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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

Mathematics

1 answer:

Rama09 [41]2 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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nasty-shy [4]

Answer:

A.) 20x + 2y = 500

B.) y-intercept = 250; its meaning is how many boxes of pencils they started with.

C.) x-intercept = 25; How many T-shirts they can sell at most

Step-by-step explanation:

2y - 500 = -20x

20x + 2y - 500 = 0

20x + 2y = 500

y-intercept = 250; its meaning is how many boxes of pencils they started with.

20x + 2y = 500

20(0) + 2y = 500

2y = 500

2y/2 = 500/2

y = 250

x-intercept = 25; How many T-shirts they can sell at most

20x + 2y = 500

20x + 2(0) = 500

20x = 500

20x/20 = 500/20

x = 25

4 0

2 years ago

#23-6: The pool concession stand made $5,800 in June and $6,300 in July. What is the percent of increase in sales? Round the ans

katrin [286]

Answer:

8.6%

Step-by-step explanation:

To find the percent change, you will need to compute the positive difference and then divide the difference by the original (the older amount).

So the positive difference will be obtain by doing larger minus smaller:

6300

- 5800

-----------

500

The older amount was 5800.

So 500/5800 is the answer as a un-reduced fraction.

I'm going to reduce it by dividing top and bottom by 100:

500/5800 = 5/58

5/58 is the answer as a reduced fraction.

5 divided by 58 gives=0.086206897 in the calculator .

Approximately 0.0862 is the answer as a decimal.

To convert this to a percentage, multiply it by a 100:

8.62%

Rounded to the nearest tenths is 8.6%

-------------

So 5800+5800(.0862) should be pretty close to 6300 (not exactly though since we rounded).

5800+5800(.0862)=6299.96 using the calculator.

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2 years ago

F(x)=16x^4-81=0 select all zeros of the function !!!

atroni [7]

Answer:

3/2, -3/2, (if it is asking for imaginary solutions as well then 3i/2 and -3i/2)

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

You want to buy an item that costs $100. Which is the most cost-effective choice for buying the item?

Lilit [14]

C. Buying it a percent discount without sales tax.

Because of not having to pay $10, so it is awesome.

5 0

2 years ago

Consumer Math The sales tax in the town where Amanda lives is 7%. Amanda paid $35 in sales tax on a new stereo. What was the pri

Natasha2012 [34]

Answer

Find out the what was the price of the stereo .

To prove

Let us assume that the price of the stereo be x .

As given

Consumer Math The sales tax in the town where Amanda lives is 7%.

7% is written in the decimal form

$= \frac{7}{100}$

= 0.07

As given

Amanda paid $35 in sales tax on a new stereo .

Than the equation becomes

x × 0.07 = 35

$x = \frac{35}{0.07}$

solving the above

x = $ 500

Therefore the price of the stereo is $ 500 .

Hence proved

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