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Diano4ka-milaya [45]
3 years ago
14

A swimming pool is a shape of a right rectangular prism if the pool is 12 3/4 yards long 5 2/3 yards wide and 9 yards deep what

is the volume of the swimming pool
Mathematics
1 answer:
Artemon [7]3 years ago
7 0

Answer:

V=650.25\ yards^3

Step-by-step explanation:

Given that,

Length = 12\dfrac{3}{4}\ yards

Width = 5\dfrac{2}{3}\ yards

Depth = 9 yards

We need to find the volume of the swimming pool. The formula for the volume of a cuboid shape is given by :

V=lbh\\\\V=12\dfrac{3}{4}\times 5\dfrac{2}{3}\times 9\\\\=\dfrac{51}{4}\times \dfrac{17}{3}\times 9\\\\V=650.25\ yards^3

So, the volume of the swimming pool is equal to 650.25\ yards^3.

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The sum of an infinite geometric series is 450, while the common ratio of the series is 4/ 5 . What is the first term of the ser
pogonyaev

Answer:

answer is 90 for first term

Step-by-step explanation:

Let the terms be  

First term x

We will use the formula s∞=x/1−r to find the sum of an infinite geometric series, where −1<r<1.  

We know the sum and the common ratio, so we'll be solving for x where r =4/5

s∞=x/1−r

450=x/1−4/5

450=x/1/5

450=5x

x=90

this is the first term x1 = 90

we know that common ratio is 4/5, so multiplying the first term by factor 4/5 to get the second term  

90 x 4/5=   72 second term  

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2 years ago
Find the first term and the common ratio <br>third term =6 and seventh term= 96​
mamaluj [8]

Answer:

First term a₁ = 3/2 and common ratio r = 2

Step-by-step explanation:

We need to find the first term and common ratio while we are given third term = 6 and seventh term = 96

Since common ratio is required so, the sequence is geometric sequence

The formula used is: a_n= a_1r^{n-1}

We are given: third term = 6 i,e

a_3=a_1r(3-1)\\6=a_1r^2----eq(1)

Seventh term = 96

a_7=a_1r(7-1)\\96=a_1r^6----eq(2)

Dividing eq(2) and eq(3)

\frac{96}{6}=\frac{a_1r^6}{a1r2}\\16=\frac{r^6}{r^2}\\16=r^{6-2}\\=> r^4=16\\Taking \ fourth \ root\\ r=2,-2,2i,-2i\\ \ We \ will \ consider \ only \ positive \ value \ of \ r \ i.e \ \textbf{ r= 2}

So, Common Ratio r = 2

Finding First term using eq(1)

a_3=a_1r^2\\6=a_1(2)^2\\6=a_1(4)\\a_1= \frac{6}{4}\\a_1= \frac{3}{2}

So, First term a₁ = 3/2 and common ratio r = 2

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