Find the x- and y-intercept of the parabola y = x² + 4x + 2
1 answer:
Answer:
x-intercept = (- 2 + √2, 0) (- 2 - √2, 0)
y-intercept = (2, 0)
Step-by-step explanation:
<u>Given expression</u>
y = x² + 4x + 2
<u>Find the x-intercept</u>
<em>Definition of x-intercept is the point that intersects with the x-axis, which means the y value is 0</em>
(0) = x² + 4x + 2
(x + 2 - √2) (x + 2 + √2) = 0
x = -2 ± √2
Therefore, the x-intercepts are
<u>Find the y-intercept</u>
<em>Definition of x-intercept is the point that intersects with the y-axis, which means the x value is 0</em>
y = (0)² + 4(0) + 2
y = 0 + 0 + 2
y = 2
Therefore, the y-intercept is
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Answer:
a) 0.012ft³
b)2.09 lb
c)0.791 lb
d) 0.012ft³
e) 6 inches
Step-by-step explanation:
a) To determine the volume of the shell of the jar we must determine the volume of the hollow cylinder:
Where r is the inside radius and R the outer radius.
convert to cubic ft:
The volume of the glass shell is 0.012 ft³
b) The weight of the cylinder can be determined because we have the volume and the density. Weight is defined as the product of volume and density:
The weight of the jar is 2.09 lb
c) The displacement of water is just the density of water mutliplied by the volume of the jar:#
0.791 lb of water will be displaced.
d) The volume of the water displaced is:
[tex]=0.791/62.5=0.01266
e) The jar will be fully submerged because the density of the jar is larger than water.