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3 years ago

Find the point on the curve y = √ x where the tangent line is parallel to the line y = x 8 .

1 answer:

7 0

If tangent to the curve y = √x is parallel to the line y = 8x, then this implies that the tangent to y = √x has the same slope as the line y = 8x. In other words, the derivative (slope) function of y = √x is equal to the slope of the line y = 8x, which is m = 8. Hence y' = 8 once we find y'

y = √x = x^(1/2)

Applying the power rule and simplifying, we find that the derivative is

y' = 1/(2√x)

Now remember that y' must equal 8

1/(2√x) = 8

Multiplying both sides by 2√x, we obtain

1 = 16√x

Dividing both sides by 16, yields

√x = 1/16

But wait a minute, √x = y. Thus 1/16 must be the y-coordinate of the point at which the tangent to y = √x is drawn.

Squaring both sides, yields

x = 1/256

This is the x-coordinate of the point on the curve where the tangent is drawn.

∴ the required point must be (1/256, 1/16)

GOOD LUCK!!!

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A picture has a height that is 2 times it’s width . It is to be enlarged to an area of 128 in 2

morpeh [17]

9514 1404 393

Answer:

8 in by 16 in

Step-by-step explanation:

In your equation, we presume that x represents the width. Solving for x, we have ...

2x² = 128 . . . . . . given equation

x² = 64 . . . . . . . . divide by 2

x = √64 = 8 . . . . square root

The enlargement will be 8 inches by 16 inches.

8 0

2 years ago

A. Solve the differential equation <img src="https://tex.z-dn.net/?f=y%27%3D2x%20%5Csqrt%7B1-y%5E2%7D%20" id="TexFormula1" title

kirill [66]

$y' = \frac{dy}{dx}$

seperable differential equations will have the form
$\frac{dy}{dx} = F(x) G(y)$

what you do from here is isolate all the y terms on one side and all the X terms on the other
$\frac{dy}{G(y)} = F(x) dx$
just divided G(y) to both sides and multiply dx to both sides

then integrate both sides
$\int \frac{1}{G(y)} dy = \int F(x) dx

$

once you integrate, you will have a constant. use the initial value condition to solve for the constant, then try to isolate x or y if the question asks for it

In your problem,
$G(y) = \sqrt{1-y^2}

F(x) = 2x$

so all you need to integrate is
$\int \frac{1}{\sqrt{1-y^2}} dy = \int 2x dx$

5 0

3 years ago

Find the surface area for the following prisms.

liubo4ka [24]

Answer:

uixis9sugwhwo19wha

Step-by-step explanation:

isisisisisisi

7 0

3 years ago

Adrienne operates the milkshake machine at Burgers and Shakes. on Monday she added whipped cream to 210 shakes.This was 70% of t

Natalka [10]

Answer:

Total number of milkshakes sold on Monday = 300

Number of milkshakes without whipped cream = 90

Step-by-step explanation:

Given:

Adrienne adds whipped cream to 210 milk shakes which is 70% of the total milk shakes sold.

To find the total milkshakes sold.

Solution:

Let the total number of milkshakes sold on Monday be = $x$

Percentage of milkshakes with whipped cream added to them = 70%

Number of milk shakes with added whipped cream can be given as:

⇒ $70\% \textrm{ of the total number of milkshakes}$

⇒ $70\% x$

⇒ $\frac{70}{100}x$ [Representing percent in fraction form]

⇒ $0.7x$ [evaluating in decimals]

We know that the number of milkshakes with whipped cream added to them = 210.

So, we have:

$0.7x=210$

Solving for $x$

Dividing both sides by 0.7

$\frac{0.7x}{0.7}=\frac{210}{0.7}$

∴ $x=300$

Thus, total number of milkshakes sold on Monday = 300

Number of milkshakes without whipped cream = $300-210$ = 90

6 0

3 years ago

A union of restaurant and foodservice workers would like to estimate the mean hourly wage, μ, of foodservice workers in the U.S.

pav-90 [236]

Answer:

$n=(\frac{1.960(2.25)}{0.35})^2 =158.76 \approx 159$

So the answer for this case would be n=159 rounded up to the nearest integer

Step-by-step explanation:

Assuming this complete question: A union of restaurant and foodservice workers would like to estimate the mean hourly wage, , of foodservice workers in the U.S. The union will choose a random sample of wages and then estimate using the mean of the sample. What is the minimum sample size needed in order for the union to be 95% confident that its estimate is within $0.35 of ? Suppose that the standard deviation of wages of foodservice workers in the U.S. is about $2.15 .

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=2.25$ represent the population standard deviation

n represent the sample size

Solution to the problem

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

And on this case we have that ME =0.35 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.960$ , replacing into formula (b) we got:

$n=(\frac{1.960(2.25)}{0.35})^2 =158.76 \approx 159$

So the answer for this case would be n=159 rounded up to the nearest integer

3 0

2 years ago