Answer: -4/15
Step-by-step explanation: To add these two fractions together,
we start by finding their <em>Least Common Denominator</em> (LCD).
Since our denominators of 5 and 3 have no factors in common,
our least common denominator is 5 · 3 or 15.
In order to get a denominator of 15 in each fraction,
we multiply top and bottom of the first fraction by 3
and top and bottom of the second fraction by 5.
That gives us -9/15 + 5/15 which simplifies to -4/15.
As your last step, make sure that the fraction
that you end up with doesn't reduce.
In this case, -4/15 does not reduce but watch out for this last step.
Steps:
1. calculate the values of y at x=0,1,2. using y=5-x^2
2. calculate the areas of trapezoids (Bottom+Top)/2*height
3. add the areas.
1.
x=0, y=5-0^2=5
x=1, y=5-1^2=4
x=2, y=5-2^2=1
2.
Area of trapezoid 1 = (5+4)/2*1=4.5
Area of trapezoid 2 = (4+1)/2*1=2.5
Total area of both trapezoids = (4.5+2.5) = 7
Exact area by integration:
integral of (5-x^2)dx from 0 to 2
=[5x-x^3/3] from 0 to 2
=[5(2-0)-(2^3-0^3)/3]
=10-8/3
=22/3
=7 1/3, slight greater than the estimation by trapezoids.
Answer:
A = 9x² + 12x
Step-by-step explanation:
The area (A) of the rectangle is calculated as
A = height × width
= 3(3x² + 4x) ← distribute parenthesis by 3
= 9x² + 12x
Answer:
You are at the top of the Empire State Building on the 102nd floor, which is located 373 m above the ground when your favorite superhero flies over the building parallel to the ground at 70.0% the speed of light.
You have never seen your favorite superhero in real life. Out of curiosity you calculate her height to be 1.57 mm . If the superhero landed next to you, how tall would she be when standing?
Step-by-step explanation:
so this problem is from Einstein's special theory of relativity about length contraction.
the formula is given by:
where 
c is speed of light 
and v is velocity of object.
L is called proper length. L' is length that the observer measure in moving frame.
here velocity of object is 70% speed of light. i.e 
so 
putting all values
