Your watch beeps every 15 seconds, and your moms watch beeps every 25 seconds. If they beep together at 3:00 pm, at what time wi
1 answer:
Answer:
The two watches will beep together for 20th time at 3:25 pm.
Step-by-step explanation:
My watch beeps every 15 seconds and mom's watch beeps every 25 seconds.
Thus both the watches beep at the same time at an interval of 75 seconds.
75 is the smallest multiple of 15 and 25.
They beep together at 3 pm and when they beep together for the 20th time , we have to add 20 times the time taken for both the watches to beep together.
This time interval = 20 75 = 1500 seconds = 25 minutes.
The two watches will beep together for 20th time at 3:25 pm.
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To find the area that is shaded red, you find the area of the rectangle and subtract it by the area of the triangle.
Area of a rectangle:
A = l × w [ l = 11 in ; w = 6in ] Plug these numbers into the equation
A = 11 · 6
A = 66 in²
Area of a triangle:
[ b = 4 in ; h = 6 in ] Plug these #s into the equation
A = 12 in²
Area of rectangle - Area of triangle = Area of the shaded region
66 in² - 12 in ² = 54 in²
Your answer is B
Cos(x) = sin(x + 20o) Use the double cos angle formula
Cos(x) = sin(x)*cos(20) + cos(x)*sin(20) Divide through by cos(x). Tanx = sin(x)/cos(x)
1 = tan(x)*cos(20) + sin(20) Subtract sin(20) from both sides.
1 - sin(20) = tan(x)*cos(20) Calculate the value of 1 - sin(20)
0.65798 = tan(x) * 0.939692 Divide by cos(20)
tan(x) = 0.65795/0.939692
tan(x) = 0.70021 Take the inverse of 0.7) = tan(x)
x = tan-1(0.70021)
x = 35 degrees as expected.
Problem Two
The easiest way to do this is to pick random values and try it. The two acute angles are complementary. So 25 and 65 are random enough.
Let A = 25
Let C = 65
A
Tan(25) = sin(25)/sin(65) ; tan(25) = 0.4663.
sin(25)/sin(65) = 0.4663 Answer
B
Sin(90 - C) = Sin(A)
Tan(90 - A) = Tan(C)
So the question becomes Cos(A) = Tan(C) / sin(A)
Cos(25) = Tan(65)/Sin(25)
0.906 = ? 5.07 This statement isn't true.
C
Sin(65) = Cos(25)/Tan(65)
.906 = 0.4226 C is not the correct answer.
D
D isn't true. The tan does not relate that away. You can find it for yourself.
Cos(A) = Tan(C) You should get 0.906 = 2.14
E
Sin(C) = Cos(A) / Tan(A) I'll leave you to show this is wrong.
Problem 3
The diagram below is for this problem. Cos(x) = 50/100 = 0.5
x = cos-1(0.5)
x = 60 degrees.
Part 2
Sin(60) = opposite / hypotenuse
opposite = sin(60) * hypotenuse
opposite = 86.61 Be sure and round this to whatever the question says to round it to.
