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Find an equation for the tangent to the curve at P and the horizontal tangent to the curve at Q. y = 5 + cot x - 2 csc x 0 1 2 3 0 2 4 x y Upper QUpper P left parenthesis StartFraction pi Over 2 EndFraction comma 3 right parenthesis

Answers

Answer 1

Answer:

Answer with explanation:

The given function in x and y is,

y= 5 +cot x-2 Cosec x

To find the equation of tangent, we will differentiate the function with respect to x

$y'= -\csc^2 x+2 \csc x* \cot x$

Slope of tangent at (π/2,3)

$y'_{((\pi)/(2),3)}= -\csc^2(\pi)/(2) +2 \csc (\pi)/(2)* \cot (\pi)/(2)\n\n=-1+2* 1 * 0\n\n= -1$

Equation of tangent passing through (π/2,3) can be obtained by

$\rightarrow (y-y_(1))/(x-x_(1))=m(\text{Slope})\n\n \rightarrow (y-3)/(x-(\pi)/(2))=-1\n\n\rightarrow 3-y=x-(\pi)/(2)\n\n\rightarrow x+y-3-(\pi)/(2)=0$

⇒There will be no Horizontal tangent from the point(π/2,3).

Related Questions

Which of the following is an example of inductive reasoning? A. The first eight marbles that Dexter has drawn from a bag containing red and blue marbles have been red. Dexter concludes that the next marble he draws will be red. B. Jacob knows that in order to get a half-hour lunch break, his work shift must be at least six hours. Jacob concludes that since he is scheduled to get a half-hour lunch break, then his work shift must be at least six hours. C. Alicia knows that in order for someone to be in band, they have to know how to play an instrument. Mindy is in band. Alicia concludes that Mindy must know how to play an instrument. D. Stewart uses the basketball rule book to determine that one point is awarded for each free throw that a player makes.
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The functions f(x) and g(x) are graphed.On a coordinate plane, a curved red line with an upward arc, labeled g of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).Which represents where f(x) = g(x)?f(2) = g(2) and f(0) = g(0)f(2) = g(0) and f(0) = g(4)f(2) = g(0) and f(4) = g(2)f(2) = g(4) and f(1) = g(1)
Find three consecutive integers whose sum is 216. (Hint: if n represents the smallest of the three integers, n + 1 and n + 2 representthe other two numbers.)

Please help me with this.

Answers

Answer:

your answer would be c because for the team's average yardage per quarter it can't be negative!

Step-by-step explanation:

C. -56÷(-4)= 14

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I've done this before.

Which one does not belong? Explain your reasoning.y = 4x + 3
y = -4x + 5
y = 1/4x + 5
y = 4x - 5

Answers

Answer:

y=-4x + 3

Step-by-step explanation:

its the only one with a negative slope

A rock falls off a balcony. It's height (in feet) is given by the formula f(x)=-16t^2+13.4t+120, where t is measured in seconds. How long will it take the rock to hit the ground? Round your answers to the nearest three decimal places.

Answers

Answer:

3.189 seconds

Step-by-step explanation:

You want f(t) = 0, so ...

0 = -16t^2 +13.4t +120

0 = t^2 -0.8375t -7.5 . . . . divide by -16

0 = (t^2 -0.8375t +0.41875^2) -7.5 -0.41875^2 . . . . complete the square*

0 = (t -0.41875)^2 -7.6753515625 . . . . write as a square

√7.6753515625 = t -0.41875 . . . . . . . . add 7.67... and take positive root

t = 0.41875 +√7.6753515625 ≈ 3.189192 . . . . add 0.41875

It will take the rock about 3.189 seconds to hit the ground.

_____

* We complete the square by adding the square of half the coefficient of the linear term (= (-0.8375/2)^2) inside parentheses and subtracting the same amount outside parentheses. This gives a form inside parentheses that is ...

(t^2 -2at +a^2) = (t -a)^2

Completing the square is complicated a little bit by a leading coefficient that is not 1. That is why we divided by -16 first.

_____

Comment on the question

We note that the rock "falls" from the 120 foot high balcony by first traveling upward at a rate of 13.4 feet per second. We also note that the height function is written f(x), but uses t as the variable. That is, it should be f(t) = ...

What is a synthetic division used for

Answers

Answer:

pooping

Step-by-step explanation:

1.poop

2.wipe.

3.eat

4.sleep

What is the value of (4-1/4) ÷ (2-1/2)?

Answers

Answer:

2.5

Step-by-step explanation:

The value of (4-1/4) divided by (2-1/2) is 2.5

You welcome, don't forget to give me the points...

Consider the following function.Step 2 of 2 : Find two points on the line to graph the function.

Answers

The twο pοints οn the line are:

A. (0, 3)

B. (3,−2)

What exactly dοes functiοn mean?

Functiοn is wοrk expressiοn the cοnnectiοns between variοus cοmpοnents that wοrk tοgether tο prοduce the same result. A utility is made up οf a variety οf distinctive cοmpοnents that cοοperate tο create distinct results fοr each input.

Here,

$$\mathrm{r(x)=3 - \frac53 (x)}$