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3 years ago

Which function increases at a faster rate on 0 to infinity, f(x) = x2 or g(x) = 2x? Explain your reasoning.

2 answers:

9 0

Using a table of values, the outputs of f(x) for whole numbers are 0, 1, 4, 9, 16, 25, 36, and so on. For the same input values, g(x) has outputs of 1, 2, 4, 8, 16, 32, and 64. Continuing to double the output each time results in larger outputs than those of f(x). The exponential function, g(x), has a constant multiplicative rate of change and will increase at a faster rate than the quadratic function.

(ed. just click all of them)

olga2289 [7]3 years ago

6 0

Answer:

Sample response: Using a table of values, the outputs of f(x) for whole numbers are 0, 1, 4, 9, 16, 25, 36, and so on. For the same input values, g(x) has outputs of 1, 2, 4, 8, 16, 32, and 64. Continuing to double the output each time results in larger outputs than those of f(x). The exponential function, g(x), has a constant multiplicative rate of change and will increase at a faster rate than the quadratic function.

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MaRussiya [10]

Answer:

The height of the second cone is 2 h₁.

Step-by-step explanation:

The volume of a cone is:

$V=\pi\ r^{2}\frac{h}{3}$

The volume of the first cone is, V₁ = 5 in³.

The volume of the second cone is, V₂ = 10 in³.

The two cones have the same base diameters.

This implies that the two radii are same, i.e. r₁ = r₂.

Compute the height of the second cone as follows:

$r_{1}=r_{2}$

$\frac{3\cdot V_{1}}{\pi\ h_{1}}=\frac{3\cdot V_{2}}{\pi\ h_{2}}$

$\frac{V_{1}}{h_{1}}=\frac{V_{2}}{ h_{2}}$

$\frac{5}{h_{1}}=\frac{10}{h_{2}}$

$h_{2}=2\ h_{1}$

Thus, the height of the second cone is 2 h₁.

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3 years ago

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Answer:

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3 years ago

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We are interested in the dimensions of a certain rectangle. this rectangle has length twice the side of the square and width thr

Mila [183]

Area of square = s^2
Area of Rectangle = lw
l = 2s

w+3 = s
solve for w, w=s-3
Now we have l and w.
Plug both into area of rectangle formula so: (2s)(s-3)
Since both areas are equal set both equations equal to each other:
(2s)(s-3)=s^2
Now simplify
2s^2-6s=s^2
s^2-6s=0, Solve for s.
Factor polynomial. s(s-6)=0 , s can be equal to 0 or 6. HOWEVER, you cannot have a side length of 0 therefore the side length has to be 6.
Now plug in s for the length formula for the rectangle:
l = 2s so... l = 2(6) so length of rectangle = 12.
Now plug in s for the width formula for the rectangle:
w+3=s so... w+3=6 so width of rectangle = 3.
Now the dimensions of the rectangle are 12 by 3. 12 being length and 3 width.
To CHECK:
Find area of rectangle:
A=lw so A=3 times 12 so A=36
Find area of square:
We know the side is equal to 6 so
A=s^2 so 6^2 = 36
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3 years ago

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Anastasy [175]

Answer:

Please find attached the required graph and

Step-by-step explanation:

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12, 450

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108 250

120 250

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156 250

168 250

180 250

192 250

204 250

216 250

228 250

240 250

252 250

264 250

276 250

288 250

300 250

312 225

324, 200

336, 175

348, 150

360, 125

372, 100

384, 75

396, 50

408, 25

420, 0

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