Given that the quadratic equation is 
We need to determine the y - value of the vertex.
<u>The x - value of the vertex:</u>
The x - value of the vertex can be determined using the formula,
where 
Substituting these values, we get;
Simplifying the terms, we get;
Thus, the x - value of the vertex is -5.
<u>The y - value of the vertex:</u>
The y - value of the vertex can be determined by substituting the x - value of the vertex ( x = -5) in the equation
Thus, we get;
Simplifying the values, we have;
Thus, the y - value of the vertex is 49.
Answer:
50% change in volume
Step-by-step explanation:
<h2>
This problem bothers on the mensuration of solid shapes.</h2>
In this problem we are to find the volume of the first cylinder and compare with the second cylinder.
Given data
Volume v = ?
Diameter d=
?
Radius r = 
Height h= 
we know that the volume of a cylinder is expressed as
Substituting our given data we have
The first cylinder as a volume of 
The change in volume is 
percentage = 
%
Answer:
<h2>
y = -⁵/₂x - 12
</h2>
Step-by-step explanation:
The point-slope form of the equation is y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope:
m = -⁵/₂
(-4, -2) ⇒ x₀ = -4, y₀ = -2
The point-slope form of the equation:
y + 2 = -⁵/₂(x + 4)
So:
y + 2 = -⁵/₂x - 10 {subtract 2 from both sides}
y = -⁵/₂x - 12 ← the slope-intercept form of the equation
Answer:
p =2 p=-18
Step-by-step explanation:
|p+8|
-------------- = 5
2
Multiply each side by 2
|p+8|
-------------*2 = 5*2
2
|p+8| =10
There is a positive and a negative solution
p+8=10 p+8=-10
Subtract 8 from each side
p+8-8=10-8 p+8-8=-10-8
p =2 p=-18
Answer:
Verified
Step-by-step explanation:
Question:-
- We are given the following non-homogeneous ODE as follows:
- A general solution to the above ODE is also given as:
- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.
Solution:-
- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.
- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:
- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.
- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:
- Therefore, the complete solution to the given ODE can be expressed as:
- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:
- Therefore, the complete solution to the given ODE can be expressed as:
