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nikklg [1K]
3 years ago
7

A polynomial function upper P left parenthesis x right parenthesis with rational coefficients has the given roots. Find two addi

tional roots of upper P left parenthesis x right parenthesis equals 0. i and 7 + 8i
Mathematics
1 answer:
mylen [45]3 years ago
5 0

Given that a polynomial function P(x) has rational coefficients.

Two roots are already given which are i and 7+8i,

Now we have to find two additional roots of P(x)=0

Given roots i and 7+8i are complex roots and we know that complex roots always occur in conjugate pairs so that means conjugate of given roots will also be the roots.

conjugate of a+bi is given by a-bi

So using that logic, conjugate of i is i

also conjugate of 7+8i is 7-8i

Hence final answer for the remaining roots are (-i) and (7-8i).

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The bending of a bean varies directly as its mas. A beam is bent 20mm by a mass 0f 40kg. how much will the beam bend with a mass
Naddik [55]

Answer:

The beam will bend by 50 mm with a mass of 100kg?

Step-by-step explanation:

The first step in solving the problem of direct variation is setting up the relation mathematically.

We can do this as follows:

The bending of the beam varies directly as its mass.

20  \alpha  40kg

\alpha here is the symbol representing direct variation. To remove this and replace it with an equality sign, we have to introduce a constant of proportionality, k

20 = k \times 40

k = 20 /40 = 0.5

We can now use this to find the distance the beam will bend with a mass of 100kg?

This will be

Bending = 0.5 \times 100 =50mm

There fore, the beam will bend by 50 mm with a mass of 100kg?

6 0
3 years ago
Read 2 more answers
Ben needs to mix 1.5 cups of lemonade concentrate with 4 cups or water to make lemonade. He has 6 cups of concentrate. How much
lubasha [3.4K]

Answer:

<u>24</u>

Step-by-step explanation:

To get your answer, you need to multiply 1.5 and 6.

<u>1.5 x 6 = 9</u>

Then you multiply 4 and 6.

<u>4 x 6 = 24</u>

Which is your final answer.

<h3><em>I hope this helps you! Good Luck!</em></h3>
4 0
3 years ago
The maximum afternoon temperature in Granderson is modeled by t=60-30 cos (x<img src="https://tex.z-dn.net/?f=%20%5Cpi%20" id="T
kicyunya [14]
The equation is t=60-30 cos (x \frac{\pi}{6})

the -30 expression, is subtracting, if negative, from the 60
if the cosine returned is negative, you'd end up with a +30,
negative * negative = positive

and then the 30 expression will ADD to the 60 amount
so the temperature "t" is highest, when the 30 expression, is
positive and and it's highest

when does that happen, when cosine is negative and at its highest,
well, cosine range is -1\le cos(\theta ) \le 1
so the lowest value cosine can provide is -1, when is cosine -1?
well, at \pi

so...  let's find a value that makes that expression to cos(\pi)

\bf t=60-30 cos (x \frac{\pi}{6}) \qquad x=6&#10;\\\\&#10;thus&#10;\\\\&#10;t=60-30 cos (6 \frac{\pi}{6})\implies t=60-30 cos (\pi )&#10;\\\\&#10;t=60-30[-1]\implies t=60+30\implies t=90

----------------------------------------------------------------------------------------
so...for August, that'll mean


\bf t=60-30 cos (x \frac{\pi}{6}) \qquad x=7&#10;\\\\&#10;t=60-30 cos (\frac{7\pi}{6})\implies t=60-30\left( -\cfrac{\sqrt{3}}{2} \right)&#10;\\\\&#10;t=60+(15\cdot \sqrt{3})\implies t\approx85.98^o


4 0
3 years ago
What is solve 5x-65=3x-17
NikAS [45]
If you would like to solve 5x - 65 = 3x - 17, you can do this using the following steps:

5x - 65 = 3x - 17
5x - 3x = 65 - 17
2x = 48
x = 48/2
x = 24

The correct result would be 24.
5 0
3 years ago
Explain how to solve linear equations.
muminat

Answer:

that means you need to find the surface area, but not the part that is touching the ground or the bottom.

3 0
3 years ago
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