R(t) = integral of r'(t) = integral of ti + e^tj + te^tk = 1/2t^2i + e^tj + (te^t - e^t)k + c
r(0) = j - k + c = i + j + k
c = i + 2k
Therefore, r(t) = (1/2t^2 + 1)i + e^tj + (te^t - e^t + 2)k
Answer:
60
Step-by-step explanation:
Let s represent the number of stickers Sophia has. Then the number Ethan has is (2/3)s. The transfer of 16 stickers can be described by the equation ...
(s -16)/(2/3s +16) = 1/2 . . . . . sophia/ethan = 1/2 after the transfer
2s -32 = 2/3s +16 . . . . . . . . .cross multiply
4/3s = 48 . . . . . . . . . . . . . . . add 32-2/3s
s = (48)(3/4) = 36 . . . . . . . . .multiply by 3/4
Together, the total number of stickers held is s +(2/3)s = (5/3)s.
5/3s = (5/3)(36) = 60 . . . . . total of Sophia's and Ethan's stickers
Together, Sophia and Ethan have 60 stickers.
15 minutes = 1/4 of an hour = 0.25
64 x 4.25 =272 miles total
We have a fraction with the unknown in the denominator, review how to treat unknowns in the denominator as a refresher for this exercise:
<span>(2/3) - (1/x + 6) = 2
</span>(2/3) - (1 + 6x)/x = <span>2
</span>(2/3) - 2 = (1 + 6x)/x
2/3 - 6/3 = (1 + <span>6x)/x
-4/3 = </span>(1 + <span>6x)/x
-4x = 3</span>(1 + <span>6x)
</span><span>-4x = 3 + 18x
</span>22x = -3
x = -3/22
Answer:
7x⁴ + 5x³ + 7x² + 6x + 5
Step-by-step explanation:
The given expression is
(5x4 + 5x3 + 4x - 9) + (2x4 + 7x2 + 2x + 14)
The first step is to open the brackets by multiplying each term inside each bracket by the term outside each bracket. Since the term outside each bracket is 1, the expression becomes
5x⁴ + 5x³ + 4x - 9 + 2x⁴ + 7x² + 2x + 14
We would collect like terms by combining each term with the same exponent or raised to the same power. The term would be arranged in decreasing order of the exponents. It becomes
5x⁴ + 2x⁴ + 5x³ + 7x² + 4x + 2x - 9 + 14
7x⁴ + 5x³ + 7x² + 6x + 5
