A ball is thrown straight out at 80 feet per second from an upstairs window that's 15 feet off the ground. It turns out that its motion can be broken down into its motion in the x-direction (horizontally) and its motion in the y-direction (vertically), and that those two components can be thought of completely independently. In other words, its horizontal motion has no influence on its vertical motion, and vice versa. I've written the two component functions here: x(t) is its position in the x-direction, and y(t) is its position in the y-direction. Which of the following choices is correct? (Ignore air resistance.) NOTE: Use a reference frame that makes all positions (x and y coordinates) of the projectile positive.
Answers
Answer:
Step-by-step explanation:
Given that ball is thrown vertically with intial velocity 80 ft per second at a height of 15 feet off the ground.
Let angle of the ball thrown with horizontal be A
Then vertical velocity = 80 sinA
HOrizontal velocity = 80 cosA
Acceleration here is negative gravity
In fps system gravity g = -32ft/sec^2
s=ut+1/2at^2
Substitute to get
h(t) = 80cos A t-16t^2 +15 (since initial height is 15 ft)
x(t) = 80 sin A t
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Answers
The value of the car in 2020 is $5532.53
What is exponential decay?
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
Given that, You purchase a car in 2010 for $25,000. The value of the car decreases by 14% annually.
The exponential decay is given by =
A = final amount
P = principal amount
r = rate of decrease.
t = 10
Therefore,
A = 25000(1-0.14)¹⁰
A = 25000×0.86¹⁰
A = 5532.53
Hence, the value of the car in 2020 is $5532.53
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Answer:
42,690
Step-by-step explanation:
it is the rule of LONG numbers
Answers
Answer:
Ashley= 15
Milan= 11
Carlos= 105
Step-by-step explanation:
Let, A, M and C denotes Ashley, Milan and Carlos respectively.
A+M+C= 131 (according to the question)
Here,
C= 7A
A= M+ 4
So, M= A - 4
Now,
A+M+C = 131
or, A+ A-4+ 7A = 131 (putting the values)
or, 9A - 4 = 131 (adding like terms i.e. A + A + 7A)
or, 9A = 131 + 4
or, 9A = 135
or, A = 135 / 9
So, A = 15
C= 7A = 7×15= 105
M= A-4 = 15 - 4 = 11
Answers
Answer:
Construction of an angle bisector is partially represented by the diagram on the baseball field.
Step-by-step explanation:
Angle bisector of an angle bisects it into two equal angles.
Construction of an angle bisector is partially represented by the diagram on the baseball field.
Consider the figure:
From point B, draw an arc by opening the compass up to the same extend as we did while drawing arc from point A.
Take the point of intersection of both the arcs as C.
Join OC.
OC is the angle bisector of the angle.
Answers
and you're asked to find the determinant of
and given that
There are two properties of the determinant that come into play here:
(1) Whenever a single row/column is scaled by a constant
(2) Adding/subtracting rows does not change the value of the determinant.
Taken together, we have that
Final answer:
Due to insufficient information, we cannot calculate the determinant of the given matrix. The determinant calculation varies based on the matrix's size and the specifics of its elements.
Explanation:
The question asked was to find the determinant of a given matrix when the det(a) = 2. However, the information provided is insufficient to determine the actual matrix determinant due to numerical errors and unrelatable data. The determinant of a matrix is calculated differently depending on the type of matrix. For a 2x2 matrix, if the matrix is [a b; c d], the determinant would be 'ad - bc'. For a 3x3 matrix, the determinant process involves more steps including finding minors and cofactors of matrix elements. However, without the actual specifics of the matrix, the determinant cannot be calculated.
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Answers
Answer:
13 pages : 1/2 hour Multiply both sides by 2
26 pages : 1 hour ------>> 26 pages/hr
Flip over 26 pages/hr ----->>> hr / 26 pages = 1 hr / 26 pages
Split up the fraction: (1/26) hr / page
Answer:
26
Step-by-step explanation:
13 in 1/2 hour
13:1/2
26:1
Answers
Answer:
Option E, two-proportion z test should be used to determine whether these data provide sufficient evidence to reject the hypothesis that the proportion of shoppers at the suburban mall who had been to a movie in the past month is the same as the proportion of shoppers in the large downtown shopping area who had been to a movie in the past month
Step-by-step explanation:
The complete question is
In a random sample of 60 shoppers chosen from the shoppers at a large suburban mall, 36 indicated that they had been to a movie in the past
month. In an independent random sample of 50 shoppers chosen from the shoppers in a large downtown shopping area, 31 indicated that
they had been to a movie in the past month. What significance test should be used to determine whether these data provide sufficient
evidence to reject the hypothesis that the proportion of shoppers at the suburban mall who had been to a movie in the past month is the same
as the proportion of shoppers in a large downtown shopping area who had been to a movie in the past month?
A one-proportion z interval B two-proportion z interval
B two-proportion z interval
C two-sample t test D one-proportion z test
D one-proportion z test
E two-proportion z test
Solution
Two proportion z test is used to compare two proportions. In this test the null hypothesis is that the two proportions are equal and the alternate hypothesis is that the proportions are not the same. The random sample of populations serve as two proportions.
Hence, option E is the best choice of answer