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Use the law of cosines to find the length of side C.

sergij07 [2.7K]

Answer:

$\text{D. 36.64}$

Step-by-step explanation:

The Law of Sines is given by $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$ and works for any triangle.

Therefore, we have the proportion:

$\frac{c}{\sin 41.5^{\circ}}=\frac{37}{\sin 42^{\circ}},\\\\c=\frac{37\sin 41.5^{\circ}}{\sin 42^{\circ}}=36.6399945706\approx \boxed{36.64}$

8 0

3 years ago

How do I solve for a, b and c?

Naya [18.7K]

Firstly expand (x - 3)(ax^2 + bx + c):
ax^3 + bx^2 + cx - 3ax^2 - 3bx - 3c

Now rearrange it so that it's in the form ax^3 + bx^2 + cx + d:
ax^3 + (b-3a)x^2 + (c-3b)x - 3c

Now we can compare both equations:
ax^3 + (b-3a)x^2 + (c-3b)x - 3c = 2x^3 - x^2 - 19x + 12

We get:
(1) a = 2
(2) b - 3a = -1
(3) c - 3b = -19
(4) -3c = 12

If we substitute (1) into (2) we get:
b - 3*2 = -1
b - 6 = -1
b = 5

Now if we solve (4) we get:
-3c = 12
c = -4

Therefor a = 2, b = 5 and c = -4

8 0

3 years ago

Mrs handson has 2 pies for a party she Calculates that if she cut it evenly they will have 1/8 of a pie how many people at the p

RUDIKE [14]

The answer is 16, half of 32 1/8 x 1/2 = 2/16 divided by 2/2 = 1/8 but since you don't need to simplify only use the denominator of 2/16 or only need to multiply 8 and 2.

5 0

3 years ago

the diagram shows a 5cm x 5cm x 5cm cube calculate the length of the diagonal AB give your answer correct to 1 decimal place

Lynna [10]

Answer:

√3 * 5 = 5√3 cm

Step-by-step explanation:

→ ABCDEFGH is a cube.

→ CF = Diagonal of cube.

→ CH = Diagonal of Base Face BCDH.

→ Let the side of Each cube = a.

Than,

in Right ∆CFH, By Pythagoras Theoram, we have,

→ CH² + FH² = CF² --------- Equation (1)

and, Similarly, in Right ∆CDH ,

→ CD² + DH² = CH² ------- Equation (2).

Putting Value of Equation (2) in Equation (1), we get,

→ (CD² + DH²) + FH² = CF²

→ a² + a² + a² = CF²

→ CF² = 3a²

→ CF = √3a .

Hence, we can say That Diagonal of a cube is √3 times of its sides.

__________________

Given:-

Side of cube = 5cm.

So,

→ Diagonal of cube = √3 * 5 = 5√3 cm. (Ans.)

4 0

3 years ago

Help a formula word problem. Thank you if you help. You're a genuis!

Ainat [17]

<h3>Answer: Choice (3) 28</h3>

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Explanation:

We start with one block at the very left side. This is algebraically written as $a_1 = 1$ . The small subscript '1' means we're dealing with the first term, and that is set equal to 1. In other words, the first term is 1.

The second term is three since we have three blocks as the next figure down the line. So $a_2 = 3$ . We can then see that $a_3 = 6$ and $a_4 = 10$

The sequence of the first four terms are: 1, 3, 6, 10.

The notation $a_n = a_{n-1} + n$ tells us "to get the nth term $a_n$ , we add the previous term ( $a_{n-1}$ ) to the value of n".

For example, if we wanted the third term, we would add the second term a2 onto the value of n = 2. In order to know a2, we need the diagram or you would have to use the recursive formula to find it.

Furthermore, it means that to find the fifth term $a_5$ , we do the following

$a_n = a_{n-1} + n\\\\a_5 = a_{5-1} + 5\\\\a_5 = a_{4} + 5\\\\a_5 = 10+5\\\\a_5 = 15$

The fifth figure will have 15 small little blocks to it. You can draw this out by copying the fourth figure, and then adding 5 smaller blocks to the very bottom portion. The sixth figure is basically a copy of the fifth one, but we have six little blocks along the bottom. This is the "plus n" being applied in the recursive formula.

So the 6th figure will have 15+6 = 21 blocks in total while the 7th figure has 21+7 = 28 blocks. This points us to choice (3).

Side note: These are known as triangular numbers. Note how the gaps between consecutive values of 1,3,6,10,15,21,28 is +2,+3,+4,+5,+6,+7.

6 0

3 years ago