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enyata [817]
3 years ago
7

Really need to someone to break this down so I can understand it

Mathematics
1 answer:
nignag [31]3 years ago
4 0

Answer:

Part A)

The slope is two.

Part B)

\displaystyle y = 2x - 7

Step-by-step explanation:

Part A)

We want to find the slope of the curve:

\displaystyle y = x^2 - 2x - 3

At the point P(2, -3) by using the limit of the secant slopes through point P.

To find the limit of the secant slopes, we can use the difference quotient. Recall that:

\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}

Since we want to find the slope of the curve at P(2, -3), <em>x</em> = 2.

Substitute:

\displaystyle f'(2) = \lim_{h \to 0} \frac{f(2 + h) - f(2)}{h}

Simplify. Note that f(2) = -3. Hence:

\displaystyle \begin{aligned}  f'(2) &= \lim_{h\to 0} \frac{\left[(2+h)^2 - 2(2+h) - 3\right] - \left[-3\right]}{h} \\ \\ &=\lim_{h \to 0}\frac{(4 + 4h + h^2)+(-4-2h)+(0)}{h}  \\ \\ &= \lim_{h\to 0} \frac{h^2+2h}{h}\\ \\&=\lim_{h\to 0} h + 2 \\ \\ &= (0) + 2 \\ &= 2\end{aligned}

(Note: I evaluated the limit using direct substitution.)

Hence, the slope of the curve at the point P(2, -3) is two.

Part B)

Since the slope of the curve at point P is two, the slope of the tangent line is also two.

And since we know it passes through the point (2, -3), we can consider using the point-slope form:

\displaystyle y - y_1 = m(x-x_1)

Substitute. <em>m</em> = 2. Therefore, our equation is:

\displaystyle y + 3 = 2(x-2)

We can rewrite this into slope-intercept if desired:

\displaystyle y = 2x - 7

We can verify this by graphing. This is shown below:

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What are the quotient and remainder of (x^5-x^3+-5) divided by (x-2)
pishuonlain [190]

Answer:

x⁴+2x³ +3x²+6x +12 r. \dfrac{19}{x-2}

Step-by-step explanation:

You can do this through synthetic division. It is a shorthand way of dividing polynomials.

First you need to make your divisor equal to zero so you can solve for what goes into the division box:

x - 2 = 0 →     x = 2

The next step is to arrange your polynomials in descending powers. All missing terms, you will put in a zero.

x⁵ - x³ + (-5)   →  x⁵ + 0x⁴- x³ + 0x² + 0x + (-5)

Now you can proceed to synthetic division. Make an upside down division box with the divisor outside and the coefficients of the dividend listed, along with their sign. Leave a space below the divident

+2 |   +1     0     -1     0     0     -5

    |<u>                                              </u>

Next you bring down the first coefficient:

+2 |   +1     0     -1     0     0     -5

    |<u>                                              </u>

        +1    

Then you multiply it by the divisor and write the product under the next coefficient:

+2 |   +1     0     -1     0     0     -5

    |<u>           +2                                   </u>

        +1    

Next add the column and put the sum below it:

+2 |   +1     0     -1     0     0     -5

    |<u>          +2                                   </u>

        +1    +2

Then multiply again and repeat until you reach the last coefficient:

+2 |   +1     0     -1     0     0     -5

    |<u>          +2    +4   +6   +12   +24 </u>

        +1    +2    +3   +6   +12    +19

Now that you have your results, add  in the x and their powers. The powers will start with the highest power but 1 less than the dividend. Since the dividend's highest power is 5, then the quotient's highest power will be 4. Then write it in descending order :

+1x⁴    +2x³    +3x²   +6x   +12   +19

Now the last coefficient is your remainder. So your results will be:

x⁴+2x³ +3x²+6x +12 r. \dfrac{19}{x-2}

7 0
3 years ago
Read 2 more answers
Plss help. I am having trouble with question (d).​
Mama L [17]

Answer:

im not sure...cuz it says 50%

its either 11.625 or 5.8125

it is the 1st one if the question means all average but if not PROBABLY only PROBABLY the right one

Step-by-step explanation:

I added all the hours together and divided it by 24 to get 11.625 but if the ans is 5.1825 ill divide 11.625 over 2

5 0
3 years ago
A machine cuts 25 circuit boards every 5 minutes. What is the unit rate of production for the machine?
irina1246 [14]

Answer:

25 divided by 5 = 5, so the unit rate is 5 circuit boards every minute.

8 0
3 years ago
Help me someone!!!!!!!!!!!!!!!!!!!!!!!
Julli [10]
Substitute answers in, a = 3 and b = 2.

(3^2 - 2^2)/(3+2)
= (9-4)/5
= 5/5
= 1
7 0
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A fisherman positions his net to -8 relative to the surface of the water. how far does he need to raise the net to bring it to t
8_murik_8 [283]

Answer: If i am correct the answer should be 9-10 because if it is -8 it takes 8 to bring it to 0 and it takes 9 to bring it to 1 and it takes 10 to bring it to 2.

Hope this helps!

6 0
3 years ago
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