Hi there!
First replace m(x) by y.
To find the inverse function we must switch the places from the variables x and y.
Now we need to isolate the y again to find the formula of the inverse function. First add 5 to both sides.
Switch sides.
And finally divide both sides by 5.
And therefore we can conclude the following:
The answer is C.
~ Hope this helps you!
Answer:
v = -0.5
Step-by-step explanation:
v = 2 + (-5 * 1/2)
v = 2 + (-2.5)
v = -0.5
Answer:
d
Step-by-step explanation:
Answer:
-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C
Step-by-step explanation:
∫ 15 sin(√(at)) dt
Use substitution:
If x = √(at), then:
dx = ½ (at)^-½ (a dt)
dx = a / (2√(at)) dt
dx = a/(2x) dt
dt = (2/a) x dx
Plugging in:
∫ 15 sin x (2/a) x dx
30/a ∫ x sin x dx
Integrate by parts:
If u = x, then du = dx.
If dv = sin x dx, then v = -cos x.
∫ u dv = uv − ∫ v du
= 30/a (-x cos x − ∫ -cos x dx)
= 30/a (-x cos x + ∫ cos x dx)
= 30/a (-x cos x + sin x + C)
Substitute back:
30/a (-√(at) cos(√(at)) + sin(√(at)) + C)
-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C
<h3><u>Option A</u></h3>
is the required equation to calculate width of rectangular frame that has a total area of 140 square inches.
<h3>
<u>Solution:</u></h3>
Given that,
Length of a rectangular frame is given as 2x + 10
Width of the rectangular frame is given as 2x + 6
Total area = 140 square inches
<em><u>The area of rectangular frame is given as:</u></em>
Plugging in values, we get
This is the required equation to calculate width of rectangular frame
Solve the above quadratic equation to get the value of "x"
<em><u>Use the quadratic equation formula:</u></em>
Here a = 4 ; b = 32 ; c = -80
x = 2 or x = -10
Now measurement cannot be negative, so taking the positve value of "x", we can calculate the width
So put "x" = 2
Width of the rectangular frame = 2x + 6 = 2(2) + 6 = 10
Thus the width of frame is 10 inches
