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3 years ago

Which interval for the graphed function contams the local maximum?

Mathematics

1 answer:

Natasha2012 [34]3 years ago

6 0

Answer:

$[0,2]$

Step-by-step explanation:

A local maximum or local minimum is the point where the tangent drawn to it is parallel to the x axis.

The crest of a wave is local maximum and the trough of wave is local minimum.

Here, in the graph, there are 2 troughs and 1 crest.

The crest is at $(1.55,10.8)$ . So, the local maximum is at $(1.55,10.8)$ .

The interval of the local maximum is between $x = 0$ and $x = 3$ .

So, the option that matches with the above interval is $[0,2]$ .

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Suppose that y varies inversely with x. Write an equation for the inverse variation. y = 6 when x = 1/3

murzikaleks [220]

Y='x'xk
6=1/3xk
K=18
Y='x'x18
Y=18x

7 0

3 years ago

Read 2 more answers

And algebra teacher drove by a farm yard full of chickens and pigs. The teacher happened to notice there were total of 70 heads

Oksanka [162]

To solve this problem, we are going to use a system of equations. Let the variable c represent the number of chickens in the farm yard and the variable p represent the number of pigs in the farm yard. If there is a total of 70 heads, this means that the total number of animals (chickens plus pigs) must be 70. This can be represent by the equation: c + p = 70. We are also told that there are 200 legs. Using our knowledge that chickens have 2 legs and pigs have 4 legs, we can construct the following equation: 2c + 4p = 200. Our system of equations is as follows:

c + p = 70

2c + 4p = 200

To solve, we are going to subtract c from both sides of the first equation so that we can get the variable p alone. Then, using this value for p in terms of c, we are going to substitute into the second equation. This method is shown below:

c + p = 70

p = 70 - c

2c + 4p = 200

2c + 4(70-c) = 200

To solve this equation, we are first going to distribute the coefficient of 4 through the parentheses on the left side of the equation to simplify.

2c + 280 - 4c = 200

Next, we are going to combine like terms on the left side of the equation. This means adding together the two terms that both have a variable c.

-2c + 280 = 200

Next, we are going to subtract 280 from both sides of the equation so that we can move all of the constant (number only) terms to the right side of the equation.

-2c = -80

Finally, we are going to divide both sides of the equation by -2 to get the variable c alone.

c = 40

We should now substitute this value for c back into one of our original equations to solve for p.

c + p = 70

40 + p = 70

To solve, simply subtract 40 from both sides of the equation to get the variable p alone.

p = 30

Therefore, your answer is that there were 40 chickens and 30 pigs.

Hope this helps!

7 0

3 years ago

NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE answer thoroughly. Chapter 9 part 2

blsea [12.9K]

9514 1404 393

Answer:

a) the degree of the polynomial

b) count the x-intercepts, with attention to multiplicity

Step-by-step explanation:

The Fundamental Theorem of Algebra tells you the number of zeros of a polynomial is equal to the degree of the polynomial. That is, for some polynomial p(x), the number of solutions to p(x)=0 will be the degree of p.

On a graph, a real zero of the polynomial will be an x-intercept. The "multiplicity" of a zero is the degree of the factor giving rise to that zero. When the multiplicity is even, the graph does not cross the x-axis at the x-intercept. The greater the multiplicity, the "flatter" the graph is at the x-intercept.

If all solutions (zeros) are distinct, then the number of real solutions can be found by counting the number of x-intercepts of the graph.

_____

By way of illustration, the attached graph is of a 6th-degree polynomial with 6 real zeros. From left to right, they are -1 (multiplicity 1), 1 (multiplicity 2), 4 (multiplicity 3). The higher multiplicities are intended to show the flattening that occurs at the x-intercept, and the fact that the graph does not cross the x-axis where the multiplicity is even.