Can anyone help with this lol-?

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

Learn more here:

brainly.com/question/20628403

3 0

3 years ago

1. is 1 5/6 closer to 1 or 2

natulia [17]

Answer:

Convert fractions into decimal, round up if the decimal is 0.5 and/or higher, and round down if less than 0.5

Example for question 1: 5/6= 0.83 ← greater than 0.5, so round up to 2

Step-by-step explanation:

1. 2

2. 5

3. 113

4.86

5. 66

6. 19

7. 72

5 0

3 years ago

What Are some ways to describe rhe relationships between sets of Numbers?

vagabundo [1.1K]

We can have the basic inequalities and equalities’ sign. (>, =, <). 
These three set of symbols can discern, describe and explain the relationship between of numbers. These signs are used varying in many mathematical operations to explain and find discrepancy between value, sets of values or numbers in single and equitable category. 
Examples includes
6 > 5; 6 is greater than 5; 5 is less than 6
 1 > -1; -1 is less than 1; 1 is greater than -1 
-2 = -2; -2 is equal to -2

7 0

4 years ago

Which shows how to find the value of this expression when x=-2 and y=5? (3x^3y^-2)2

Gnoma [55]

Put x = -2 and y = 5 to the expression.

$(3x^3y^{-2})^2$

$\left[3\cdot(-2)^3(5)^{-2}\right]^2=\left[3(-8)\cdot\dfrac{1}{5^2}\right]^2=\left(-24\cdot\dfrac{1}{25}\right)^2=\left(-\dfrac{24}{25}\right)^2\\\\=\dfrac{24^2}{25^2}=\dfrac{576}{625}$

explanation

$(-2)^3=(-2)(-2)(-2)=-8\\\\a^{-n}=\dfrac{1}{a^n}\to5^{-2}=\dfrac{1}{5^2}=\dfrac{1}{(5)(5)}=\dfrac{1}{25}\\\\a^2\geq0\ \text{for any real number}\to\left(-\dfrac{24}{25}\right)^2=\left(\dfrac{24}{25}\right)^2\\\\\left(\dfrac{a}{b}\right)^2=\dfrac{a^2}{b^2}\to\left(\dfrac{24}{25}\right)^2=\dfrac{24^2}{25^2}=\dfrac{(24)(24)}{(25)(25)}=\dfrac{576}{625}$

6 0

4 years ago

-4(-3x - 7) whats the answer

kiruha [24]

12x+28 is the simplified expression

8 0

3 years ago

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