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4 years ago

What do both of these functions have in common?

Mathematics

2 answers:

Troyanec [42]4 years ago

7 0

Answer:

Option D- They have the same horizontal translation.

Step-by-step explanation:

Given: $f(x)=2log10(x-1)-4$

$g(x)=10(x-1)^2+4$

To find: what is common in both the function

Solution : As we see to both the function there is a right shift in both the function of 1 unit i.e (x-1) which is common in both.

therefore, they have the same horizontal translation -Option D

antiseptic1488 [7]4 years ago

5 0

Got the question again i'm going to try vertical stretch
23

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Hello from MrBillDoesMath!

Answer:

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Discussion:

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3 years ago

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3 years ago

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3 years ago

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 .

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

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

$\rule{200}2$

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

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3 years ago