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2 years ago

Use the remainder theorem to find P(2) for P(x) = x^4 - 3x^3 - 6x^2 + 9 .

Mathematics

1 answer:

kramer2 years ago

4 0

Step-by-step explanation:

soln;

given; p(x) = x^4 - 3x^3 - 6x^2 + 9

using remainder theorem;

p(x) = p(a)

= p(2)

= (2)^4 - 3(2)^3 - 6(2)^2 + 9

= -23

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A committee consisting of 4 faculty members and 5 students is to be formed. Every committee position has the same duties and vot

Zina [86]

Answer:

The number of ways to form the committee is formed = 637065

Solution:

The number of combinations of n things such that m things taken together are given by:-

$C_{(\boldsymbol{n}, \boldsymbol{m})}=\frac{n !}{m !(\boldsymbol{n}-\boldsymbol{m}) !}$

Given Data:

A committee consisting of 4 faculty members and 5 students is to be formed. There are 12 faculty members and 13 students eligible to serve on the committee.

Then, the number of ways to form the committee is formed given by :-

$\begin{array}{l}{12 C_{4} \times 13 C_{5}} \\\\ {=\frac{12 !}{4 !(12-4) !} \times \frac{13 !}{5 !(13-5) !}} \\\\ {=\frac{12 !}{4 ! 8 !} \times \frac{13 !}{5 ! 8 !}} \\\\ {\frac{12 \times 11 \times 10 \times 9 \times 8 !}{27 \times 8 !} \times \frac{13 \times 12 \times 11 \times 10 \times 9 \times 8}{120 \times 8 !}} \\\\ {=637065}\end{array}$

Hence, the number of ways to form the committee is formed = 637065

7 0

2 years ago

a motorboat travels 305km in 5 hours going upstream and 651km in 7 hours going downstream. What is the rate of the boat in still

Ghella [55]

Recall your d = rt, distance = rate * time.

b = speed rate of the boat.

c = speed rate of the current.

keeping in mind that, as the boat goes Upstream, against the current, it's speed is not "b", but is really " b - c ", because the current is subtracting speed from it.

likewise, when the boat is going Downstream, because is going with the current, is really going faster at " b + c ".

$\bf \begin{array}{lccclll}
&\stackrel{km}{distance}&\stackrel{kmh}{rate}&\stackrel{hours}{time}\\
&------&------&------\\
Upstream&305&b-c&5\\
Downstream&651&b+c&7
\end{array}
\\\\\\
\begin{cases}
305=(b-c)(5)\implies 61=b-c\implies 61+c=\boxed{b}\\
651=(b+c)(7)\implies 93=b+c\\
----------------------\\
93=\boxed{61+c}+c
\end{cases}
\\\\\\
93=61+2c\implies 32=2c\implies \cfrac{32}{2}=c\implies 16=c$

what is the speed of the boat? well, 61 + c = b.

6 0

3 years ago

PLZ HELP, 20 pts and brainliest awarded, plz ASAP!!!!!! see image below

Amiraneli [1.4K]

Answer:

Option B

Step-by-step explanation:

we have

$f(x)=x^{3}-x^{2}-9x+9$

we know that

The vertical line test is a visual way to determine if a curve is a function or not. A function can only have one value of y for each unique value of x

In this problem

The given function passes the vertical line test

therefore

f(x) is a function

The Horizontal Line Test is a test use to determine if a function is one-to-one

If a horizontal line intersects a function's graph more than once, then the function is not one-to-one.

In this problem

The given function fails the horizontal line test

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8 0

3 years ago

Please help me out.

grandymaker [24]

Answer:

it's 4

Step-by-step explanation:

big brainnnnnnnnnn

6 0

2 years ago

Read 2 more answers

a farmer is buying fencing to surround a square field of area 3600m^2. What length of fencing does he need to buy?

kirill115 [55]

Answer:

240 m

Step-by-step explanation:

The area of a square field is 3600 m².

We need to find the length of fencing he needs to buy. It means we need to find the perimeter of the field.

The area of a square field is given by :

A = side²

So,

$s=\sqrt{3600} \ m\\\\s=60\ m$

Length of fencing = perimeter

= 4(s)

= 4(60)

= 240 m

So, he would need to buy 240 m of fencing.

8 0

2 years ago