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3 years ago

Solve for x. Round your answer to two decimal places. Show your work for full credit.

Mathematics

1 answer:

omeli [17]3 years ago

5 0

Answer:

x ≈ 14.30

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Trigonometry

sin∅ = opposite over hypotenuse

Step-by-step explanation:

Step 1: Define variables

∅ = 39°

opposite leg = 9

hypotenuse = x

Step 2: Solve for x

Substitute: sin39° = 9/x
Multiply x on both sides: xsin39° = 9
Isolate x: x = 9/sin39°
Evaluate: x = 14.3011
Round: x ≈ 14.30

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An object is launched from a launching pad 208 ft. above the ground at a velocity of 192ft/sec. what is the maximum height reach

loris [4]

Answer:

The maximum height is 784 feet

Step-by-step explanation:

In this problem we use the kinematic equation of the height h of an object as a function of time

$h(t) = -16t ^ 2 + v_0t + h_0$

Where $v_0$ is the initial velocity and $h_0$ is the initial height.

We know that

$v_0 = 192\ \frac{ft}{sec}$

$h_0 = 208\ ft.$

Then the equation of the height is:

$h(t) = -16t ^ 2 + 192t +208$

For a quadratic function of the form $ax ^ 2 + bx + c$

where $a$

the maximum height of the function is at its vertex.

The vertice is

$x = -\frac{b}{2a}\\\\y = f(\frac{-b}{2a})$

In this case

$a = -16\\b = 192\\c = 208$

Then the vertice is:

$t = -\frac{192}{2(-16)}\\\\t = 6\ sec$

Now we calculate h (6)

$h(6) = -16(6) ^ 2 +192(6) +208\\\\h(6) = 784\ feet$

The maximum height is 784 feet

8 0

3 years ago

How to rationalize <img src="https://tex.z-dn.net/?f=%5Cfrac%7B17%7D%7B4%5Csqrt%7B1%7D7%20%7D" id="TexFormula1" title="\frac{17}

dem82 [27]

Answer:

$\frac{\sqrt{17}}{4}$

Step-by-step explanation:

Rationalizing the denominator of a fraction is when one multiplying fraction such that it removes any radical from the denominator. This can be done by multiplying both the numerator and the denominator by the radical that is present in the denominator. In fractional terms, a number over itself is equal to one, therefore, doing this would keep the equation true. After multiplying, one will simplify the resulting fraction.

$\frac{17}{4\sqrt{17}} * \frac{\sqrt{17}}{\sqrt{17}}\\\\= \frac{17\sqrt{17}}{4(17)}\\$