Answer:
- x ≈ -0.107760269824
- x ≈ 1.98779489573
Step-by-step explanation:
The quadratic portion of f(x) factors as (-4x)(x -2), so has zeros at x=0 and x=2. The cosine portion of f(x) will have a value of 1 at x=0 and a value of about -0.15 at x=2. Thus, we might expect roots to be slightly negative and near x=2. (It turns out that a not-unreasonable approximation of the cosine function as cos(x) ≈ 1-x²/2 can be usefully used to get better approximations of the roots in each case.)
A graphing calculator makes it easy to find initial approximations of the two roots. The graph shows them to be -0.108 and 1.988.
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Many graphing calculators also include the ability to determine a numerical value of the derivative of a function. This makes it possible to write an iteration function after the fashion of Newton's Method iteration:
g(x) = x -f(x)/f'(x)
where g(x) gives a new value for old guess x, and f'(x) is the derivative of f(x).
The calculator we used is interactive, so the value of g(x) is found even as you type the argument value x. That makes it possible to achieve full calculator accuracy for the root estimate simply by copying the approximate value into the expression g(x).
x ∈ {−0.107760269824, 1.98779489573}
Answer:
$0.8 per raisin and
1 1/4 ounces of raisin
Step-by-step explanation:
Jason bought 5 ounces of raisins for $4.
Cost of each raisin = cost of raisins / no. of raisins per ounce
That’s $4/5
= $0.8
Each raisin cost $0.8 per ounce .
Also, if
$4 = 5 ounces
$1 = A ounces
Cross multiply
4 x A = 1 x 5
Divide both sides by 4
A = 5/4
A = 1 1/4
1 1/4 ounces of raisins can be bought for $1
Answer:17.14%
Step-by-step explanation:
145 x
_____=_____
175 100
145(100)=175(x)
14500=175x
__________
175 175
x=82.86
100-82.86=17.14%
Answer:
y=5x+3
Step-by-step explanation:
You have the points (1,8) (2,13) (3,18) (4,23)
first you want to find the slope. The equation to find a slope is y2-y1 / x2-x1
your points (1,8) and (2,13) are really all you need
1 would be your x1 and your 2 would be your x2.
8 would be your y1 and 2 your y2
so you want to plug those into your equation y2-y1/x2-x1
13-8 /2-1 you get 5/1
Simplify your answer is 5 for your slope
Now finding the y intercept or "b" I normally just find the pattern of the sequence so in this case when you add one to the top your adding five to the bottom like
x 1 2 3 4
y 8 13 18 23
so to get to your y intercept which is (0,y)
subtract 1 from the top to get zero and subtract 5 from the bottom to get 3 so your y intercept is 3.
Hope this helps.