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Nataly [62]
3 years ago
13

Locate the absolute extrema of the function f(x)=cos(πx) on the closed interval [0,3/4] .

Mathematics
1 answer:
ivann1987 [24]3 years ago
3 0

Answer:

b) absolute max: f(0)=1, absolute min: f(3/4)=cos3π/4

Step-by-step explanation:

Find the derivative.

f'(x) = -π sin(πx)

Set to 0 and solve.

0 = -π sin(πx)

πx = 0 + kπ

x = 0 + k

On the interval [0, 3/4], x = 0 is an extrema (either local min or local max).

Now evaluate the end points.

f(0) = cos(0) = 1

f(3/4) = cos(3π/4) = -√2/2

Absolute max at f(0) = 1, absolute min at f(3/4) = cos(3π/4).

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Answer:

2496 cubic feet

Step-by-step explanation:

Dimension of storage unit 13 ft x 16 ft x 12 ft.

Since there are three sides it can be safely assumed that storage unit is rectangular in shape.

Volume of rectangular body is given by length * width * height

Using the above formula in the given dimension we have

volume of storage unit = length of storage unit * width of storage unit  * height of storage unit

volume of storage unit = 13 ft * 16 ft * 12 ft = 2,496 cubic feet

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3 years ago
Rewrite using powers of ten 32,000,000
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Which of the following is true of the discriminant for the graph below
aniked [119]

Answer:

Step-by-step explanation:

The discriminant is used to determine the number and nature of the zeros of a quadratic. If the discriminant is positive and a perfect square, there are 2 rational zeros; if the discriminant is positive and not a perfect square, there are 2 rational complex zeros; if the discriminant is 0, there is 1 rational root; if the discriminant is negative, there are no real roots.

The roots/solutions/zeros of a quadratic are where the graph goes through the x axis. Those are the real zeros, even if they don't fall exactly on a number like 1 or 2 or 3; they can fall on 1.32, 4.35, etc. They are still real. If the graph doesn't go through the x-axis at all, the zeros are imaginary because the discriminant was negative and you can't take the square root of a negative number. As you can see on our graph, the parabola never goes through the x-axis. Therefore, the zeros are imaginary because the discriminant was negative. Choice C.  Get familiar with your discriminants and the nature of quadratic solutions. Your life will be much easier!

4 0
3 years ago
Juan went out to lunch with five friends. They decided to divide the bill evenly among them. Juan estimated that his lunch cost
Lina20 [59]
Juan’s lunch would have costed less if he paid separately. his lunch is 5.25
the bill 37.20
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alexandr1967 [171]

Answer:

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Step-by-step explanation:

First term is -2

The term to term rule is 'square and subtract 3'

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Third term=(1)^{2} -3=-2

Fourth term=(-2)^{2} -3=1

Fifth term=(1)^{2} -3=-2

Sixth term=(-2)^{2} -3=1

The first six numbers are -2,1,-2,1,-2,1

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