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2 years ago

Write the quadratic function in the form f (x) = a (x - h)2 +k.

Mathematics

1 answer:

Yakvenalex [24]2 years ago

6 0

The awnser would be f(x) = 2x2 -4x +4

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1. Sand falling from a chute forms a conical pile whose altitude is always equal to 4/3 the radius of the base. (a) How fast is

solong [7]

Answer:

The volume is increasing at a rate of 16286 in³/min.

Step-by-step explanation:

a) The volume of a cone is given by:

$V = \frac{1}{3}h\pi r^{2}$

Where:

r: is the radius

h: is the height

The rate of change of the volume can be calculated by using the chain rule:

$\frac{dV}{dt} = \frac{\pi}{3}[\frac{dh}{dt}r^{2} + h\frac{d(r^{2})}{dt}]$

Since h = 4/3 r we have:

$\frac{dV}{dt} = \frac{\pi}{3}[\frac{d(\frac{4r}{3})}{dt}r^{2} + \frac{4r}{3}\frac{d(r^{2})}{dt}]$

$\frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + r\frac{d(r^{2})}{dt}]$

$\frac{dV}{dt} = \frac{4\pi}{9}[\frac{dr}{dt}r^{2} + 2r^{2}\frac{dr}{dt}]$ (1)

With:

$\frac{dr}{dt}$ = 3 in/min

$r = 3 ft*\frac{12 in}{1 ft} = 36 in$

And by entering the above values into equation (1) we have:

$\frac{dV}{dt} = \frac{4\pi}{9}[(3 in/min)*(36 in)^{2} + 2*(36 in)^{2}*3 in/min]$

$\frac{dV}{dt} = 16286 in^{3}/min$

Therefore, the volume is increasing at a rate of 16286 in³/min.

I hope it helps you!

3 0

3 years ago

Shelly states that the triangles below are similar. Which proportion supports her statement?

OLga [1]

Answer:

$\frac{NO}{ST}$ = $\frac{NM}{SR}$ = $\frac{OM}{RT}$

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

What is the slope of the line? A. 0 B. 1 C. undefined D. infinity

Tanya [424]

Learn this...
HOY -- horizontal line, 0 slope, represented by y = a number
VUX -- vertical line, undefined slope, represented by x = a number

ok....so ur graph shows a vertical line....and a vertical line has an undefined slope

7 0

2 years ago

Help please

algol [13]

An Ecosystem is a community of living organisms in conjunction with the nonliving components of their environment, interacting as a system. These biotic and abiotic components are linked together through nutrient cycles and energy flows. Energy enters the system through photosynthesis and is incorporated into plant tissue. By feeding on plants and on one another, animals play an important role in the movement of matter and energy through the system. They also influence the quantity of plant and microbial biomass present. By breaking down dead organic matter, decomposers release carbon back to the atmosphere and facilitate nutrient cycling by converting nutrients stored in dead biomass back to a form that can be readily used by plants and other microbes.

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6 0

2 years ago

HURRY

malfutka [58]

Answer:

x = 3.

Step-by-step explanation:

1. Add 2 + 7, and you get 9.

2. Now find what 3 multiplied by what equals 9.

3. 3 x 3 = 9.

4. Therefore, x = 3.

5. 3 x 3 - 2 = 7.

4 0

3 years ago

Read 2 more answers