Answer:
3rd option - 14 m²
Step-by-step explanation:
First we know that the square's area will be 2×2 = 4
To calculate the area of a triangle we know the vertical height is 2.5 and the base length is 2 so we can use the formula b×h/2 to give the area of one triangle:
2.5×2 = 5
5÷2 = 2.5
So the area of 1 triangle is 2.5 m²
Since there are 4 triangles we multiply the area of 1 traingle by 4:
2.5×4 = 10
We add the area of the 4 triangles to the area of the square to give our final answer of :
10 + 4 = 14
14 m²
a+b+c=68
b-3=a
c-5=b
now just solve the system of equations, substitue so that there are only b's in the equation:
a+b+c=68
(b-3) + b + (b+5) = 68
3b=66
b=22
Therefore Barbara is 22
Answer:
The overall change in field position is 7yds, 0 - 5 + 12 = 7, if that isn't a "sum of integers" I apologize.
Step-by-step explanation:
<h2>
Rate at which area is increasing is 1.08 m²/s.</h2>
Step-by-step explanation:
Area of triangle is with side a and b and angle C between them is given by
A = 0.5 ab SinC
Here we need to find how area changes with a and b fixed and C is changing,
We have
a = 8 m
b = 9 m
Substituting
Rate at which area is increasing is 1.08 m²/s.
We know that sin2x=2sinxcosx
(search the net for proof if you wish)
So the original equation becomes
2sinxcosx-sinx=0
The two terms both have sinx that can be taken out to get:
sinx(2cosx-1)=0
This is true if sinx=0 or 2cosx-1=0 , rewritten: cosx=1/2
sinx=0 than x=2kπ
cosx=1/2 than x=π/3+2kπ
where k is an integer
