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4 years ago

Use linear approximation to estimate 15^.25 ...?

2 answers:

8 0

Let f(x) = sqrt(x). Use linear approximation about x = 25, since 24 is close to 25, and since it is easy to take the square root of 25. Note that f ' (x) = 1/[2sqrt(x)] from the power rule. About x = 25, f(x) is approximately f(25) + f ' (25)(x - 25). So sqrt(24) = f(24) is approximately f(25) + f ' (25)(24 - 25) = sqrt(25) + {1/[2sqrt(25)]}(-1) = 5 - 1/10 = 4.9 .

kvv77 [185]4 years ago

8 0

A linear approximation of f(x) in a neighborhood of a


f(x) ~ f(a) + f'(a) (x-a) 


f(x) = x^1/4 

2^4 = 16 i.e. a = 16 

f(15) ~ f(16) + f'(16) (15-16) 

f'(x) = 1/4 x^(-3/4) 

f(15) ~ 2 + 1/4 (16)^-3/4 (-1) 

~ 2 - 1/(32) = 1.96875

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3 years ago

In the diagram, ∠ADE ≅ ∠ABC. The ratios___ and ___ are equal.

DiKsa [7]

Answer:

$\frac{AD}{AB}$ = $\frac{AE}{AC}$ = $\frac{DE}{BC}$

Step-by-step explanation:

triangle ADE and triangle ABC are similar

therefore, the ratio of their corresponding sides are equal

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3 years ago

Paul went on a bike ride of 30 miles. He realized that if he had gone 8 mph faster, he would have arrived 12 hours sooner. How f

lara [203]

Answer: He actually rode 2 miles per hour on his trip

Step-by-step explanation: Maybe unconventional, but express the time it took, then figure the speed.

Time = distance /speed t will represent time, s is the speed: t = 30/s Use the rime it would have taken at the higher speed to create an equation:

t-12 = 30/s+8 replace the y with the 30/s

30/s -12 = 30/s+8

(s)(30/s -12 ) = (s)(30/s+8 ) Cross multiply to cancel denominators

(s-8)(30 -12s) = (s-8)(30s/s+8 ) ==> 30s +240 -12s² -96s =30s Simplify:

(-1)(-12s² -96s +240 ) =0 ==> 12s² +96s -240 divide all by 12

s² + 8s -20 = 0 Factor and solve for s

(s +10)(s -2) =0 s-2=0 S= 2

Proof:

30/2 = 15 hours for original trip at 2mph,

increase speed by 8mph 2 + 8 = 10mph

30 miles at 10mph takes 3 hours; that is 12 hours less than his actual trip.

(Brainilest, please :-)

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4 years ago

What is the equation of this graph? a) x=-7 b) y=-7

sergiy2304 [10]

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3 years ago

As of April 2006, roughly 50 million web domain names were registered (e.g., ). How many domain names consisting of just two let

Furkat [3]

Answer:

a) 676, 1296

b) 17576, 46656

c) 456976, 1679616

Step-by-step explanation:

firstly we know that there are 26 letters in the alphabet.

there are 26 ways of choosing the first character and 26 ways choosing the second character,

Therefore, the possible number of domains with two leeter is;

n = 26²

= 26 × 26

= 676

now when the digits are allowed, there are 26 + 10 = 36 characters to be used in total

therefore the possible number of domains with two characters is;

n = 36²

= 36 × 36

= 1296

there are 26 ways of choosing each character

therefore, the possible number of domains with three letters is

n = 26³

= 26 × 26 × 26

= 17576

when the digits are allowed, there are 26 + 10 = 36 characters to be used in total

therefore , the possible number of domains with three characters is;

n = 36³

= 36 × 36 × 36

= 46656

there are 26 ways of choosing each character, therefore the possible number of domains with four letters is;

n = 26⁴

n = 26 × 26 × 26 × 26

n = 456976

when the digits are allowed, there are 26 + 10 = 36 characters to be used in total

therefore, the possible number of domains with four characters is;

n = 36⁴

n = 36 × 36 × 36 × 36

= 1679616

7 0

3 years ago