Answer:
Step-by-step explanation:
Try dividing the first equation by 3. The result will be identical to the second equation. Thus, we have two lines that coincide, and therefore there are an infinite number of solutions.
Answer:
Step-by-step explanation:
let it's breadth be x
area of rectabgle=l*b
259=18.5*b
259/18.5=b
14=b
perimeter of rectangle=2(l+b)
=2(18.5+14)
=2*32.5
=65 cm
<h3>
Answer: y = x+1</h3>
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Explanation:
f(x) = x^3 - 2x + 3
f ' (x) = 3x^2 - 2 ..... apply the power rule
f ' (1) = 3(1)^2 - 2 ... plug in x coordinate of given point
f ' (1) = 1
If x = 1 is plugged into the derivative function, then we get the output 1. This means the slope of the tangent line at (1,2) is m = 1. It's just a coincidence that the x input value is the same as the slope m value.
Now apply point slope form to find the equation of the tangent line
y - y1 = m(x - x1)
y - 2 = 1(x - 1)
y - 2 = x - 1
y = x - 1 + 2
y = x + 1 is the equation of the tangent line.
The graph is shown below. I used GeoGebra to make the graph.
Let

where we assume |r| < 1. Multiplying on both sides by r gives

and subtracting this from
gives

As n → ∞, the exponential term will converge to 0, and the partial sums
will converge to

Now, we're given


We must have |r| < 1 since both sums converge, so


Solving for r by substitution, we have


Recalling the difference of squares identity, we have

We've already confirmed r ≠ 1, so we can simplify this to

It follows that

and so the sum we want is

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?
Answer:
Factor:
x^2+5x-300=0
(x-15)(x+20)=0
x=15 is the width
x+5=20 is the length
Step-by-step explanation: