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Reptile [31]
3 years ago
6

If X = 18 inches, Y = 80 inches, and Z = 82 inches, what is the cosine of B?

Mathematics
1 answer:
svetoff [14.1K]3 years ago
8 0
Cosine is probably either opp/hyp or adj/hyp
You might be interested in
A cardboard box without a lid is to have a volume of 8,788 cm3. Find the dimensions that minimize the amount of cardboard used.
Montano1993 [528]

Answer:

  x = y = 26 cm; z = 13 cm

Step-by-step explanation:

The generic solution for the minimum material in an open-top box is that the box is square and half as high as it is wide. It is half a cube of twice the volume.

The dimensions of the square base are ...

  ∛(2·8788 cm³) = 26 cm

Then the height is half that, or 13 cm.

  x = y = 26 cm; z = 13 cm

_____

If you need to see the development, you can use the method of Lagrange multipliers to find the minimum area for the given volume;

  area = xy +2(xz +yz)

  volume = xyz = 8788

We require each of the partial derivatives of L with respect to x, y, z, and λ to be zero.

  L = xy +2(xz +yz) +λ(xyz -8788)

  partial with respect to x: 0 = y+2z +λyz

  partial with respect to y: 0 = x +2z +λxz

  partial with respect to z: 0 = 2x+2y +λxy

  partial with respect to λ: 0 = xyz -8788

From the first two equations, we have ...

  λ = (y +2z)/(yz) = 1/z +2/y

  λ = (x +2z)/(xz) = 1/z +2/x

Equating these expressions for λ, we find ...

  1/z +2/y = 1/z +2/x   ⇒   x = y

The third equation then tells us ...

  λ = (2x +2y)/(xy) = 2/y +2/x

Comparing this to either of the first two expressions for λ, we see ...

  1/z +2y = 2/x +2/y   ⇒   z = x/2

This is the result we started the answer with:

  x = y = 2z = ∛(2·8788 cm³)

7 0
2 years ago
Polygon CCC has an area of 404040 square units. K 2ennan drew a scaled version of Polygon CCC using a scale factor of \dfrac12 1
nikdorinn [45]

Answer:

<em>Area of polygon D = 10 square units</em>

Step-by-step explanation:

<u>Given:</u>

Polygon <em>C </em>has an area of 40 square units.

It is scaled with a scale factor of \frac{1}2 to form a new polygon D.

<u></u>

<u>To find:</u>

The area of polygon D = ?

<u>Solution:</u>

When any polygon is scaled to half, then all the sides of new polygon are half of the original polygon.

And the area becomes one-fourth of the original polygon.

Let us consider this by taking examples:

  • First of all, let us consider a right angled triangle with sides <em>6, 8 and 10 units.</em>

Area of a right angled triangle is given by:

A = \dfrac{1}{2} \times Base \times Height\\\Rightarrow A = \dfrac{1}{2} \times 6 \times 8 = 24\ sq\ units

If scaled with a factor \frac{1}{2}, the sides will be 3, 4 and 5.

New area, A':

A' =\dfrac{1}{2} \times 3 \times 4 = 6\ sq\ units = \dfrac{1}4\times A

i.e. Area becomes one fourth.

  • Let us consider a rectangle now.

Sides be 8 and 10 units.

Area of a rectangle, A = Length \times Width = 8 \times 10 = 80 sq units.

Now after scaling, the sides will be 4 and 5 units.

New Area, A' = 4 \times 5 =20 sq units

So, \bold{A' = \frac{1}4 \times A}

Now, we can apply the same in the given question.

\therefore Area of polygon D = \bold{\frac{1}{4}}\times Area of polygon C

Area of polygon D = \bold{\frac{1}{4}}\times 40 = <em>10 sq units</em>

4 0
2 years ago
If ∠A and ∠B are supplementary and m∠A = 37°45', then m∠B = ______.
xenn [34]

Answer: 142°15'

Explanation:

Supplementary angles are angles that add up to make a straight angle (180^{\circ}).

Therefore, we must find the angle ∠B such that

∠A + ∠B = 180° (1)

We know that ∠A = 37°45', so we can re-arrange equation (1) to find the magnitude of ∠B:

∠B = 180° - ∠A = 180° - 37°45' = 142°15'

So, the correct answer is

142°15'

6 0
3 years ago
Read 2 more answers
If a*b means 2a + b , then what is 2*5 ?
NeX [460]

Answer:

9

Step-by-step explanation:

let a = 2

b = 5

2a + b

Substituting the values,

=> 2(2) + 5

=> 4 + 5

=> 9

3 0
3 years ago
For the inverse variation equation xy = k, what is the value of x when y = 4 and k = 7? 3 28
Oliga [24]

Answer:

The value of x is \frac{7}{4}.

Step-by-step explanation:

It is given that the inverse variation equation is

xy=k                  ..... (1)

The value of y is 4 and the value of k is 7.

Substitute y=4 and k=7 in equation (1).

x\times 4=7

Divide both sides by 4.

\frac{x\times 4}{4}=\frac{7}{4}

x=\frac{7}{4}

Therefore the value of x is \frac{7}{4}.

7 0
3 years ago
Read 2 more answers
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