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3 years ago

If you fill a 4.92 cm prism with cubes who’s sides lengths are less than 1 cm what size would be the best

Mathematics

1 answer:

Marrrta [24]3 years ago

8 0

Answer:

See explanation below: either 0.984 cm or 0.85 cm depending on the complete question.

Explanation:

The question is incomplete and, thus, ambiguos.

There are two plausible interpretations: either each side of the prism has a leght of 4.92 cm, or the the units of the given measured is not cm but cm³ and 4.92 is the volume of the prism.

Considering the first option:

The best side length is the first decimal number that divides exactly 4.92cm

That is 4.92/5 = 0.984 cm

Considering the second option

The correct question would be "If you fill a 4.92 cm³ prism with cubes who’s sides lengths are less than 1 cm what size would be the best"

The best size of the sides lentgths is one that occupies the greatest part of each length.

Assume the prism is a cube. Then, the legth of each side is:

$\sqrt[3]{4.92}=1.70$

The greatest decimal number that divides 1.70 exactly is:

1.70cm/2 = 0.85cm

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3 years ago

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What is the perimeter of the rectangle? Write your answer in scientific notation. The area is 2.76 x 10 pw12

MrRa [10]

We know that
area of a rectangle=length*width
length=area/width
area=2.76 x 10^12 units²
width=4.6 x 10^5 units
length=2.76 x 10^12/4.6 x 10^5 ------> 6 x 10^6 units

perimeter of a rectangle=2*[length+width]
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the answer is
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3 years ago

Use summation notation to write the series 49 + 54 + 59 +... for 14 terms.

My name is Ann [436]

Answer:

Arithmetic sequence states that a sequence of numbers such that the difference between the consecutive terms is constant.

it is given by: $a_n = a+(n-1)d$ where a is the first term , n is the number of term and d is the common difference.

Given the series: $49 + 54 + 59+ ......$

here, Common difference(d) = 5

First term(a) = 49

by definition we have;

For nth term

$a_n = a+(n-1)d$

$a_n = 49+(n-1)5$

$a_n =49+5n -5$ = 5n + 44

To write the series using summation notation for 14 terms

Summation symbol $'\sum'$

The series for 14th terms is given by;

$\sum_{n=1}^{14}(5n +44)$

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3 years ago

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Explain how you know which method you should use to solve a rational equation.

notsponge [240]

Methods to solve rational equation:

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A rational equation is an equation containing at least one rational expression.

Method 1:

The method for solving rational equations is to rewrite the rational expressions in terms of a common denominator. Then, since we know the numerators are equal, we can solve for the variable.

For example,

$\frac{1}{2}=\frac{x}{2}\Rightarrow x=1$