Let <span>the town courthouse be the origin of coordinate plane, the positive direction of x-axis is west and negative direction is east, the positive direction of y-axis is north and negative direction is south. Then a lawyer home has coordinates (-2,3) and lawyer office has coordinates (5, -21).
</span>
Use the distance formula
to get the <span>distance between lawyer's home and office:
</span><span>
</span><span />
.
Answer: 25 miles.
Answer:
Step-by-step explanation:
g(5)= (-5)^2 + 5(-2) - 4
25 - 10 - 4
15 - 4 = 11
f(11)= (11)^2 + 2(11) + 3
121 + 22 + 3
143 + 3 = 146
Answer:
8 = x
y = 29
Step-by-step explanation:
4x + 17 = y + 20 because vertical angles theorem.
y + 20 = 5x + 9 because interior angles theorem.
4x + 17 = 5x + 9 because same side interior angles theorem.
Subtract 9 from both sides and subtract 4x from both sides.
8 = x
Plug 8 in for x and solve.
5 times 8 is 40, plus 9 equals 49. Subtract 20 from both sides and you get 29.
5(8) + 9 = y + 20
49 = y + 20
29 = y
I hope this helps!
#teamtrees #WAP (Water And Plant)
9514 1404 393
Answer:
8000π mm^3/s ≈ 25,133 mm^3/s
Step-by-step explanation:
The rate of change of volume is found by differentiating the volume formula with respect to time.
V = 4/3πr^3
V' = 4πr^2·r'
For the given numbers, this is ...
V' = 4π(20 mm)^2·(5 mm/s) = 8000π mm^3/s ≈ 25,133 mm^3/s
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<em>Additional comment</em>
By comparing the derivative to the area formula for a sphere, you see that the rate of change of volume is the product of the area and the rate of change of radius. This sort of relationship will be seen for a number of different shapes.
