All categories

3 years ago

Given that cosine theta = -1/2 and theta is obtuse find sin4theta

Mathematics

1 answer:

igomit [66]3 years ago

5 0

Answer:

0.8660

Step-by-step explanation:

cosine theta = -1/2

theta = cosinearctan(-0.5)

theta = 120

sine4theta = sine 4(120)

= sine480

= 0.8660

You might be interested in

Two intersecting lines have ______ of point(s) in common.

Vladimir79 [104]

They only have 1 common point

5 0

4 years ago

Read 2 more answers

Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another br

Lina20 [59]

Answer:

The differential equation for the amount of salt A(t) in the tank at a time t > 0 is $\frac{dA}{dt}=12 - \frac{2A(t)}{500+t}$ .

Step-by-step explanation:

We are given that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.

The concentration of the solution entering is 4 lb/gal.

Firstly, as we know that the rate of change in the amount of salt with respect to time is given by;

$\frac{dA}{dt}= \text{R}_i_n - \text{R}_o_u_t$

where, $\text{R}_i_n$ = concentration of salt in the inflow $\times$ input rate of brine solution

and $\text{R}_o_u_t$ = concentration of salt in the outflow $\times$ outflow rate of brine solution

So, $\text{R}_i_n$ = 4 lb/gal $\times$ 3 gal/min = 12 lb/gal

Now, the rate of accumulation = Rate of input of solution - Rate of output of solution

= 3 gal/min - 2 gal/min

= 1 gal/min.

It is stated that a large mixing tank initially holds 500 gallons of water, so after t minutes it will hold (500 + t) gallons in the tank.

So, $\text{R}_o_u_t$ = concentration of salt in the outflow $\times$ outflow rate of brine solution

= $\frac{A(t)}{500+t} \text{ lb/gal } \times 2 \text{ gal/min}$ = $\frac{2A(t)}{500+t} \text{ lb/min }$

Now, the differential equation for the amount of salt A(t) in the tank at a time t > 0 is given by;

= $\frac{dA}{dt}=12\text{ lb/min } - \frac{2A(t)}{500+t} \text{ lb/min }$

or $\frac{dA}{dt}=12 - \frac{2A(t)}{500+t}$ .

4 0

3 years ago

Alexa and her children went into a movie theater where

slega [8]

1 Pretzel and 5 Bags of Popcorn
(WORK SHOWN BELOW)

7 0

2 years ago

Which expression is less than 3? 3 x 4/4, 3 x 15/8, 3 x 4/9, 3 x 1 1/8

pav-90 [236]

Answer:

3 × 4/9

Step-by-step explanation:

Remember that 4/4 is equal to 1, so 3 × 4/4 = 3

15 is bigger than 8, so we know that 15/8 is equal to 1 point something, you can find out the answer by a simple division, once you know the answer (1.875), you multiply it by 3, and get 5.625, this is larger than 3 so it is not the answer.

4 is smaller than 9, so we know that 4/9 is equal to 0 point something, again, we divide and get 0.444..., now we know that multypling something by 0 pint something is almost the same as dividing, so we can that this result is less than 3 (its 1.333).

1 and 1/8 is a mixed fraction so we know it is larger than 1, meaning that if we multiply it by 3, we will get a number larger than 3 (3.375)

8 0

3 years ago

For the x-values 1, 2, 3, and so on, the yvalues of a function form a geometric

Tema [17]

Answer:

exponential function

Step-by-step explanation:

A geometric sequence is a representation of an exponential function.

There are a couple of ways an exponential function can decrease in value. It can be a decaying function, or it can be a growth function that is reflected across the x-axis.

4 0

3 years ago