Write the polynomial in standard form. –9x + x3

The image shows a ray of light bending at the boundary of a glass block. According to a law of optics, = n, where n is a constan

UkoKoshka [18]

The formula for the light bend would be n1*sin i= n2 * sin r

If you use "sin (90-x)= cos x" principle, you can change the sin in the equation into
n1*sin i= n2 * sin r
n1 * cos a= n2 * cos b
n2/n1= cos a/ cos b

Assuming the n constant is the ratio of the glass compared to water then the answer would be: cos a/ cos b

3 0

2 years ago

Write the polynomial of least degree with roots -2, 5, and 7.

fomenos

For roots of -2, 5, and 7.

x = -2, x = 5, and x = 7

x = -2 x = 5    x = 7

(x + 2) = 0 (x - 5) = 0    (x - 7) = 0

The polynomial of least degree would be:
(x -2)(x - 5)(x - 7) = 0

(x -2)(x -5) = x(x - 5) - 2(x -5)

   = x² - 5x - 2x + 10

   = x² - 7x + 10

(x² - 7x + 10)(x -7)

x(x² - 7x + 10) - 7(x² - 7x + 10)

x³ - 7x² + 10x - 7x² + 49x - 70

x³ - 7x² - 7x² + 10x + 49x - 70

x³ - 14x² + 59x - 70

The least is   x³ - 14x² + 59x - 70

3 0

2 years ago

The heights (in cm) and arm spans (in cm) of 31 students were measured. The association between x(height) and y(arm span) is sho

abruzzese [7]

Answer:

27.385 cm longer would we expect Mike's arm span to be than George's.

Step-by-step explanation:

We have to find how many centimeters longer would we expect Mike's arm span to be than George's using the equation:

y= 4.5x + 0.977 x

where y= arm span

and x= height

Given:

Mike's height=x = 175 cm

so Mike's arm span= y= 4.5 x + 0.977 x

= 4.5* (175) + 0.977* (175)

= 787.5 + 170.975

= 958.475 cm

George's height = x = 170 cm

so George's arm span= y= 4.5 x + 0.977 x

= 4.5* (170) + 0.977* (170)

= 765 + 166.09

= 931.09 cm

Mike's arm span longer than George's = Mike's arm span - George's arm span

= 958.475 - 931.09

= 27.385 cm.

8 0

2 years ago

The graph below represents a polynomial.

AleksAgata [21]

Answer:

C

Step-by-step explanation:

The polynomial on the graph has zeros or x-intercepts at x = -3, 0, 2, 4. These come from the factors x (x+3)(x-2)(x-4). Notice at 4 it doesn't cross but just touches. This means it has a degree of 2. So the factors are $x(x+3)(x-2)(x-4)^2$ . This matches to C.

6 0

2 years ago

If you take out a $15,000 loan for a period of 36 months at a 5.4% annual interest rate, how much of your first monthly payment

Tems11 [23]

Answer:

The amount that will go towards the balance is 385.71.

Step-by-step explanation:

The information provided is:

P = Principal of loan = $15,000

r = interest rate = 5.4% p.a. = $\frac{0.054}{12}= 0.0045$

n = number of periods = 36

The amount of the monthly payment that will go towards the balance is:

Amount towards the balance = EMI - Interest

First compute the Equated monthly installments (EMI) as follows:

$EMI=\frac{P\times r\times (1+r)^{n}}{(1+r)^{n}-1} \\=\frac{15000\times0.0045\times(1+0.0045)^{36}}{(1+0.0045)^{36}-1} \\=\frac{79.3125}{0.175}\\=453.21$

Now compute the interest as follows:

$Interest=P\times r\\=15000\times0.0045\\=67.5$

The amount that will go towards the balance is,

Amount towards the balance = EMI - Interest

= 453.21 - 67.5

= 385.71

Thus, the amount that will go towards the balance is 385.71.

4 0

2 years ago

Read 2 more answers

Write the polynomial in standard form. –9x + x3 – x4 + 3