Answer:
a) -36
b) y = -36x +34
Step-by-step explanation:
a) The slope is found using the derivative of the function.
f'(x) = dy/dx = 0 -9(2x) = -18x
Then at x=2, the slope is ...
f'(2) = -18·2 = -36
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b) The point-slope form of the equation can be written as ...
y = -36(x -2) -38
Simplifying to slope-intercept form, we get ...
y = -36x +34
If she went 10 miles upstream in the same time as she went 20 miles downstream, that means the downstream speed is twice the upstream speed.
The speed is still water is 9 mph.
The speed of the current is c.
Going downstream, the current adds speed, so the sped downstream is 9 + c.
The speed upstream is 9 - c.
9 + c is twice 9 - c.
9 + c = 2(9 - c)
9 + c = 18 - 2c
3c = 9
c = 3
Answer: The speed of the current is 3 mph.
Check:
9 + c = 12
9 - c = 6
By taking into the account the speed of the current, the downstream speed, 12 mph, is indeed twice the upstream sped, 6 mph.
<span>Coffee mug is cylindrical in shape.
So, volume of cylinder = V=π r² h
Mass of coffee = 400 g which is filled to a depth of 8.00 cm. so, h=8.00 cm
density of water = 1 g/cmÂł
Density = mass/volume
1 g/cmÂł = 400g / volume
volume = (400g) / (1 g/cmÂł)
volume = 400 cmÂł
As,
volume of cylinder -
V=π r² h
400 cm³ = π r^2 x 8.00 cm
π r² = (400 cm³) / (8.00 cm)
π r² = 50 cm²
r² = (50)/ π
r² = 15.924 cm²
Taking square root on both sides -
r =3.99 cm
r =4.00 cm
Answer: Thhe inside radius of coffee mug is 4.00 cm</span>
