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arsen [322]
3 years ago
12

Building a model of an object "to scale" means that the height of the object is ____________ to the height of the model.

Mathematics
1 answer:
Zina [86]3 years ago
8 0
The height of the object is EQUAL to the height of the model. We can see this in advertising when for example cereal is being advertised and on the box is says "actual size" because the cereal is drawn to scale.
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A. ¿Cuál es el valor de la expresión -2 +3(8+-13)?
Nostrana [21]

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5 0
3 years ago
A 4 x 5 x 8 rectangular prism is cut parallel to one of its faces into two prisms. Which could be the dimensions of the resultin
ivolga24 [154]

Answer:

<u><em>d</em></u>

Step-by-step explanation:

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5 0
3 years ago
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For any triangle ABC note down the sine and cos theorems ( sinA/a= sinB/b etc..)
SCORPION-xisa [38]

Answer:

Step-by-step explanation:

Law of sines is:

(sin A) / a = (sin B) / b = (sin C) / c

Law of cosines is:

c² = a² + b² − 2ab cos C

Note that a, b, and c are interchangeable, so long as the angle in the cosine corresponds to the side on the left of the equation (for example, angle C is opposite of side c).

Also, angles of a triangle add up to 180° or π.

(i) sin(B−C) / sin(B+C)

Since A+B+C = π, B+C = π−A:

sin(B−C) / sin(π−A)

Using angle shift property:

sin(B−C) / sin A

Using angle sum/difference identity:

(sin B cos C − cos B sin C) / sin A

Distribute:

(sin B cos C) / sin A − (cos B sin C) / sin A

From law of sines, sin B / sin A = b / a, and sin C / sin A = c / a.

(b/a) cos C − (c/a) cos B

From law of cosines:

c² = a² + b² − 2ab cos C

(c/a)² = 1 + (b/a)² − 2(b/a) cos C

2(b/a) cos C = 1 + (b/a)² − (c/a)²

(b/a) cos C = ½ + ½ (b/a)² − ½ (c/a)²

Similarly:

b² = a² + c² − 2ac cos B

(b/a)² = 1 + (c/a)² − 2(c/a) cos B

2(c/a) cos B = 1 + (c/a)² − (b/a)²

(c/a) cos B = ½ + ½ (c/a)² − ½ (b/a)²

Substituting:

[ ½ + ½ (b/a)² − ½ (c/a)² ] − [ ½ + ½ (c/a)² − ½ (b/a)² ]

½ + ½ (b/a)² − ½ (c/a)² − ½ − ½ (c/a)² + ½ (b/a)²

(b/a)² − (c/a)²

(b² − c²) / a²

(ii) a (cos B + cos C)

a cos B + a cos C

From law of cosines, we know:

b² = a² + c² − 2ac cos B

2ac cos B = a² + c² − b²

a cos B = 1/(2c) (a² + c² − b²)

Similarly:

c² = a² + b² − 2ab cos C

2ab cos C = a² + b² − c²

a cos C = 1/(2b) (a² + b² − c²)

Substituting:

1/(2c) (a² + c² − b²) + 1/(2b) (a² + b² − c²)

Common denominator:

1/(2bc) (a²b + bc² − b³) + 1/(2bc) (a²c + b²c − c³)

1/(2bc) (a²b + bc² − b³ + a²c + b²c − c³)

Rearrange:

1/(2bc) [a²b + a²c + bc² + b²c − (b³ + c³)]

Factor (use sum of cubes):

1/(2bc) [a² (b + c) + bc (b + c) − (b + c)(b² − bc + c²)]

(b + c)/(2bc) [a² + bc − (b² − bc + c²)]

(b + c)/(2bc) (a² + bc − b² + bc − c²)

(b + c)/(2bc) (2bc + a² − b² − c²)

Distribute:

(b + c)/(2bc) (2bc) + (b + c)/(2bc) (a² − b² − c²)

(b + c) + (b + c)/(2bc) (a² − b² − c²)

From law of cosines, we know:

a² = b² + c² − 2bc cos A

2bc cos A = b² + c² − a²

cos A = (b² + c² − a²) / (2bc)

-cos A = (a² − b² − c²) / (2bc)

Substituting:

(b + c) + (b + c)(-cos A)

(b + c)(1 − cos A)

From half angle formula, we can rewrite this as:

2(b + c) sin²(A/2)

(iii) (b + c) cos A + (a + c) cos B + (a + b) cos C

From law of cosines, we know:

cos A = (b² + c² − a²) / (2bc)

cos B = (a² + c² − b²) / (2ac)

cos C = (a² + b² − c²) / (2ab)

Substituting:

(b + c) (b² + c² − a²) / (2bc) + (a + c) (a² + c² − b²) / (2ac) + (a + b) (a² + b² − c²) / (2ab)

Common denominator:

(ab + ac) (b² + c² − a²) / (2abc) + (ab + bc) (a² + c² − b²) / (2abc) + (ac + bc) (a² + b² − c²) / (2abc)

[(ab + ac) (b² + c² − a²) + (ab + bc) (a² + c² − b²) + (ac + bc) (a² + b² − c²)] / (2abc)

We have to distribute, which is messy.  To keep things neat, let's do this one at a time.  First, let's look at the a² terms.

-a² (ab + ac) + a² (ab + bc) + a² (ac + bc)

a² (-ab − ac + ab + bc + ac + bc)

2a²bc

Repeating for the b² terms:

b² (ab + ac) − b² (ab + bc) + b² (ac + bc)

b² (ab + ac − ab − bc + ac + bc)

2ab²c

And the c² terms:

c² (ab + ac) + c² (ab + bc) − c² (ac + bc)

c² (ab + ac + ab + bc − ac − bc)

2abc²

Substituting:

(2a²bc + 2ab²c + 2abc²) / (2abc)

2abc (a + b + c) / (2abc)

a + b + c

8 0
3 years ago
Please helppp maybe write out the equation too
jolli1 [7]
84 and 6 i believe not sure tho

complementary adds to 90°
7 0
2 years ago
Read 2 more answers
Given the two sets, what is A ∩ B ? <br><br> A = {1, 2, 3, 4, 5, 6}<br><br> B = {2, 3, 5, 7}
topjm [15]

Answer:

2, 3, 5

Step-by-step explanation:

A∩B means "A intersection B" which includes all elements that are shared in BOTH sets. This would be the middle crossover section of a Venn diagram.

Hence, 2 and 3 and 5 are shared in both sets.

5 0
3 years ago
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