Given points H, I and J and HI = 9,1J = 9 and HJ = 16 . Are the three points collinear?

A shooting star forms a right triangle with the Earth and the Sun, as shown below:

Semmy [17]

I found this!!!!

The scientist can use these two measurements to calculate the distance between the Sun and the shooting star by applying one of the trigonometric functions: Cosine of an angle.

- The scientist can substitute these measurements into cos\alpha=\frac{adjacent}{hypotenuse}cosα=

hypotenuse

adjacent

and solve for the distance between the Sun and the shooting star (which would be the hypotenuse of the righ triangle).

Step-by-step explanation:

You can observe in the figure attached that "AC" is the distance between the Sun and the shooting star.

Knowing the distance between the Earth and the Sun "y" and the angle x°, the scientist can use only these two measurements to calculate the distance between the Sun and the shooting star by applying one of the trigonometric functions: Cosine of an angle.

This is:

cos\alpha=\frac{adjacent}{hypotenuse}cosα=

hypotenuse

adjacent

In this case:

\begin{gathered}\alpha=x\°\\\\adjacent=BC=y\\\\hypotenuse=AC\end{gathered}

α=x\°

adjacent=BC=y

hypotenuse=AC

Therefore, the scientist can substitute these measurements into cos\alpha=\frac{adjacent}{hypotenuse}cosα=

hypotenuse

adjacent

, and solve for the distance between the Sun and the shooting star "AC":

cos(x\°)=\frac{y}{AC}cos(x\°)=

AC

y

AC=\frac{y}{cos(x\°)}AC=

cos(x\°)

y

7 0

2 years ago

Write the standard form of the line that passes through the given points.<br> 4, 7) and (0, 7)

zubka84 [21]

(4,7)(0,7)

notice how ur points have the same y values....this means this is a horizontal line with a slope of 0.

equation is : y = 7...or y = 0x + 7...but we need it in standard form...
0x + y = 7 <== standard form

6 0

3 years ago

out of 1200 student served at lunch 660 of the students get hamburgers what is the percent of people who got hamburgers

Mars2501 [29]

Answer:

45% of students got hamburgers :)

Step-by-step explanation:

3 0

2 years ago

After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is modelled by the function C(t)=8(e

Alexxx [7]

Answer:

the maximum concentration of the antibiotic during the first 12 hours is 1.185 $\mu g/mL$ at t= 2 hours.

Step-by-step explanation:

We are given the following information:

After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is modeled by the function where the time t is measured in hours and C is measured in $\mu g/mL$

$C(t) = 8(e^{(-0.4t)}-e^{(-0.6t)})$

Thus, we are given the time interval [0,12] for t.

We can apply the first derivative test, to know the absolute maximum value because we have a closed interval for t.
The first derivative test focusing on a particular point. If the function switches or changes from increasing to decreasing at the point, then the function will achieve a highest value at that point.

First, we differentiate C(t) with respect to t, to get,

$\frac{d(C(t))}{dt} = 8(-0.4e^{(-0.4t)}+ 0.6e^{(-0.6t)})$

Equating the first derivative to zero, we get,

$\frac{d(C(t))}{dt} = 0\\\\8(-0.4e^{(-0.4t)}+ 0.6e^{(-0.6t)}) = 0$

Solving, we get,

$8(-0.4e^{(-0.4t)}+ 0.6e^{(-0.6t)}) = 0\\\displaystyle\frac{e^{-0.4}}{e^{-0.6}} = \frac{0.6}{0.4}\\\\e^{0.2t} = 1.5\\\\t = \frac{ln(1.5)}{0.2}\\\\t \approx 2$