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monitta
3 years ago
6

Alex drives at an average speed that is

Mathematics
1 answer:
densk [106]3 years ago
5 0

Answer:

The answer is 162.5

Step-by-step explanation:

you divide 2 by 3 and then figure out how many examples where given to find the average and multiply by that much and you get the answer.

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Consider the function f(x) = x3 − 4x2 + 2. Calculate the limit of the difference quotient at x0 = 3 for f(x).
m_a_m_a [10]
<h2>Part 1.</h2>

Answer: \boxed{f'(x)=3x^2-8x}

The limit of the difference quotient is simply the derivative, so we can express this as follows:

f'(x)=\underset{\Delta x\rightarrow0}{lim}\frac{\triangle y}{\Delta x}=\frac{f(x+\Delta x)-f(x)}{\Delta x}

So our function is:

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

Taking the derivative, we have:

f'(x)=3x^2-8x

So the correct option is:

\boxed{f'(x)=3x^2-8x}

<h2>Part 2.</h2>

Answer: \boxed{y=3x-16}

The equation of the line that passes through the same point can be found as:

y-y_{0}=m(x-x_{0})

Where x_{0}=3, so we need to find y_{0}. Plug in that x-value in the function we have:

y_{0}=f(3)=(3)^3-4(3)^2+2 \\ \\ y_{0}=-7 \\ \\ \\ So \ the \ point \ is: \\ \\ P(x_{0},y_{0})=(3,-7)

And the slope is:

m=f'(3)=3(3)^2-8(3) \\ \\ m=3

Then, the equation of the line is:

y-(-7)=3(x-3) \\ \\ \therefore y+7=3x-9 \\ \\ \boxed{y=3x-16}

<h2 /><h2>Part 3.</h2>

Answer: Shown below

As you can see below, the graph of the function of f is continuous. This is so because we have plotted a polynomial function whose domain is the set of all real numbers. So the function is defined at the point P(3,-7), so the derivative exists at this point, hence we can calculate a tangent line there. In conclusion, we get the graph shown below. The blue line is the tangent line while the red curve is the graph of f

3 0
3 years ago
In Los Angeles, a taxi owner charges $5 to rent a taxi and then $1 for each mile. Find the cost
jasenka [17]

Answer:

All in the explanation

Step-by-step explanation:

It would be a dollar for every mile traveled, in this case 10 dollars as Ms. Robinson travels 10 miles.

The starting cost would be 5 dollars to rent it and then 1 dollar for every mile.

Equation would be 1(x) + 5

The cost of Ms. Robinsons trip would be 1(10) + 5 = 15 dollars.

4 0
3 years ago
Read 2 more answers
Is $36 for 4 baseball hat equivalent to $56 for 7 baseball hat
Iteru [2.4K]
It is not.
First, divide 36 by 4.
= 9
So, 9 for each hat.
9 x 7 =63
In conclusion, it is in fact not equivalent.
4 0
3 years ago
HELLLP ME PLEASE ❤️ which one do you think it is?
Arte-miy333 [17]
3/7 for sure hope this helps
8 0
3 years ago
Read 2 more answers
PLS HELP ME I WILL MARK THE BRAINLIEST
Serga [27]

Answer:

1. 155 yd², 2. 379.54 ft², 5. x = 65.82π

Step-by-step explanation:

1. A = (1/2) · (3 + 13) · 8

A = (1/2)(16)(8)
A = 64
A = bh
A = 13*7
A = 91
64 + 91 = 155
155 yd²

2. A = bh
A = 25x25
A = 625
A = πr²
A = 3.14*12.5²
A = 3.14*156.25
A = 490.625
490.925/2 = 245.4625
625 - 245.4625 = 379.5375
379.54 ft²

3. and 4. Sorry, I don't know how to solve these

5. A = πr²
A = 3.14*7²
A = 3.14*49
A = 153.86
x/154 = 153.86π/360
360x = 154*153.86π
360x = 23694.44π
x = 65.8178889π
x = 65.82π

Hope this helps :)

7 0
3 years ago
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