Perimeter = 2(l + w)
Thus,
102 = 2(l + w)
l = 6 + 2w
102 = 2( 6 + 2w + w)
102 = 12 + 4w +2 w
102 = 12 + 6w
90 = 6w
Thus, w = 15.
Length = 6 + 2w
= 6 + 30
= 36.
Thus, the length is 36 meters and width is 15 meters.
Answer:
20
Step-by-step explanation:
If the ratio of boys is 9 there are 90 boys. If 9=90 then 1= 10. 10 x 2 = 20
I hope this helps :0)
5 red, 3 blue, 7 white.....total of 15
probability of 1st drawn being red : 5/15 reduces to 1/3
without replacement
probability of 2nd being red : 4/14 reduces to 2/7
probability of both : 1/3 * 2/7 = 2/21 <==
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
