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3 years ago

What is the axis of symmetry and y- intercept for the equation y = 3x² + 6x - 7 ?

1 answer:

4 0

Axis of symmetry is
x
=
1
, vertex is at
(
1
,
15
)
.
Explanation:
f
(
x
)
=
−
3
x
2
+
6
x
+
12
=
−
3
(
x
2
−
2
x
)
+
12
=
−
3
(
x
2
−
2
x
+
1
)
+
3
+
12
=
−
3
(
x
−
1
)
2
+
15
. Comparing with standard vertex form of equation
f
(
x
)
=
a
(
x
−
h
)
2
+
k
;
(
h
,
k
)
being vertex.
Here
h
=
1
,
k
=
15
. So vertex is at
(
1
,
15
)
.
Axis of symmetry is
x
=
1

graph{-3x^2+6x+12 [-40, 40, -20, 20]} [Ans]

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I need help with this problem from the calculus portion on my ACT prep guide

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Given a series, the ratio test implies finding the following limit:

$\lim _{n\to\infty}\lvert\frac{a_{n+1}}{a_n}\rvert=r$

If r<1 then the series converges, if r>1 the series diverges and if r=1 the test is inconclusive and we can't assure if the series converges or diverges. So let's see the terms in this limit:

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Then the limit is:

$\lim _{n\to\infty}\lvert\frac{a_{n+1}}{a_n}\rvert=\lim _{n\to\infty}\lvert\frac{n5^{n+1}}{2^n}\cdot\frac{2^{n+1}}{\mleft(n+1\mright)5^{n+2}}\rvert=\lim _{n\to\infty}\lvert\frac{2^{n+1}}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^{n+1}}{5^{n+2}}\rvert$

We can simplify the expressions inside the absolute value:

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Since none of the terms inside the absolute value can be negative we can write this with out it:

$\lim _{n\to\infty}\lvert\frac{2}{5}\cdot\frac{n}{n+1}\rvert=\lim _{n\to\infty}\frac{2}{5}\cdot\frac{n}{n+1}$

Now let's re-writte n/(n+1):

$\frac{n}{n+1}=\frac{n}{n\cdot(1+\frac{1}{n})}=\frac{1}{1+\frac{1}{n}}$

Then the limit we have to find is:

$\lim _{n\to\infty}\frac{2}{5}\cdot\frac{n}{n+1}=\lim _{n\to\infty}\frac{2}{5}\cdot\frac{1}{1+\frac{1}{n}}$

Note that the limit of 1/n when n tends to infinite is 0 so we get:

$\lim _{n\to\infty}\frac{2}{5}\cdot\frac{1}{1+\frac{1}{n}}=\frac{2}{5}\cdot\frac{1}{1+0}=\frac{2}{5}=0.4$

So from the test ratio r=0.4 and the series converges. Then the answer is the second option.

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1 year ago

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So for the first given:

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So for the second given:

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4 years ago

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From the figure we can see that a right angled triangle with angles 45°, 45°, 90° and hypotenuse = 32

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3 years ago

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Gekata [30.6K]

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Datos dados

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Obtenga más información sobre el interés compuesto aquí:

brainly.com/question/24924853

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