Answer:
0.1 rad/s
Step-by-step explanation:
Since the distance from or to the flagpole is not given, I will assume. And my assumption is 50 ft
Now, the elevation angle A = 45 degrees, converting to radians, we have π/4 radians
Remember that the tan of an angle is OPP/HYP, and so
tan A = h/25, on differentiating, we have
d tan A/dA = sec^2 A = (1/25) dh/dA
Next, we have
25 sec^2 A * dA/dt= dh/dt = 5
Making dA/dt the subject of formula, we have
dA/dt = (1/5) cos^2 A
but cos^2 A from trigonometry = 1/2, this means that
dA/dt = .1 radians/second
If you want to convert to degrees, your have
.1 Rad/s( 180 deg/rad) = 18 degrees/second
X= number of dimes
x+6= number of quarters
5(x+6)= number of nickels
$5.40= 540 cents
Add the number of each coin and set it equal to the total in cents.
x + (x + 6) + 5(x + 6)= $5.40
multiply 5 by parentheses; change dollar total to cents
x + (x + 6) + (5 * x) + (5 * 6)= 540
x + (x + 6) + 5x + 30= 540
combine like terms
7x + 36= 540
subtract 36 from both sides
7x= 504
divide both sides by 7
x= 72 dimes
x + 6= 78 quarters
5(x + 6)= 390 nickels
CHECK
72 + 78 + 390= 540
540= 540
ANSWER: There are 72 dimes, 78 quarters and 390 nickels.
Hope this helps! :)
Answer:
42
Step-by-step explanation:
39+39 = 78
162 - 78 = 2 lengths =84
84/2 = 42
First, let's convert each line to slope-intercept form to better see the slopes.
Isolate the y variable for each equation.
2x + 6y = -12
Subtract 2x from both sides.
6y = -12 - 2x
Divide both sides by 6.
y = -2 - 1/3x
Rearrange.
y = -1/3x - 2
Line b:
2y = 3x - 10
Divide both sides by 2.
y = 1.5x - 5
Line c:
3x - 2y = -4
Add 2y to both sides.
3x = -4 + 2y
Add 4 to both sides.
2y = 3x + 4
Divide both sides by 2.
y = 1.5x + 2
Now, let's compare our new equations:
Line a: y = -1/3x - 2
Line b: y = 1.5x - 5
Line c: y = 1.5x + 2
Now, the rule for parallel and perpendicular lines is as follows:
For two lines to be parallel, they must have equal slopes.
For two lines to be perpendicular, one must have the negative reciprocal of the other.
In this case, line b and c are parallel, and they have the same slope, but different y-intercepts.
However, none of the lines are perpendicular, as -1/3x is not the negative reciprocal of 1.5x, or 3/2x.
<h3><u>B and C are parallel, no perpendicular lines.</u></h3>
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