Can anyone help me with my last math test question pls my grades are depending on this test so pls help and get me the right ans
wer I will give a brainlest plsss!!!
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Answer:
see attached
Step-by-step explanation:
At 1100 ft per second for 18 seconds, the sound travels 19,800 ft, or 3.75 miles farther to my friend's house. The set of points that lie 3.75 miles farther from my friend's house than from my house form a hyperbolic curve. This is illustrated by the blue line in the attached graph. (My house is the red dot on the left; my friend's house is the red dot on the right.)
The lightning occurred somewhere on the blue curve.
___
If the lightning occurred on the line between our houses, it was 1/8 mile from my house and 3 7/8 mile from my friend's house. (That's close!)
_____
The formula for the curve in the graph is the distance formula applied to the set of points (x, y). It equates the difference of distance from the two houses to 3.75 miles. If one were to write the equation of the hyperbola in standard form, the equation would look a little different and a restriction would need to be applied so the formula would describe only one branch of the hyperbola.
Hi there!
To find the Trigonometric Equation, we have to isolate sin, cos, tan, etc. We are also given the interval [0,2π).
<u>F</u><u>i</u><u>r</u><u>s</u><u>t</u><u> </u><u>Q</u><u>u</u><u>e</u><u>s</u><u>t</u><u>i</u><u>o</u><u>n</u>
What we have to do is to isolate cos first.
Then find the reference angle. As we know cos(π/3) equals 1/2. Therefore π/3 is our reference angle.
Since we know that cos is negative in Q2 and Q3. We will be using π + (ref. angle) for Q3. and π - (ref. angle) for Q2.
<u>F</u><u>i</u><u>n</u><u>d</u><u> </u><u>Q</u><u>2</u>
<u>F</u><u>i</u><u>n</u><u>d</u><u> </u><u>Q</u><u>3</u>
<u></u>
Both values are apart of the interval. Hence,
<u>S</u><u>e</u><u>c</u><u>o</u><u>n</u><u>d</u><u> </u><u>Q</u><u>u</u><u>e</u><u>s</u><u>t</u><u>i</u><u>o</u><u>n</u>
Isolate sin(4 theta).
Rationalize the denominator.
The problem here is 4 beside theta. What we are going to do is to expand the interval.
Multiply whole by 4.
Then find the reference angle.
We know that sin(π/4) = √2/2. Hence π/4 is our reference angle.
sin is negative in Q3 and Q4. We use π + (ref. angle) for Q3 and 2π - (ref. angle for Q4.)
<u>F</u><u>i</u><u>n</u><u>d</u><u> </u><u>Q</u><u>3</u>
<u></u>
<u>F</u><u>i</u><u>n</u><u>d</u><u> </u><u>Q</u><u>4</u>
Both values are in [0,2π). However, we exceed our interval to < 8π.
We will be using these following:-
Hence:-
<u>F</u><u>o</u><u>r</u><u> </u><u>Q</u><u>3</u>
We cannot use any further k-values (or k cannot be 4 or higher) because it'd be +8π and not in the interval.
<u>F</u><u>o</u><u>r</u><u> </u><u>Q</u><u>4</u>
Therefore:-
Then we divide all these values by 4.
Let me know if you have any questions!