Answer:
Answer =C
Step-by-step explanation:
F= 9
So teh answer is 9
The plane you want is parallel to another plane, <em>x</em> - <em>y</em> + <em>z</em> = -5, so they share a normal vector. In this case, it's ⟨1, -1, 1⟩.
The plane must also pass through the point (0, 4, 4) since it contains <em>r</em><em>(t)</em>. Then the equation of the plane is
⟨<em>x</em>, <em>y</em> - 4, <em>z</em> - 4⟩ • ⟨1, -1, 1⟩ = 0
<em>x</em> - (<em>y</em> - 4) + (<em>z</em> - 4) = 0
<em>x</em> - <em>y</em> + <em>z</em> = 0
Answer:
-2x³+4x
Step-by-step explanation:
g(x) + f(x)
(2x) + (-2x³+2x)
-2x³+4x
Answer:
n = 3
Step-by-step explanation:
Given
4n = 2n + 6 ( subtract 2n from both sides )
2n = 6 ( divide both sides by 2 )
n = 3
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)!!!
