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2 years ago

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Mathematics

1 answer:

Vladimir [108]2 years ago

6 0

Answer:

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Step-by-step explanation:

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The function f(t) = 4t^2 − 8t + 6 shows the height from the ground f(t), in meters, of a roller coaster car at different times t

andreev551 [17]

Answer:

C - f(t) = 4(t − 1)^2 + 2; the minimum height of the roller coaster is 2 meters from the ground.

Step-by-step explanation:

Here we're asked to rewrite the given equation f(t) = 4t^2 − 8t + 6 in the form f(t) = a(t - h)^2 + k (which is known as the "vertex form of the equation of a parabola.") Here (h, k) is the vertex and a is a scale factor.

Let's begin by factoring 4 out of all three terms:

f(t) = 4 [ t^2 - 2t + 6/4 ]

Next, we must "complete the square" of t^2 - 2t + 6/4; in other words, we must re-write this expression in the form (t - h)^2 + k.

(To be continued)

3 0

2 years ago

Allometric relations often can be modeled by f(x)= x^b, where a and b are constants. One study showed that for a male fiddler

dolphi86 [110]

Answer:

a) $f(2)= 0.448 (2)^{1.21}= 1.036 grams$

b) $0.5 = 0.448 x^{1.21}$

Dividing both sides by 0.448 we got:

$\frac{0.5}{0.448} = x^{1.21}$

We can appy the exponent $\frac{1}{1.21}$ in both sides of the equation and we got:

$(\frac{0.5}{0.448})^{\frac{1}{1.21}} = x= 1.095grams$

Step-by-step explanation:

For this case we know the following function:

$f(x) = 0.448 x^{1.21}$

The notation is: x is the weight of the crab in grams, and the output f(x) is the weight of the claws in grams.

Part a

For this case we just need to replace x = 2 gram in the function and we got:

$f(2)= 0.448 (2)^{1.21}= 1.036 grams$

Part b

For this case we know tha value for $f(x) =0.5$ and we want to find the value of x who satisfy this condition:

$0.5 = 0.448 x^{1.21}$

Dividing both sides by 0.448 we got:

$\frac{0.5}{0.448} = x^{1.21}$

We can appy the exponent $\frac{1}{1.21}$ in both sides of the equation and we got:

$(\frac{0.5}{0.448})^{\frac{1}{1.21}} = x= 1.095grams$

8 0

2 years ago

Suppose you had to find 4 x 57. How are the expanded algorithm and the standard algorithm alike? And how are they different?

Nookie1986 [14]

The expanded algorithm is given as follows:

4 x 57 = (4 x 50) + (4 x 7) = 200 + 28 = 228

The standard algorithm is given as follows:

$\ \ \ \ \ \ {_2}\\{ \ \ \ \ \ \ 5 \ 7} \\ \times \ \ \ \ \ 4 \\ = \overline{\underline{2\ 2\ 8}}$