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3 years ago

What types of numbers can not be written as a fraction

Mathematics

1 answer:

Nataly [62]3 years ago

6 0

Answer:

THE answer is D Irrational number

Step-by-step explanation:

Pi is an irrational number because it cannot be expressed as a ratio (fraction) of two integers: it has no exact decimal equivalent, although 3.1415926 is good enough for many applications. The square root of 2 is another irrational number that cannot be written as a fraction.

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Answer: 4 in. wide

Step-by-step explanation: to get from 8 to 2, you divide by 4.

if you divide 16 by 4, the answer is 4

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2 years ago

Find an equation of the plane that contains the points p(5,−1,1),q(9,1,5),and r(8,−6,0)p(5,−1,1),q(9,1,5),and r(8,−6,0).

topjm [15]

Given plane passes through:
p(5,-1,1), q(9,1,5), r(8,-6,0)

We need to find a plane that is parallel to the plane through all three points, we form the vectors of any two sides of the triangle pqr:
pq=p-q=<5-9,-1-1,1-5>=<-4,-2,-4>
pr=p-r=<5-8,-1-6,1-0>=<-3,5,1>

The vector product pq x pr gives a vector perpendicular to both pq and pr. This vector is the normal vector of a plane passing through all three points
pq x pr
=
i j k
-4 -2 -4
-3 5 1
=<-2+20,12+4,-20-6>
=<18,16,-26>

Since the length of the normal vector does not change the direction, we simplify the normal vector as
N = <9,8,-13>

The required plane must pass through all three points.
We know that the normal vector is perpendicular to the plane through the three points, so we just need to make sure the plane passes through one of the three points, say q(9,1,5).

The equation of the required plane is therefore
Π : 9(x-9)+8(y-1)-13(z-5)=0
expand and simplify, we get the equation
Π : 9x+8y-13z=24

Check to see that the plane passes through all three points:
at p: 9(5)+8(-1)-13(1)=45-8-13=24
at q: 9(9)+8(1)-13(5)=81+9-65=24
at r: 9(8)+8(-6)-13(0)=72-48-0=24
So plane passes through all three points, as required.

3 0

3 years ago

A radioactive substance decreases in the amount of grams by one-third each year. If the starting amount of the

katovenus [111]

Answer:

The sequence is geometric. The recursive formula is $a_{n}=2/3a_{n-1}$

Step-by-step explanation:

In order to solve this problem, you have to calculate the amount of the substance left after the end of each year to obtain a sequence and then you have to determine if the sequence is arithmetic or geometric.

The substance decreases by one-third each year, therefore:

After 1 year:

$1452-\frac{1}{3}(1452)$

Using 1452 as a common factor and solving the fraction:

$1452(1-\frac{1}{3})=1452(\frac{2}{3})=968$

You can notice that in general, after each year the amount of grams is the initial amount of the year multiplied by 2/3

After 2 years:

$968(\frac{2}{3})=\frac{1936}{3}$

After 3 years:

$\frac{1936}{3}(\frac{2}{3})=\frac{3872}{9}$

The sequence is:

1452,968,1936/3,3872/9....

In order to determine if the sequence is geometric, you have to calculate the ratio of two consecutive terms and see if the ratio is the same for all two consecutive terms. The ratio is obtained by dividing a term by the previous term.

The sequence is arithmetic if the difference of two consecutive terms is the same for all two consecutive terms.

-Calculating the ratio:

For the first and second terms:

968/1452=2/3

For the second and third terms:

1936/3 ÷ 968 = 2/3

In conclussion, the sequence is geometric because the ratio is common.

The recursive formula of a geometric sequence is given by:

$a_{n}=ra_{n-1}$

where an is the nth term, r is the common ratio and an-1 is the previous term.

In this case, r=2/3

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3 years ago