Chau bought 28 pounds of flour for $12. How many dollars did he pay per pound of flour?

Mathematics

1 answer:

Nostrana [21]3 years ago

5 0

Answer:

Step-by-step explanation: 28 divided by 12 = $2.33 per pound of flour.

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saveliy_v [14]

Answer:

After 1.5 second of throwing the ball will reach a maximum height of 44 ft.

Step-by-step explanation:

The height in feet of a ball after t seconds of throwing is given by the function

h = - 16t² + 48t + 8 .......... (1)

Now, condition for maximum height is

$\frac{dh}{dt} = 0 = - 32t + 48$ {Differentiating equation (1) with respect to t}

⇒ $t = \frac{48}{32} = 1.5$ seconds.

Now, from equation (1) we get

h(max) = - 16(1.5)² + 48(1.5) + 8 = 44 ft.

Therefore, after 1.5 seconds of throwing the ball will reach a maximum height of 44 ft. (Answer)

4 0

3 years ago

The boundary of the lawn in front of a building is represented by the parabola . The parabola is represented on the coordinate p

Colt1911 [192]

The boundary of the lawn in front of a building is represented by the parabola

y = (x^2) /16 + x - 2

And you have three questions which require to find the focus, the vertex and the directrix of the parabola.

Note that it is a regular parabola (its symmetry axis is paralell to the y-axis).

1) Focus:

It is a point on the symmetry axis => x = the x-component of the vertex) at a distance equal to the distance between the directrix and the vertex).

In a regular parabola, the y - coordinate of the focus is p units from the y-coordinate of the focus, and p is equal to 1/(4a), where a is the coefficient that appears in this form of the parabola's equation: y = a(x - h)^2 + k (this is called the vertex form)

Then we will rearrange the standard form, (x^2)/16 + x - 2 fo find the vertex form y = a(x-h)^2 + k

What we need is to complete a square. You can follow these steps.

1) Extract common factor 1/16 => (1/16) [ (x^2) + 16x - 32]

2) Add (and subtract) the square of the half value of the coefficent ot the term on x =>

16/2 = 8 => add and subtract 8^2 => (1/16) [ (x^2) + 16 x + 8^2 - 32 - 8^2]

3) The three first terms inside the square brackets are a perfect square trinomial: =>

(1/16) [ (x+8)^2 - 32 - 64] = (1/16) [ (x+8)^2 - 96] =>

(1/16) [(x+8)^2 ] - 96/16 =>

(1/16) (x +8)^2 - 6

Which is now in the form a(x - h)^2 + k, where:

a = 1/16 , h = - 8, and k = -6

(h,k) is the vertex: h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

=> a = 1/16 => p =1/4a = 16/4 = 4

y-componente of the focus = -6 + 4 = -2

x-component of the focus = h = - 8

=> focus = (-8, -2)

2) Vertex

We found it above, vertex = (h,k) = (-8,-6)

3) Directrix

It is the line y = p units below the vertex = > y = -6 - 4 = -10

y = -10

4 0

4 years ago

three points have coordinates A(-1,2),B(3,10)and C(p,8).Find the value (s) of p if AC is perpendicular to BC.

Reil [10]

Step-by-step explanation:

All steps are in pic above.

Note:if you have any questions about it let me know.