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2 years ago

13

A meteorologist records the number of clear days in a given year in each of 21 different U.S. cities. The results are shown belo

w. Find the midrange. 72 143 52 84 100 98 101 120 99 121 86 60 59 71 125 130 104 74 83 55 169

1 answer:

deff fn [24]2 years ago

3 0

Answer:

Midrange = 85 (Approx.)

Step-by-step explanation:

Given:

72 143 52 84 100 98 101 120 99 121 86 60 59 71 125 130 104 74 83 55 169

Find:

Midrange

Computation:

Number of data = 21

Midrange = [72 + 143 + 52 + 84 + 100 + 98 + 101 + 120 + 99 + 121 + 86 + 60 + 59 + 71 + 125 + 130 + 104 + 74 + 83 + 55 + 169] / 21

Midrange = 1,786/21

Midrange = 85 (Approx.)

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Find the general solution to the homogeneous differential equation. d2ydx2−1dydx−30y=0 d2ydx2−1dydx−30y=0 Use c1c1 and c2c2 in y

lukranit [14]

Answer:

The general solution of second order homogeneous differential equation is $y(x)=c_1e^{6x}+c_2e^{-5x}$

Step-by-step explanation:

To find the general solution of this second order homogeneous differential equation $\frac{d^2y}{dx^2}-\frac{dy}{dx}-30y=0$ we are going to use this Theorem:

<em>Given the differential equation $a \ddot{y}+b\dot{y}+cy =0, a\neq 0$ , consider the quadratic polynomial $ax^2+bx+c$ , called the</em><em> characteristic polynomial.</em><em> Using the quadratic formula, this polynomial always has one or two roots, call them $r$ and $s$ . The general solution of the differential equation is:</em>

<em>(a) $\ds y=Ae^{rt}+Be^{st}$ if the roots $r$ and $s$ are real numbers and $r\not=s$ .</em>

<em>(b) $\ds y=Ae^{rt}+Bte^{rt}$ , if $r=s$ is real.</em>

<em>(c) $\ds y=A\cos(\beta t)e^{\alpha t}+B\sin(\beta t)e^{\alpha t}$ , if the roots $r$ and $s$ are complex numbers $\alpha+\beta i$ and $\alpha-\beta i$ </em>

Applying the above Theorem we have:

$\mathrm{Substitute\quad }\frac{d^2y}{dx^2},\:\frac{dy}{dx}\mathrm{\:with\:}\ddot{y},\dot{y}$

$\ddot{y}-\dot{y}-30y=0$

The characteristic polynomial is $x^2-x-30$ and we find the roots as follows:

$\mathrm{Break\:the\:expression\:into\:groups}$

$\left(x^2+5x\right)+\left(-6x-30\right)$

$\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+5x\mathrm{:\quad }x\left(x+5\right)$

$\mathrm{Factor\:out\:}-6\mathrm{\:from\:}-6x-30\mathrm{:\quad }-6\left(x+5\right)$

$\mathrm{Factor\:out\:common\:term\:}x+5$

$\left(x+5\right)\left(x-6\right)$

The roots of characteristic polynomial are $r=-5$ and $s=6$

Therefore the general solution of second order homogeneous differential equation is $y(x)=c_1e^{6x}+c_2e^{-5x}$

5 0

3 years ago

Y is equal to one less than the square of x

mixas84 [53]

Answer: y= x^2- 1

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Solve 4(2a-1) = -10(a-5)

densk [106]

Firstly, you've got to expand the brackets, this becomes;
8a-4= -10a+ 50
You've then got to eliminate the -10a and you do this by adding 10a to both sides,
This then becomes 18a-4=50
You've then got to add 4, to eliminate this, which then becomes 18a=54
You've then got to divide both sides by 18, and this becomes 3.
Therefor, a=3
Hope this helps :)

4 0

2 years ago

Read 2 more answers

if a right angle has a hypotenuse of 19 units and a leg with the length of 7 units, find the length of the other leg

anyanavicka [17]

Square root of 19^2-7^2=17.66
Answer 17.6

8 0

2 years ago

What is the markup percent on a diamond for which the markup is $870 and the selling price is $2870?

ryzh [129]

Answer:

30.31%

Step-by-step explanation:

Mark up on selling price is given by markup*100%/selling price

In this case, markup is given as $870 while the selling price is $2870 hence the percentage of narkup to selling price will be given by $\frac {870\times 100}{2870}=30.313588850174\approx 30.31$

Therefore, the percentage of markup to selling price is approximately 30.31%

3 0

2 years ago