Use Pythagorean theorem for side1 = a, side2 = 3, and hypotenuse = 2a
a² + b² = c²
a² + (3)² = (2a)
a² + 9 = 4a²
9 = 3a²
3 = a²
√3 = a
side1 = a = √3 ft
side2 = 3 ft (this was given in the problem)
hypotenuse = 2a = 2√3 ft
Answer:
the error is in step 2.
0.25x was added to -0.75x with an incorrect result of +0.50x.
Step-by-step explanation:
The incorrect step is ...
Step 2: negative 1.50 = 0.50 x
This is the result of an attempt to add 0.25x to both sides of the equation. The correct step would be ...
-1.50 -0.25x = -0.75x . . . . . . . result from Step 1
-1.50 -0.25x +0.25x = -0.75x +0.25x . . . . . add 0.25x to both sides
-1.50 = -0.50x . . . . . . . . . . . . . the correct result from the addition (Step 2)
__
The correct result is ...
x = -1.50/-0.50 = 3 . . . . . Step 3
Answer:
cp is RS 300
Step-by-step explanation:
let cp be x
sp= 115x/100 ---(when 15%gain)
sp = 88x/100------(when 12% loss
according to question
115x/100 - 88x/100 = 81
or, (115x-88x)= 8100
or, 27x = 8100
or, x= 8100/27
x = 300
hence cp is RS 300
Answer:
see below
Step-by-step explanation:
y' = -2e⁻ˣcos(x) -sin(x)2e⁻ˣ +e⁻ˣsin(x)-cos(x)e⁻ˣ = e⁻ˣ(-2cos(x)-2sin(x)+sin(x) -cos(x))
=e⁻ˣ(-3cos(x)-sin(x))
y'' = -e⁻ˣ(-3cos(x)-sin(x)) + (3sin(x)-cos(x))e⁻ˣ
y'' = e⁻ˣ[3cos(x)+sin(x) + 3sin(x)-cos(x)] = e⁻ˣ[2cos(x)+4sin(x)]
y''+2y'+2y = 0
e⁻ˣ[2cos(x)+4sin(x)] + 2[e⁻ˣ(-3cosx-sinx)] + 2[2e⁻ˣ cos(x)−e⁻ˣ sin(x)]
e⁻ˣ[2cos(x)+4sin(x)-6cos(x)-2sin(x)+4cos(x)-2sin(x)]
e⁻ˣ[-4cos(x)+2sin(x)+4cos(x)-2sin(x)]
e⁻ˣ[0cos(x)+0sin(x)] = 0
Answer:
Step-by-step explanation:
given the expresseon that relates the number of ounces y and number of pounds x as y = 16x
The equation is a directly proportionality with a Proportionality constant of 16.
Thus means that the value of y keeps increasing by a factor of 16 for any value of x.
The ordered pairs that represent the number of pounds and the number of ounces are;
If x = 3
y = 16(3) = 48
Hence (3, 16) is an ordered pair
also if x = 10
y = 16(10) = 160
Therefore (10, 160) is another ordered pair
Hence the correct ordered pairs are (3, 16) and (10, 160)
