
x + 2 = 41 + 2 = 43
x + 4 = 41 + 4 = 45
Hope this helped!
<h3>~AH1807</h3>
<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.
Answer:
581
Step-by-step explanation:
<u>Population of Grizzlys</u>
1970 >>> 270
2005 >>> 115% INCREASE
We need to find 115% of 270 and increase 270 by that amount. Firstly, converting percentage to decimal (division by 100):
115/100 = 1.15
So, that would be now:
1.15 * 270 = 310.5
Increasing, we get:
270 + 310.5 = 580.5
We round to 581
In 2005, the population was about 581