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vampirchik [111]
3 years ago
7

Find all solutions for a triangle with A = 30°, a = 4, and b = 8.

Mathematics
1 answer:
Artemon [7]3 years ago
5 0
The answer will be b
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Jorge is asked to build a box in the shape of a rectangular prism. The maximum girth of the box is 20 cm. What is the width of t
MariettaO [177]

Answer:

The width of the box is 6.7 cm

The maximum volume is 148.1 cm³

Step-by-step explanation:

The given parameters of the box Jorge is asked to build are;

The maximum girth of the box = 20 cm

The nature of the sides of the box = 2 square sides and 4 rectangular sides

The side length of square side of the box = w

The length of the rectangular side of the box = l

Therefore, we have;

The girth = 2·w + 2·l = 20 cm

∴ w + l = 20/2 = 10

w + l = 10

l = 10 - w

The volume of the box, V = Area of square side × Length of rectangular side

∴ V = w × w × l = w × w × (10 - w)

V = 10·w² - w³

At the maximum volume, we have;

dV/dw = d(10·w² - w³)/dw = 0

∴ d(10·w² - w³)/dw = 2×10·w - 3·w² = 0

2×10·w - 3·w² = 20·w - 3·w² = 0

20·w - 3·w² = 0 at the maximum volume

w·(20 - 3·w) = 0

∴ w = 0 or w = 20/3 = 6.\overline 6

Given that 6.\overline 6 > 0, we have;

At the maximum volume, the width of the block, w = 6.\overline 6 cm ≈ 6.7 cm

The maximum volume, V_{max}, is therefore given when w = 6.\overline 6 cm = 20/3 cm  as follows;

V = 10·w² - w³

V_{max} = 10·(20/3)² - (20/3)³ = 4000/27 = 148.\overline {148}

The maximum volume, V_{max} = 148.\overline {148} cm³ ≈ 148.1 cm³

Using a graphing calculator, also, we have by finding the extremum of the function V = 10·w² - w³, the coordinate of the maximum point is (20/3, 4000/27)

The width of the box is;

6.7 cm

The maximum volume is;

148.1 cm³

5 0
3 years ago
The measure of the supplement of an angle is seven times as large as the measure of its complement find the measure of the angle
8090 [49]

Answer: original angle = 75°

Its supplement 105°

Its complement = 15°

Step-by-step explanation:

We know that,

  • Sum of supplementary angles is 180 degrees.
  • Sum of complementary angles is 90 degrees.

Let x be the original angle , then its supplement = 180° - x

its complement = 90° - x

As per given,

180° - x = 7(90° - x)

⇒ 180° - x = 630° - 7x

⇒  7x- x = 630° -180°

⇒  6 x = 450°

⇒  x = 75°  [divide both sides by 6]

So, original angle = 75°

Its supplement =  180° - 75° = 105°

Its complement = 90° -75° = 15°

Hence,  original angle = 75°

Its supplement 105°

Its complement = 15°

4 0
3 years ago
Andy wrote the equation of a line that has a slope of Step 2: y plus 2 equals StartFraction 3 Over 4 EndFraction x minus StartFr
nlexa [21]

answer is C

He made an error in Step 3. He should have subtracted 2 from both sides.

4 0
3 years ago
Read 2 more answers
What do you call two angles that have a sum of 90 degrees?
melomori [17]
The answer to this would be complementary angles.

8 0
3 years ago
The measure of angle ABC is<br> A<br> D<br> 60<br> 40°
Umnica [9.8K]
The measure of angle ABC is 100 because all you do is add the 60 to the 40 and get 100.
4 0
2 years ago
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