Answer:
3.1
Step-by-step explanation:
ok so
4.7j-6.8k J=5 k=3 plug in the values
4.7(5)-6.8(3)
23.5-20.4
3.1
<em><u>The proportion that could be used to solve for the variable is:</u></em>
![\frac{16}{40} = \frac{3}{h}](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B40%7D%20%3D%20%5Cfrac%7B3%7D%7Bh%7D)
h = 7.5
<em><u>Solution:</u></em>
Given that,
16 walls in 40 hours 3 walls in h hours
Which means,
16 walls build in 40 hours
Then 3 walls in h hours
We have to write a proportion
The number of walls and the number of hours are proportion
Therefore, we get,
![\frac{16}{40} = \frac{3}{h}](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B40%7D%20%3D%20%5Cfrac%7B3%7D%7Bh%7D)
Cross multiply and solve for h
![16 \times h = 3 \times 40\\\\16h = 120\\\\h = \frac{120}{16}\\\\h = 7.5](https://tex.z-dn.net/?f=16%20%5Ctimes%20h%20%3D%203%20%5Ctimes%2040%5C%5C%5C%5C16h%20%3D%20120%5C%5C%5C%5Ch%20%3D%20%5Cfrac%7B120%7D%7B16%7D%5C%5C%5C%5Ch%20%3D%207.5)
Thus the proportion is solved
The solution set of the equation x^2 + 2x - 48 = 0 is x = -1 ± 7
<h3>How to determine the solution set of the equation?</h3>
The equation is given as:
x^2 + 2x - 48 = 0
A quadratic equation is represented as:
ax^2 + bx + c = 0
By comparing both equations, we have
a = 1, b = 2 and c = -48
The solution of the quadratic equation is then calculated using
x = (-b ± √(b^2 - 4ac))/2a
Substitute values for a, b and c in the above equation
x = (-2 ± √(2^2 - 4 * 1 * -48))/2 * 1
This gives
x = (-2 ± √196)/2
Evaluate the square root of 196
x = (-2 ± 14)/2
Divide through by 2
x = -1 ± 7
Hence, the solution set of the equation x^2 + 2x - 48 = 0 is x = -1 ± 7
Read more about quadratic equation at:
brainly.com/question/1214333
#SPJ1
Complete Question:
Alejandro jumped from a cliff into the ocean in Acapulco while vacationing with some friends.
![h(t)=-16t^2 + 16t + 480](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E2%20%2B%2016t%20%2B%20480)
Where t is the time in seconds and h is the height in feet
(a) How long did it take for Alejandro to reach his maximum height
(b) What was the highest point Alejandro reached
(c) Alejandro hits the water after how many seconds
Answer:
(a) 0.5 seconds
(b) 484 feet
(c) 6 seconds
Step-by-step explanation:
Given
![h(t)=-16t^2 + 16t + 480](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E2%20%2B%2016t%20%2B%20480)
Solving (a): Time to reach maximum height
This is the maximum of the function and it is calculated using:
![t = -\frac{b}{2a}](https://tex.z-dn.net/?f=t%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D)
Where
![a = -16; b = 16; c =480](https://tex.z-dn.net/?f=a%20%3D%20-16%3B%20b%20%3D%2016%3B%20c%20%3D480)
So:
![t = -\frac{16}{2*-16}](https://tex.z-dn.net/?f=t%20%3D%20-%5Cfrac%7B16%7D%7B2%2A-16%7D)
![t = \frac{16}{32}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B16%7D%7B32%7D)
![t = 0.5](https://tex.z-dn.net/?f=t%20%3D%200.5)
Solving (b): Highest point reached
Time to reach the highest point is 0.5.
So, the highest point is: h(0.5)
![h(t)=-16t^2 + 16t + 480](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E2%20%2B%2016t%20%2B%20480)
![h(0.5) = -16 * 0.5^2 + 16 * 0.5 + 480](https://tex.z-dn.net/?f=h%280.5%29%20%3D%20-16%20%2A%200.5%5E2%20%2B%2016%20%2A%200.5%20%2B%20480)
![h(0.5) = 484](https://tex.z-dn.net/?f=h%280.5%29%20%3D%20484)
Solving (c): Time he hits water.
At this point, h(t) = 0
So;
![h(t)=-16t^2 + 16t + 480](https://tex.z-dn.net/?f=h%28t%29%3D-16t%5E2%20%2B%2016t%20%2B%20480)
![-16t^2 + 16t + 480 = 0](https://tex.z-dn.net/?f=-16t%5E2%20%2B%2016t%20%2B%20480%20%3D%200)
Factorize
![-16(t^2 - t -30) = 0](https://tex.z-dn.net/?f=-16%28t%5E2%20-%20t%20-30%29%20%3D%200)
Divide both sides by -16
![t^2 - t -30 = 0](https://tex.z-dn.net/?f=t%5E2%20-%20t%20-30%20%3D%200)
Expand
![t^2 + 5t - 6t - 30 = 0](https://tex.z-dn.net/?f=t%5E2%20%2B%205t%20-%206t%20-%2030%20%3D%200)
Factorize
![t(t + 5)-6(t + 5) =0](https://tex.z-dn.net/?f=t%28t%20%2B%205%29-6%28t%20%2B%205%29%20%3D0)
![(t -6)(t + 5) =0](https://tex.z-dn.net/?f=%28t%20-6%29%28t%20%2B%205%29%20%3D0)
![t =6\ or\ t = -5](https://tex.z-dn.net/?f=t%20%3D6%5C%20or%5C%20t%20%3D%20-5)
Time can't be negative.
So:
![t = 6](https://tex.z-dn.net/?f=t%20%3D%206)