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2 years ago

Find the square root of 15129 by division method

1 answer:

7 0

$\underline{\ \ \ \ \ \ 123}\\1\ \ \ |15129\\\underline{\ \ \ \ \|1}\\22\ |\ 51\\\underline{\ \ \ \ |\ 44}\\243|\ \ 729\\\underline{\ \ \ \ \ |\ 729}\\.\qquad\ \ \ 0$

$\sqrt{15129}=123$

$\begin{array}{c|c}15129&3\\5043&3\\1681&41\\41&41\\1\end{array}15129=3\cdot3\cdot41\cdot41=3^2\cdot41^2\\\\\sqrt{15129}=\sqrt{3^2\cdot41^2}=\sqrt3^2}\cdot\sqrt{41^2}=3\cdot41=123$

$Used:\\\\\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{a^2}=a\ for\ a\geq0$

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You are typing a paper. At 4:04pm you have typed 275 words. By 4:18pm you have 765 words. Find the rate of change in words per m

alekssr [168]

You start at 4:04pm and end at 4:18pm. This means 14 minutes have passed

Now you had 275 word typed and now you have 765. To find the amount that were added simply subtract 765 by 275 and you'll get 490.

Finally, to find the average amount of words typed per minute, you'd divide 490 by 14 for each minute which is 35

Your answer is 35 words per minute

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2 years ago

There is a 0.9991 probability that a randomly selected 31-year-old male lives through the year. A life insurance company charge

jarptica [38.1K]

Answer:

a) Monetary values corresponding to the two events are:

-In case of surviving the year = -166$

-In case of a death in the year = 89834$

b) Expected value of the purchasing the insurance is -85 $

c) Yes, insurance company can make a profit with this policy.

Step-by-step explanation:

a) The man need to pay 166$ first to enroll the insurance policy. If he survives within a year, he will lose 166$. Otherwise, if he dies within a year he will profit 89834$.

b) Expected value of the purchasing the insurance as following:

-In case of surviving the year:

Value: -166$

Probability: 0,9991

-In case of death in a year

Value: 89834$

Probability: 0,0009

Expected value is E(x) = -166×0,9991 + 89834×0,0009 = -85 $

c) Lets consider that 10000 different 31 year old man enrolled to this insurance policy. According to probability of death, 9 out of 10000 man expected to be dead within the year. Therefore, company need to pay 9*90000 = 810000$ to their costumers. But, company will collect 10000*166=1660000$ from their costumers in the beginning of the year

So, it is expected that company is going to profit 1660000-810000=850000$ per year.

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2 years ago

The graphs of the quadratic functions f(x) = 6 – 10x2 and g(x) = 8 – (x – 2)2 are provided below. Observe there are TWO lines si

natta225 [31]

Answer:

a) y = 7.74*x + 7.5

b) y = 1.148*x + 6.036

Step-by-step explanation:

Given:

f(x) = 6 - 10*x^2

g(x) = 8 - (x-2)^2

Find:

(a) The line simultaneously tangent to both graphs having the LARGEST slope has equation

(b) The other line simultaneously tangent to both graphs has equation,

Solution:

- Find the derivatives of the two functions given:

f'(x) = -20*x

g'(x) = -2*(x-2)

- Since, the derivative of both function depends on the x coordinate. We will choose a point x_o which is common for both the functions f(x) and g(x). Point: ( x_o , g(x_o)) Hence,

g'(x_o) = -2*(x_o -2)

- Now compute the gradient of a line tangent to both graphs at point (x_o , g(x_o) ) on g(x) graph and point ( x , f(x) ) on function f(x):

m = (g(x_o) - f(x)) / (x_o - x)

m = (8 - (x_o-2)^2 - 6 + 10*x^2) / (x_o - x)

m = (8 - (x_o^2 - 4*x_o + 4) - 6 + 10*x^2)/(x_o - x)

m = ( 8 - x_o^2 + 4*x_o -4 -6 +10*x^2) /(x_o - x)

m = ( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x)

- Now the gradient of the line computed from a point on each graph m must be equal to the derivatives computed earlier for each function:

m = f'(x) = g'(x_o)

- We will develop the first expression:

m = f'(x)

( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x) = -20*x

Eq 1. (-2 - x_o^2 + 4*x_o + 10*x^2) = -20*x*x_o + 20*x^2

And,

m = g'(x_o)

( -2 - x_o^2 + 4*x_o + 10*x^2) /(x_o - x) = -20*x

-2 - x_o^2 + 4*x_o + 10*x^2 = -2(x_o - 2)(x_o - x)

Eq 2 -2 - x_o^2 + 4*x_o+ 10*x^2 = -2(x_o^2 - x_o*(x + 2) + 2*x)

- Now subtract the two equations (Eq 1 - Eq 2):

-20*x*x_o + 20*x^2 + 2*x_o^2 - 2*x_o*(x + 2) + 4*x = 0

-22*x*x_o + 20*x^2 + 2*x_o^2 - 4*x_o + 4*x = 0

- Form factors: 20*x^2 - 20*x*x_o - 2*x*x_o + 2*x_o^2 - 4*x_o + 4*x = 0

20*x*(x - x_o) - 2*x_o*(x - x_o) + 4*(x - x_o) = 0

(x - x_o)(20*x - 2*x_o + 4) = 0

x = x_o , x_o = 10x + 2

- For x_o = 10x + 2 ,

(g(10*x + 2) - f(x))/(10*x + 2 - x) = -20*x

(8 - 100*x^2 - 6 + 10*x^2)/(9*x + 2) = -20*x

(-90*x^2 + 2) = -180*x^2 - 40*x

90*x^2 + 40*x + 2 = 0

- Solve the quadratic equation above:

x = -0.0574, -0.387

- Largest slope is at x = -0.387 where equation of line is:

y - 4.502 = -20*(-0.387)*(x + 0.387)

y = 7.74*x + 7.5

- Other tangent line:

y - 5.97 = 1.148*(x + 0.0574)

y = 1.148*x + 6.036

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1 year ago

you have housing and fixed expenses of $631.72/month and they are 33% of your realized income. What is our realized income per m

nikklg [1K]

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2 years ago

Read 2 more answers

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Mariulka [41]

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2 years ago