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4 years ago

9

What is the explicit formula for the sequence? 7, 14, 21, 28, 35, . . .

2 answers:

qaws [65]4 years ago

7 0

Count By 7's Each Time

larisa86 [58]4 years ago

6 0

You’re supposed to +7 each time

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Help with this question, ASAP PLEASE!! SHOW YOUR WORK!!

r-ruslan [8.4K]

Simplest polynomial function is $x^4-x^3-11x^2+9x+18.$

Solution:

Given data:

Zeroes are 3i, –1, 2.

3i is a complex root of the function.

If 3i is a zero of the polynomial then –3i is also a zero of the polynomial.

Therefore zeroes are 3i, –3i –1, 2.

By factor theorem,

If a is zero of the function, then (x – a) is a factor of the polynomial.

So, the factors are (x – 3i), (x + 3i), (x + 1), (x –2).

On multiplying the factors, we get the polynomial.

$(x - 3i) (x + 3i) (x + 1) (x -2)$

$=(x^2+3ix-3ix+(3i)^2)(x^2-2x+x-2)$

$=(x^2-9)(x^2-x-2)$

Since the value of $i^2=-1$

$=x^2(x^2-x-2)-9(x^2-x-2)$

$=x^4-x^3-2x^2-9x^2+9x+18$

$=x^4-x^3-11x^2+9x+18$

Simplest polynomial function is $x^4-x^3-11x^2+9x+18.$

5 0

3 years ago

How do you find the length of an equilateral triangle with the area?

max2010maxim [7]

Formula used for an equilateral triangle is
Root3 a^2/4
Hope this helps.!!

7 0

3 years ago

How do you round 32.697 to the nearest one tents and hundreths.

natulia [17]

Neaest tenths is 32.7

6 0

4 years ago

Read 2 more answers

Match each spherical volume to the largest cross sectional area of that sphere

zlopas [31]

Answer:

Part 1) $324\pi\ units^{2}$ ------> $7,776\pi\ units^{3}$

Part 2) $36\pi\ units^{2}$ ------> $288\pi\ units^{3}$

Part 3) $81\pi\ units^{2}$ ------> $972\pi\ units^{3}$

Part 4) $144\pi\ units^{2}$ ------> $2,304\pi\ units^{3}$

Step-by-step explanation:

we know that

The largest cross sectional area of that sphere is equal to the area of a circle with the same radius of the sphere

Part 1) we have

$A=324\pi\ units^{2}$

The area of the circle is equal to

$A=\pi r^{2}$

so

$324\pi=\pi r^{2}$

Solve for r

$r^{2}=324$

$r=18\ units$

Find the volume of the sphere

The volume of the sphere is

$V=\frac{4}{3}\pi r^{3}$

For $r=18\ units$

substitute

$V=\frac{4}{3}\pi (18)^{3}$

$V=7,776\pi\ units^{3}$

Part 2) we have

$A=36\pi\ units^{2}$

The area of the circle is equal to

$A=\pi r^{2}$

so

$36\pi=\pi r^{2}$

Solve for r

$r^{2}=36$

$r=6\ units$

Find the volume of the sphere

The volume of the sphere is

$V=\frac{4}{3}\pi r^{3}$

For $r=6\ units$

substitute

$V=\frac{4}{3}\pi (6)^{3}$

$V=288\pi\ units^{3}$

Part 3) we have

$A=81\pi\ units^{2}$

The area of the circle is equal to

$A=\pi r^{2}$

so

$81\pi=\pi r^{2}$

Solve for r

$r^{2}=81$

$r=9\ units$

Find the volume of the sphere

The volume of the sphere is

$V=\frac{4}{3}\pi r^{3}$

For $r=9\ units$

substitute

$V=\frac{4}{3}\pi (9)^{3}$

$V=972\pi\ units^{3}$

Part 4) we have

$A=144\pi\ units^{2}$

The area of the circle is equal to

$A=\pi r^{2}$

so

$144\pi=\pi r^{2}$

Solve for r

$r^{2}=144$

$r=12\ units$

Find the volume of the sphere

The volume of the sphere is

$V=\frac{4}{3}\pi r^{3}$

For $r=12\ units$

substitute

$V=\frac{4}{3}\pi (12)^{3}$

$V=2,304\pi\ units^{3}$

5 0

3 years ago

Read 2 more answers

Write mixed number as a fraction 5 1/2

Virty [35]

Answer:11/2

Step-by-step explanation:You multiply 5 and 2, the answer will be 10. Plus 1, 11. So, 11/2

3 0

3 years ago

Read 2 more answers