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mylen [45]
3 years ago
15

Henry is designing a model for a dome shaped glasshouse. He creates the model and records the horizontal distance from the edge

of the greenhouse of the dome over its vertical height from the base of the model. The table shows the horizontal distance from the edge of the greenhosue, in inches, x, over its verital height from the base, in inches, f(x). Use data in table to create standard form of the function that models this situation.

Mathematics
2 answers:
dolphi86 [110]3 years ago
8 0

Answer:

Correct choice is B

Step-by-step explanation:

All given options represent quadratic function. Let the equation of this quadratic function be

f(x)=ax^2+bx+c.

Then

1. f(0)=2=a\cdot 0^2+b\cdot 0+c\Rightarrow c=2;

2. f(1)=7.5=a\cdot 1^2+b\cdot 1+c\Rightarrow 7.5=a+b+2;

3. f(2)=12=a\cdot 2^2+b\cdot 2+c\Rightarrow 12=4a+2b+2.

Solve the system of two equations:

\left\{\begin{array}{l}a+b+2=7.5\\4a+2b+2=12\end{array}\right.\Rightarrow\left\{\begin{array}{l}a=5.5-b\\4(5.5-b)+2b=10\end{array}\right.

Then

22-4b+2b=10,\\ \\-2b=-12,\\ \\b=6,\\ \\a=5.5-6=-0.5.

Thus, the equation of the function is

f(x)=-\dfrac{1}{2}x^2+6x+2.

Note that

f(3)=-\dfrac{1}{2}\cdot 3^2+6\cdot 3+2=-4.5+20=15.5;

f(4)=-\dfrac{1}{2}\cdot 4^2+6\cdot 4+2=18.

lara31 [8.8K]3 years ago
5 0

Answer:

Step-by-step explanation:

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Interesting problem.

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(PLEASE ANSWER QUICK) Which prisms do Sophia use exactly 18 unit cubes to build? Choose all the correct answers. The options are
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Step-by-step explanation:

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Step-by-step explanation:

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What is the volume of this container?
Keith_Richards [23]

Answer:

The volume of the container is 56\ in^{3}

Step-by-step explanation:

we know that

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