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Y_Kistochka [10]
2 years ago
12

F(x) = (x - 1) (4x + 3) (3x - 8) has zeros at x = 3/4, x= 1, and x = 8/3.

Mathematics
1 answer:
inn [45]2 years ago
8 0

Using the given roots, it is found that on the interval -\frac{3}{4} < x < 1, the function is positive.

The function is:

f(x) = (x - 1)(4x + 3)(3x - 8)

The zeroes are:

x = -\frac{3}{4}, x = 1, x = \frac{8}{3}

Between two zeroes, the function has the same sign, hence, to find the sign on the interval -\frac{3}{4} < x < 1, we find the <u>numeric value of the function of a value of x on the interval</u>, for example f(0), for x = 0.

Then:

f(0) = (0 - 1)[4(0) + 3][3(0) - 8] = (-1)(3)(-8) = 24

Since f(0) is positive, the function is positive on the interval -\frac{3}{4} < x < 1.

A similar problem, in which it is desired to find the sign of the function, is given at brainly.com/question/4787253

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Goryan [66]

The disk method will only involve a single integral. I've attached a sketch of the bounded region (in red) and one such disk made by revolving it around the y-axis.

Such a disk has radius x = 1/y and height/thickness ∆y, so that the volume of one such disk is

π (radius) (height) = π (1/y)² ∆y = π/y² ∆y

and the volume of a stack of n such disks is

\displaystyle V_n = \sum_{i=1}^n \pi {y_i}^2 \Delta y

where y_i is a point sampled from the interval [1, 5].

As we refine the solid by adding increasingly more, increasingly thinner disks, so that ∆y converges to 0, the sum converges to a definite integral that gives the exact volume V,

\displaystyle V = \lim_{n\to\infty} V_n = \int_1^5 \frac{\pi}{y^2} \, dy

V = -\dfrac\pi y\bigg|_{y=1}^{y=5} = \boxed{\dfrac{4\pi}5}

8 0
2 years ago
When (3,-2) is reflected across the x-axis the resulting image point is:
tankabanditka [31]

<em>3,2</em>

Step-by-step explanation:

Reflection across the x-axis:

(x,y) -> (x,-y)

In other words, you want to <u>change the sign of the y</u>.

(3,-2) -> (3,2)

4 0
2 years ago
A sales person earns $80 for every computer he sells. He earns an additional $250 for every 10 computers he sells that month. Ho
Georgia [21]

Answer

23 computer

Step-by-step explanation:

if he sold 20 computers he would make 2100 which then he would need 240 more dollars to reach his goal and to find the answer you would then divide 240 by 80.

4 0
2 years ago
Find the Area of this figure.
grin007 [14]

Answer:

158 m²

Step-by-step explanation:

I made this into 3 rectangles.

Figure 1:

9•8=72

The 9 is from the 13 m side, but I've taken 4 m off from the overlapping square.

Figure 2:

6•7=42

The 7 is from the 10 m side, but I've taken 4m off from the overlapping square again.

Remaining Area:

If you extend the lines into figures 1 and 2 from the top left corner and bottom right corner vertically, you will get a rectangle that is (11 m) x (4 m). This is not yet accounted for.

11•4=44

Add together: 72 + 42 + 44 = <u>158</u>

*Note: You could also find the area of the squares a much easier way by subtracting the overlapping part after finding the area of both figures , but this is how I did it*

5 0
2 years ago
Chocolate chip and peanut butter cookies are randomly chosen from a cookie jar and placed onto a plate. The first plate had four
soldier1979 [14.2K]

Answer:

3 peanut cookies

Step-by-step explanation:

Given that :

Plate 1:

Number of chocolate chip = 4

Number of peanut butter cookies = 1

Probability of drawing chocolate chip cookies from plate 1 :

Probability =( number of required outcome / Total possible outcomes)

P(chocolate chip) = 4 / 5

Plate 2:

Number of chocolate chip = 2

Number of peanut butter cookies = p

P(chocolate chip) = 2 / (2 + p)

Probability of drawing chocolate chip from plate 1 and then plate 2 = 8/ 25

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8 / (10 + 5p) = 8/ 25

8(10 + 5p) = 8 * 25

80 + 40p = 200

40p = 200 - 80

40p = 120

p = 3

7 0
2 years ago
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