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2 years ago

Evaluate the expression P(6,1)

Mathematics

1 answer:

klasskru [66]2 years ago

5 0

Answer:

p(6,3)=120

Step-by-step explanation:

In the pic is how to do it

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find the equations of the tangents to the curve y= x(x-1)(x+2) at the points where the curve cuts the x axis

antoniya [11.8K]

First of all, we compute the points of interest, i.e. the points where the curve cuts the x axis: since the expression is already factored, we have

$x(x-1)(x+2) = 0 \iff x=0\ \lor\ x-1=0\ \lor\ x+2=0$

Which means that the roots are

$x=0\ \lor\ x=1\ \lor\ x=-2$

Next, we can expand the function definition:

$y = x(x-1)(x+2) = x^3 + x^2 - 2x$

In this form, it is much easier to compute the derivative:

$y' = 3x^2+2x-2$

If we evaluate the derivative in the points of interest, we have

$y'(-2) = 6,\quad y'(0)=-2,\quad y'(1)=3$

This means that we are looking for the equations of three lines, of which we know a point and the slope. The equation

$y-y_0=m(x-x_0)$

is what we need. The three lines are:

$y-0=6(x+2) \iff y = 6x+12$ This is the tangent at x = -2

$y-0=-2(x-0) \iff y = -2x$ This is the tangent at x = 0

$y-0=3(x-1) \iff y = 3x-3$ This is the tangent at x = 1

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2 years ago

Samantha needs 9 feet of fencing to make repairs from a storm. If the hardware store sells fencing only in yards, how much

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It's C. because 3 yards is 9 feet

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2 years ago

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Dilate a triangle with vertices (0,0), (0,2) and (2,0) using the scale factor k=3. What is the value of the ratio (new to origin

seropon [69]

Answer:

Part a) The ratio of the perimeters is $3$

Part b) The ratio of the areas is $9$

Step-by-step explanation:

Part A) What is the value of the ratio (new to original) of the perimeters?

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z-----> the scale factor

x-----> the perimeter of the new triangle

y-----> the perimeter of the original triangle

$z=\frac{x}{y}$

we have

$z=3$

substitute

$\frac{x}{y}=3$

Part B) What is the value of the ratio (new to original) of the areas?

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

x-----> the area of the new triangle

y-----> the area of the original triangle

$z^{2}=\frac{x}{y}$

we have

$z=3$

substitute

$\frac{x}{y}=3^{2}$

$\frac{x}{y}=9}$

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3 years ago

What can i do to inprove my math skills

myrzilka [38]

Answer:

Practice, study, get involved in school activities involving math, don’t get too stressed out when it doesn't work, and always try again.

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2 years ago

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A road is made in such a way that the center of the road is higher off the ground than the sides of the road, in order to allow

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Remark.

The problem is a bit indistinct. Where exactly are the two edges of the road? I'm going to say that they are the x intercepts, but that may not be true. Certainly it does not have to be true at all.

Graph.

A graph has been made for you. The maximum is marked for you. It is an approximation The actual height can be more accurately found.

Height

y = (-1/200)(x - 16)(x + 16)

y = (-1/200)*(x^2 - 256)

The maximum height for this graph only is when x = 0.Other graphs require completing the square.

y = (-1/200) * (-256)

y = 1.28 exactly. I thought the graph might be rounding the answer. It is not.

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3 years ago

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