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2 years ago

What is the range of the function f(x) = 4 − 2(x + 3)^2?

Mathematics

1 answer:

mash [69]2 years ago

4 0

Answer:

(-infinity, 4]

Step-by-step explanation:

The range is the possible y values

The smallest that (x+3)^2 can be is zero

f(x) = 4 − 2(x + 3)^2

f(x) = 4 -2(0) = 4

This is the maximum value

As the square term gets bigger we are subtracting a larger amount and it will get more negative

Let x = infinity, x+3 = infinity and infinity ^2 = infinity and 2* infinity = infinity

f(x) = 4 - infinity

= -infinity

The range is -infinity to 4

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The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in min

Deffense [45]

Answer:

f'(t) is negative

The unit is degC/min

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.

Step-by-step explanation:

From the question we are told we are told that

The equation for the temperature of a cup of coffee place on a counter is

$H= f(t)$

Here t is the time in minutes the coffee was put on the counter

Generally f(t)' is the derivative of f(t) at it represents the change of the temperature of the cup of coffee with respect to time

Generally for the coffee placed on the counter after a couple of minutes the temperature will decrease hence f(t)' is negative

Generally the unit of the temperature is in degrees Celsius while that of time is in minutes

So the change in temperature with time f(35)' will be in degrees Celsius/minutes (i.e degC/min)

From the question we are told that

$|f(35)'| = 1.5$

i.e the rate of change of temperature after 35 minutes is 1.5

and

$|f(35)| = 68$

i.e the temperature of the cup of coffee after 35 minutes is 67 degC

Now after another t= 30 seconds = $\frac{30}{60}= 0.5 \ minutes$ the rate of change of the temperature of the cup of coffee is

$R = |f(35)'| * t$

=> $R = 1.5 * 0.5$

=> $R = 0.75$

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.

5 0

3 years ago

if a toy rocket is launced vertically upward from ground level with an inital velocity of 128 feet per second, then its high h,

makkiz [27]

The toy rocket hits the ground when h(t) = 0.
So, h(t) = 0 = -9t^2 + 81.

Solving the equation,
-9t^2 = -81
Dividing by -9
t^2 = 9
Taking the square root.
t = 3

The answer is 3 seconds.

7 0

3 years ago

A golf course charges $16 for a package including the full 18-hole course. The course also sells buckets of

MA_775_DIABLO [31]

16x + 21y = 555

Step-by-step explanation:

Let x be the no. of 18-hole course

And y be the no. of golf balls

16x + 21y = 555

6 0

3 years ago

Each face of a number cube is a square with a side length of 16 millimeters. What is the total area of all of the faces of the n

kupik [55]

Answer:

1536² mm

Step-by-step explanation:

16 x 16 = 256

256 x 6 = 1536 (6 = number of faces)

1536²mm

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2 years ago

Which of the following is not a diameter? SV RU WT

snow_tiger [21]

WT
It does not perfectly cut the circle in half.

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2 years ago

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