Answer:
r = -12cos(θ)
Step-by-step explanation:
The usual translation can be used:
Putting these relationships into the formula, we have ...
(r·cos(θ) +6)² +(r·sin(θ))² = 36
r²·cos(θ)² +12r·cos(θ) +36 +r²·sin(θ)² = 36
r² +12r·cos(θ) = 0 . . . . subtract 36, use the trig identity cos²+sin²=1
r(r +12cos(θ)) = 0
This has two solutions for r:
r = 0 . . . . . . . . a point at the origin
r = -12cos(θ) . . . the circle of interest
Answer:
-3.47 inches per minute
Step-by-step explanation:
Let the height be 'h' for any time 't'.
Given:
Length of the prism (L) = 10 in
Width of the prism (w) = 16 in
The rate of change of volume of prism is, (The negative sign implies the volume decreases with time.)
Now, rate of change of height of prism =
Length and width remains constant.
Now, we know that, volume of a rectangular prism is given as:
Volume = Length × width × Height
Now, differentiating both sides with respect to time 't', we get:
Plug in the given values and solve for . This gives,
The negative sign implies the height decreases with time.
Therefore, the the rate of change, in inches per minute, of the height when the height is 3 inches is -3.47 inches per minute.
9514 1404 393
Answer:
-10
Step-by-step explanation:
The first step is to write what you mean. We think you mean (-1000)^(1/3).
If you've been paying attention to place-value, and/or cubes of small integers, you already know that 10^3 = 1000. Since we're concerned with an odd power, we also know ...
-1000 = (-10)^3
Then your expression is ...
(-1000)^(1/3) = ((-10)^3)^(1/3) = (-10)^(3/3) = (-10)^1 = -10
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Some calculators can evaluate this for you (see attached).
Some calculators and spreadsheets use logarithms to compute roots or fractional powers, so will give you an error when you try to compute this. You should know that an odd-index root of a negative number (here, 3rd root of -1000) has the same sign as the number: negative. Then you can use your calculator to compute the positive root and add the sign yourself:
(-1000)^(1/3) = -(1000^(1/3)) = -(10) = -10
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Of course, a 1/3 power is the same as a cube root. Your calculator may have a cube root button that works just fine with negative numbers.
