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Ad libitum [116K]

1 year ago

15

. A rocket carrying fireworks is launched from a hill above a lake. The rocket will fall into lake after exploding at its maximu

m height. The rocket's height above the surface of the lake is given by h(t) = −16t 2 + 64t + 80, where h is in feet and t is in seconds

1 answer:

RoseWind [281]1 year ago

8 0

Answer:

Step-by-step explanation:

Since we are not told what to find, we can as well find the time taken by the rocket to reach its maximum height as shown

The rocket reaches its maximum height when the velocity is zero

v = dh/dt

v = -32t+64

Since v = 0 at maximum height

0 = -32t+64

32t = 64

t = 64/32

t = 2secs

Hence the rocket reaches the maximum height after 2secs

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Let d(t) be the total number of miles Joanna has cycled, and let t represent the number of hours after stopping for a break duri

katrin [286]

For this case we have the following equation:
$d (t) = 12t + 20
$
The variables are:
t: time in hours
d (t): distance traveled in miles.
We evaluate the distance traveled after 4 hours.
So we have that for t = 4:
$d (4) = 12 (4) +20

d (4) = 48 + 20

d (4) = 68$
Answer:
d (4) = 68
This means that after 4 hours Joanna cycled for 68 miles total

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2 years ago

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what are the solution(s) to the quadratic equation x2 – 25 = 0? x = 5 and x = –5 x = 25 and x = –25 x = 125 and x = –125 no real

sattari [20]

The left hand side expression of the given equation is a difference of two squares. The first term, x², is a square of x and the second term, 25 is the square of 5. The factors of the expression are (x - 5) and (x + 5).
(x - 5)(x + 5) = 0
The values of x from the equation above are x = -5 and x = 5.

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2 years ago

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A waterbed filled with water has the dimensions 8ft by 7 ft by .75 ft taking the density of water to be 1.00/gm cubed how many k

monitta

By definition, the density is given by:

$D = \frac{m}{V}$

Where,

m: mass

V: volume

Clearing the mass we have:

$m = DV$

The volume is given by:

$V = (8) * (7) * (0.75)$

$V = 42ft ^ 3$

Then, we have the following conversion:

$1foot = 0.3048m$

Applying the conversion we have:

$V = 42 * (0.3048) ^ 3$

$V = 1.19m ^ 3$

On the other hand we have the following conversions:

$1m = 100cm$

$1Kg = 1000g$

Applying the conversions for the density we have:

$D = (1\frac{g}{cm^3})((\frac{100}{1})^3\frac{cm^3}{1m^3})(\frac{1}{1000}\frac{Kg}{g})=1000\frac{Kg}{m^3}$

Then, the mass of the water is:

$m = (1000) * (1.19)$

$m = 1190$

Answer:

1190 kilgrams of water are required to fill the waterbed

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1 year ago

The product of a binomial and a trinomial is x 3 + 3 x 2 − x + 2 x 2 + 6 x − 2. Which expression is equivalent to this product a

valkas [14]

Answer:

$x^3+3x^2+5x+2$

Step-by-step explanation:

The product of a binomial and a trinomial is

$x^3+3x^2-x+2 \times 2 +6x-2$

we have to simplify that

$x^3+3x^2-x+4+6x-2$

bringing the like terms together we get

$x^3+3x^2-x+6x+4-2$

$-x+6x = 5x$

$-2+4 = 2$

hence our expression becomes

$x^3+3x^2-x+6x+4-2=x^3+3x^2+5x+2$

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1 year ago

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14.75x - 2.3 = 5.25x + 45.2

Cerrena [4.2K]

14.75x - 23=5.25x+45.2
14.75x-23-5.25x=5.25x+45.2-5.25x
14.75-5.25x=9.5
9.5x-23=45.2
9.5x-23+23=45.2+23
9.5x=68.2
9.5x/9.5=68.2/9.5
x=7.178947

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1 year ago

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