Complementary angles If G= (6x-15)° and H= (3x+6)° find the x value and H

Mathematics

1 answer:

Liula [17]3 years ago

5 0

Answer:

x = 11 and H = 39°

Step-by-step explanation:

Complementary angles add up to 90 degrees, so angles G and H will add up to 90 degrees.

Create an equation by adding the expressions together and setting it equal to 90.

(6x - 15) + (3x + 6) = 90

Solve for x by adding like terms first:

9x - 9 = 90

Isolate x and solve:

9x = 99

x = 11

Then, find H by plugging in 11 as x into the expression:

3x + 6

3(11) + 6

33 + 6

= 39

So, x = 11 and H = 39°

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A rocket is fired upward from some initial distance above the ground. Its height in feet, h,above the ground, t seconds after

kirill115 [55]

Check the picture below.

$\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\
\begin{array}{lccclll}
h(t) = &{{ -16}}t^2&{{ +96}}t&{{ +2560}}\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad 
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)$

so.. the maximum point is at $\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}~~~ft$

and it happened after $\bf -\cfrac{{{ b}}}{2{{ a}}}~~~seconds$

--------------------------------------------------------------------------

now, when the rocket reaches the ground, as you saw on the picture, y = 0, thus

$\bf h(t)=-16t^2+96t+2560\implies 0=-16t^2+96t+2560
\\\\\\
0=-16(t^2-6t-160)\implies 0=t^2-6t-160
\\\\\\
0=(t-16)(t+10)\implies t=
\begin{cases}
\boxed{16}\\
-10
\end{cases}$

"t" is an amount in seconds, for this specific phenomena, it cannot be negative, so -10 is not a feasible value.