Answer:
1)
a)
We are given one leg of triangle as 6 km and the other leg is of length of 8 km.
Hence, the hypotenuse is calculated using Pythagorean theorem as:
Hence, the hypotenuse of the triangle or the missing side x=10 cm.
Now we calculate trignometric ratio with respect to angle a and b as:
b)
We know that:
Sine of an angle is ratio of perpendicular to hypotenuse.
Cosine of an angle is ratio of base and hypotenuse.
And tangent of an angle is ratio of perpendicular and base.
<u>Angle a:</u>
We have perpendicular=8
Base=6
Hypotenuse=10
Hence,
sin a=8/10
cos a=6/10
tan a=8/6
<u>Angle b:</u>
Perpendicular =6
Base=8
Hypotenuse=10
Hence,
sin b=6/10
cos b=8/10
tan b=6/8
Answer:
The value of the stock can be found by: x × 1.26.
Step-by-step explanation:
The value of the stock in year one can be found by multiplying x by 1.4. This will represent a 40% increase in value. The following year, the stock decreases in value by 10%; this is represented by multiplication by 0.9. For example, if the value of the stock was $5:
5 × 1.4 = 7 (A 40% increase in value)
(5 × 1.4) * 0.90 = 6.3 (A further 10% decrease in value)
Rather than writing out the long version, we can simplfify by multiplying 1.4 by 0.9 to get 1.26 .We can also replace 5 with x to get a more general equation.
I really don’t know sadly...
Answer:
Incorrect
Step-by-step explanation:
150 students are 100%,
82 students are x%
(82*100)/150=54,67%, so that is more than half of all students
For the given function f(t) = (2t + 1) using definition of Laplace transform the required solution is L(f(t))s = [ ( 2/s²) + ( 1/s) ].
As given in the question,
Given function is equal to :
f(t) = 2t + 1
Simplify the given function using definition of Laplace transform we have,
L(f(t))s = 
= ![\int\limits^\infty_0[2t +1] e^{-st} dt](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%5Cinfty_0%5B2t%20%2B1%5D%20e%5E%7B-st%7D%20dt)
= 
= 2 L(t) + L(1)
L(1) = 
= (-1/s) ( 0 -1 )
= 1/s , ( s > 0)
2L ( t ) = 
= ![2[t\int\limits^\infty_0 e^{-st} - \int\limits^\infty_0 ({(d/dt)(t) \int\limits^\infty_0e^{-st} \, dt )dt]](https://tex.z-dn.net/?f=2%5Bt%5Cint%5Climits%5E%5Cinfty_0%20e%5E%7B-st%7D%20-%20%5Cint%5Climits%5E%5Cinfty_0%20%28%7B%28d%2Fdt%29%28t%29%20%5Cint%5Climits%5E%5Cinfty_0e%5E%7B-st%7D%20%5C%2C%20dt%20%29dt%5D)
= 2/ s²
Now ,
L(f(t))s = 2 L(t) + L(1)
= 2/ s² + 1/s
Therefore, the solution of the given function using Laplace transform the required solution is L(f(t))s = [ ( 2/s²) + ( 1/s) ].
Learn more about Laplace transform here
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