Jakes batting average for softball season is 0.368 what is Jake’s batting average written in expanded form

For the function g(x)=3-8(1/4)^2-x

Reika [66]

Using function concepts, it is found that:

a) The y-intercept is y = 2.5.

b) The horizontal asymptote is x = 3.

c) The function is decreasing.

d) The domain is $(-\infty,\infty)$ and the range is $(-\infty,3)$ .
e) The graph is given at the end of the answer.

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The given function is:

$g(x) = 3 - 8\left(\frac{1}{4}\right)^{2-x}$

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Question a:

The y-intercept is g(0), thus:

$g(0) = 3 - 8\left(\frac{1}{4}\right)^{2-0} = 3 - 8\left(\frac{1}{4}\right)^{2} = 3 - \frac{8}{16} = 3 - 0.5 = 2.5$

The y-intercept is y = 2.5.

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Question b:

The horizontal asymptote is the limit of the function when x goes to infinity, if it exists.

$\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2+\infty} = 3 - 8\left(\frac{1}{4}\right)^{\infty} = 3 - 8\frac{1^{\infty}}{4^{\infty}} = 3 -0 = 3$

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$\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2-\infty} = 3 - 8\left(\frac{1}{4}\right)^{-\infty} = 3 - 8\times 4^{\infty} = 3 - \infty = -\infty$

Thus, the horizontal asymptote is x = 3.

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Question c:

The limit of x going to infinity of the function is negative infinity, which means that the function is decreasing.

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Question d:

Exponential function has no restrictions in the domain, so it is all real values, that is $(-\infty,\infty)$ .
From the limits in item c, the range is: $(-\infty,3)$

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The sketching of the graph is given appended at the end of this answer.

A similar problem is given at brainly.com/question/16533631

8 0

3 years ago

In order to successfully perform a trick, a flying trapeze artist must swing along a parabolic path that is equidistant from the

DaniilM [7]

Recall that the focus of a parabola is a point inside the parabola along the axis of symmetry of the parabola with the same distance from the vertex of the parabola as the directrix of the parabola.

Given that the focus of the parabola is (8, 16) i.e. a y-value of 16. The vertex of a parabola is halfway the distance between the y-values of the focus and the directrix.
i.e. the vertex of the parabola will have a y-value of (16 + (-8)) / 2 = (16 - 8) / 2 = 8 / 2 = 4.
Thus the vertex of the parabola is (8, 4)

Let point (x, y) be any point on the parabola, the distance between point (x, y) and the focus is
$\sqrt{(x-8)^2+(y-16)^2}$
while the distance between the point (x, y) and the directrix is
$|y-(-8)|=|y+8|$

Now, by definition, the distance between any point in a parabola and the focus is equal to the distance between that point and the directrix.
i.e.
$\sqrt{(x-8)^2+(y-16)^2}=|y+8| \\ (x-8)^2+(y-16)^2=(y+8)^2 \\ x^2-16x+64+y^2-32y+256=y^2+16y+64 \\ 16y+32y=x^2-16x+256 \\ 48y=x^2-16x+256 \\ y= \frac{1}{48} x^2- \frac{1}{3} x+ \frac{16}{3}$

6 0

4 years ago

- 4a = 36 find the value of a<br>

goblinko [34]

Answer:

-9 = a

Step-by-step explanation:

Divide both sides by -4 to isolate a: a = -36/4 = -9 = a

4 0

4 years ago

Anna wants to take fitness classes. She compares two gyms to determine which would be the best deal for her. Fit Fast charges a

lutik1710 [3]

The number of classes Anna can take so the total cost for the month will be the same is 5.

The monthly cost would be $37.50.

<h3>When would the total cost be the same?</h3>

When the monthly cost is equal, both equations would be equal: 7.5x = 5.5x + 10

In order to determine the value of x, take the following steps:

Combine similar terms: 7.5x - 5.5x = 10
Add similar terms: 2x = 10
Divide both sides by 2 : 10 /2 = 5

Monthly cost when the cost is the same: 7.5 x 5 = $37.50

To learn more about cost, please check: brainly.com/question/25711114

#SPJ1

7 0

2 years ago

PLs help with this its urgent (due tomorrow)

Alchen [17]

Answer:

Step-by-step explanation:

we are given that 1 angle equals 27 and the other two are equal.

180-27=153. and the other two are equal so they each equal 76.5 (153 divided by 2) now since one of the angles is supplementary with angle x, they together must equal 180 so: 180-76.5=x, x=103.5

6 0

3 years ago