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2 years ago

Math help please Let f(x)=x2+5 and g (x)=3x+4; find (g o f)(7); (g o f)(7)=; help me solve!! Please!

Mathematics

1 answer:

lorasvet [3.4K]2 years ago

5 0

f(x) = 2x

g(x) = x + 3

First let us find (fog)(x)

(fog)(x) = f(g(x)

= f(x+3)

= 2(x+3)

= 2x + 6

==> (fog)(x) = 2x + 6

Now let us find (gof)(x):

(gof)(x) = g(f(x)

= g(2x)

= 2x + 3

==> (gof)(x) = 2x + 3

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Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms

miv72 [106K]

Hint :-

Break the given sequence into two parts .
Notice the terms at gap of one term beginning from the first term .They are like $\dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ . Next term is obtained by multiplying half to the previous term .
Notice the terms beginning from 2nd term , $4,7,10,13$ . Next term is obtained by adding 3 to the previous term .

Solution :- 

We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,

$\implies S_1 = \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8}$ .

We can see that this is in Geometric Progression where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,

$\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]$

Notice the term $\dfrac{1}{2^{25}}$ will be too small , so we can neglect it and take its approximation as 0 .

$\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]$

$\\\implies \boxed{ S_1 \approx 1 }$

$\rule{200}2$

Now the second sequence is in Arithmetic Progression , with common difference = 3 .

$\implies S_2=\dfrac{n}{2}[2a + (n-1)d]$

Substitute ,

$\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}$

Hence sum = 908 + 1 = 909

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2 years ago

Three minus the product of two and a number xxx.

pav-90 [236]

Answer: 3 - 2x

I’m not sure if you meant xxx or not.

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3 years ago

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steposvetlana [31]

Answer:

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Step-by-step explanation:

(x 1,y1) = (-10,5)

(x2, y2) = (3,4)

y2 - y1 / x2 - x1

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3 years ago

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Aubrey finished 2/9 of a project on Monday and 1/4 of the project of Tuesday. How much of the project has Aubrey completed?

riadik2000 [5.3K]

Answer:

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Step-by-step explanation:

We have to find a common denominator, so the first common denominator for 4 and 9 is 36. 9x4=36, so we multiply 2 by 4, which equals 8. 4x9-36, so we multiply the 1 by 9, and get 9. Then we add the numerators, 8 and 9, and get 17. So it's 17/36

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3 years ago

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AURORKA [14]

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3 years ago

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