Answer:
the cost of the four meal is $4.00
Answer:
y"(2, 1) = -5
Step-by-step explanation:
Step 1: Define implicit differentiation
5 - y² = x²
Step 2: Find dy/dx
- Take implicit differentiation: -2yy' = 2x
- Isolate y': y' = 2x/-2y
- Isolate y': y' = -x/y
Step 3: Find d²y/dx²
- Quotient Rule: y'' = [y(-1) - y'(-x)] / y²
- Substitute y': y" = [-y - (-x/y)(-x)] / y²
- Simplify: y" = [-y - x²/y] / y²
- Multiply top/bottom by y: y" = (-y² - x²) / y³
- Factor negative: y" = -(y² + x²) / y³
Step 4: Substitute and Evaluate
y"(2, 1) = -(1² + 2²) / 1³
y"(2, 1) = -(1 + 4) / 1
y"(2, 1) = -5/1
y"(2, 1) = -5
This will give us
That is the second option.
Please mark me as brainliest.
4. To solve this problem, we must simply subtract the volume of the smaller box from the volume of the larger box. The formula for volume of a rectangular prism is length * width * height. So we know that the bigger box has a height of 20 inches, a length of 15 inches, and a height of 9 inches. We can multiply these together to get the volume.
20 * 15 = 300
300 * 9 = 2700
The bigger box has a volume of 2,700 cubic inches.
Now for the smaller box. This box has a length of 12 inches, a width of 8 inches, and a height of 4 inches. Let us multiply this together:
12 * 8 = 96
96 * 4 = 384
The smaller box has a volume of 384 cubic inches.
Now, we just need to subtract.
2700 - 384 = 2316
There are 2,316 cubic inches of space left in Jeff's bigger box.
5. Mrs. Nelson has plans for a flower box that has two constant side lengths, the length and height (5 feet and 2 feet). The width can be any whole number (counting number) only up to 5 feet, so there are 5 different volumes she could have. Those are:
5 * 2 * 1 = 10 cubic feet
5 * 2 * 2 = 20 cubic feet
5 * 2 * 3 = 30 cubic feet
5 * 2 * 4 = 40 cubic feet
and
5 * 2 * 5 = 50 cubic feet
The possible volumes for Mrs. Nelson's flower box are 10, 20, 30, 40, and 50 cubic feet.
So there you have it!
Hope that helped! =)
