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3 years ago

Is this a A.M or P.M activity? Thank you in advance.

Mathematics

1 answer:

Margarita [4]3 years ago

3 0

This is an A.M. activity because normally, you would go to classes during the morning.
Hope this helps!

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Please help me with these calculus bc questions

zhannawk [14.2K]

4. Compute the derivative.

$y = 2x^2 - x - 1 \implies \dfrac{dy}{dx} = 4x - 1$

Find when the gradient is 7.

$4x - 1 = 7 \implies 4x = 8 \implies x = 2$

Evaluate $y$ at this point.

$y = 2\cdot2^2-2-1 = 5$

The point we want is then (2, 5).

5. The curve crosses the $x$ -axis when $y=0$ . We have

$y = \dfrac{x - 4}x = 1 - \dfrac4x = 0 \implies \dfrac4x = 1 \implies x = 4$

Compute the derivative.

$y = 1 - \dfrac4x \implies \dfrac{dy}{dx} = -\dfrac4{x^2}$

At the point we want, the gradient is

$\dfrac{dy}{dx}\bigg|_{x=4} = -\dfrac4{4^2} = \boxed{-\dfrac14}$

6. The curve crosses the $y$ -axis when $x=0$ . Compute the derivative.

$\dfrac{dy}{dx} = 3x^2 - 4x + 5$

When $x=0$ , the gradient is

$\dfrac{dy}{dx}\bigg|_{x=0} = 3\cdot0^2 - 4\cdot0 + 5 = \boxed{5}$

7. Set $y=5$ and solve for $x$ . The curve and line meet when

$5 = 2x^2 + 7x - 4 \implies 2x^2 + 7x - 9 = (x - 1)(2x+9) = 0 \implies x=1 \text{ or } x = -\dfrac92$

Compute the derivative (for the curve) and evaluate it at these $x$ values.

$\dfrac{dy}{dx} = 4x + 7$

$\dfrac{dy}{dx}\bigg|_{x=1} = 4\cdot1+7 = \boxed{11}$

$\dfrac{dy}{dx}\bigg|_{x=-9/2} = 4\cdot\left(-\dfrac92\right)+7=\boxed{-11}$

8. Compute the derivative.

$y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b$

The gradient is 8 when $x=2$ , so

$2a\cdot2 + b = 8 \implies 4a + b = 8$

and the gradient is -10 when $x=-1$ , so

$2a\cdot(-1) + b = -10 \implies -2a + b = -10$

Solve for $a$ and $b$ . Eliminating $b$ , we have

$(4a + b) - (-2a + b) = 8 - (-10) \implies 6a = 18 \implies \boxed{a=3}$

so that

$4\cdot3+b = 8 \implies 12 + b = 8 \implies \boxed{b = -4}$ .

5 0

2 years ago

Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.

m_a_m_a [10]

Answer:

Line of "rise": (0, 3) to (0, 0) ==> -3 units

Line of "run": (0, 0) to (1, 0) ==> 1 unit

Slope: rise/run ==> -3/1

Step-by-step explanation:

Slope is basically a ratio of changes in the y-value to changes in the x-value. What I mean by that is the slope shows how much the line goes up or down compared to how much the line goes left or right. In this case, the line goes right one unit for every 3 units the line goes down. Taking a look at the portion of the line in Quadrant 1 (top right quadrant), the line starts at (0, 3) and ends at (1, 0). I guess that's another way to figure out slope, too: line up the two coordinates (the leftmost one above the rightmost one), and add or subtract.

Like this:

(0, 3)

+1 -3

Since the formula for slope is rise/run (y-difference/x-difference), the slope is therefore -3/+1, or simply -3/1. (You don't include plus signs.)

3 0

3 years ago

A runner did the 100 meter dash in 9.9 seconds and the 100 yard dash in the same amount of time . In which race did he run the f

RideAnS [48]

He ran the fastest in the second run

4 0

3 years ago

-a^2b^2c^2(a+b-c) find the product

irakobra [83]

Answer:

-a^3b^2c^2-a^2b^3c^2+a^2b^2c^3

I hope it will be useful.

5 0

3 years ago

PLEASE HELP

Dima020 [189]

Answer:

55565555555 bLa bla.bla bla bla.bla uebsuenIemekmjenejnsjNejiyneiyneiyneiyneisneIneInJeJeE

3 0

3 years ago