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3 years ago

In △ABC, m∠A=19°, a=13, and b=14. Find c to the nearest tenth.

1 answer:

34kurt3 years ago

3 0

We know that
Applying the law of sines

step 1
Find the value of angle B
a=13
b=14
A=19°
so

$\frac{a}{sin A} = \frac{b}{sin B} \\ a*sin B=b*sin A \\ sin B= \frac{b}{a}*sin A \\ sin B= \frac{14}{13} *sin 19 \\ sin B=0.3506 \\ B=arc sin(0.3506) \\ B=20.5$ °

step 2
with angle A and angle B find the angle C
A+B+C=180-----> solve for C
C=180-(A+B)------> C=180-(19+20.5)-----> C=140.5°

step 3
$\frac{a}{sin A} = \frac{c}{sin C} \\ a*sin C=c*sin A \\ c=a* \frac{sin C}{sin A} \\ c=13* \frac{sin 140.5}{sin 19} \\ c=25.4$

the answer is
the value of c is 25.4

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At a picnic there were 3 times as many adults as children and twice as many women as men. If there was a total of x men, women,

Dennis_Churaev [7]

Answer:

$\dfrac{x}{4}$

C is correct.

Step-by-step explanation:

At a picnic,

Number of adults is 3 times as number of children.

Number of women is twice as number of men.

Total number of men, women and children at the picnic be x

Let number of children be c

Let number of men be m

Let number of women be w

# Number of women is twice as number of men, w = 2m

# Number of adults is 3 times as number of children, w + m = 3c

2m + m = 3c (∴ w=2m )

c = m

Total number of men, women and children at the picnic be x

∵ c + m + w = x

m + m + 2m = x

4m = x

Number of men, $m=\dfrac{x}{4}$

Hence, The total number of men will be $\dfrac{x}{4}$

5 0

3 years ago

Pls help in a middle of an exam

KIM [24]

Answer:

$\frac{2x^2+4x-9}{(2x-3)(2x+3)(x-1)}$

Step-by-step explanation:

$\frac{2x}{4x^2-9} + \frac{3}{2x^2+x-3}$ can be simplified to:
$\frac{2x}{(2x-3)(2x+3)}+\frac{3}{(2x+3)(x-1)}$

Make them have common denominators so:
$\frac{(2x)(x-1) +3(2x-3)}{(2x-3)(2x+3)(x-1)}$

Simplify:
$\frac{2x^2-2x+6x-9}{(2x-3)(2x+3)(x-1)} = \frac{2x^2+4x-9}{(2x-3)(2x+3)(x-1)}$

I don't think you can simplify that fraction further so that's the answer.

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2 years ago

The population of a town increases by 4 % every year . In the last year the population of the town was 110000.

TEA [102]

Answer:

114,400 and 118,976.

Step-by-step explanation:

Let's represent this using a function. Let's let:

$P(y)$ represent the total population, and $y$ represent the total number of years since last year.

We know that the population grows by 4% every year or 0.04 every year. This is exponential growth. We can write this as:

$P(y)=110000(1.04)^y$

Note that the coefficient is 110000 because that is the year we are starting with. Also, note that it is 1.04 because we are essentially adding .04 to the original population.

Anyways, to find the present population, set y equal to 1 (because 1 year after last year is the present year)

$P(1)=110000(1.04)^1=114400$