Answer:
8.
Step-by-step explanation:
Since this cannot be further simplified, we will calculate the square root of 57 with our calculators.
We find that the square root of 57 is 7.549834435, and since the tenths place is a 5, we will round up to the next whole number. So, the point on the number line that best represents the square root of 57 is 8.
Hope this helps!
This is how the first one would be done. sorry if it’s a little messy the answer is 9. but try using photomath for the rest. it gives you the answer and explains how to do it
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
For the series 3/2 + 3/4 + 3/8 + 3/16 + ...the sum will be calculated by the formula 
.
<h3>What is number series?</h3>
When the numbers are arranged in a series with some logic then it is called as the number series.
here we have a series:
The sum of the series will be given as:
Hence for the series 3/2 + 3/4 + 3/8 + 3/16 + ...the sum will be calculated by the formula
To know more about number series follow
brainly.com/question/6561461
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Answer:
(5)2
Step-by-step explanation:
As we know that the equation of circle with center at (h,k) ad radius r is given as-
(x−h)
2
+(y−k)
2
=r
2
Given that the centre of circle is (1,4) and radius is 5.
Therefore the equation of circle is-
(x−1)
2
+(y−4)
2
=(5)
2
