Answer:
84.71 cm^3
Step-by-step explanation:
Volume = Base * height
Base = 19.7
Height = 4.3
Base * Height = 19.7 * 4.3 = 84.71 = Area
9514 1404 393
Answer:
c = -3; d = 5
Step-by-step explanation:
The function is differentiable if it is continuous and the derivative is continuous.
This function will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
5(3^2) +c = 45 +c
From the right, the limit is ...
d(3^2) -3 = 9d -3
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The derivative will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...
f'(x) = 10x
= 10(3) = 30
From the right, the limit is ...
f'(x) = 2dx
= 2d(3) = 6d
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This gives us a pair of simultaneous equations in 'c' and 'd':
45 +c = 9d -3
6d = 30
The latter tells us d = 5. Then the former tells us ...
45 +c = 9(5) -3 ⇒ c = -3
The function is differentiable if c = -3 and d = 5.
_____
<em>Additional comment</em>
With these values, the function becomes ...
![f(x)=\begin{cases}5x^2-3&\text{if }x\le 3\\5x^2-3&\text{if }x>3\end{cases}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cbegin%7Bcases%7D5x%5E2-3%26%5Ctext%7Bif%20%7Dx%5Cle%203%5C%5C5x%5E2-3%26%5Ctext%7Bif%20%7Dx%3E3%5Cend%7Bcases%7D)
Answer:
Distance between two point = 3.6 (Approx.)
Step-by-step explanation:
Given:
Coordinate;
(-4, -6) and (-1, -4)
Find:
Distance between two point
Computation:
Distance between two point = √(x1 - x2)² + (y1 - y2)²
Distance between two point = √(-4 + 1)² + (-6 + 4)²
Distance between two point = √(-3)² + (-2)²
Distance between two point = √9 + 4
Distance between two point = √13
Distance between two point = 3.6 (Approx.)
Answer:
The investment will generate a NPV of $2,731.
Step-by-step explanation:
Cost of an investment (PV) = $5,000
Annual cash flows = $3,000
Period of investment = 3 years
Interest rate of return = 8%
Annuity Factor = 2.577 (for 3 years at 8% per year)
Present value of the annuity = $3,000 * 2.577 = $7,731
NPV = Annuity PV minus PV of investment cost
= $7,731 - $5,000
= $2,731
b) The NPV (net present value) of $2,731 is the difference between the present value of the annual cash flows $7,731 and the investment cost of $5,000. The resulting NPV is positive and the investment should be accepted.
Answer:
Rational Number
Step-by-step explanation:
A rational number is, by definition, a number that can be expressed as the quotient or fraction of p/q of two integers, a numerator <em>p</em> and a non-zero denominator <em>q</em>. 33/3 is a fraction of p/q of two integers, a numerator <em>p</em>, or 33, and a non-zero denominator <em>q</em>, or 3. This makes 33/3 a rational number.