Answer:
- as written, -2
- with denominator parentheses, 0
- with f(x)=ln(x) and denominator parentheses, -1/2
Step-by-step explanation:
The problem as stated asks for the limit as x approaches 2 of (0/x) -2.
As written, the limit is (0/2) -2 = -2.
<u>Explanation</u>: f(x) is a constant, so the numerator is 0. The ratio 0/x -2 is defined as -2 everywhere except x=0. So, the value at x=2 is 0/2 -2 = -2.
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If you mean (f(2) -f(x))/(x -2), that limit is the limit of 0/(x-2) = 0 as x approaches 2.
<u>Explanation</u>: f(x) is a constant, so the numerator is 0. The ratio 0/(x-2) is zero everywhere except at x=2. The left limit and right limit are both 0 as x approaches 2. Since these limits agree, the limit is said to be 0.
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If you mean f(x) = ln(x) and you want the limit of (f(2) -f(x))/(x -2), that value will be -1/2.
<u>Explanation</u>: The value of the ratio is 0/0 at x=2, so we can find the limit using L'Hôpital's rule. Differentiating numerator and denominator, we have ...
lim = (-1/x)/(1)
The value is -1/2 at x=2.
Jennifer have 8 quarters, 12 dimes and 36 nickels.
Step-by-step explanation:
Given,
Worth of coins = $5.00 = 5*100 = 500 cents
One quarter = 25 cents
One dime = 10 cents
One nickel = 5 cents
Let,
x = number of quarters
y = number of dimes
z = number of nickels
According to given statement;
25x+10y+5z=500 Eqn 1
y = x+4 Eqn 2
z = 3y
z = 3(x+4) => z = 3x+12 Eqn 3
Putting value of y and z from Eqn 2 and 3 in Eqn 1
Dividing both sides by 50
Putting x = 8 in Eqn 2
Putting x=8 in Eqn 3
Jennifer have 8 quarters, 12 dimes and 36 nickels.
Keywords: linear equation, substitution method
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The line y = mx + c has a slope of m.
Parallel line:
A parallel line will also have a slope of m, and should be of the form
y = mx + k
Because the line passes through the point (a,b), therefore
ma + k = b
k = b - ma
The equation of a parallel line is
y = mx + b - ma
= m(x-a) + b
Perpendicular line:
A perpendicular line will have a slope of -1/m, because the product of slopes should be -1.
The equation for a perpendicular line is of the form
y = -(1/m)x + k
Because the line passes through (a,b), therefore
-(1/m)a + k = b
k = b + a/m
The equation for a perpendicular line is
y = -(x/m) + b + a/m
= -(1/m)(x-a) + b
Answer:
Parallel line:
Perpendicular line:
Y = x/4 - <span>€
y = (1/4)x - </span><span>€
</span><span>
y = 0.25x - </span>€ comparing to y = mx + c
m = slope = 0.25 or (1/4)
Answer:
2x + 9y = 60
10x + 5y = 60
The price of each bag of popcorn is $6.
Step-by-step explanation:
Let each drink costs $x and the price of each bag of popcorn is $y.
So, from the given two conditions we can write two different equations as
2x + 9y = 60 ............... (1) and
10x + 5y = 60 ................. (2)
Now, solving those two equations we get,
5(60 - 9y) + 5y = 60
⇒ 300 - 45y + 5y = 60
⇒ 40y = 240
⇒ y = 6
Therefore, the price of each bag of popcorn is $6. (Answer)
