1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ycow [4]
3 years ago
12

Solve 2cos(x)-4sin(x)=3 [0,360]

Mathematics
1 answer:
Korvikt [17]3 years ago
3 0
2cos(x) - 4sin(x) = 3

use identity  [cos(x)]^2 +[ sin(x)]^2 = 1 => cos(x) = √[1 - (sin(x))^2]

2√[1 - (sin(x))^2] - 4 sin(x) = 3

2√[1 - (sin(x))^2] = 3 + 4 sin(x)

square both sides

4[1 - (sin(x))^2] = 9 + 24 sin(x) + 16 (sin(x))^2

expand, reagrup and add like terms

4 - 4[sin(x)]^2 = 9 + 24sin(x) + 16sin^2(x)

20[sin(x)]^2 + 24sin(x) +5 = 0

use quadratic formula and you get sin(x) = -0.93166 and sin(x) = -0.26834

Now use the inverse functions to find x:

arcsin(-0.93166) = 76.33 degrees

arcsin(-0.26834) = 17.30 degrees






You might be interested in
A box is to be made where the material for the sides and the lid cost​ $0.20 per square foot and the cost for the bottom is ​$0.
Reika [66]

Answer:

The dimension of the box is l×w×h =  (2.274 × 2.274 × 1.934) ft³

Step-by-step explanation:

From the given information;

Let a be the cost of the box

Let b  be one side of the square base ;    &

h to be the height  of the box

We know that the volume of the box = 10 cubic feet

Then;

a²h = 10

h = 10/a²

The base = (0.65)a²

The top = (0.2)a²

The side = (0.2) a × 25/a²

= 5/a

For the four sides of the box now ;

= (0.2) 4a × 25/a²

= 0.8  × 25/a

= 20 /a

The total cost of the box is:

b = 0.65a² + 0.2a² + 20 /a

b = 0.85 a² + 20 /a

Taking differential of b with respect to a ;we have:

db/da = 1.7a - 1/a²(20) = 0

1.7 a³ - 20 = 0

1.7 a³  = 20

a³ = 20/1.7

a³ = 11.77

a = \sqrt[3]{11.77}

a = 2.274 ft

Thus; the cost for the base of the box = (0.65)a²

the cost for the base of the box =(0.65) × ( 2.274)²

the cost for the base of the box = 3.362

The top of the box = (0.2)a²

The top of the box = (0.2)× ( 2.274)²

The top of the box = 1.034

The four sides of the box = 20 /a

The four sides of the box = 20/2.274

The four sides of the box = 8.795

the total cost = b = 0.85 a² + 20 /a

the total cost = 0.85 (2.274)² + 20 /2.274

the total cost = 4.395 + 8.795

the total cost = 13.19

Recall that:

the volume of the box = 10 cubic feet

Then;

a²h = 10

h = 10/a²

h = 10/ 2.274²

h  1.934

The dimension of the box is l×w×h =  (2.274 × 2.274 × 1.934) ft³

7 0
3 years ago
The graph of y=x^3 is transformed as shown in the graph below. Which equation represents the transformed function?
omeli [17]

Answer:

y = (-x)^3 - 4

Step-by-step explanation:

Ok, for the function:

y = x^3

When x = 0, we have:

y = 0^3  = 0

So the original graph passes through the point (0, 0)

If we look at the given graph, we can see that the y-intercept (the value of y when x = 0) is:

y = -4

So, this is the graph of y = x^3 moved down 4 units.

You can also see that the graph goes downward as x increases (and up as x decreases) while for the function:

y = x^3

as x increases, we should see that y also increases.

Then we have a reflection across the x-axis.

Ok, now let's describe a vertical shift.

For a general function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

if N is positive, the shift is upwards

if N is negative, the shift is downwards.

And for a function f(x), a reflection across the x-axis is written as:

g(x) = - f(x)

Here we first apply the reflection across the x-axis, so we get:

g(x) = -f(x)

now we apply the shift 4 units downwards

g(x) = - f(x) - 4

replacing f(x) by our function, x^3

we get:

g(x) = -x^3 - 4

And because of the odd power, we can write:

-x^3 = (-x)^3

Then the function is:

g(x) = (-x)^3 - 4

The correct option is the last one.

y = (-x)^3 - 4

3 0
3 years ago
Please help me! I will give you Brainlist if you get it right!​
Sedaia [141]

Answer:

B

Step-by-step explanation:

find the area of the rectangle and then find the area of the semi circle, then add the 2 together

6 0
3 years ago
A team of 17 softball players need to choose three players to refill the water cooler. How many different ways are there to sele
KATRIN_1 [288]
<h3>Answer: 680 different combinations</h3>

=======================================================

Explanation:

If order mattered, then we'd have 17*16*15 = 4080 different permutations. Notice how I started with 17 and counted down 1 at a a time until I had 3 slots to fill. We count down by 1 because each time we pick someone, we can't pick them again.

So we have 4080 different ways to pick 3 people if order mattered. But again order doesn't matter. All that counts is the group itself rather than the individual or how they rank. There are 3*2*1 = 6 ways to order any group of three people, which means there are 4080/6 = 680 different combinations possible.

An alternative is to use the nCr formula with n = 17 and r = 3. That formula is

_n C _r = \frac{n!}{r!*(n-r)!}

where the exclamation marks indicate factorials

5 0
3 years ago
What is the property ??
hram777 [196]

The distributive property is being displayed here. The distributive property shows if you have a problem like 3(a+c), it can be converted into 3a+3c. It shows itself in this because it is distributing -2 to both a and b.

Answer: The distributive property is being shown here.

Hope I helped!

4 0
3 years ago
Other questions:
  • How many hundredths are egual to six tenths?
    9·2 answers
  • Fill in the blanks to make the solution correct: <br> 5._4 - (_.8_)=-3.61
    13·1 answer
  • What is the distance between the points (21, 16) and (9, 11)?
    8·1 answer
  • Convert (CAB) 16 to decimal<br><br>need help asap
    8·2 answers
  • "Use distributive property, show work: 7(2x1)"
    9·2 answers
  • A recipe called for 2/9 cup of chopped tomatoes and 4/7 cup of diced tomatoes. In total how many cups of tomatoes did the recipe
    15·2 answers
  • A line passes through (-1, 7) and (2, 10) Which answer is the equation of the line?
    7·1 answer
  • To skate at Roller Heaven, each person must pay a membership fee (m) and a fee for each session (f). Art attended five sessions
    9·1 answer
  • A circle has a radius of 5 ft, and an arc of length 7 ft is made by the intersection of the circle with a central angle. Which e
    12·1 answer
  • Which expression is equivalent to x ^ 2 + 7x + 6 ? pls show work
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!