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.
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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.
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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.
The complete question in the attached figure
Part A) find the perimeter
[perimeter of the garden]=[perimeter square 1]+[perimeter a quarter circle]+[perimeter square 2]
[perimeter square 1]=5+5+5-----> 15 ft
[perimeter square 2]=5+5+5-----> 15 ft
[perimeter a quarter circle]=(2*pi*r)/4------> 2*pi*5/4-----> 7.85 ft
[perimeter of the garden]=[15]+[7.85]+[15]-------> 37.85 ft
the answer Part A) isthe perimeter of the garden is 37.85 ftPart B) Find the area of the garden
[Area of the garden]=[Area square 1]+[Area a quarter circle]+[Area square 2]
[Area square 1]=5*5-----> 25 ft²
[Area square 2]=5*5-----> 25 ft²
[Area a quarter circle]=(pi*r²)/4------> pi*5²/4-----> 19.625 ft²
[Area of the garden]=[25]+[19.625]+[25]-------> 69.625 ft²
the answer Part B) isthe Area of the garden is 69.625 ft²
The answer is 4. If the relay is 1/4 mile, and each person runs 1/16 mile, then to get the answer you divide 1/4 by 1/6 and get 4. 4 people would be needed to run this relay. Hope this helps! :)
Answer:
y = 3/4x + 4
Step-by-step explanation:
to put it into slope intercept form, you need to find the y intercept or b becasue the slope intercept form is y = mx + b where b is the y intercetpt and m is the slope. To find b you insert the points you were given so 1 = -4(3/4) + b
which simplifies to 4 = b so then you can put in your slope and y intercept into slope intercept form
Answer:
The larger number is -6, the smaller number is -15
Step-by-step explanation:
We have two numbers, a and b.
We know that one number is larger than another by 9.
Then we can write:
a = b + 9
then a is larger than b by 9 units.
If the greater number is increased by 10 (a + 10) and the lesser number is tripled (3*b), the sum of the two would be -41:
(a + 10) + 3*b = -41
So we got two equations:
a = b + 9
(a + 10) + 3*b = -41
This is a system of equations.
One way to solve this is first isolate one variable in one of the two equations:
But we can see that the variable "a" is already isolated in the first equation, so we have:
a = b + 9
now we can replace that in the other equation:
(a + 10) + 3*b = -41
(b + 9) + 10 + 3*b = -41
now we can solve this for b.
9 + b + 10 + 3b = -41
(9 + 10) + (3b + b) = -41
19 + 4b = -41
4b = -41 -19 = -60
b = -60/4 = -15
b = -15
then:
a = b + 9
a = -15 + 9 = -6
a = -6
