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leva [86]
4 years ago
13

How many 1.1 centimeter lengths can be made from a string that is 5.093 centimeters long? Enter a numerical answer only.

Mathematics
1 answer:
Alexandra [31]4 years ago
5 0
The number of 1.1 cm in 5.093 cm can be calculated through finding the ratio of:
(longer length)/(shorter length)
longer length=5.093 cm
shorter length=1.1 cm
thus the ratio will be:
5.093/1.1
=4.63
This means that 1.1 cm length will go into 5.093 cm length by a factor of 4.63

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Answer:

The explicit form for this sequence is f(n)=f(1)-\frac{n-1}{10} for all n\geq 1.

Step-by-step explanation:

The explicit form of an arithmetic sequence  of numbers   is given by the formula  f(n)=f(1)+(n-1)d, where  f(1)  is the first term of the sequence,  d  is the difference between two consecutive terms of the sequence, and n\geq 1.

We know that  the first four elements for the arithmetic sequence are {f(1)=\frac{1}{5},f(2)=\frac{1}{10},f(3)=0, f(4)=-\frac{1}{10}}.

To find the general formula for this problem we only need to calculate d in the above formula.

For n=2, we have

f(2)=f(1)+(2-1)d=f(1)+d

if we replace f(1)=\frac{1}{5} and f(2)=\frac{1}{10} and solve for d we obtain  

\frac{1}{10}=\frac{1}{5}+d

d=\frac{1}{10}-\frac{1}{5}=-\frac{1}{10}

Therefore the explicit form is  f(n)=f(1)-\frac{n-1}{10} for all  n\geq 1.

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3 years ago
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jeka57 [31]

Answer:

The scale factor is \frac{3}{2}

Step-by-step explanation:

The volume of the original prism is V_P=980cm^3

The volume of the dilated prism is V_Q=3307.5cm^3

Let the scale factor be k.

To find the volume of the dilated prism, we multiplied by k^3.

\Rightarrow 980k^3=3307.5

\Rightarrow k^3=\frac{3307.5}{980}

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\Rightarrow k=\sqrt[3]{\frac{27}{8}}

\Rightarrow k=\frac{3}{2}

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