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inn [45]
3 years ago
13

Consider the curve y = x − x^3, find the slope of the tangent line to the curve at the point (1, 0).

Mathematics
1 answer:
lbvjy [14]3 years ago
7 0

The derivative of a function, such as the one given above, represents the slope of the tangent line to the curve at the given point.

In this case, y = x − x^3, and dy/dx = 1 - 3x^2.  Letting x = 1, we get the slope of the tangent line at the point (1,0):  1 - 3(1^2) = -2 (answer)

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A rectangular parking lot has a length that is 5 yards greater than the width the area of the parking lot is 300 yd.² find the l
ArbitrLikvidat [17]

Answer:

width=5yd and length=10yd

Step-by-step explanation:

To solve this problem, you need to start by asking what you do and don't know (always where to start with word problems)

We know that Area (A) = Length (L) * Width (W)

You know Area (A) = 50 sq. yds.

You don't know anything about the width, so let's just say Width (W) = x

And you know that the length is 5 yds longer than the width, so L = W + 5yd and, since W = x, we can say L = x + 5yd

Now, we recall that A = L * W, and, since A = 50, we can say 50 sq yd = L * W.

Well, now just plug in. What does W equal and L equal?

From above we plug in and can say that 50 sq yd = x * (x + 5 yd).

Multiply it out and you get 50 = x^2 + 5x (removing units for a moment so they don't clutter the lines).

Now there are a number of ways to solve this. You can tell (because of the "x^2") that it is quadratic. So let's get it equal to zero:

0 = x^2 + 5x - 50

Now you can factor it, use your quadratic formula, or (if you hated yourself) do it as a completing the square problem. I'm going to factor.

I can see from going through a list in my head that the factors 10 and -5 multiply to -50 and add to 5, so I know that

0 = x^2 + 5x - 50 = (x + 10)(x - 5)

And so you know that x = -10 or 5.

Well, you know the parking lot cannot be -10 yd long. So we must say that W = x = 5, and, since L = W + 5, then L = 5+5 = 10. So your width is 5 yd and length is 10 yd.

<h2>mark me brainlist</h2>
6 0
2 years ago
I need to know how to solve these
My name is Ann [436]
1. make an equation
4x+7(20) = 5(x+20)
2. multiply the numbers and distribute 5 through the parenthesis
4x+140 = 5x+100
3. move variables to the left side and change its sign and move constant to the right side and change its sign
4x-5x = 100-140
4. collect the like terms and calculate the difference
-x = -40
5. change the signs on both sides of the equation
x = 40
he needs to use 40 pounds of the cheaper coffee.
hope this helped!
4 0
3 years ago
Please help ASAP
sashaice [31]
I don’t know I’m only in 7th grade but 56
3 0
3 years ago
1. What is the y-intercept in the table below?
11Alexandr11 [23.1K]

Answer:

EWAN KO DYA DI AKO MATH EXPERT

Step-by-step explanation:

POIU

5 0
3 years ago
The length of a rectangle is five inches less than twice it’s width. If the rectangle has a perimeter of 80 inches, find the len
yawa3891 [41]

Answer:

Width of the rectangle  = 15 inches

Length of the rectangle  = 25 inches

Step-by-step explanation:

Let the width of the rectangle =  k inches

So, the length of the rectangle =   (2k -5) inches

Perimeter = 80 in

Perimeter of a rectangle = 2 (Length + Width)

⇒  80 = 2(k + (2k -5)

or 80 = 6k - 10

⇒ 6k = 80 + 10 = 90

or  k = 90 / 6

⇒ k = 15

So the width of the rectangle  = k  = 15 inches

And the length of the rectangle =  2k -5 = 2 x 25  - 5 = 25 inches

5 0
3 years ago
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