The ordered pair (-3, 1) is not a solution to system because it makes at least one of the equations false
<em><u>Solution:</u></em>
<em><u>Given system of equations are:</u></em>
x - 4y = 6 ------- eqn 1
3x + y = -8 ------------ eqn 2
Given ordered pair is (-3, 1)
We have to check if the options are true
<em><u>Let us substitute (x, y) = (-3, 1) in eqn 1</u></em>
Thus the given ordered pair (-3, 1) did not satisfy the first equation
<em><u>Substitute (x, y) = (-3, 1) in eqn 2</u></em>
Thus the given ordered pair (-3, 1) satisfied the second equation
But for a ordered pair to be a solution to system of equations, it must satisfy both the equations
Thus the ordered pair (-3, 1) is not a solution to system because it makes at least one of the equations false
A) Ms.Wright receive $12 as interest at the end of 1/2 year.
B) Ms.Wright receive $24 as interest at the end of 1 year.
Step-by-step explanation:
The sum deposited in the bank = Principle = $800
The rate of simple interest = 3%
The time = 6 months = (6/12) years = 0.5 years
So, here simple interest = $12.
So Ms.Wright receive $12 as interest at the end of 1/2 year.
B) Now here Time = 1 year
so, Simple interest =
So Ms.Wright receive $24 as interest at the end of 1 year.
Answer:
-0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.
Step-by-step explanation:
Let
x= distance between the wall and ladder
Ф = angle between the ladder and ground
The rate of change is: dx/dt = 0.8 ft/s
We need to find dФ/dt when x = 8 ft/s
From the triangle in the figure we see that:
cos Ф = x/10
=> x = 10 cosФ
Now, the rate of change will be
d(x)/dt = d/dt (10cosФ)
dx/dt = -10 sin Ф dФ/dt
dx/dt = 0.8 (given)
to find dФ/dt
we need to find sin Ф when x = 8
By Pythagoras theorem
(hypotenuse)^2 = (Perpendicular)^2+(base)^2
(10)^2 = (8)^2+ (Perpendicular)^2
100 = 64 + (Perpendicular)^2
=> (Perpendicular)^2 = 100-64
(Perpendicular)^2 = 36
Perpendicular = 6
sin Ф = Perpendicular/hypotenuse
sin Ф = 6/10 = 3/5
Putting values in:
dx/dt = -10 sin Ф dФ/dt
0.8 = -10(3/5) dФ/dt
0.8 = -6 dФ/dt
=> dФ/dt = 0.8 / -6
dФ/dt = - 0.133 radians/s
So, -0.133 radians/s is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall.
