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2 years ago

Find the two x-intercepts of the function f and show that f '(x) = 0 at some point between the two x-intercepts.

Mathematics

1 answer:

suter [353]2 years ago

7 0

Step-by-step explanation:

f(x) = x√(x+8)

When f(x) = 0,

0 = x√(x+8)

x = 0, x + 8 = 0

x = -8

f'(x) = (1)√(x+8) + x • ½(x+8)^(-½) = 0

0 = √(x+8) + 1/[2√(x+8)] (x)

-2(x+8) = x

-2x - 16 = x

x = -16/3

(-8 < -16/3 < 0)

Therefore, x-intercept of f'(x) = 0 is somewhere between the two x-intercepts, ranging from -8 to 0.

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2 years ago

Kanye wants to make a triangular flower bed using logs with the lengths 3 ft, 4 ft, and 8ft. Can Kanye form a triangle with the

valina [46]

Way 1:
a triangle with sides 3,4,5 will make a triangle. because this isn't 3,4,5 triangle it wont work.

way 2:
By using Heron's formula you can find the area of the flower bed.
s=(a+b+c) ÷2
Area =√s(s-a)(s-b)(s-c)
so, 3+4+8= 15
15÷2 =7.5
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2 years ago

Todd Holland from NY grows pumpkins. He studied his past records carefully and concluded that his biggest pumpkins are distribut

ehidna [41]

Answer:

$P(X>1000)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>1000)=P(\frac{X-\mu}{\sigma}>\frac{1000-\mu}{\sigma})=P(Z>\frac{1000-950}{50})=P(z>1)$

And we can find this probability using the complement rule and the normal standard table and we got:

$P(z>1)=1-P(z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(950,50)$