Simplify. 2x²-x-1 2x+x

Solve using law of sines or law of cosines!

malfutka [58]

Answer:

Part 5) The length of the ski lift is $1.15\ miles$

Part 6) The height of the tree is 18.12 m

Step-by-step explanation:

Part 5)

Let

A -----> Beginning of the ski lift

B -----> Top of the mountain

C -----> Base of mountain

we have

$b=0.75\ miles$

$A=20\°$

$C=180\°-50\°=130\°$ ----> by supplementary angles

Find the measure of angle B

Remember that the sum of the interior angles must be equal to 180 degrees

$B=180\°-A-C$

substitute

$B=180\°-20\°-130\°=30\°$

Applying the law of sines

$\frac{b}{sin(B)}=\frac{c}{sin(C)}$

substitute

$\frac{0.75}{sin(30\°)}=\frac{c}{sin(130\°)}$

$c=\frac{0.75}{sin(30\°)}(sin(130\°))$

$c=1.15\ miles$

Par 6)

see the attached figure with letters to better understand the problem

Applying the law of sines in the right triangle BDC

In the right triangle BDC 20 degrees is the complement of 70 degrees

$\frac{BC}{sin(70\°)}=\frac{x}{sin(20\°)}$

$BC=(sin(70\°))\frac{x}{sin(20\°)}$ -----> equation A

Applying the law of sines in the right triangle ABC

In the right triangle ABC 50 degrees is the complement of 40 degrees

$\frac{BC}{sin(40\°)}=\frac{x+15}{sin(50\°)}$

$BC=(sin(40\°))\frac{x+15}{sin(50\°)}$ -----> equation B

Equate equation A and equation B and solve for x

$(sin(70\°))\frac{x}{sin(20\°)}=(sin(40\°))\frac{x+15}{sin(50\°)}\\\\2.7475x=0.8391(x+15)\\\\2.7475x=0.8391x+12.5865\\\\2.7475x-0.8391x=12.5865\\\\x=6.60\ m$

Find the value of BC

$BC=(sin(70\°))\frac{6.6}{sin(20\°)}$

$BC=18.12\ m$

therefore

The height of the tree is 18.12 m

5 0

4 years ago

Ashley deposits $1000 into an account that earns 4% interest compounded 2 times per year. how much money will Ashley have in her

loris [4]

The equation for compound interest is $A=P(1+\frac{r}{n})^{nt}$ , where:
P is the original deposit (or "principal")
r is the rate of the interest (in decimal form)
n is the number of times per year that the interest is compounded
t is the time passed in years

Plugging in your values, we see that the equation becomes $A=1000(1+\frac{.04}{2})^{(2)(5)}=1000(1.02)^{10}$

which equals, to the nearest cent, $1218.99, which is answer C.

3 0

4 years ago

Can someone solve this?

RoseWind [281]

I can the company sold 3,00 units in 2008, and 5,00 in 2012

3 0

3 years ago

Which function has a constant additive rate of change of -1/4?

VladimirAG [237]

Answer:

The first graph (in other words A)

Step-by-step explanation:

bc it is going down 1/4 at a constant rate!!!

Hope This Helps!!!

<3

7 0

3 years ago

Evaluate -6y - 5 for y = 1/2

saul85 [17]

Answer:

15

Step-by-step explanation:

-6y-5

Substitute 1/2 for y.

-6y-5

-6(1/2)-5

-3(-5)

15

5 0

2 years ago