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bearhunter [10]
2 years ago
11

Use the function f(x) to answer the questions.

Mathematics
1 answer:
fiasKO [112]2 years ago
3 0

Answer:

Below in bold.

Step-by-step explanation:

A. −16x2 + 24x + 16 = 0

-8(2x2 - 3x - 2) = 0

-8(2x + 1 )(x - 2) = 0

x = -0.5, 2.

So the x-intercepts are (-0/5, 0) and (2, 0).

B.  As the leading coefficients is negative (-16) the vertex of the graph will be a Maximum.

To find its coordinates we convert the function to vertex form:

f(x) =  −16x2 + 24x + 16

=  -16(x^2 - 1.5x) + 16

Completing the square on  contents of the parentheses:

= -16 [(x - 0.75)^2  - 0.75^2] + 16

= -16(x - 0.75)^2  - 16 * -0.75^2 + 16

= -16(x - 0.75)^2 + 9 + 16

= -16(x - 0.75)^2 + 25.

So the coordinates of the vertex are (0.75, 25)

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I don’t know how to use the triangle area to calculate the area of the inscribed polygons
Trava [24]

First of all, let's recall the area of a triangle, knowing its base (b) and height (h):

A = \cfrac{bh}{2}

The exercise is showing you that, if you inscribe a polynomial with more and more side, the area of the polynomial will approximate the area of the circle better and better (you can see youself that the polygon is "filling" the circle more and more as the number of sides increase).

Now, the second column tells you the area of each of the triangles the polygon is split into. So, we can see that the first polygon is split into 3 triangles, each of them having base 1.73 and height 0.5.

So, the area of each triangle is

A = \cfrac{1.73 \cdot 0.5}{2} = 0.4325

There are three of these triangles, so the area of the whole polygon is

A = 0.4325 \cdot 3 = 1.2975

In the second case, you have six triangles, each with base 1 and height 0.87. So, the whole area is

A = 6 \cdot \cfrac{1\cdot 0.87}{2} = 0.87 \cdot 3 = 2.61

Finally, in the last case you have 8 triangles, each with base 0.77 and height 0.92. So, the whole area is

A = 8 \cdot \cfrac{0.77\cdot 0.92}{2} = 0.77\cdot 0.92 \cdot 4 = 2.8336

3 0
2 years ago
Can you help me graph and list the (Zeros, Maximums, Minimums, Asymptotes)
Marina86 [1]

The zero of the function is at 33.69 degree , the graph is plotted and attached with the answer.

<h3>What is a Function ?</h3>

A function is a law that relates a dependent variable and an independent variable with each other

It is given that

y = 2tan (x - π/2) +3

To find the zeroes of a function that function has to be equated to zero.

2tan (x - π/2) +3 = 0

2tan (x - π/2)  = -3

tan (x - π/2)  = -3/2

x - 90 = -56.31

x = 33.69 degree

The zero of the function is at 33.69 degree

For finding the maxima /minima

the derivative is

dy/dx = 2 sec² (x - π/2)

the point at which the slope is zero is substituted in the second derivative to find maxima/minima

d²y/dx² = 4 sec² (x - π/2) tan (x - π/2)

if the value is negative then it is a maxima and if it is positive it is a minima.

The vertical asymptote is found by finding the values that make the function undefined

x = 0+ πn

No horizontal or oblique asymptote

To know more about Function

brainly.com/question/12431044

#SPJ1

5 0
1 year ago
A line is drawn so that it passes through the points (-3,0) and (1.4). What is the slope of the line?
vladimir2022 [97]

Answer: m=1

Step-by-step explanation:

For this exercise you can use the following formula for calculate the slope:

m=\frac{y_2-y_1}{x_2-x_1}

In this case you know that the given line passes through the points (-3,0) and (1.4). Therefore you can identify that:

y_2=0\\y_1=4\\\\x_2=-3\\x_1=1

Then, in order to calculate the slope of this line, you must substitute the coordinates of the points into the formula:

m=\frac{0-4}{-3-1}

Finally, evaluating, you get that the slope of this line is the following:

m=\frac{-4}{-4}\\\\m=1

4 0
3 years ago
It is 9:00. What is the measure of the smaller angle between the hour hand
Ksivusya [100]

Answer:

The hour hand is three-fourths of the way from the "4" to the "5; that is, ... What is the angle between the hour hand and the minute hand at 4:40? ... What is the measure of the smaller angle formed by the hands of an analog watch if the hour hand is on the ... One has to account, however, for the 10 minutes that have passed.Step-by-step explanation:

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A one year membership to metro gym costs $460. There is a fee of $40 when you join, and the rest is paid monthly. Write an equat
zysi [14]

Answer: The equation that would help members to find how much they would pay per month is

40 + 12x = 460

Step-by-step explanation:

Let x represent the amount of money that members would pay per month.

Let y represent the number of months for which a member uses the gym.

There is a fee of $40 when you join, and the rest is paid monthly. This means that the cost of using the gym for x months would be

40 + xy

A one year membership to metro gym costs $460. Therefore are 12 months in a year. Therefore,

40 + 12x = 460

12x = 460 - 40 = 420

x = 420/12 = 35

The equation that would help members to find how much they would pay per month is

8 0
2 years ago
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