180^2 + 235^2 = (cliff base to point on bridge)^2
32400 + 55225 = 87625
so cliff base to point on bridge = sqrt of 87625.
Then notice 87625 + d^2 = (x+180)^2
since x^2 +235^2 = d^2,
substitute (x^2 + 235^2) for d^2, like this:
87625 + x^2 + 235^2 = (x+180)^2
87625 + x^2 + 55225 = x^2 + 360x + 32400
87625 + 55225 - 32400 = x^2 - x^2 +360x
360x = 110450
x = about 306.8 feet
h = x+180, so h = 486.8 feet
Remember d^2 = x^2 + 235^2, so
d^2 = 306.8^2 + 235^2
d^2 = 149354.6489
d = about 386.46 feet
The sequence is geometric. Any exponential function models geometric growth. Recall the general nth term of a geometric sequence is a*(r)^(n-1) which is very similar to the form y = a*b^x. The big difference is that the x function is continuous while the function in terms of n is discrete. In this case, the common ratio is r = 1.10 to indicate we have 10% growth. Notice how 100%+10% = 1.00+0.10 = 1.10
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The first quadrant is where x and y are both positive. Since x is the time in years, it doesn't make sense to talk about negative years or negative years have passed by. We can have a negative balance in a bank account, so it makes sense to have y be negative. However, Mr Sullivan starts with some positive amount and his account grows every year. So there's no way that y can be negative in this case.
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The point (0,200) is the y intercept. It represents the starting amount he deposited into the account, which was the $200. Keep in mind that no other deposits were made, and he cannot pull money out of the account if he wants his account to grow according to the graph. Also, the interest rate must remain at 10%.
Can of baked beans = x
packet of brown sugar = y
packet of biscuit = z
5x + 4y + 2z = 150 - 26 ⇒ 5x + 4y + 2z = 124 is the total cost of all items.
can of baked beans = x = 1/2 of z
packet of sugar = y = z - 3
5(z/2) + 4(z-3) + 2z = 124
5z/2 + 4z - 12 + 2z = 124
5z/2 + 6z = 124 + 12
2(5z/2 + 6z) = 2(136)
5z + 12z = 272
17z = 272
z = 16 cost of a packet of biscuit.
x = 1/2 of z = 16/2 = 8 cost of a can of baked beans
y = z - 3 = 16 - 3 = 13 cost of a packet of sugar
5x + 4y + 2z = 124
5(8) + 4(13) + 2(16) = 124
40 + 52 + 32 = 124
124 = 124
8(8) + 1(13) + 6(16) = 64 + 13 + 96 = 173 total cost on question 3.
Answer:
2nd quadrant.
Step-by-step explanation:
