A triangle is placed in a semicircle with a radius of 9 cm

1 answer:

4 0

Considering that the shaded area is the part of the semi circle outside the triangle:
Area of circle= Pi x radius2 (this means radius squared)
Area of triangle= 1/2 x base x height
1/2 (because it is a semi circle) x 3.14 (in replacement of pi as directed by question) x 9squared= 127.17

127.17 - (1/2 x 18 x 9) = 46.17cmsquared

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Assume the exponential growth model A(t)equals=Upper A 0 e Superscript ktA0ekt and a world population of 5.95.9 billion in 2006

Whitepunk [10]

Answer:

1.4% is the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

Step-by-step explanation:

We are given the following in the question:

The exponential growth model is given by:

$A(t) = A_0e^{kt}$

where k is the growth rate, t is time in years and $A_0$ is constant.

The world population is 5.9 billion in 2006.

Thus, t = 0 for 2006

$A_0 = 5.9\text{ billions}$

We have to find the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

Putting these values in the growth model, we have,

$24 = 5.9e^{100k}\\\\k = \dfrac{1}{100}\ln \bigg(\dfrac{24}{5.9}\bigg)\\\\k = 0.01403\\k = 0.01403\times 100\% = 1.4\%$

1.4% is the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

8 0

3 years ago

1. ) Consider the function f(x)=5−7x2,−5≤x≤1

Marat540 [252]

1.) The interval of the value of x is from -5 to 1, inclusive. Remember that what is asked is the absolute value, thus the sign does not matter even if you have to subtract x from 5. Thus, the maximum value would be obtained if the x is smaller, which is 1. The minimum value is obtained when x=-5.

Absolute maximum value: x = - 5
f(-5) = ║5 - 7(-5)^2║ = ║-170║=170

Absolute minimum value: x = 1
f(1) = ║5 - 7(1)^2║ = ║-2║= 2

2.) The Mean Value Theorem (MVT) applies to functions that are continuous and differentiable on the closed and open interval of a to b, respectively. Since the function is a quadratic function, MVT can be applied. Then, this means that there is a value of c which is between a and b. This could be determined using this formula according to MVT:

$f'(c)= \frac{f(b)-f(a)}{b-a}$

The differentiated form would be f'(x) = -2x. Then,

$-2c = \frac{(4- 0^{2} )-(4- (-1)^{2}) }{0--1}=1$

$c=- \frac{1}{2}$

Thus, x = -1, x = -1/2, and x=0 all lie in the function 4-x^2.

3 0

4 years ago

If you have a spinner with 5 slots, what is the compound probability of spinning an even number, then an odd number? Expressed a

Minchanka [31]

Since the spinner has 5 slots it contains 3 odd and 2 evens,