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:
LCM = 4590
Step-by-step explanation:
1. Find the prime factorization of 306
306 = 2 × 3 × 3 × 17
2. Find the prime factorization of 270
270 = 2 × 3 × 3 × 3 × 5
3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2 × 3 × 3 × 3 × 5 × 17
X-3y=-5
-(x+3y=1)
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-6y=-6
y=1
x=-2
Y=(x-h)^2+k where (h,k) is the vertex
So, equation of new parabola is:
y=(x+1)^2+7
Answer:
The length of one side of the square is 3.
Step-by-step explanation:
The perimeter of any given shape is all of the sides added together. So, the perimeter of the triangle is 5x + 4x + 3x. Added together, 12x.
The perimeter of the square is (x + 2)*4. Distributed, it's 4x + 8. Since we know they're equal, set it up like this:
12x = 4x + 8
You then find that x = 1. Plug that into one side of the square, x + 2, to get 3.
