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3 years ago

12

What type of angle is angle M?

1 answer:

Darina [25.2K]3 years ago

4 0

Answer:

B

Step-by-step explanation:

right

have a good day, hope this helps

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Solve the oblique triangle where side a has length 10 cm, side c has length 12 cm, and angle beta has measure thirty degrees. Ro

strojnjashka [21]

Answer:

The missing side is $B = 6.0\ cm$

The missing angles are $\alpha = 56.2$ and $\theta = 93.8$

Step-by-step explanation:

Given

$A = 10\ cm$

$C = 12\ cm$

$\beta = 30$

The implication of this question is to solve for the missing side and the two missing angles

Represent

Angle A with $\alpha$

Angle B with $\beta$

Angle C with $\theta$

Calculating B

This will be calculated using cosine formula as thus;

$B^2 = A^2 + C^2 - 2ACCos\beta$

Substitute values for A, C and $\beta$

$B^2 = 10^2 + 12^2 - 2 * 10 * 12 * Cos30$

$B^2 = 100 + 144 - 240 * 0.8660$

$B^2 = 100 + 144 - 207.8$

$B^2 = 36.2$

Take Square root of both sides

$B = \sqrt{36.2}$

$B = 6.0$ <em>(Approximated)</em>

Calculating $\alpha$

This will be calculated using cosine formula as thus;

$A^2 = B^2 + C^2 - 2BCCos\alpha$

Substitute values for A, B and C

$A^2 = B^2 + C^2 - 2BCCos\alpha$

$10^2 = 6^2 + 12^2 - 2 * 6 * 12 * Cos\alpha$

$100 = 36 + 144 - 144Cos\alpha$

Collect Like Terms

$100 - 36 - 144 = -144Cos\alpha$

$-80 = -144Cos\alpha$

Divide both sides by -144

$\frac{-80}{-144} = Cos\alpha$

$0.5556 = Cos\alpha$

$\alpha = cos^{-1}(0.5556)$

$\alpha = 56.2$ <em>(Approximated)</em>

Calculating $\theta$

This will be calculated using cosine formula as thus;

$C^2 = B^2 + A^2 - 2BACos\theta$

Substitute values for A, B and C

$12^2 = 6^2 + 10^2 - 2 * 6 * 10Cos\theta$

$144 = 36 + 100 - 120Cos\theta$

Collect Like Terms

$144 - 36 - 100 = -120Cos\theta$

$8 = -120Cos\theta$

Divide both sides by -120

$\frac{8}{-120} = Cos\theta$

$-0.0667= Cos\theta$

$\theta = cos^{-1}(-0.0667)$

$\theta = 93.8$ <em>(Approximated)</em>

4 0

4 years ago

A red candle is 8 inches y'all and burns at a rate of 7 divided by 10 inch per hour. A blue candle is 6 inches tall and burns at

lorasvet [3.4K]

Answer:

Both candles will have the same height after 4 hours.

Step-by-step explanation:

The equation for the amount of candle remaining can be given by the following equations:

$Q(t) = Q(0) - at$

In which Q(t) is the amount after t hours, Q(0) is the initial amount and a is how much it decreases, in inches, per hour.

Red candle:

8 inches tall and burns at a rate of 7 divided by 10 inch per hour. This means that $Q(0) = 8, a = 7/10 = 0.7$ . So

$Q_{r}(t) = 8 - 0.7t$

Blue candle:

6 inches tall and burns at a rate of 1 divided by 5 inch per hour. This means that $Q(0) = 6, a = 1/5 = 0.2$ . So

$Q_{b}(t) = 6 - 0.2t$

After how many hours will both candles be the same height ?

This is t when

$Q_{r}(t) = Q_{b}(t)$

$8 - 0.7t = 6 - 0.2t$

$0.2t - 0.7t = 6 - 8[/yrc][tex]-0.5t = -2$

Multiplying by (-1)

$0.5t = 2$

$t = \frac{2}{0.5}$

$t = 4$

Both candles will have the same height after 4 hours.

6 0

4 years ago

The population of a small town was 10,800 in 2002. Since then the population has decreased at a rate of 2.5% each year. Write an

lozanna [386]

Answer:

See below

Step-by-step explanation:

A 2.5 % decrease means 97.5 % remains (.975)

population = 10800 ( .975) ^n where n = years past 2002

in 2020 n = 18

10800 (.975)^18 = 6847 people

6 0

2 years ago

Solve for the value of y in the triangle below.

german

Answer:

d

Step-by-step explanation:

6 0

3 years ago

Solve for x: (6x-3). QUICK!!!

Nana76 [90]

3(2x-1 does this help you?

3 0

3 years ago