Answer:
<em>x = 11.83°</em>
Step-by-step explanation:
<u>Equations</u>
The figure shows two parallel lines crossed by a line. We have completed the figure with another variable y. Please see the attached image.
Angles y and 4x+28 are linear, thus their sum is 180°:
y + 4x + 28 = 180
Angles y and 8x + 10 are corresponding, thus
y = 8x + 10
Substituting:
8x + 10 + 4x + 28 = 180
Simplifying:
12x + 38 = 180
Subtracting 38:
12x = 142
Dividing by 12
x = 11.83°
Po = 2500
r = 6.9% = 0.069
t = 10
P = Po * e^(rt)
= 2500*e^(0.069*10)
=2500*1.994
=4984.289
=4984 or approximately 5000
the answer is option e. *answer needs to be 20 characters long this should do :)
Answer: m=-7/4
Step-by-step explanation: subtract 1-8 and 6-2 but keep them in fraction form
Answer:
Laplace transform of the original differential equation:
.
Given that and , solve for to obtain:
.
Apply inverse Laplace transform to obtain:
.
Step-by-step explanation:
<h3>Apply Laplace transform</h3>
Apply these two rules to replace all , , and in the original equation with their Laplace transforms:
.
<h3>Solve for Y(s)</h3>
Substitute in the values and .
.
Solve for after rearranging this equation:
.
Note that if denominator is the left-hand side of a quadratic equation, this equation would have no real root. Hence, complete the square in the denominator:
.
<h3>Invert Laplace Transform</h3>
Look up a table of Laplace transforms. Apply the rule , where and .
.