Answer:
what is your question
Step-by-step explanation:
You are given the length of a rectangular prism of 3x^2, width of 2x and height of x^2 + 3x +5. You are required to find the volume of a rectangular prism. Using the equation V = l x w x h, we multiply the three dimensions.
V = l x w x h
V = (3x^2)(2x)( x^2 + 3x +5)
V = 2x (3x^4 + 9x^3 + 15x^2)
V = 6x^5 + 18x^4 + 30x^3
The volume of the rectangular prism is 6x^5 + 18x^4 + 30x^3.
Answer: 11
Step-by-step explanation:
Exponential Functions:
y=ab^x
y=ab
x
a=\text{starting value = }550
a=starting value = 550
r=\text{rate = }18.8\% = 0.188
r=rate = 18.8%=0.188
\text{Exponential Decay:}
Exponential Decay:
b=1-r=1-0.188=0.812
b=1−r=1−0.188=0.812
\text{Write Exponential Function:}
Write Exponential Function:
y=550(0.812)^x
y=550(0.812)
x
Put it all together
\text{Plug in y-value:}
Plug in y-value:
60=550(0.812)^x
60=550(0.812)
x
\frac{60}{550}=\frac{550(0.812)^x}{550}
550
60
=
550
550(0.812)
x
Divide both sides by 550
0.109091=0.812^x
0.109091=0.812
x
\log 0.109091=\log 0.812^x
log0.109091=log0.812
x
Take the log of both sides
\log 0.109091=x\log 0.812
log0.109091=xlog0.812
use power rule to bring x to the front
\frac{\log 0.109091}{\log 0.812}=\frac{x\log 0.812}{\log 0.812}
log0.812
log0.109091
=
log0.812
xlog0.812
Divide both sides by log(0.812)
10.638757=x
10.638757=x
x\approx 11
x≈11
15 performances can be accommodated
<em><u>Solution:</u></em>
Given that,
Each performer for the talent show has 7 minutes for his or her performance
The introduction for the talent show is 25 minutes long
The entire show including the introduction, will last 130 minutes
Thus the remaining time for performances is:
Performance time = 130 minutes - 25 minutes
Performance time = 105 minutes
To find, the number of performances, divide the 105 by 7 minutes
Thus 15 performances can be accommodated
