FOR THE FIRST PROBLEM:
Differentiating p^2 + 2q^2 = 1100 with respect to time => 2p(dp/dt) + 4q(dq/dt) = 0
<span>dp/dt = -2q/p(dq/dt) </span>
<span>R = pq </span>
<span>dR/dt = p(dq/dt) + q(dp/dt) = -p²/2q(dp/dt) + q(dp/dt) = (2q² - 1100)/2q * (dp/dt) + q(dp/dt) </span>
<span>A = (2q - 550/q)
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13,200
because you would take 165,000 and mulitply it by .08 (because it is a percent just move the decimal 2 places to the left to get it in decimal form) which would then give you 13,200
Answer:
There are ways for quickly multiply out a binomial that's being raised by an exponent. Like
(a + b)0 = 1
(a + b)1 = a + b
(a + b)2 = a2 + 2ab + b2
(a + b)3 = (a + b)(a + b)2 = (a + b)(a2 + 2ab + b2) = a3 + 3a2b + 3ab2 + b3
and so on and so on
but there was this mathematician named Blaise Pascal and he found a numerical pattern, called Pascal's Triangle, for quickly expanding a binomial like the ones from earlier. It looks like this
1 1
2 1 2 1
3 1 3 3 1
4 1 4 6 4 1
5 1 5 10 10 5 1
Pascal's Triangle gives us the coefficients for an expanded binomial of the form (a + b)n, where n is the row of the triangle.
Hope this helps!
Answer:
x=4.375
Step-by-step explanation:
-3(2x-7)+5=2x-9
-6x+21+5=2x-9
-6x+26=2x-9
-6x-2x+26=2x-2x-9
-8x+26=-9
-8x+26-26=-9-26
-8x=-35
-8x/-8=-35/-8
x=4.375
Answer:
10 seconds
Step-by-step explanation:
mark two points on the line the use the slope rule to calculate it you'll find it's -5 m/s
