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Artist 52 [7]
3 years ago
12

What is the constant term of the quotient when 2x^3-3x^2 + 4x-2 is divided by x^2-x+2?

Mathematics
1 answer:
AlladinOne [14]3 years ago
6 0

Answer:

  -1

Step-by-step explanation:

See the attachment for the polynomial long division. The constant in the quotient is -1.

_____

Here, there is a remainder of -x. If there were no remainder the constant in the quotient is the ratio of the constant in the dividend to the constant in the divisor: -2/2 = -1.

That could be a first guess in a "guess and check" solution approach.

<em>Guess</em>: first term of binomial quotient is (2x^3)/x^2 = 2x; last term of binomial quotient is -2/2 = -1. So, the quotient is guessed to be (2x -1).

<em>Check</em>: (2x -1)(x^2 -x +2) = 2x^3 -3x^2 +5x -2

Subtracting this from the actual dividend gives a remainder of -x. This has a lower degree than the divisor, so no further adjustment of the quotient is required.

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an engineer decides to use similar triangles to find the distance across the river she makes the diagram below which triangles t
sergiy2304 [10]
<h2>Explanation:</h2><h2 />

The missing diagram is shown below. Remember that shapes are similar if you can turn one into the other by moving, rotating, flipping, or scaling. So this means you can make the object bigger or smaller. So in this case, we know that ΔABC is similar to ΔDEF. If so, we can establish the following proportion:

\frac{h}{56.7}=\frac{17.2}{52.4} \\ \\ h=56.7\times \frac{17.2}{52.4} \\ \\ h=18.61m

Our goal is to find x. So by Pythagorean theorem:

x=\sqrt{17.2^2+18.61^2} \\ \\ \boxed{x=25.34m}

Conclusion:

<em>ΔABC ~ΔDEF</em>

<em>Distance across the river is 25.34m </em>

8 0
3 years ago
A prime number is a number that is evenly divisible only by 1 and itself. The prime numbers less than 100 are listed below.2 3 5
Usimov [2.4K]

Answer:

a. 0.96 = 96% probability that the number is odd.

b. 0.48 = 48% probability that the sum of the digits is odd.

c. 0.24 = 24% probability that the number is greater than 70.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

We are given the prime numbers less than 100, they are:

2,3,5,7,11,13,17,19,23,29,31,37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

There are 25 prime numbers less than 100.

a. The number is odd

Of the 25, 24 are odd, only the number 2 is even. So

24/25 = 0.96 = 96%

0.96 = 96% probability that the number is odd.

b. The sum of the digits is odd

The sum of the digits is odd for:

3, 5, 7, 23, 29, 41, 43, 47, 61, 67, 83, 89. So for 12 of them

12/25 = 0.48 = 48%

0.48 = 48% probability that the sum of the digits is odd.

c. The number is greater than 70

71, 73, 79, 83, 89, 97. 6 of them

6/25 = 0.24 = 24%

0.24 = 24% probability that the number is greater than 70.

5 0
3 years ago
Use the Change of Base Formula to evaluate log3 48. Then convert log3 48 to a logarithm in base 5. Round to the nearest thousand
Romashka [77]

Answer:

Log 48 base 3 on changing base is3.524 and log X base 5 on solving is290.385

Step-by-step explanation:

Given log48 base 3

To change the base to natural logarithm for easy simplification

Log M base n is equal to log M /log n

Hence log3 48= log48/log 3= 1.6821/0.4771= 3.524

Changing to base 5

Log X base 5 is 3.524

log5 X=3.524

Recall that loga b=x

a^x=b

So

5^3.524=290.385 =X

5 0
3 years ago
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