Answer:
Step-by-step explanation:
g(x) = 3x + 5
g(3) = 3(3) + 5
g(3) = 9 + 5
g(3) = 14
-----------------------
f(x) = 2x² + 3
f(g(3)) = 2(g(3)) + 3
f(14) = 2(14²) + 3
f(14) = 2(196) + 3
f(14) = 392 + 3
f(14) = 395
-----------------------------
f(g(3)) = 395
X=2.5 the triangles are 2x the scale of the other one so if you divide the numbers on the triangle by 2 then you will get the answer for x
Answer:
£2121.80 he would have earned £121.80
Step-by-step explanation:
2000 × 1.03 = £2060
2060 × 1.03 = £2121.80
(2 Year's)
£2121.80 - £2000 = £121.80
V=abc
a=2(ab+act+bc)
hope it helps
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>
