The total area of square TUVW is 160 meters.
<h3>Find out the sides of PQRS:</h3>
Total area: side x side
256 m = side x side
side = √ 256
side= 16 m
This means PQ, QR, RS, SP = 16 m
<h3>Find out the area of one triangle:</h3>
Area: 1/2 x base x height
Let's find out the area of the triangle UVR although all triangles are the same.
Base: 4 meters
Height:
RQ= 16
QU= 4
16-4 = 12
Area: 1/2 x 4 x 12 = 24
<h3>Find the total area of the triangles:</h3>
24 x 4 = 96
Finally, find out the total area of the grey square:
Total area of the grey square = Total area of the white square - area of the triangles
Total area = 256 - 96
Total area= 160
Learn more about squares in: brainly.com/question/13747846
The question says the machine uses up m gallons of oil each hour on weekends.
This means that if the machine works for 24 hours each day, it implies that:
There are only two days on weekends i.e. Saturday and Sunday.
This means that if the amount of oil used in 1 day in the weekend is 24m, then we can say:
Saturday: oil used is 24m
Sunday: oil used is 24m
Total oil used during the weekend is:
There are 2 short sides x and 1 long side y.
x+x+y=1,800
2x+y=1,800
y=1,800-2x
The area of the rectangle is A=x(1,800-x).
A is a function with variable x. Moreover it is a quadratic (second degree) function.
The graph of the function is a parabola which opens downwards, because the signs of the leading coefficients of the factors, multiply to minus:
(x)(-x)=-x^2.
This means that the highest point of the parabola, is its vertex V(h,k), so the function takes its largest value for x=h.
The roots of A=x(1,800-x) are x=0 and x=1,800, thus the x coordinate of the vertex, must be the midpoint of 0 and 1,800, that is 900.
Answer:
A=x(1,800-x)
largest area is when x=900
Answer:
<em>y = - cos ( </em>
<em> x + </em>
<em> ) </em>
Step-by-step explanation:
y = A cos ( Bx + C) + D
Vertical shift D = 0
A = - 1
Compression / Stretching B
Period of given function is 
Period of cos x is 2π
= 
⇒ B =
Horizontal shift is C ÷ B
Horizontal shift of given function is 
= C ÷ ⇒ C =
So, the equation of given function is
<em>y = - cos ( </em><em> x + </em><em> ) </em>
Answer:
5.0 ft - 5.6 ft
Step-by-step explanation:
Given that the structure is to be made using two 12 foot boards, then we expect the total perimeter to be equal to (2*12)= 24 ft.
Using the angle of elevation, 40° and the width of 8 ft then you can apply the formula for tangent of a triangle where ;
Tan α = opposite side length/adjacent length
Tan 40°= h/8
h= 8 tan 40° = 6.71 ft
Applying the cosine of an angle formula to find the length of the sliding side
Cosine β = adjacent length /hypotenuse
Cosine 40°= 8/ sliding side length
sliding side length = 8/cosine 40° =10.44 ft
Checking the perimeter = 10.44 +8+6.71= 25.15 ft
This is more than the total lengths of the boards, so you need to adjust the height as;
24 - 18.44 = 5.56 ft ,thus the height should be less or equal to 5.56 ft
h≤ 5.6 ft
