Answer:
RS = 2
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
RS² + RT² = TS² , that is
RS² + 6² = 8²
RS² + 36 = 64 ( subtract 36 from both sides )
RS² = 28 ( take the square root of both sides )
RS = 
= 
= 2 ≈ 5.3 ( to 1 dec. place )
QUESTION A
The given points are
and 
The slope can be found using the formula;
We substitute the point to obtain;
This simplifies to
Therefore the slope is 5.
QUESTION 2
A positive slope indicates a rising line
A negative slope indicates a rising line
A zero slope means the line is horizontal.
An undefined slope means the line is vertical.
The correct answer is
A. The line rises from left to right.
Answer:
y = 2cos5x-9/5sin5x
Step-by-step explanation:
Given the solution to the differential equation y'' + 25y = 0 to be
y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.
According to the boundary condition y(0) = 2, it means when x = 0, y = 2
On substituting;
2 = c1cos(5(0)) + c2sin(5(0))
2 = c1cos0+c2sin0
2 = c1 + 0
c1 = 2
Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given
y(x) = c1cos5x + c2sin5x
y'(x) = -5c1sin5x + 5c2cos5x
If y'(π) = 9, this means when x = π, y'(x) = 9
On substituting;
9 = -5c1sin5π + 5c2cos5π
9 = -5c1(0) + 5c2(-1)
9 = 0-5c2
-5c2 = 9
c2 = -9/5
Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation
y = c1 cos(5x) + c2 sin(5x) will give
y = 2cos5x-9/5sin5x
The final expression gives the required solution to the differential equation.
Answer:
B. 1/4
Step-by-step explanation:
Even though A is a fraction it is also an integer (4)
Answer:
they are both alike because you're dividing both equations by 2 . in both equations you're trying to get the variable by itself .
they are both different because both of the equations have a different x= . in equation 1 you subtract and in equation 2 you would add .
Step-by-step explanation:
For 2x+4=20 you would make +4 negative 4 to get the variable by itself .
then you'd subtract the numbers 20-4=16
then divide both sides by 2 2÷2 and 16÷2
x=8 is your answer
for 2x-4=20 you would make -4 and make it positive 4 to get the variable by itself
then you'd add the numbers 20+4
then divide both sides by 2 2÷2 and 24÷2
x=12
