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Leni [432]
3 years ago
12

Please help me with these questions! Will mark brainlist!

Mathematics
2 answers:
Sophie [7]3 years ago
7 0

Answer:

For part one 30000 and the slope for part two is -2000 and for part three it is y=30000=2000x.

Step-by-step explanation:

If it starts at 30,000 then that is on the 0 on the x-axis.

While the plane is descending by 2000 so that is the slope but because it is descending and not rising it is -2000. If it was rising it would be 2000.

And for part three because it starts and 30000 and it goes down 2000 by the x-axis.

Hope this helps.

Zielflug [23.3K]3 years ago
4 0

Answer:

-2,000

30,000

Y = 30,000-2,000X

Step-by-step explanation:

It decscends - 2000 feet

it has a [asitive slope and that is 30,000

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How many solutions are there to x - 2 = 5? How many solutions are there to x - 2 > 5? Explain, use complete sentences. ( 30 P
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There is only one solution on the first one since you can't get 5 any other time then it being 7.

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Can someone please help me with this
Mama L [17]

Answer:

27.

<em>Equation of 2 tangent lines at the given curve going through point P is:</em>

<em>y = -7x + 1</em>

<em>y = x + 1</em>

28.

<u>Part 1:</u>  400 feet

<u>Part 2:</u>  Velocity is +96 feet/second (or 96 feet/second UPWARD)  & Speed is 96 feet per second

<u>Part 3:</u>  acceleration at any time t is -32 feet/second squared

<u>Part 4:</u>  t = 10 seconds

29.

<u>Part 1:</u>  Average Rate of Change = -15

<u>Part 2:</u>  The instantaneous rate of change at x = 2 is -8  &  at x = 3 is -23

<u />

Step-by-step explanation:

27.

First of all, the equation of tangent line is given by:

y-y_1=m(x-x_1)

Where m is the slope, or the derivative of the function

Now,

If we take a point x, the corresponding y point would be x^2-3x+5, so the point would be  (x,x^2-3x+5)

Also, the derivative is:

f(x)=x^2-3x+5\\f'(x)=2x-3

Hence, we can equate the DERIVATIVE (slope) and the slope expression through the point given (0,1) and the point we found (x,x^2-3x+5)

The slope is  \frac{y_2-y_1}{x_2-x_1}

So we have:

\frac{x^2-3x+5-1}{x-0}\\=\frac{x^2-3x+4}{x}

Now, we equate:

2x-3=\frac{x^2-3x+4}{x}

We need to solve this for x. Shown below:

2x-3=\frac{x^2-3x+4}{x}\\x(2x-3)=x^2-3x+4\\2x^2-3x=x^2-3x+4\\x^2=4\\x=-2,2

So, this is the x values of the point of tangency. We evaluate the derivative at these 2 points, respectively.

f'(x)=2x-3\\f'(-2)=2(-2)-3=-7\\f'(2)=2(2)-3=1

Now, we find 2 equations of tangent lines through the point (0,1) and with respective slopes of -7 and 1. Shown below:

y-y_1=m(x-x_1)\\y-1=-7(x-0)\\y-1=-7x\\y=-7x+1

and

y-y_1=m(x-x_1)\\y-1=1(x-0)\\y-1=x\\y=x+1

<em>So equation of 2 tangent lines at the given curve going through point P is:</em>

<em>y = -7x + 1</em>

<em>y = x + 1</em>

<em></em>

28.

<u>Part 1:</u>

The highest point is basically the maximum value of the position function. To get maximum, we differentiate and set it equal to 0. Let's do this:

s(t)=160t-16t^2\\s'(t)=160-32t\\s'(t)=0\\160-32t=0\\32t=160\\t=\frac{160}{32}\\t=5

So, at t = 5, it reaches max height. We plug in t = 5 into position equation to find max height:

s(t)=160t-16t^2\\s(5)=160(5)-16(5^2)\\=400

max height = 400 feet

<u>Part 2:</u>

Velocity is speed, but with direction.

We also know the position function differentiated, is the velocity function.

Let's first find time(s) when position is at 256 feet. So we set position function to 256 and find t:

s(t)=160t-16t^2\\256=160t-16t^2\\16t^2-160t+256=0\\t^2-10t+16=0\\(t-2)(t-8)=0\\t=2,8

At t = 2, the velocity is:

s'(t)=v(t)=160-32t\\v(2)=160-32(2)\\v(2)=96

It is going UPWARD at this point, so the velocity is +96 feet/second or 96 feet/second going UPWARD

The corresponding speed (without +, -, direction) is simply 96 feet/second

<u>Part 3:</u>

We know the acceleration is the differentiation of the velocity function. let's find it:

v(t)=160-32t\\v'(t)=a(t)=-32

hence, the acceleration at any time t is -32 feet/second squared

<u>Part 4:</u>

The rock hits the ground when the position is 0 (at ground). So we equate the position function, s(t), to 0 and find time when it hits the ground. Shown below:

s(t)=160t-16t^2\\0=160t-16t^2\\16t^2-160t=0\\16t(t-10)=0\\t=0,10

We disregard t = 0 because that's basically starting. So we take t = 10 seconds as our answer and we know rock hits the ground at t = 10 seconds.

29.

<u>Part 1:</u>

The average rate of change is basically the slope, which is

Slope = Change in y/ Change in x

The x values are given, from 2 to 3, and we need to find corresponding y values by plugging in the x values in the function. So,

When x = 2,  y=f(2)=-(2)^3 + 4(2) + 2=2

When x = 3,  y=f(3)=-(3)^3 + 4(3) + 2=-13

Hence,

Average Rate of Change = \frac{-13-2}{3-2}=-15

<u>Part 2:</u>

The instantaneous rate of change is got by differentiating the function and plugging the 2 points and finding the difference.

First, let's differentiate:

f(x)=-x^3+4x+2\\f'(x)=-3x^2+4

Now, find the derivative at 3,

f'(x)=-3x^2+4\\f'(3)=-3(3)^2+4=-23

finding derivative at 2,

f'(x)=-3x^2+4\\f'(2)=-3(2)^2+4=-8

The instantaneous rate of change at x = 2 is -8  &  at x = 3 is -23

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