An intersection point, is a shared coordinate. If the equations share a coordinate we can say they are "equal". There are two ways (algebraically) to find this point. Substitution or linear combination. Because the coefficients are different, let's use linear combination
First stack the equations on top of each other.
2x + 3y = 5
3x + 4y = 6
Next let's manipulate one or both of the equations to get coefficients that are equal, but opposite. For this I'm going to turn the coefficient of x into 6 and -6 respectively by multiplying the first equation by 3 and the second by -2 to get
6x + 9y = 15
-6x -8y = -12
Now we can combine the equations with addition and the x's will cancel leaving a single variable (which we can solve)
y = 3
Now plug this back into either original equation to find the x coordinate.
2x + 3(3) = 5
2x + 9 = 5
2x = -4
x = -2.
So your intersection point is (-2,3)
I believe that the answer would be to add 10 to both sides, srry if I'm incorrect!
Answer:
d
Step-by-step explanation:
Answer:
V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π
Step-by-step explanation:
Since we have the radius of the sphere R = 4, we have R² = r² + z² where r = radius of cylinder in z-plane and z = height² of cylinder.
So, r = √(R² - z²)
r = √(4² - z²)
r = √(16 - z²)
Since the region is above the plane z = 2, we integrate z from z = 2 to z = R = 4
Our volume integral in cylindrical coordinates is thus
V = ∫∫∫rdrdθdz integrating from z = 2 to z = 4, r = 0 to √(16 - z²) and θ = 0 to 2π
The answer is: Find the mean of the differences with the other numbers in the set<span>. Add the squared differences and then divide the total by the number of items in </span>data<span> in your </span>set; t<span>ake the square root of this mean of differences to </span>find<span> the standard </span>deviation.
