Given:
Lateral Area = π * r * (√h² + r²)
Lateral Area = 100 in² ; height = 5 in
I find it hard to derive the formula of r because of the radical sign. So, I'll just plug each radius to the formula to check confirm the given lateral area.
a) r = 1.52138 ⇒ LA = 24.98
b) r = 4.658 ⇒ LA = 100
c) r = 78 ⇒ LA = 19152.68
d) r = 6.7432 ⇒ LA = 177.84
The radius is B.) r = 4.658 inches
Answer:
<h3>AB ≈ 70m</h3>
Step-by-step explanation:
Check the attachment for the diagram.
You can see from the diagram that it is a right angled triangle with opposite side AB and adjacent side BC. Using SOH, CAH, TOA trig identity to get the length of AB. According to TOA;
tan 35° = opposite/adjacent
tan 35° = AB/BC
tan 35° = AB/100
AB = 100tan35°
AB = 100 * 0.7002
AB = 70.02m
Hence the distance across a lake between A and B is approximately 70m
Both the general shape of a polynomial and its end behavior are heavily influenced by the term with the largest exponent. The most complex behavior will be near the origin, as all terms impact this behavior, but as the graph extends farther into positive and/or negative infinity, the behavior is almost totally defined by the first term. When sketching the general shape of a function, the most accurate method (if you cannot use a calculator) is to solve for some representative points (find y at x= 0, 1, 2, 5, 10, 20). If you connect the points with a smooth curve, you can make projections about where the graph is headed at either end.
End behavior is given by:
1. x^4. Terms with even exponents have endpoints at positive y ∞ for positive and negative x infinity.
2. -2x^2. The negative sign simply reflects x^2 over the x-axis, so the end behavior extends to negative y ∞ for positive and negative x ∞. The scalar, 2, does not impact this.
3. -x^5. Terms with odd exponents have endpoints in opposite directions, i.e. positive y ∞ for positive x ∞ and negative y ∞ for negative x ∞. Because of the negative sign, this specific graph is flipped over the x-axis and results in flipped directions for endpoints.
4. -x^2. Again, this would originally have both endpoints at positive y ∞ for positive and negative x ∞, but because of the negative sign, it is flipped to point towards negative y ∞.
Answer:
10.2 years
gain is $2,704.00
rate of return is 22%
Step-by-step explanation:
The it would take for mutual to double can be determined the future value formula as shown below:
=nper(rate,pmt,-pv,fv)
rate is the rate of return of 7% per year
pmt is the periodic amount placed in the mutual fund and it not applicable here
pv is the original amount invested which is $7,500
fv is the future worth of $15,000
=nper(7%,0,-7500,15000)=10.2 years
cost of shares=actual cost of purchase+broker's commission
=(800*$15.34)+$20=$12,292.00
gain on shares=sales proceeds-cost=(800*$18.77)-$20-$12,292.00=$2,704.00
rate of return=gain/original cost=$2,704.00/$12,292.00 =22%
Answer:
The Standard Deviation
Step-by-step explanation:
Your concentration should be on what the standard deviation tells us about the data. The standard deviation is a number which measures how far the data are spread from the mean. Let a calculator or computer do the arithmetic. The standard deviation, s or σ , is either zero or larger than zero.
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