Joe borrowed $7000 from the bank at a rate of 7% simple interest per year how much interest did he pay in six years
2 answers:
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Given the vertex, (2, -4) as the minimum point, and that it is an upward-facing parabola that passes point (1, -2):
We could substitute these values into the vertex form of the quadratic function,
f(x) = a(x - h)^2 + k
where:
(h,k) is the vertex
The axis of symmetry is the vertical line x = 2
The value of “a” determines whether the graph opens up or down, and makes the parent function wider or narrower.
The value of “h” determines how far left or right the parent function is translated.
The value of “k” determines how far up or down the parent function is translated.
Now that we’ve established these definitions, we can substitute the given values into the vertex form:
f(x) = a(x - 2)^2 - 4
In order to determine the value of “a”, we must substitute the values of the other given point, (1, -2) into the equation:
f(x) = a(x - 2)^2 - 4
-2 = a(1 - 2)^2 - 4
-2 = a(-1)^2 - 4
-2 = a - 4
Add 4 to both sides to solve for “a”
-2 + 4 = a - 4 + 4
2 = a
Now that we have the value of a = 2, we can establish our quadratic function in vertex form:
f(x) = 2(x - 2)^2 - 4
I’m also including a screenshot of the graph of the function we came up with.
Please mark my answers as the Brainliest if you find my explanations helpful :)
We could substitute these values into the vertex form of the quadratic function,
f(x) = a(x - h)^2 + k
where:
(h,k) is the vertex
The axis of symmetry is the vertical line x = 2
The value of “a” determines whether the graph opens up or down, and makes the parent function wider or narrower.
The value of “h” determines how far left or right the parent function is translated.
The value of “k” determines how far up or down the parent function is translated.
Now that we’ve established these definitions, we can substitute the given values into the vertex form:
f(x) = a(x - 2)^2 - 4
In order to determine the value of “a”, we must substitute the values of the other given point, (1, -2) into the equation:
f(x) = a(x - 2)^2 - 4
-2 = a(1 - 2)^2 - 4
-2 = a(-1)^2 - 4
-2 = a - 4
Add 4 to both sides to solve for “a”
-2 + 4 = a - 4 + 4
2 = a
Now that we have the value of a = 2, we can establish our quadratic function in vertex form:
f(x) = 2(x - 2)^2 - 4
I’m also including a screenshot of the graph of the function we came up with.
Please mark my answers as the Brainliest if you find my explanations helpful :)
The answer is 15 in³.
The volume of the cone is:
where:
V₁ - the volume of the cone
r₁ - the radius of the cone
h₁ - the height of the cone
The volume of the cylinder is:
where:
V₂ - the volume of the cone
r₂ - the radius of the cone
h₂ - the height of the cone
Since <span>the cone fits exactly inside of the cylinder, they have the same radius and the height:
r</span>₁ = r₂
h₁ = h₂
Also:
V₁ = 5
Now, let's write two volume formulas together:
<span>
</span>
We can include V₂ into V₁:
⇒
The volume of the cone is:
where:
V₁ - the volume of the cone
r₁ - the radius of the cone
h₁ - the height of the cone
The volume of the cylinder is:
where:
V₂ - the volume of the cone
r₂ - the radius of the cone
h₂ - the height of the cone
Since <span>the cone fits exactly inside of the cylinder, they have the same radius and the height:
r</span>₁ = r₂
h₁ = h₂
Also:
V₁ = 5
Now, let's write two volume formulas together:
<span>
We can include V₂ into V₁:
⇒