A rocket is launched with an initial upward velocity of 320 feet per second from an initial height of 15 feet. The function h (t) = -1672 + 320t + 15 models the height of the rocket, in feet, t seconds after it was
launched. For how many seconds is the height of the rocket greater than or equal to 1.039 feet?

The height of the rocket is greater than or equal to 1.039 feet during first 19.936 seconds.

Step-by-step explanation:

The height of the rocket launched from the ground is modelled after the following expression:

(1)

Where:

- Time, measured in seconds.

- Height, measured in feet.

After a careful reading to the statement, we translate all relevant information into the following mathematical inequation:

(2)

After some algebra, we get the equivalent inequation:

Which means that the following conditions must be observed to satisfy the inequation above:

The height of the rocket is greater than or equal to 1.039 feet during first 19.936 seconds.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: