Determine the direction that this parabola opens y=-5x^2-10x-15

1 answer:

8 0

The parabola opens down.

If the a value is positive it opens up. If it's negative it opens down. If it is 0, it's not quadratic. The a value here is -5

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a solid sphere is cut into 3 equal wedges. the volume of each wedge is V=4/9π^3. solve the formula for r

algol13

$\\ \qquad\quad\sf{:}\dashrightarrow V=\dfrac{4}{9}πr^3$

It is one third of the solid. sphere

$\\ \qquad\quad\sf{:}\dashrightarrow V_{(Sphere)}$

$\\ \qquad\quad\sf{:}\dashrightarrow 3\left(\dfrac{4}{9}πr^3\right)$

$\\ \qquad\quad\sf{:}\dashrightarrow \dfrac{4}{3}\pi r^3$

Now

$\\ \qquad\quad\sf{:}\dashrightarrow \pi r^3=\dfrac{3V}{4}$

$\\ \qquad\quad\sf{:}\dashrightarrow r^3=\dfrac{3V}{4\pi}$

$\\ \qquad\quad\sf{:}\dashrightarrow r=\sqrt[3]{\dfrac{3V}{4\pi}}$

4 0

3 years ago

Read 2 more answers

Ann is adding water to a swimming pool at a constant rate. The table below shows the amount of water in the pool after different

N76 [4]

Answer:

(a) As time increases, the amount of water in the pool increases.

11 gallons per minute

(b) 65 gallons

Step-by-step explanation:

From inspection of the table, we can see that as time increases, the amount of water in the pool increases.

We are told that Ann adds water at a constant rate. Therefore, this can be modeled as a linear function.

The rate at which the water is increasing is the rate of change (which is also the slope of a linear function).

Choose 2 ordered pairs from the table:

$\textsf{let}\:(x_1,y_1)=(8, 153)$

$\textsf{let}\:(x_2,y_2)=(12,197)$

Input these into the slope formula:

$\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{197-153}{12-8}=\dfrac{44}{4}=11$

Therefore, the rate at which the water in the pool is increasing is:

11 gallons per minute

To find the amount of water that was already in the pool when Ann started adding water, we need to create a linear equation using the found slope and one of the ordered pairs with the point-slope formula:

$y-y_1=m(x-x_1)$