A and B start from the same point and travel west and north, respectively. A travels 3 miles per hour faster than B. At the end of two hours, they are 30 miles apart. Find their distances.
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Answer:
Step-by-step explanation:
I believe you're actually looking for their respective rates. If A travels directly west and B travels directly north, and the distance between them is 30 miles, what we have is a right triangle situation. The hypotenuse of the triangle is 30. If the distance an object travels at a certain rate for given time is d = rt, then for B, our formula for distance is d = 2r (since the time each traveled is 2 hours). A traveled 3 miles per hour faster, so the formula for distance for A is d = (r + 3)2. Again, each traveled for 2 hours, so t = 2. Distributing we get that d = 2r + 6. Now that we have each expression for A and B, we use them in Pythagorean's Theorem to find the only unknown we have which is r. That's why I said in the beginning that I believe what you're actually looking for is the rate that each traveled. Our equation is:
and
and
Putting everything on one side and setting the quadratic equal to 0 to factor, we get
You can factor out an 8 to make the numbers a bit smaller:
Factor to get
8(r - 9)(r + 12)=0
That means, by the Zero Product Property, that 8 = 0, r - 9 = 0, or r + 12 = 0. We all know that 8 doesn't = 0, so forget that one!! If r - 9 = 0, then r = 9. If r + 12 = 0. then r = -12. We all know that rate cannot be negative (velocity can, but we are not using vector math here), so we discount rate as -12. That means that r = 9. B's rate is 9 then and A's rate is 12. There you go!
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Find a possible formula for P(x)
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remember the roots of a polynomial is
P(x)=(x-r1)(x-r2)...(x-rn)
so we have 5th degreee, means all exponents shoud add to 5
leading coeficient of 1, that means
P(x)=1x^n+bx^(n-1)...zx^0
means highest power coefience it 1
roots of multiplicity 2 at x=2 and x=0, means those roots show up 2 times each
root at x=2 means (x-2), it has multiplicity 2 so (x-2)^2
root at x=0 means (x-0), it has multiplicyt 2 so (x-0)^2
last one, multiplicity 1 and root at x=-4
(x-(-4))^1=(x+4)
so the polynomial is
7) 12, 7, 2, -3,...
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Answer:
Let's find the recursive formula, explicit formula, and the indicated term for the given arithmetic sequences.
Sequence 1: 1, 4, 1, 10, ...
To find the recursive formula, we need to identify the pattern between consecutive terms. Looking at the sequence, we can see that each term alternates between adding 3 and subtracting 3.
Recursive formula:
a1 = 1 (the first term)
an = an-1 + (-1)^(n+1) * 3
For example, to find the 4th term (a4) using the recursive formula:
a1 = 1 (the first term)
a2 = a1 + (-1)^(2+1) * 3 = 1 + (-1) * 3 = -2
a3 = a2 + (-1)^(3+1) * 3 = -2 + 1 * 3 = 1
a4 = a3 + (-1)^(4+1) * 3 = 1 + (-1) * 3 = -2
Explicit formula:
To find the explicit formula, we need to identify the common difference. In this case, since the terms alternate between adding 3 and subtracting 3, the common difference is not constant.
Indicated term:
To find the indicated term, we need to know which term is being referred to. Please provide the term number or the position of the term in the sequence so that I can assist you further.
-----------------------------------------------------------
Sequence 2: 12, 7, 2, -3, ...
To find the recursive formula, we need to identify the pattern between consecutive terms. Looking at the sequence, we can see that each term decreases by 5.
Recursive formula:
a1 = 12 (the first term)
an = an-1 - 5
For example, to find the 4th term (a4) using the recursive formula:
a1 = 12 (the first term)
a2 = a1 - 5 = 12 - 5 = 7
a3 = a2 - 5 = 7 - 5 = 2
a4 = a3 - 5 = 2 - 5 = -3
Explicit formula:
To find the explicit formula, we need to identify the common difference. In this case, the common difference is -5.
Explicit formula:
an = 12 + (n - 1)(-5)
Indicated term:
To find the indicated term, we need to know which term is being referred to. Please provide the term number or the position of the term in the sequence so that I can assist you further.
Please provide the term number or the position of the term in the sequence so that I can help you find the indicated term.
Step-by-step explanation:
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Answer:
u can look up the title and the entire answer key will come up
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