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statuscvo [17]
3 years ago
11

What is half of the product of 8 1/7 and 7 4/5

Mathematics
1 answer:
UNO [17]3 years ago
6 0

First we must convert these mixed numbers to improper fractions:

8\frac{1}{7}=\frac{57}{7}

7\frac{4}{5}=\frac{39}{5}

So then we need the product of these two numbers. That means to multiply:

\frac{57}{7}* \frac{39}{5}= \frac{2,223}{35}

But then we need the value of half of this product. So then let's multiply by one-half:

\frac{2,223}{35} *\frac{1}{2} =\frac{2,223}{70}

Then we can convert this from an improper fraction to a mixed number:

\frac{2,223}{70} =31\frac{53}{70}

And so this number is half of the product of the initial two numbers.

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In a G.P the 3rd term is 4 times the 1st term and the sum of the 2nd term and the 4th term is 30.find the common ratio,find the
STALIN [3.7K]

Answer:

the common ratio is either 2 or -2.

the sum of the first 7 terms is then either 765 or 255

Step-by-step explanation:

a geometric sequence or series of progression (these are the most common names for the same thing) means that every new term of the sequence is created by multiplying the previous term by a constant factor which is called the common ratio.

so,

a1

a2 = a1×f

a3 = a2×f = a1×f²

a4 = a3×f = a1×f³

the problem description here tells us

a3 = 4×a1

and from above we know a3 = a1×f².

so, f² = 4

and therefore the common ratio = f = 2 or -2 (we need to keep that in mind).

again, the problem description tells us

a2 + a4 = 30

a1×f + a1×f³ = 30

for f = 2

a1×2 + a1×2³ = 30

2a1 + 8a1 = 30

10a1 = 30

a1 = 3

for f = -2

a1×-2 + a1×(-2)³ = 30

-10a1 = 30

a1 = -3

the sum of the first n terms of a geometric sequence is

sn = a1×(1 - f^(n+1))/(1-f) for f <>1

so, for f = 2

s7 = 3×(1 - 2⁸)/(1-2) = 3×-255/-1 = 3×255 = 765

for f = -2

s7 = -3×(1 - (-2)⁸)/(1 - -2) = -3×(1-256)/3 = -3×-255/3 =

= -1×-255 = 255

4 0
2 years ago
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Answer:

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Step-by-step explanation:

5a + 3b = 6b

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5a=3b

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Step-by-step explanation:

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dsp73

Answer:

2 Answers By Expert Tutors

Consider as an example a box of length L, width W, and height H. If all linear dimension are doubled the area becomes 4 (22) times the original

Step-by-step explanation:

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3 years ago
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