Find the equation of the tangent line to the curve y=2sinxy
2
sin
x
at the point (π/6,1)
π
6
1
.

The equation of this tangent line can be written in the form y=mx+b
y
m
x
b
where

Answers

Answer 1

Answer:

Final answer:

To find the equation of the tangent line to the curve y=2sinx at the point (π/6,1), we take the derivative to find the slope and then use the point-slope form of the line equation. The result is y = √3x + 1 - √3π/6.

Explanation:

The subject of this question is calculus and focuses specifically on finding the equation of the tangent line to the curve y=2sinx at a given point. To do this, we use the formula y=mx+b.

Firstly, the slope of the tangent line is obtained by taking the derivative of the function at the point of tangency. The derivative of y=2sinx is y'=2cosx. For the given point (π/6,1), the slope (m) would be 2cos(π/6) = √3.

Secondly, we use the point-slope form of the line equation to find b. Inserting the values of the slope (m) and the given point into the equation, we get 1 = √3(π/6) + b. Solving for b gives b = 1 - √3π/6.

Finally, the equation of the tangent line is y = √3x + 1 - √3π/6.

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Answer 2

Answer: Hello
f(x) = 2sin(x)
f(π/6) = 1
f'(x) 2cos(x)
f'(π/6) = 2×co(π/6) = 2 × root(3)×0.5 =root(3)
The equation of this tangent line is : y= root(3)(x-π/6)+1
y = root(3)x+1 - π/6(root(x)) in the form y=mx+b
m = root(3) and b = 1 - π/6(root(x))

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Answers

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Peter is reading a 193-page book. He has read three pages more than one-fourth of the number of pages he hasn’t yet read. How many pages has he not yet read?

Answers

Let X be amount of pages that he has NOT yet read.
So he read (x/4+3) pages
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Four hundred vouchers were sold for a carwash. Vouchers to wash trucks were $4, while vouchers to wash compact cars were $3. If the total sales were $1350, how many of each type of voucher were sold?

Answers

Answer:

150 vouchers to wash trucks were sold

250 vouchers to wash compact cars were sold

Step-by-step explanation:

Here, we are interested in calculating the number of each type of vouchers sold.

Let the number of vouchers to wash trucks be x while the number of vouchers to wash compact trucks be y.

Firstly, we know that both sums up to be 400.

Mathematically;

x + y = 400 •••••••••(i)

Secondly,

since a voucher to wash trucks sell $4, and we sold a total of x, the amount generated from selling is 4 * x = $4x

Same way for the vouchers to wash compact cars, we have a total of $3 * y = $3y

The sum of both gives $1350, which is the total sales.

Mathematically;

4x + 3y = 1350 ••••••(ii)

So we have two equations to solve simultaneously;

x + y = 400

4x + 3y = 1350

Multiply equation i by 4 , we have;

4x + 4y = 1600

4x + 3y = 1350

Subtract equation ii from i, we have 4y-3y = 1600-1350

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From equation 1, we know that

x + y = 400

This means that;

x = 400 -y

x = 400 -250

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2x-2

Answers

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How can b^2+9b+14 be re-written?1) (b+7) (b-7)
2) (b-7) (b-2)
3) (b+7) (b-2)
4) (b+7) (b+2)

Answers

$b^2+9b+14 =\n \n=b^2+9b-2b + 2b +14 =\n \n =b^2+7b +2b +14 = \n \n = b(b+7)+2(b+7)=\n \n=(b+7)(b+2) \n \n Answer: \ 4. ) \ (b+7)(b+2)$

Please, help me I’m so dumb

Answers

Answer:

Step-by-step explanation:

You know that 9 = 10 - 1.

Then 9 of something is equal to 10 of it less one of it. Here, that "something" is four.

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_____

Comment on this math

This illustrates a shortcut for multiplying by 9 that can be convenient for mental arithmetic. The idea is to multiply by 10, which just involves adding 0 (or moving the decimal point), then subtract the original number.

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