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3 years ago

Let a = 0.9876 and b = 0.9887 with N = 2, calculate the midpoint.

Mathematics

1 answer:

rodikova [14]3 years ago

5 0

Answer:

For a=0.9876 and b=0.9887 mid point will be 0.98815

Step-by-step explanation:

We have given a = 0.9876 and b = 0.9887

And N = 2

We have to find the mid point

For finding mid point we know that formula

Midpoint $=\frac{a+b}{2}$ , here we have given a=0.9876 and b = 0.9887

So midpoint will be $=\frac{0.9876+0.9887}{2}=\frac{1.9763}{2}=0.98815$

So for a=0.9876 and b=0.9887 mid point will be 0.98815

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2 years ago

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Part a)

Answer: 5*sqrt(2pi)/pi

-----------------------

Work Shown:

r = sqrt(A/pi)
r = sqrt(50/pi)
r = sqrt(50)/sqrt(pi)
r = (sqrt(50)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(50pi)/pi
r = sqrt(25*2pi)/pi
r = sqrt(25)*sqrt(2pi)/pi
r = 5*sqrt(2pi)/pi

Note: the denominator is technically not able to be rationalized because of the pi there. There is no value we can multiply pi by so that we end up with a rational value. We could try 1/pi, but that will eventually lead back to having pi in the denominator. I think your teacher may have made a typo when s/he wrote "rationalize all denominators"

============================================================

Part b)

Answer: 3*sqrt(3pi)/pi

-----------------------

Work Shown:

r = sqrt(A/pi)
r = sqrt(27/pi)
r = sqrt(27)/sqrt(pi)
r = (sqrt(27)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(27pi)/pi
r = sqrt(9*3pi)/pi
r = sqrt(9)*sqrt(3pi)/pi
r = 3*sqrt(3pi)/pi

Note: the same issue comes up as before in part a)

============================================================

Part c)

Answer: sqrt(19pi)/pi

-----------------------

Work Shown:

r = sqrt(A/pi)
r = sqrt(19/pi)
r = sqrt(19)/sqrt(pi)
r = (sqrt(19)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(19pi)/pi

8 0

2 years ago

Read 2 more answers

An investment services company experienced dramatic growth in the last two decades. The following models for the company's reven

zlopas [31]

Answer: a) 138.32 and b) 35 years approx.

Step-by-step explanation:

Since we have given that

$R(t)=21.4e^{0.13t}\\\\C(t)=18.6e^{0.13t}$

So, Profit is given by

$Profit=R(t)-C(t)\\\\Profit=21.4e^{0.13t}-18.6e^{0.13t}\\\\Profit=e^{0.13t}(21.4-18.6)\\\\Profit=2.8e^{0.13t}$

Difference in years of 1990 and 2020=30

So, Profit becomes :

$P(30)=2.8e^{0.13\times 30}\\\\P(30)=2.8\times 49.40\\\\P(30)=138.32$

(b) How long before the profit found in part (a) is predicted to double? (Round your answer to the nearest whole number.) years after 1990.

So, profit doubles , we get :

$138.32\times 2=2.8e^{0.13t}\\\\276.65=2.8e^{0.13t}\\\\\dfrac{276.65}{2.8}=e^{0.13t}\\\\98.80=e^[0.13t}\\\\\ln 98.80=0.13t\\\\4.593=0.13t\\\\\dfrac{4..593}{0.13}=t\\\\35.33=t$

Hence, a) 138.32 and b) 35 years approx.

6 0

3 years ago