Answer:
The total distance traveled by the particle is S = 30.
Step-by-step explanation:
Given that velocity,
v(t) = 2t + 1
To find the total distance travel, we integrate the velocity function, v(t), to obtain the distance function s(t), and evaluate the resulting distance at the interval given. That is at t = 0 to t = 5.
Integrating v(t) with respect to t, we have
s(t) = t² + t + C.
At t = 5
s(5) = 5² + 5 + C
= 25 + 5 + C
= 30 + C
At t = 0
S(0) = 0 + 0 + C
= C
The required distance is now
S(5) - S(0)
= 30 + C - C
= 30.
Answer:
114 ft
Step-by-step explanation:
Imagine or construct a right triangle with the 46 ft leg lying on the ground. This is the "adjacent side" of the triangle; it lies immediately adjacent to the 68 degree angle. The side opposite this angle is h, the height of the tree.
The tangent function includes angle, opp side and adj side:
tan 68 degrees = opp / adj = h / (46 ft), and so:
(46 ft)*tan (68 degrees) = opp = h
Then the height of the tree is h = (46 ft)(2.47) = 114 ft
Answer:
First you have to multiply negative four in parentheses, then add minus two
-4×(-8+3x)=32-12x
2+32-12x=34-12x
34-12x=82
-12x=48
x=-4
Answer: the cost of each bush is $15
the cost of each flower is $2
Step-by-step explanation:
Let x represent the cost of each bush.
Let y represent the cost of each flower.
Portia bought 12 bushes and 30 flowers for $240 to plant in her yard. This is expressed as
12x + 30y = 240- - - - - - - - - - -1
Later, she realized she did not have enough plants and bought 7 more bushes and 10 more flowers for $125. This is expressed as
7x + 10y = 125- - - - - - - - - - -2
Multiplying equation 1 by 7 and equation 2 by 12, it becomes
84x + 210y = 1680
84x + 120y = 1500
Subtracting, it becomes
90y = 180
y = 180/90
y = 2
Substituting y = 2 into equation 1, it becomes
12x + 30 × 2 = 240
12x + 60 = 240
12x = 240 - 60 = 180
x = 180/12
x = 15
