marie made a model (shown below) of the square pyramid she plans to build when she grows up. Find the surface area of the model.

What are the quotient and remainder of (x^5-x^3+-5) divided by (x-2)

pishuonlain [190]

Answer:

x⁴+2x³ +3x²+6x +12 r. $\dfrac{19}{x-2}$

Step-by-step explanation:

You can do this through synthetic division. It is a shorthand way of dividing polynomials.

First you need to make your divisor equal to zero so you can solve for what goes into the division box:

x - 2 = 0 → x = 2

The next step is to arrange your polynomials in descending powers. All missing terms, you will put in a zero.

x⁵ - x³ + (-5) → x⁵ + 0x⁴- x³ + 0x² + 0x + (-5)

Now you can proceed to synthetic division. Make an upside down division box with the divisor outside and the coefficients of the dividend listed, along with their sign. Leave a space below the divident

+2 | +1 0 -1 0 0 -5

|

Next you bring down the first coefficient:

+2 | +1 0 -1 0 0 -5

|

+1

Then you multiply it by the divisor and write the product under the next coefficient:

+2 | +1 0 -1 0 0 -5

| +2

+1

Next add the column and put the sum below it:

+2 | +1 0 -1 0 0 -5

| +2

+1 +2

Then multiply again and repeat until you reach the last coefficient:

+2 | +1 0 -1 0 0 -5

| +2 +4 +6 +12 +24

+1 +2 +3 +6 +12 +19

Now that you have your results, add in the x and their powers. The powers will start with the highest power but 1 less than the dividend. Since the dividend's highest power is 5, then the quotient's highest power will be 4. Then write it in descending order :

+1x⁴ +2x³ +3x² +6x +12 +19

Now the last coefficient is your remainder. So your results will be:

x⁴+2x³ +3x²+6x +12 r. $\dfrac{19}{x-2}$

7 0

3 years ago

Read 2 more answers

If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar

sleet_krkn [62]

This question is incomplete, the complete question is;

If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in increasing order but are not necessarily distinct.

In other words, how many 5-tuples of integers ( h, i , j , m ), are there with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1 ?

Answer:

the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120

Step-by-step explanation:

Given the data in the question;

Any quintuple ( h, i , j , m ), with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1

this can be represented as a string of ( n-1 ) vertical bars and 5 crosses.

So the positions of the crosses will indicate which 5 integers from 1 to n are indicated in the n-tuple'

Hence, the number of such quintuple is the same as the number of strings of ( n-1 ) vertical bars and 5 crosses such as;

$\left[\begin{array}{ccccc}5&+&n&-&1\\&&5\\\end{array}\right] = \left[\begin{array}{ccc}n&+&4\\&5&\\\end{array}\right]$

= [( n + 4 )! ] / [ 5!( n + 4 - 5 )! ]

= [( n + 4 )!] / [ 5!( n-1 )! ]

= [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120

Therefore, the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120

4 0

2 years ago

The kinetic energy (K) that an object has varies jointly with its mass (m) and the square of its velocity (v). The equation that

lord [1]

The kinetic energy of the bowling ball with the mass and traveling at the given velocity is 10.14 Joules.

<h3>What is Kinetic Energy?</h3>

Kinetic energy is simply a form of energy a particle or object possesses due to its motion.

It is expressed as;

K = (1/2)mv²

Where m is mass of the object and v is its velocity.

Given that;

Mass of the bowling ball m = 3kg

Velocity of the bowling ball v = 2.6m/s

Kinetic energy K = ?

We substitute the given values into the above equation.

K = (1/2)mv²

K = 0.5 × 3kg × (2.6m/s)²

K = 0.5 × 3kg × 6.76m²/s²

K = 10.14kgm²/s²

K = 10.14J

Therefore, the kinetic energy of the bowling ball with the mass and traveling at the given velocity is 10.14 Joules.

Learn more about kinetic energy here: brainly.com/question/12669551

#SPJ1

6 0

1 year ago

Nine yards of ribbon are used to make bows. How many yards of ribbon does each bow use?

Juliette [100K]

15 inches of ribbon for each

6 0

2 years ago

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Write your answer without using negative exponents

Reil [10]

Answer:

$\frac{1}{ {u}^{42} }$

Step-by-step explanation:

From law of indices

5 0

2 years ago