Answer:
If a certain cone with a height of 9 inches has volume V = 3πx2 + 42πx + 147π, what is the cone’s radius r in terms of x?
Step-by-step explanation:
V = 3πx2 + 42πx + 147π
V=3π(x2 + 14x +49)
9.42(x2 + 14x +49)
9.42(x2 + 14x +14) -14 + 49= 0
9.42(x + 7)^2 + 35= 0
9.42(9.42(x + 7)^2 = - 35)9.42
(x + 7)^2 = - 35/9.42)
√(x + 7)^2=√- 35/9.42
x + 7 = - 1.927
x= - 1.927 - 7
x= - 8.927
V = 3π(- 8.927)^2 + 42π(- 8.927) + 147π
V=750.69 - 1177.29 + 461.58
<u>V=34.98</u>
h= 9 inches
V = 13πr2h
34.98 = 13(3.14) (r^2) (h)
34.98 = 40.82 (r^2) 9
34.98 = 367.38 r^2
34.98/ 367.38 = 367.38 r^2/ 367.38
0.095= r^2
Answer:
(See step-by-step)
Step-by-step explanation:
Let’s start by making A-(X) and W-(Y). So, when substituting the variables you get x=210-35y. When x=0, the answer to the equation is 6. So, the y-intercept (when x=0) is 6 or (0,6). When y=0, the answer to the equation/x-intercept(y=0) is 210 or (210,0). The graph itself looks like the image included.
The domain, realistically, is x>=0 however on the graph itself, the domain is x= All Real Numbers. The range realistically is y>=0, but on the graph it is also All Real Numbers.
The x-intercept is the account when no weeks have passed and no money is lost (210) and the y-intercept is the maximum amount of weeks before there is no more money in the account (6).
Answer:
The answer is > because 9.63 is greater than 1.82
Step-by-step explanation:
9.63 is a larger number than 1.82
Answer:
it is 1/2
Step-by-step explanation:
The population size after 6 years and after 8 years are 147 and 169 population respectively
<h3>Exponential functions</h3>
The standard exponential function is expressed as y = ab^x
where
a is the base
x is the exponent
Given the function that represents the population size P (t) of the species as shown;
![p(t)=\frac{550}{1+5e^{-0.1t}} \\](https://tex.z-dn.net/?f=p%28t%29%3D%5Cfrac%7B550%7D%7B1%2B5e%5E%7B-0.1t%7D%7D%20%5C%5C)
For the population size after 6 years
![p(t)=\frac{550}{1+5e^{-0.1(6)}} \\P(6)=\frac{550}{3.744}\\ P(6)=147 population](https://tex.z-dn.net/?f=p%28t%29%3D%5Cfrac%7B550%7D%7B1%2B5e%5E%7B-0.1%286%29%7D%7D%20%5C%5CP%286%29%3D%5Cfrac%7B550%7D%7B3.744%7D%5C%5C%20P%286%29%3D147%20population)
For the population after 8 years
![p(t)=\frac{550}{1+5e^{-0.1(8)}} \\P(8)=\frac{550}{3.2466}\\ P(8)=169 population](https://tex.z-dn.net/?f=p%28t%29%3D%5Cfrac%7B550%7D%7B1%2B5e%5E%7B-0.1%288%29%7D%7D%20%5C%5CP%288%29%3D%5Cfrac%7B550%7D%7B3.2466%7D%5C%5C%20P%288%29%3D169%20population)
Hence the population size after 6 years and after 8 years are 147 and 169 population respectively
Learn more on exponential function here: brainly.com/question/2456547
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