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777dan777 [17]
3 years ago
8

72b384 is a number in which one of its digits is ‘b'. If the number is a multiple of 9, what is the numerical value of ‘b'?

Mathematics
1 answer:
Maslowich3 years ago
7 0

A number is divisible by 9 if and only if the sum of its digits is divisible by 9.

So, the sum of the digits of your number is

7+2+b+3+8+4 = 24+b

Since b ranges from 0 to 9 (it is a digit and it can't have any other values), 24+b ranges from 24 to 33. The only multiple of 9 in this range is 27, which we obtain by choosing b=3.

So, the only way to choose a value for b in order to make your number divisible by 9 is choosing b=3 and thus getting the number 723384, and indeed we have

\dfrac{723384}{9}=80376

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A sector with a radius of 15 cm has a central angle measure of 8π/5 what is the area of the sector
Inessa05 [86]

Answer:

area of the sector = 360π cm²

Step-by-step explanation:

To calculate the area of the sector, we will follow the steps below;

First write down the formula for calculating the area of a sector.

If angle Ф is measured in degree, then

area of sector = Ф/360   × πr²

but if angle Ф is measured in radians, then

area of sector = 1/2 × r² × Ф

In this case the angle is measured in radiance, hence we will use the second formula

From the question given, radius = 15 cm  and angle Ф = 8π/5

area of sector = 1/2 × r² × Ф  

                         =1/2 × 15² ×  8π/5

                         =1/2 ×225 × 8π/5

                          =360π cm²

area of the sector = 360π cm²

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2 years ago
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2 years ago
Find the 75th term of the arithmetic sequence -17, -13, -9....
Sphinxa [80]

Answer:

The 75th term of the arithmetic sequence -17, -13, -9.... is:

a_{75}=279

Step-by-step explanation:

Given the sequence

-17, -13, -9....

An arithmetic sequence has a constant difference 'd' and is defined by  

a_n=a_1+\left(n-1\right)d

computing the differences of all the adjacent terms

-13-\left(-17\right)=4,\:\quad \:-9-\left(-13\right)=4

The difference between all the adjacent terms is the same and equal to

d=4

The first element of the sequence is:

a_1=-17

now substitute d=4 and a_1=-17 in the nth term of the sequence

a_n=a_1+\left(n-1\right)d

a_n=4\left(n-1\right)-17

a_n=4n-21

Now, substitute n = 75 in the a_n=4n-21 sequence to determine the 75th sequence

a_n=4n-21

a_{75}=4\left(75\right)-21

a_{75}=300-21

a_{75}=279

Therefore,  the 75th term of the arithmetic sequence -17, -13, -9.... is:

a_{75}=279

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Answer:

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