Answer:
Step-by-step explanation:
a. Since the parabola is compressed by a factor of 1/3 we can state:
- a parabola is written this way : y=(x-h)²+k
- h stands for the translation to the left ⇒ 2*3=6
- k for the units down ⇒4*3=12
So the equation is : y=(x-6)²+12
b.Here the parabola is stretched by a factor of 2 so we must multiply by 1/2
- We khow that a parabola is written this way : y=(x-h)²+k
- (h,k) are the coordinates of the vertex
- the maximum value is 7*0.5=3.5
- we khow tha the derivative of a quadratic function is null in the maximum value
- so let's derivate (x-h)²+k= x²+h²-2xh+k
- f'(x)= 2x-2h h is 1 since the axe of simmetry is x=1
- f'(x)=2x-2 ⇒2x-2=0⇒ x= 1
- Now we khow that 1 is the point where the derivative is null
- f(1)=3.5
- 3.5=(x-1)²+k
- 3.5= (1-1)²+k⇒ k=3.5
So the equation is : y=(x-1)²+3.5
7.
the maximum height is where the derivative equals 0
- h= -5.25(t-4)²+86
- h= -5.25(t²-8t+16)+86
- h=-5.25t²+42t-84+86
- h=-5.25t²+42t+2
Let's derivate it :
- f(x)= -10.5t+42
- -10.5t+42=0
- 42=10.5t
- t= 42/10.5=4
When the height was at max t=4s
- h(max)= -5.25(4-4)²+86 = 86 m
h was 86m
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Inequalities are used to show the relationship between unequal expressions.
The inequalities that represent the maximum weights are:
- <em>2 axles - </em><em>.</em>
- <em>3 axles - </em><em>.</em>
- <em>4 axles - </em><em>.</em>
<em />
Let the maximum weight be represented with x
In inequality, maximum means less than or equal to i.e.
<u>(a) 2 axles</u>
The maximum weight, here is 40000.
So, the inequality is:
<u>(b) 3 axles</u>
The maximum weight, here is 60000.
So, the inequality is:
<u>(c) 4 axles</u>
The maximum weight, here is 80000.
So, the inequality is:
<em>See attachment for the graphs of each inequality</em>
Read more about inequalities at:
brainly.com/question/11612965
Answer:
the numbers of cars pf various colors in a parking lot
Answer:
x=7
Step-by-step explanation:
8(1X/4 +12 - 1 x 1/2X)=82
8(X/4 +12-1 x 1/2 x X)=82
8(X/4+ 12 - 1/2x)=82
8 X x/4 + 96+8 X -x/2=82
2x +96 +8 X -x/2=82
2x +96+ 8(-1)/2=82
2x +96 -8x/2 =82
2x+96-4x=82
-2x+96=82
-2x=-14
x=7
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