Answer:
Part a. t = 7.29 years.
Part b. t = 27.73 years.
Part c. p = $3894.00
Step-by-step explanation:
The formula for continuous compounding is: A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.
Part a. It is given that p = $2000, r = 2.5%, and A = $2400. In this part, t is unknown. Therefore: 2400 = 2000*e^(2.5t). This implies 1.2 = e^(0.025t). Taking natural logarithm on both sides yields ln(1.2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(1.2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(1.2)/0.025. This means that t = 7.29 years (rounded to the nearest 2 decimal places)!!!
Part b. It is given that p = $2000, r = 2.5%, and A = $4000. In this part, t is unknown. Therefore: 4000 = 2000*e^(2.5t). This implies 2 = e^(0.025t). Taking natural logarithm on both sides yields ln(2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(2)/0.025. This means that t = 27.73 years (rounded to the nearest 2 decimal places)!!!
Part c. It is given that A = $5000, r = 2.5%, and t = 10 years. In this part, p is unknown. Therefore 5000 = p*e^(0.025*10). This implies 5000 = p*e^(0.25). Making p the subject gives p = 5000/e^0.25. This means that p = $3894.00(rounded to the nearest 2 decimal places)!!!
Answer:
The length is 16 ft, and the width is 3 ft.
Step-by-step explanation:
Let L = length & let W = width.
The perimeter of a rectangle is
P = 2(L + W)
The area of a rectangle is
A = LW
We know the perimeter and the area, so we substitute those values int he equations above and we switch sides in both equations.
Perimeter: 2(L + W) = 38
Divide both sides by 2:
L + W = 19
Area: LW = 48
We have a system of two equations in two unknowns:
L + W = 19
LW = 48
Solve the first equation for L and substitute it into the second equation.
L = 19 - W
(19 - W)W = 48
19W - W^2 - 48 = 0
Multiply both sides by -1, and rearrange the order of the terms.
W^2 - 19W + 48 = 0
(W - 16)(W - 3) = 0
W - 16 = 0 or W - 3 = 0
W = 16 or W = 3
Use W = 3 to find L
L = 19 - W
L = 19 - 3
L = 16
Answer: The length is 16 ft, and the width is 3 ft.
Answer:
960
Step-by-step explanation:
This is a triangular prism. It has 5 faces. Two faces are congruent triangles. The other 3 faces are rectangles.
SA = 2 × ½bh + L₁W₁ + L₂W₂ + L₃W₃
SA = 2 × ½ × 10 in. × 24 in. + 10 in. × 12 in. + 26 in. × 12 in. + 24 in. × 12 in.
SA = 960 in.²
Answer:
8/24=1/3
Step-by-step explanation:
just do math
