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3 years ago

(3x + 8)

Mathematics

1 answer:

slava [35]3 years ago

6 0

A or b I just know it

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Whats the next two terms in order are p+q, p , p-q

Law Incorporation [45]

Answer:

p - 2q and p - 3q

Step-by-step explanation:

A Series is given to us and we need to find the next two terms of the series . The given series to us is ,

$\rm\implies Series = p+q , p , p - q$

Note that when we subtract the consecutive terms we get the common difference as "-q" .

$\rm\implies Common\ Difference = p - (p + q )= p - p - q =\boxed{\rm q}$

Therefore the series is Arithmetic Series .

Arithmetic Series:- The series in which a common number is added to obtain the next term of series .

And here the Common difference is -q .

Fourth term :-

$\rm\implies 4th \ term = p - q - q = \boxed{\blue{\rm p - 2q}}$

Fifth term :-

$\rm\implies 4th \ term = p - 2q - q = \boxed{\blue{\rm p - 3q}}$

Therefore the next two terms are ( p - 2q) and ( p - 3q ) .

5 0

3 years ago

Find the standard deviation of the following data. Answers are rounded to the nearest tenth. 5, 5, 6, 12, 13, 26, 37, 49, 51, 56

kogti [31]

Answer:

24.2(to the nearest tenth)

Step-by-step explanation:

The question is ungrouped data type

standard deviation =√ [∑ (x-μ)² / n]

mean (μ)=∑x/n

= $\frac{5+5+6+12+13+26+37+49+51+56+56+84}{12}$

=33.3

x-μ for data 5, 5, 6, 12, 13, 26, 37, 49, 51, 56, 56, 84 will be

-28.3, -28.3, -27.3, -21.3, -7.3, 3.7, 15.7,17.7, 22.7,22.7,50.7

(x-μ)² will be 800.89, 800.89,745.29,453.69,53.29,13.69,246.49,313.29,515.29,515.29,2570.49

∑ (x-μ)² will be = 7028.59

standard deviation = √(7028.59 / 12)

=24.2

6 0

4 years ago

Find the point P on the graph of the function y=√x closest to the point (9,0)

Sphinxa [80]

Answer:

$\displaystyle \frac{17}{2}$ .

Step-by-step explanation:

Let the $x$ -coordinate of $P$ be $t$ . For $P\!$ to be on the graph of the function $y = \sqrt{x}$ , the $y$ -coordinate of $\! P$ would need to be $\sqrt{t}$ . Therefore, the coordinate of $P \!$ would be $\left(t,\, \sqrt{t}\right)$ .

The Euclidean Distance between $\left(t,\, \sqrt{t}\right)$ and $(9,\, 0)$ is:

$\begin{aligned} & d\left(\left(t,\, \sqrt{t}\right),\, (9,\, 0)\right) \\ &= \sqrt{(t - 9)^2 +\left(\sqrt{t}\right)^{2}} \\ &= \sqrt{t^2 - 18\, t + 81 + t} \\ &= \sqrt{t^2 - 17 \, t + 81}\end{aligned}$ .

The goal is to find the a $t$ that minimizes this distance. However, $\sqrt{t^2 - 17 \, t + 81}$ is non-negative for all real $t\!$ . Hence, the $\! t$ that minimizes the square of this expression, $\left(t^2 - 17 \, t + 81\right)$ , would also minimize $\sqrt{t^2 - 17 \, t + 81}\!$ .

Differentiate $\left(t^2 - 17 \, t + 81\right)$ with respect to $t$ :

$\displaystyle \frac{d}{dt}\left[t^2 - 17 \, t + 81\right] = 2\, t - 17$ .

$\displaystyle \frac{d^{2}}{dt^{2}}\left[t^2 - 17 \, t + 81\right] = 2$ .

Set the first derivative, $(2\, t - 17)$ , to $0$ and solve for $t$ :

$2\, t - 17 = 0$ .

$\displaystyle t = \frac{17}{2}$ .

Notice that the second derivative is greater than $0$ for this $t$ . Hence, $\displaystyle t = \frac{17}{2}$ would indeed minimize $\left(t^2 - 17 \, t + 81\right)$ . This $t\!$ value would also minimize $\sqrt{t^2 - 17 \, t + 81}\!$ , the distance between $P$ $\left(t,\, \sqrt{t}\right)$ and $(9,\, 0)$ .

Therefore, the point $P$ would be closest to $(9,\, 0)$ when the $x$ -coordinate of $P\!$ is $\displaystyle \frac{17}{2}$ .

8 0

3 years ago

Binomial ( 5x - y ) ^ 10 terms ax ^ 2 y ^8

iragen [17]

$\bf (5x-y)^{10}\implies 
\begin{array}{llll}
term&coefficient&value\\
-----&-----&-----\\
1&+1&(5x)^{10}(-y)^0\\
2&+10&(5x)^9(-y)^1\\
3&+45&(5x)^8(-y)^2\\
4&+120&(5x)^7(-y)^3\\
5&+210&(5x)^6(-y)^4\\
6&+252&(5x)^5(-y)^5\\
7&+210&(5x)^4(-y)^6\\
8&+120&(5x)^3(-y)^7\\ 9&+45&(5x)^2(-y)^8
\end{array}$

now, how do we get the coefficients? well, the first coefficient is 1, any subsequent is " the product of the current terms's coefficient and the exponent of the first element, divided by the exponent of the second element in the next term", now that's a mouthful, but for example,

how did get 210 for the 5th expanded term? well is just 120 * 7 / 4

how about 252 of the 6th term? 210 * 6 / 5.

how about 45 of the 9th one? 120 * 3 / 8.

of course, the exponents for each is simple, as you'd already know from the binomial theorem.

so, just expand away the 9th expanded term.

3 0

3 years ago

3) A data set has 11 numbers in it. Each number is a whole number and there are no repeats. The bottom 2 values of the data set

NNADVOKAT [17]

C) 18 is your answer

Hope this brings you luck ^o^ ^_^

7 0

3 years ago