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ivanzaharov [21]
3 years ago
15

Picking a month of the year in the day of the week (fundamental counting principle)

Mathematics
1 answer:
inysia [295]3 years ago
8 0
Since you mentioned the fundamental counting principle, I assume you are looking for the total number of possibilities.

If you are picking a month, there are 12 options.
If you are selecting a day of the week, there are 7 options.

If you are doing both, you multiply the two numbers together.
12 x 7 = 84
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To obtain the area of a sector, what fraction is multiplied by the area of a circle (A = πr2)?
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Let r be a radius of a given circle and α be an angle, that corresponds to a sector.

The circle area is A=\pi r^2 and denote the sector area as A_1. 
Then  \dfrac{A_1}{A}= \dfrac{\alpha}{2\pi}  (the ratio between area is the same as the ratio between coresponding angles).

A_1=\dfrac{\alpha}{2\pi} \cdot A=\dfrac{\alpha}{2\pi} \cdot \pi r^2= \dfrac{r^2\alpha}{2}.

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Kryger [21]
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yan [13]
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Find the value of a and of b for which<br>(a) the solution of x2 + ax &lt; b is<br>-2&lt;x &lt; 4​
KengaRu [80]

Answer: a = -2

b = 8

Step-by-step explanation:

Given :

x^{2} +ax

re - writing the equation , we have

x^{2} +ax-b

we need to find the value of a and b for which -2<x < 4 , this means that the roots of the quadratic equation are -2<x < 4.

The formula for finding the quadratic equation when the roots are known is :

x^{2} - sum of roots(x) + product of root = 0

sum of roots = -2 + 4 = 2

product of roots = -2 x 4 = -8

substituting into the formula , we have:

x^{2} -2x-8=0 , which could be written in inequality form as

x^{2} -2x-8

comparing with x^{2} +ax-b , it means that :

a = -2

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3 years ago
Help for good luck<br> and a lot of money
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