Which expression has a value of -10?

1. Find the value of

spin [16.1K]

9514 1404 393

Answer:

-√5
3/5
-4/5

Step-by-step explanation:

The relevant relations are ...

sec = ±√(tan² +1)

cos = 1/sec

csc = 1/sin = ±1/√(1 -cos²)

Sine and Cosecant are positive in quadrants I and II. Cosine and Secant are positive in quadrants I and IV.

__

1. sec(θ) = -√((-2)² +1) = -√5

2. cos(θ) = 1/sec(θ) = 1/(5/3) = 3/5

3. csc(θ) = -1/√(1 -(-3/5)²) = -√(16/25) = -4/5

8 0

2 years ago

A 12 ounce bottle of shampoo lasted Nina 8 weeks how long would an 18 once bottle of shampoo last her

natali 33 [55]

Answer:

12 weeks

Step-by-step explanation:

set up a proportion of ounces/weeks = ounces/weeks

12/8 = 18/w

12w = 144

w = 12

4 0

2 years ago

Solve the system of equations algebraically. Verify your

xz_007 [3.2K]

Answer:

The solution is the point (0.5,-3)

Step-by-step explanation:

we have

$y=4x-5$ ----> equation A

$y=-3$ ----> equation B

Solve the system by substitution

Substitute equation B in equation A

$-3=4x-5$

Solve for x

Adds 5 both sides

$-3+5=4x$

$2=4x$

Divide by 4 both sides

$x=0.5$

therefore

The solution is the point (0.5,-3)

Verify your answer using the graph

using a graphing tool

Remember that the solution of the system of equations is the intersection point both graphs

The intersection point is (0.5,-3)

therefore

The solution is the point (0.5,-3)

see the attached figure

8 0

3 years ago

Read 2 more answers

A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of

belka [17]

Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.

Salt flows into the tank at a rate of

(2 gal/min) (6 lb/gal) = 12 lb/min

and flows out at a rate of

(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min

so that the net rate at which salt is exchanged through the tank is

ds(t)/dt = 12 - s(t)/150 … (lb/min)

Solve for s(t). The DE is separable, so we have

ds/dt = 12 - s/150

150 ds/dt = 1800 - s

150/(1800 - s) ds = dt

Integrate both sides to get

-150 ln|1800 - s| = t + C

Solve for s :

ln|1800 - s| = -t/150 + C

1800 - s = exp(-t/150 + C )

1800 - s = C exp(-t/150)

s = 1800 - C exp(-t/150)

Now given that s(0) = 50, we solve for C :

50 = 1800 - C exp(-0/150)

50 = 1800 - C

C = 1750

Then the amount of salt in the tank at any time t ≥ 0 is

s(t) = 1800 - 1750 exp(-t/150)

To find the time it takes for the tank to hold 100 lb of salt, solve for t in

100 = 1800 - 1750 exp(-t/150)

1700 = 1750 exp(-t/150)

34/35 = exp(-t/150)

ln(34/35) = -t/150

t = -150 ln(34/35) ≈ 4.348

So it would take approximately 4.348 minutes.

By the way, we didn't have to solve for s(t), we could have instead stopped with

-150 ln|1800 - s| = t + C

Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so

-150 ln|1800 - 50| = 0 + C

C = -150 ln|1750|

==> t = 150 ln(1750) - 150 ln|1800 - s|

Then s(t) = 100 lb when

t = 150 ln(1750) - 150 ln(1700)

t = 150 ln(1750/1700)

t = 150 ln(35/34)

t ≈ 4.348

5 0

3 years ago

A punch makes 16 pints.If 10 guests equally share the punch,how many pints will each guest drink?

m_a_m_a [10]

Answer:

1.6 pints

Step-by-step explanation:

A punch=16 pints

If 10 guest shares the punch equally

Each guest get=16 pints/10

=1.6 pints

Each guest will drink 1.6 pints of punch

8 0

2 years ago