Answer:
- max for 5th-degree: 4 turns. This function: 2 turns.
- max for 7th-degree: 6 turns. This function: 0 turns.
Step-by-step explanation:
In general, the graph of an n-th degree function can make n-1 turns. However, in specific cases, the number of turns is limited by the number of real zero-crossings of the derivative.
__
1. This 5th-degree function can have at most 4 turns. However, the derivative, f'(x) = 5x^4 -3, has only two (2) real zeros. Hence the graph of this function can only have 2 turns.
__
2. This 7th-degree function can have at most 6 turns. However, the derivative, f'(x) = -7x^6 -35x^4-12x^2, has an even-multiplicity root at x=0 only. The derivative never crosses 0. Hence the graph makes no turns.
So, you have to have your equation in terms of dimes. What you said about what he has: four more nickels than dimes in his pocket. Will help with our equation.
We know what a nickel and dime is worth. A nickel is .05 and a dime is .1
We don't know how many dimes are in his pocket, since we're trying to solve it.
.1x+(4+x).05=1.25;
In the parenthesis, it shows how there are four more nickels. Let's solve it now.
.1x + (4+x).05=1.25
.1x + .2+ .05x = 1.25; Let's add like terms.
.15x + .2 = 1.25; Subtract .2 from both sides.
.15x= 1.05
1.05÷.15= 7 =x
There are 7 dimes in his pocket, let's check our answer.
We now know there are 11 nickels, since there are four more nickels than dimes.
11(.05) +.1(7) = 1.25
.55+ .7 = 1.25
Now that we've tried it, we know there are 7 dimes in his pocket.
Tell me if this helps!
Answer:
55
Step-by-step explanation:
Let x represent the middle integer. Then the smallest is x-2 and the largest is x+2. Your requirement is that ...
(x-2)/(x+2) > 2/3
3x -6 > 2x +4 . . . . cross multiply
x > 10 . . . . . . . . . . .add 6-2x
The smallest integer satisfying this requirement is x=11. The sum of the 5 integers is 5x = 55.
The smallest sum is 55.
Answer:
The coefficient of the squared expression in the parabola equation is
Step-by-step explanation:
The equation of a parabola in its vertex form is:
Where the vertex of the parabola is the point (h, k)
a is the ceoficiente of the term to the square.
We need to find the equation of a parabola that has its vertex in the point:
(-5, -2)
So:
Therefore the equation is:
We know that the point (-4, 2) belongs to this parable. Then we can find the value of a by replacing the point in the equation of the parabola
Finally the coefficient is a = 4
Answer:
Step-by-step explanation: