The slope of this line is____.
2 answers:
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Answer:
The amount of the chemical flows into the tank during the firs 20 minutes is 4200 liters.
Step-by-step explanation:
Consider the provided information.
A chemical flows into a storage tank at a rate of (180+3t) liters per minute,
Let is the amount of chemical in the take at <em>t </em>time.
Now find the rate of change of chemical flow during the first 20 minutes.
So, the amount of the chemical flows into the tank during the firs 20 minutes is 4200 liters.
Answer:
The coordinates of the centroid are (0, 5)
Step-by-step explanation:
The coordinates of the centroid of a triangle whose vertices (x1, y1), (x2, y2), and (x3, y3) are ( ,
)
In Δ ABC
∵ A = (-20, 0), B = (0, 15), C = (20, 0)
∴ x1 = -20, x2 = 0, x3 = 20
∴ y1 = 0, y2 = 15, y3 = 0
∴ The centroid = ( ,
) = (
,
) = (0, 5)
∴ The coordinates of the centroid of Δ ABC are (0, 5)
In Δ DBE
∵ D = (-15, 0), B = (0, 15), E = (15, 0)
∴ x1 = -15, x2 = 0, x3 = 15
∴ y1 = 0, y2 = 15, y3 = 0
∴ The centroid = ( ,
) = (
,
) = (0, 5)
∴ The coordinates of the centroid of Δ DBE are (0, 5)
In Δ FBG
∵ F = (-5, 0), B = (0, 15), G = (5, 0)
∴ x1 = -5, x2 = 0, x3 = 5
∴ y1 = 0, y2 = 15, y3 = 0
∴ The centroid = ( ,
) = (
,
) = (0, 5)
∴ The coordinates of the centroid of Δ FBG are (0, 5)
∵ The three triangles are symmetric about the y-axis
→ That means they have the same centroid and it lies on the y-axis
∴ The coordinates of the centroid are (0, 5)
Answer:
f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}
Step-by-step explanation:
To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.
__
<h3>Left Piece</h3>The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.
The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.
The first piece can be written ...
f(x) = x-3 for x ≤ -1
__
<h3>Right Piece</h3>The domain is shown as 5 to ∞, with 5<em> not included</em>.
The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...
y -(-1) = -3(x -5)
y = -3x +15 -1 = -3x +14
The second piece can be written ...
f(x) = -3x +14 for x > 5
__
<h3>Whole function</h3>Putting these pieces together, we have ...
_____
<em>Additional comment</em>
Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.