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2 years ago

F(1) =3 and f (n+1)= f(n)^2+3 then find the value of f(4)

Mathematics

1 answer:

Tcecarenko [31]2 years ago

6 0

Answer:

f(4) = 1612

Step-by-step explanation:

using the recursive formula and f(1) = 3 , then

f(2) = f(1)² + 3 = 3² + 3 = 9 + 3 = 12

f(3) = f(2)² + 3 = 144 + 3 = 147

f(4) = f(3)² + 3 = 147² + 3 = 1609 + 3 = 1612

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Help please!!!!!!!!!!!!

creativ13 [48]

Answer:

$\frac{\pi }{3},\:\frac{2\pi }{3}$

Step-by-step explanation:

Let a=THETA (angle)

$1+\sin \left(a\right)-1=\frac{\sqrt{3}+2}{2}-1\\\sin \left(a\right)=\frac{\sqrt{3}+2}{2}-1\\a=\arcsin \left(\frac{\sqrt{3}+2}{2}-1\right)+2\pi n,\:a=\pi -\arcsin \left(\frac{\sqrt{3}+2}{2}-1\right)+2\pi n\\a=\frac{\pi }{3},\:a=\frac{2\pi }{3}$

7 0

3 years ago

A box has a volume of 308 cm cubed. Its height is 4 cm greater than its length. Its length is 3 cm greater than its width. What

kifflom [539]

Answer:

4 cm.

Step-by-step explanation:

Given:

A box has a volume of 308 cm cubed.

Its height is 4 cm greater than its length.

Its length is 3 cm greater than its width.

Question asked:

What is the width of the box?

Solution:

Let width = $x\ cm$

Length = $x+3\ cm$

Height = $x+3+4=x+7\ cm$

As we know:

$Volume\ of\ box=length\times width\times height$

$308=(x+3)\times x\times(x+7)\\ \\ 308=(x^{2} +3x)(x+7)\\ \\ 308=x^{2} (x+7)+ 3x(x+7)\\ \\ 308=x^{3} +7x^{2} +3x^{2} +21x\\ \\ 308=x^{3} +10x^{2} +21x\\ \\ Subtract\ 308\ from\ both\ sides\\ \\ x^{3} +10x^{2} +21x-308=0\\ \\ factor\ left\ side\ of\ equation\\ \\ (x-4)(x^{2} +14x+77)=0\\ \\ Set\ factors\ equal\ to\ 0.\\ \\ x-4=0 \ or\ x^{2} +14x+77=0\\ \\ \\$

As width can never be in negative, $x= 4\ cm$

By substituting the value:-

Width = $x\ cm$ = 4 cm

Thus, width of the box is 4 cm.

4 0

3 years ago

The length of a rectangle is 8 inches more than twice its width. The area of the rectangle is 120 square inches. How many inches

Irina-Kira [14]

Answer:

L = 20 inches

Step-by-step explanation:

w = width

L = length

area = 120

W x L = 120

L - 8 = 2W then L = 2W + 8

substitute for L:

W x (2W + 8) = 120

2W² + 8W -120 = 0

(2W - 12)(W + 10) = 0

2W-12 = 0

2W = 12

W = 6

L = 20

7 0

3 years ago

What is the estimate of 137,638 plus 52,091

polet [3.4K]

The answer is 189,729
If to be rounded answer would be 190,000 I would say best estimate would be 180,000

3 0

3 years ago

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A boy has as many sisters as brothers, but each sister has only half as many sisters as brothers. How many brothers and sisters

Elenna [48]

The boy would have 3 brothers and 3 sisters therefore in the family there would be 4 boys and 3 girls

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3 years ago