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3 years ago

What is the equation of the tangent drawn for f(x)=x-x^2 which is parallel to the line 4x-y-3=0

Mathematics

1 answer:

V125BC [204]3 years ago

8 0

Answer:

y = 4x + 9/4

Step-by-step explanation:

4x − y − 3 = 0

y = 4x − 3

The slope of the line is 4.

The slope of the tangent line is:

f(x) = x − x²

f'(x) = 1 − 2x

Setting the slope equal to 4:

4 = 1 − 2x

2x = -3

x = -3/2

The point on f(x) is:

f(-3/2) = -3/2 − (-3/2)²

f(-3/2) = -3/2 − 9/4

f(-3/2) = -15/4

Using point-slope form:

y − (-15/4) = 4 (x − (-3/2))

y + 15/4 = 4 (x + 3/2)

y + 15/4 = 4x + 6

y = 4x + 9/4

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2 years ago

A rectangular parking lot must have a perimeter of 440 feet and an area of at least 8000 square feet. Describe the possible leng

tangare [24]

Answer:

The possible parking lengths are 45.96 feet and 174.031 feet

Step-by-step explanation:

Let x be the length of rectangular plot and y be the breadth of rectangular plot

A rectangular parking lot must have a perimeter of 440 feet

Perimeter of rectangular plot =2(l+b)=2(x+y)=440

2(x+y)=440

x+y=220

y=220-x

We are also given that an area of at least 8000 square feet.

So, $xy \leq 8000$

So, $x(220-x) \leq 8000$

$220x-x^2 \leq 8000$

So, $220x-x^2 = 8000\\-x^2+220x-8000=0$

General quadratic equation : $ax^2+bx+c=0$

Formula : $x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-220 \pm \sqrt{220^2-4(-1)(-8000)}}{2(-1)}\\x=\frac{-220 + \sqrt{220^2-4(-1)(-8000)}}{2(-1)} , \frac{-220 - \sqrt{220^2-4(-1)(-8000)}}{2(-1)}\\x=45.96,174.031$

So, The possible parking lengths are 45.96 feet and 174.031 feet

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2 years ago

Two numbers have the same digits in the millions period, The same digits in the thousands period, and the same digits in the one

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2 years ago

What is the circumference of the largest circle that can fit a rectangle with dimension 8 x 12?

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The number that will fit there is 93

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2 years ago

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At the end of 8 years, Anna paid $400 interest for a loan. If the simple annual interest rate was 4%, how much did Anna borrow?

Valentin [98]

Answer:

$1,250

Step-by-step explanation:

You can find the answer using the following formula:

i = Prn

i= interest= $400

P= principal

r= rate of interest=0.04

t= time periods= 8

You can replace the values you have in the formula and then, isolate P:

400= P*0.04*8

400=P*0.32

P= 400/0.32

P= 1250

According to this, the answer is that Anna borrowed $1,250.

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2 years ago

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