What is 1.7 expressed as a fraction in simplest form?

bekas [8.4K]

Looking at this question again, I don't understand why you're told "for y=11". That doesn't seem relevant at all... So you can disregard the answer I posted a few minutes ago on your other question.

a) With $x^2=-2+y+5\cos y$ , differentiate both sides with respect to $x$ to get

$2x=\dfrac{\mathrm dy}{\mathrm dx}-5\sin y\dfrac{\mathrm dy}{\mathrm dx}$

$\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x}{1-5\sin y}$

b) The point P occurs at $x=2$ , which corresponds to a $y$ -coordinate of

$4=-2+y+5\cos y\implies y\approx4.928$

The slope of the line tangent to this point is approximately

$\dfrac{\mathrm dy}{\mathrm dx}\approx\dfrac{2(2)}{1-5\sin(4.928)}\approx0.68$

so the equation of the tangent line is approximately

$y-4.928=0.68(x-2)\implies y=0.68x+3.57$

c) The tangent line to the graphed curve is vertical when $\dfrac{\mathrm dy}{\mathrm dx}$ is undefined. This happens when $1-5\sin y=0$ , or $y=\pi-\sin^{-1}\dfrac15+2n\pi$ and $y=\sin^{-1}\dfrac15+2n\pi$ where $n$ is any integer.

In case you're not sure where the general solution came from: We have

$\sin y=\dfrac15$

which has an infinite number of solutions. $\sin^{-1}\dfrac15$ is one of them, which we obtain by taking the inverse sine of both sides of this equation. Since $\sin(\pi-x)=\sin x$ , we also know that $\pi-\sin^{-1}\dfrac15$ is a solution. And since $\sin(x+2n\pi)=\sin x$ for integers $n$ , we also know that we can add any multiple of $2\pi$ to these two solutions to get infinitely more solutions.

3 0

3 years ago

Determine whether the situation calls for a survey, an observational study, or an experiment.

grandymaker [24]

Survey

By conducting a survey, you can ask people who have seen the new movie what they think about it. This will be the best approach to get a straightforward answer from these people.

3 0

3 years ago

How many units down does susan need to move to get to the fourth point on the number line a. 1/2 b. 3/2 c. 2 d. 4 e. 6

ddd [48]

Answer:

e. 6

Step-by-step explanation:

Hello there!, since there is no prior information concerning the activities performed by Susan, I will explain what a number line is and try as much as possible to answer your question from the definition.

A number line is a line on which integers are usually drawn as points separated by a uniform distance. This way, the number line makes addition and subtraction easier, which is very useful when you want to teach someone these operations.

Now, let assume Susan starts from 0 on the number line, to get to the fourth point, Susan needs to move 4 blocks, where each block contains 10 units.

Now, let's assume that Susan is at the third block and the fourth unit, it will take Susan an additional 6 units to get to the fourth point.

NOTE: The solution to this question was provided based on assumption since no much information was given in the question.

4 0

3 years ago

Solve for y: 6x-3y=24

geniusboy [140]

Answer:

$y=2x-8$

Step-by-step explanation:

Isolate the variable and divide by the coefficient to solve for a variable.

$6x-3y=24 \\ \\ -3y=-6x+24 \\ \\ y=2x-8$

3 0

3 years ago

Enter the phrase as an algebraic expression.<br> p divided by 8<br> The algebraic expression is

mote1985 [20]

Answer: p/8

Step-by-step explanation: p is being divided by 8, meaning that in a fraction, p would be the numerator and 8 would be the denominator.

I hope this helps, have a good day.

4 0

3 years ago