A cylinder has a volume of 320 pi cu. in. and a height of 5". Find the radius of the cylinder.
1 answer:
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The solution of the word problem is a = 2
Word Problems are mathematical problems presented in complete languages, rather than in mathematical notations.
Example: Let a number is divided by half, the result is added to itself to give 6, what is the number?
Solution: Let the number be a
Now, dividing a by half, we get
a ÷ = 2a
Now, adding the result to the number itself, we will get 6 i.e.,
2a + a = 6
3a = 6
Dividing both the sides by 3, we get
a = 2
Therefore, the solution is a = 2
Complete question: Write your own word problem and share it with the group. Then translate your problem into its resulting math equation. What steps would you then follow to solve for the variable?
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Answer:
Step-by-step explanation:
Given equation is,
y = 3x² - 6x + 11
a). y = 3x² - 6x + 11
= 3(x² - 2x) + 11
= 3(x² -2x + 1 - 1) + 11
= 3(x² - 2x + 1) - 3 + 11
= 3(x - 1)² + 8
Comparing this equation with y = a(x - b)² + c
a = 3, b = 1 and c = 8
b). For minimum value of x,
Since, vertex of the graph is given by (b, c),
Minimum value of x will be,
x = b
x = 1
c). Vertex of the parabola → (b, c)
→ (1, 8)
For y-intercept,
By substituting x = 0 in the equation,
y = 3(0 - 1)² + 8
y = 11
Now we can sketch the graph by using the table of input - output values.
x -2 -1 0 1 2 3
y 35 20 11 8 11 20
(-2, 5) Minimum
Step-by-step explanation:
y-5=(1/3)(x + 2)²
y-5=(1/3)(x²+4x+4))
y-5=1/3x²+4/3x+4/3
y=1/3x²+4/3x+4/3+5
y=1/3x²+4/3x+4/3+15/3
y=1/3x²+4/3x+19/3
graph is attached
x= -b/2a
x= (-4/3)/2(1/3)
x= (-4/3)/(2/3)
x= (-4/3)*(3/2)
3's cancel
x= (-4/1)*(1/2)
x = -4/2
x = -2
plug -2 back into
y=1/3x²+4/3x+19/3
y=1/3*4+4/3*-2+19/3
y=4/3-8/3+19/3
y=15/3
y=5
(-2,5)
if a is positive
graph looks like a smile
so minimum
if a is negative
graph looks like a frown
so maximum
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