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soldier1979 [14.2K]
3 years ago
13

Given that F(x) =x^2+2, evaluate F(2)

Mathematics
1 answer:
maria [59]3 years ago
5 0

Answer:

F(2) = 6

Step-by-step explanation:

Given that F(x) =x^2+2, evaluate F(2).

The above equation is a function of x

Such that for every value of x at a given time, the equation results to equation takes a different value at that time. For every value of x, the value is simply substituted into the equation to find the solution of the equation at that point. The above equation is a quadratic function since the highest power of x is 2.

F(x) =x^2+2,

To evaluate F(2),

Substitute x = 2 in equation x^2+2

It becomes

2^2 + 2 = 4 + 2 = 6

So F(2) = 6

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4 years ago
While traveling to and from a certain destination, you realized increasing your speed by 40 mph saved 4 hours on your return. If
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The speed driven while returning is 88 mph.

Step-by-step explanation:

We are given that while traveling to and from a certain destination, you realized increasing your speed by 40 mph saved 4 hours on your return.

Also, the total distance of the roundtrip was 420 miles.

Let the speed driven while returning be 'x mph' which means that the speed driven while going was '(x - 40) mph' because it has been given that while returning we have increased the speed by 40 mph.

As we know that the Speed-Distance-Time formula is given by;

                         \text {Speed} = \frac{\text{Distance}}{\text{Time}}   or  \text {Time} = \frac{\text{Distance}}{\text{Speed}}

So, according to the question;

\frac{420}{x-40} -\frac{420}{x} = 4 \text{ hours}       where Distance = 420 miles

\frac{420x-420(x-40)}{x(x-40)} = 4

\frac{420x-420x+16800}{x^{2} -40x} = 4

\frac{16800}{x^{2} -40x} = 4

4x^{2} -160x= 16800

4x^{2} -160x- 16800=0

x^{2} -40x- 4200=0

Now finding the roots of the above equation;

Here a = 1, b = -40 and c = -4200

D = b^{2} -4ac

   =  (-40)^{2} -4(1)(-4200) = 18400

Now, the roots of a quadratic equation is given by;

x = \frac{-b\pm \sqrt{D} }{2a}

x = \frac{-(-40)\pm \sqrt{18400} }{2\times 1}

So, the two roots of x are : x = \frac{40-\sqrt{18400} }{2}  and  x = \frac{40+\sqrt{18400} }{2}

Solving these two we get; x = -47.8  and  x = 87.8

Here we ignore the negative value of x, so the speed driven while returning is 87.8 ≈ 88 mph.

8 0
3 years ago
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