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son4ous [18]
2 years ago
9

If f(x) = arcsinx, then f' (√3/2)=

Mathematics
1 answer:
Irina-Kira [14]2 years ago
4 0

You can either use the inverse function theorem or compute the general derivative using implicit differentiation. The first method is slightly faster.

The IFT goes like this: if f(x) is invertible and f(a) = b, then finv(b) = a (where "finv" means "inverse of f").

By definition of inverse functions, we have

f(finv(x)) = finv(f(x)) = x

Differentiating both sides of the second equality with respect to x using the chain rule gives

finv'(f(x)) * f'(x) = 1

When x = a, we get

finv'(b) * f'(a) = 1

or

finv'(b) = 1/f'(a)

Now let f(x) = sin(x), which is invertible over the interval -π/2 ≤ x ≤ π/2. In the interval, we have sin(x) = √3/2 when x = π/3. We also have f'(x) = cos(x).

So we take a = π/3 and b = √3/2. Then

arcsin'(√3/2) = 1/cos(π/3) = 1/(1/2) = 2

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Ghella [55]
Elliot drove 31.2 miles per gallon of gasoline 
6 0
3 years ago
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If B equals 7 what is the value of the expression 2 + (10 - B )?
avanturin [10]

We just need to <u>plug in 7 for B! </u>

Let's do it !

2 + (10 - 7)

<em>We always start with the parenthesis first ! It's just a rule in math :) </em>

10 - 7 = ?

10 - 7 = 3

Now we have ...

2 + 3

2 + 3 = 5

Your final answer is 5!

I hope I helped :) Just comment if you have any questions and remember to vote me "brainliest" if you like my answer !!!

6 0
3 years ago
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One number is 7 less than another. If 4 times the smaller number plus 2 times the larger number is 62, find the two numbers.
Nana76 [90]
X=Y-7

4X+2Y=62

4(Y-7)+2Y=62

4Y-28+2Y=62

6Y=62+28

6Y=90

Y=90/6

Y=15
Larger number^

X=15-7=8
Smaller number^
PROOF:
4*8+2*15=62

32+30=62

62=62
Hope this helps.
4 0
3 years ago
What percent of 1.60 is 6
JulsSmile [24]
N% x 1.60 = 6   (I turned it from English to math)
Can't move n% back two places to make it a decimal so I will move the number I am multiplying by n% back two places instead.
Here is a sample to show you why it works.    .34 x 57 = 34 x .57

So
.016n = 6   (.016 is 1.60 decimal moved back two places)

Now divide both sides by .016
<u>.016</u>n   = <u>6
</u><u />.016     .016      n = 375%     

Why is the percent over 100% you might ask?

What % of 1.60 is 1.60  (Answer - all of it or 100%)
So What % of 1.60 is 6  - the number 6 being much bigger than 1.60, it is not surprising that the percent is more than 100.

What % of 1.60 is 1.60  - 100%
What %  of 1.60 is 3.20 - 200%   (notice that 3.20 is twice 1.60)
What % of 1.6 is 4.80   - 300%   (notice that 4.80 is three times 1.60)
What % of 1.6 is  6.40   - 400%  (notice that  6.40 is four times 1.60)
6 (the number in the problem) is just a bit less than 6.40  so 375% makes a lot a sense.
Hope you found this helpful. 

6 0
3 years ago
There are 20 blue marbles and 10 red marbles in a bag .if a marble is drawn at random once ,what is the probability that it will
andrew11 [14]

Answer:

2/3

Step-by-step explanation:

First, you figure out how many marbles are in total, which is the denominator. The total number of marbles is 30.

Then, you figure out how many marbles are blue, which is the numerator. There are 20 blue marbles.

Finally, you simplify the fraction. 20/30=2/3.

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