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3 years ago

At what point on the graph of y=1/4x^4 is the tangent line parallel to the line 24x -3y=8

Mathematics

1 answer:

Rama09 [41]3 years ago

3 0

Answer:

a) dy/dx = 4/(2y+1)^2.

(b) y = 4/9 x - 14/9

Step-by-step explanation:

You have the following equation

(1)

(a) You first derivative implicitly the equation (1) respect to x:

next, you solve the last result for dy/dx:

(2)

(b) The equation for the tangent line is given by:

(3)

with yo = -2 and xo = -1

To find the slope m you use the result of the equation (2), because dy/dx evaluated in (-1,-2) is the slope at such point:

m =

Hence, by replacing in the equation (3) you obtain:

hence, the equation for the tangent line is y = 4/9 x - 14/9

(4)

the second derivative for the point (-1,-2) is obtained by replacing y=-2 and dy/dx=m=4/9 in the equation (4):

hence, d2y/dx2 evaluated in (-1,-2) is -64/243

Step-by-step explanation:

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What is the radius of the circle defined by x2 + 2x + y2 + 6y − 39 = 0? 49 9 7 81

Bond [772]

radius = 7

the equation of a circle in standard form is

(x-a)² + (y-b)² = r²

where (a, b) are the coordinates of the centre and r is the radius

To obtain this form ' complete the square ' on both the x and y terms

x² + 2(1)x + 1 + y² + 2(3)y + 9 = 39 + 1 + 9

(x+1)² + (y+3)² = 49 ← in standard form

with centre (1, 3) and r = √49 = 7

7 0

3 years ago

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An art gallery is increasing the asking price of its paintings by 60%. A painting now costs $400.00. How much was the painting b

Lera25 [3.4K]

The goal here is to find the cost of the painting BEFORE the 60% increase.

To find the cost of the painting, we must take in the information we already have:

Increase percent: 60%
Original price: unknown
Price after increase: $400

$400 is the price of the painting AFTER the increase has been added. So this equals the cost of the painting before the increase, plus the total amount of the increase (which is 60% of the original price).

The total must be (100% + 60% = 160%) 160% of the original painting price.

To find the original price, we must divide the increased price by the new percentage (160%). But how do we get here?

Well, we have 160% and our (fraction) $400/1%. We will have to switch the 160% and the 1%, giving us..

1% $400/160%

We take 400/160, which is 2.5. But this is only 1% of the original price! We want 100%.

So now, we multiply the 2.5 by 100 to get our answer: $250.

I hope this helps! If you have any questions, feel free to ask.

5 0

3 years ago

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Put these numbers in descending order.

barxatty [35]

Answer:

0.098 > 0.059 > 0.046 > 0.01

Step-by-step explanation:

try to make them in same number of digits.

0.098

0.059

0.046

0.010

you can add 0 to right side after the decimal :)

so just compare the last two digits of these numbers.

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3 years ago

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Given f(x)=3x+12, find f(f^-1(0))

mamaluj [8]

Answer:

Step-by-step explanation:

METHOD 1.

We know:

$f\bigg(f^{-1}(x)\bigg)=x$

Therefore

$f\bigg(f^{-1}(0)\bigg)=0$

METHOD 2.

$\text{Find}\ f^{-1}(x)$

$f(x)=3x+12\to y=3x+12$

exchange x to y and vice versa:

$x=3y+12$

solve for y:

$3y+12=x$ subtract 12 from both sides

$3y=x-12$ divide both sides by 3

$y=\dfrac{x-12}{3}\to f^{-1}(x)=\dfrac{x-12}{3}$

$f\bigg(f^{-1}(x)\bigg)\to$ replace x in f(x) with the expression $\dfrac{x-12}{3}$

$f\bigg(f^{-1}(x)\bigg)=3\cdot\dfrac{x-12}{3}+12=x-12+12=x$

$f\bigg(f^{-1}(0)\bigg)\to$ put x = 0 to $f\bigg(f^{-1}(x)\bigg)=x$

$f\bigg(f^{-1}(0)\bigg)=0$

METHOD 3.

$\text{Find}\ f^{-1}(x)$

$f^{-1}(x)=\dfrac{x-12}{3}$

Calculate the value of f ⁻¹(x) for x = 0:

$f^{-1}(0)=\dfrac{0-12}{3}=\dfrac{-12}{3}=-4$

Calculate the value of f(x) for x = -4:

$f(4)=3(-4)+12=-12+12=0$

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3 years ago

According to the Center for Disease Control and Prevention (CDC), the mean life expectancy in 2015 for non‑Hispanic white males

wolverine [178]

Answer:

The 95% confidence interval for the mean life expectancy of non-hispanic white males is (73.3 years, 79.3 years).

Step-by-step explanation:

This is the 95% confidence interval for the mean life expectancy of non-hispanic white males.

Our sample size is 100

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

$df = 100-1 = 99$

Then, we need to subtract one by the confidence level $\alpha$ and divide by 2. So:

$\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025$

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 99 and 0.025 in the two-sided t-distribution table, we have $T = 1.984$

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

$s = \frac{15}{\sqrt{100}} = 1.5$

Now, we multiply T and s

$M = T*s = 1.984*1.5 = 2.976$

Then

The lower end of the confidence interval is the mean subtracted by M. So:

$L = 76.3 - 2.976 = 73.3$

The upper end of the confidence interval is the mean added to M. So:

$L = 76.3 + 2.976 = 79.3$

The 95% confidence interval for the mean life expectancy of non-hispanic white males is (73.3 years, 79.3 years).

5 0

2 years ago

At what point on the graph of y=1/4x^4 is the tangent line parallel to the line 24x -3y=8￼￼

At what point on the graph of y=1/4x^4 is the tangent line parallel to the line 24x -3y=8