So it tells us that g(3) = -5 and g'(x) = x^2 + 7.
So g(3) = -5 is the point (3, -5)
Using linear approximation
g(2.99) is the point (2.99, g(3) + g'(3)*(2.99-3))
now we just need to simplify that
(2.99, -5 + (16)*(-.01)) which is (2.99, -5 + -.16) which is (2.99, -5.16)
So g(2.99) = -5.16
Doing the same thing for the other g(3.01)
(3.01, g(3) + g'(3)*(3.01-3))
(3.01, -5 + 16*.01) which is (3.01, -4.84)
So g(3.01) = -4.84
So we have our linear approximation for the two.
If you wanted to, you could check your answer by finding g(x). Since you know g'(x), take the antiderivative and we will get
g(x) = 1/3x^3 + 7x + C
Since we know g(3) = -5, we can use that to solve for C
1/3(3)^3 + 7(3) + C = -5 and we find that C = -35
so that means g(x) = (x^3)/3 + 7x - 35
So just to check our linear approximations use that to find g(2.99) and g(3.01)
g(2.99) = -5.1597
g(3.01) = -4.8397
So as you can see, using the linear approximation we got our answers as
g(2.99) = -5.16
g(3.01) = -4.84
which are both really close to the actual answer. Not a bad method if you ever need to use it.
Answer:
A. 30
Step-by-step explanation:
sin theta = opposite side / hypotenuse
sin B = 8/16
sin B = 1/2
Take the arcsin of each side
arcsin sin(B) = arcsin (1/2)
B = arcsin (1/2)
B = 30
Answer:
its correct
Step-by-step explanation:
because if u take away 1 and add for take away 2 and get 3
Because it accurately depicts the distribution of values for many natural occurrences, it is the most significant probability distribution in statistics.
The most significant probability distribution in statistics for independent, random variables is the normal distribution, sometimes referred to as the Gaussian distribution. In statistical reports, its well-known bell-shaped curve is generally recognized.
The majority of the observations are centered around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean. The probabilities for values that are farther from the mean taper off equally in both directions. Extreme values in the distribution's two tails are likewise rare. Not all symmetrical distributions are normal, even though the normal distribution is symmetrical. The Student's t, Cauchy, and logistic distributions, for instance, are all symmetric.
The normal distribution defines how a variable's values are distributed, just like any probability distribution does. Because it accurately depicts the distribution of values for many natural occurrences, it is the most significant probability distribution in statistics. Normal distributions are widely used to describe characteristics that are the sum of numerous distinct processes. For instance, the normal distribution is observed for heights, blood pressure, measurement error, and IQ scores.
Learn more about probability distribution here:
brainly.com/question/28021875
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Answer:
171.65
Step-by-step explanation:
A=2AB+(a+b+c)h
AB=s(s﹣a)(s﹣b)(s﹣c)
s=a+b+c
2
Solving forA
A=ah+bh+ch+1
2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=5·10+5·10+5·10+1
2·﹣54+2·(5·5)2+2·(5·5)2﹣54+2·(5·5)2﹣54≈171.65064
