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A firework is fired into the air from the top of a barn. Tis hight (h) above the ground in yards after (t) seconds is given by t

Grace [21]

The given function for the height of the firework is a quadratic function

1. Time at which the firework reaches the maximum height is 1 seconds

2. The maximum height of the firework, is 25 yards

3. Time after which the firework will fall to the ground is (1 + √5) seconds

Reason:

The given function that represents the height of the fireworks with time is

presented as follows;

h(t) = -5·t² + 10·t + 20

1. The time at which the firework reaches its maximum height is given by

the maximum point of the given function as follows;

The x-value of the maximum point of a quadratic function is $x = \dfrac{b}{2 \cdot a}$

Where;

a, and b, are the coefficient of x² and x, in the general form of a quadratic function f(x) = a·x² + b·x + c

By comparison, we have;

$t = -\dfrac{10}{2 \times (-5)} = 1$

The time at which the firework reaches the maximum height is t = 1 seconds

2. The maximum height is given by plugging in the value of t, at the maximum point into the given function as follows;

h(1) = -5×1² + 10×1 + 20 = 25

The maximum height of the firework, f(1) = 25 yards

3 The time at which the firework will fall to the ground, is given by the zero of the function as follows;

When the firework falls to the ground, h(t) = 0 = -5·t² + 10·t + 20

Dividing both sides by (-5) gives;

$\dfrac{0}{-5} = \dfrac{ -5 \cdot t^2 + 10 \cdot t + 20}{-5} = t^2 - 2 \cdot t - 4$

t² - 2·t - 4 = 0

By the quadratic formula $x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}$ , we get;

$t = \dfrac{2\pm \sqrt{(-2)^{2}-4\times 1\times (-4)}}{2\times 1} = \dfrac{2\pm \sqrt{20}}{2\times 1} = \dfrac{2\pm 2 \times \sqrt{5}}{2\times 1} = 1 \pm \sqrt{5}$

Therefore;

The time after which the firework will fall to the ground, t = 1 + √5 seconds

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Evaluate -8-(12)/4 Please help

liq [111]

-11

Step-by-step explanation:

your always have to do division multiplication first

-8-(12)/4=

-8-3=

-11

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Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5,

Mkey [24]

Answer:

C. {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}

Step-by-step explanation:

I just did the quiz. Basically all you do is switch the x and y values for each coordinate pair in order to see if it would pass the line test. If it has double X values, it is not a function with an inverse function.

5 0

4 years ago

Which set of numbers is the most reasonable to describe the number of desks in a classroom?

VladimirAG [237]

Whole numbers are reasonable to describe the number of desk.

5 0

4 years ago

Read 2 more answers

What is (f−g)(x)? f(x)=5x^4+4x^3+3x^2+2x+1 g(x)=x^4+2x^3+3x^2+4x+5. Enter your answer, in standard form, in the box.

Naddika [18.5K]

Answer:

$(f-g)(x)=4x^{4}+2x^3}-2x-4$

Step-by-step explanation:

Let f and g be two functions that are defined in the same interval and have the same independent variable. Then, the Subtraction of Function is defined as:

$(f-g)(x)=f(x)-g(x)$

Let's solve (f-g)(x) with $f(x)=5x^{4}+4x^3}+3x^{2}+2x+1$ and $g(x)=x^{4}+2x^{3}+3x^{2}+4x+5$

$(f-g)(x)=(5x^{4}+4x^3}+3x^{2}+2x+1)-(x^{4}+2x^{3}+3x^{2}+4x+5)\\(f-g)(x)=5x^{4}+4x^3}+3x^{2}+2x+1-x^{4}-2x^{3}-3x^{2}-4x-5\\(f-g)(x)=4x^{4}+2x^3}-2x-4$

.

6 0

3 years ago