Each term has a common divisor of 
:
133 = 7*19, so the number in the blanks is .
1. 10
2. 5√2 in
1. The ratio for a 30-60-90 triangle is x:x√3:2x
x is the shortest leg so 2*x =2*5 = 10
2. the ratio of a 45-45-90 triangle is x:x:x√2
x is one leg so x * √2 = 5*√2 = 5√2
The area are in the ratio of the squares of corresponding sides.
That is 15^2 : 20^2 = 225:400
so the area of the smaller figure = (225/400) * 64
= 0.5625 * 64
= 36 cm^2 (answer)
Answer:
<h2><em>
2ft by 2ft by 1 ft</em></h2>
Step-by-step explanation:
Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;
S = lw+2wh+2lh ... 1
Given the volume V = lwh = 4ft³ ... 2
From equation 2;
h = 4/lw
Substituting into r[equation 1;
S = lw + 2w(4/lw)+ 2l(4/lw)
S = lw+8/l+8/w
Differentiating the resulting equation with respect to w and l will give;
dS/dw = l + (-8w⁻²)
dS/dw = l - 8/w²
Similarly,
dS/dl = w + (-8l⁻²)
dS/dw = w - 8/l²
At turning point, ds/dw = 0 and ds/dl = 0
l - 8/w² = 0 and w - 8/l² = 0
l = 8/w² and w =8/l²
l = 8/(8/l² )²
l = 8/(64/I⁴)
l = 8*l⁴/64
l = l⁴/8
8l = l⁴
l³ = 8
l = ∛8
l = 2
Hence the length of the box is 2 feet
Substituting l = 2 into the function l = 8/w² to get the eidth w
2 = 8/w²
1 = 4/w²
w² = 4
w = 2 ft
width of the cardboard is 2 ft
Since Volume = lwh
4 = 2(2)h
4 = 4h
h = 1 ft
Height of the cardboard is 1 ft
<em>The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft</em>
Height over shadow
H/S
9 in is 9/12=.75
So
Boys height /shadow. Flags height /shadow
4.75/6= X/19
Cross multiply
6x= 90.25
Divide by 6
X= 15.0
