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
Evgen [1.6K]
3 years ago
6

Solve sin4x cosx-sinx cos4x = sqrt(2)/2 for [0, 2pi)

Mathematics
1 answer:
natita [175]3 years ago
4 0

Answer:

x = π/12, π/4, 3π/4, 11π/12, 17π/12, 19π/12

Step-by-step explanation:

sin(4x) cos x − sin x cos(4x) = √2 / 2

Use angle difference formula.

sin(4x − x) = √2 / 2

sin(3x) = √2 / 2

3x = π/4 + 2kπ, 3π/4 + 2kπ

x = π/12 + 2kπ/3, π/4 + 2kπ/3

x = π/12, π/4, 3π/4, 11π/12, 17π/12, 19π/12

You might be interested in
( 3 + 2i ) + ( 6 - 8i )
natta225 [31]
9-6i is the answer, combine like terms
4 0
3 years ago
Four hundred sixty-nine and eight hundredths can also be written as ​
svet-max [94.6K]

Answer:469.08

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
What is 3 ln 3 - ln 9 expressed as a single natural logarithm?
marusya05 [52]
Answer: In 3
SOLVINGS
What is 3 ln 3 - ln 9 expressed as a single natural logarithm

Since ln (m^n) = n⋅ln (m)                 … natural logarithmic property
We can further simplify the expression 3 ln 3
3 In 3 = In (3^3)
Therefore, 3 ln 3 - ln 9 = In (3^3) – In 9

Since ln(m/n) =ln(m) – ln(n)         … natural logarithmic property
We can further simplify the expression In (3^3) – In 9
In (3^3) – In 9 = In [(3^3)/(9)]
= In (27/9)
= In 3

Therefore, 3 ln 3 - ln 9 expressed as a single natural logarithm is In 3.
4 0
3 years ago
Read 2 more answers
Rhonda hiked 260.4 feet and hiked 3 more hours and I got that by adding 1.5+1.5=3 but what do I do
Hunter-Best [27]
1.5 + 1.5 + 2 = 5 hours 
All you must do is: 260.4 / 5 = ? 
6 0
3 years ago
Please solve i will give brainiest 100 point question ****** do the whole page please need to pass or i will fail its my final t
dmitriy555 [2]

Answer:

1. Find the difference between the areas.

<u>Area of the small rectangle</u>: (x+2)(x+7)=x^2+7x+2x+14=x^2+9x+14

<u>Area of the big rectangle</u>: (x+9)(x+11)=x^2+11x+9x+99=x^2+20x+99

The difference is: 11x+85

( x^2+20x+99)- (x^2+9x+14)=x^2+20x+99-x^2-9x-14=11x+85

2.

You can solve this question just by looking at the graph.

a) The height is 4 meters.

f(d)=h=-2d^2+7d+4

To find the height of the bleachers, we should consider the moment before the shoot, when the distance is equal to 0.

f(0)=h=-2(0)^2+7(0)+4

h=4

The height is 4 meters.

b) 9 meters.

For d=1

f(1)=h=-2(1)^2+7(1)+4

f(1)=h=-2+7+4

h=9

b) The ball travels 4 meters.

But to calculate it, it is when h=0

0=-2d^2+7d+4

Using the quadratic formula:

$d=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$d=\frac{-7 \pm \sqrt{7^2-4\left(-2\right)4}}{2\left(-2\right)}$

$d=\frac{-7\pm\sqrt{81}}{-4}$

$d=\frac{-7\pm9}{-4}$

It will give us to solutions, once it is a quadratic equation, but we are talking about a positive distance.

$d=-\frac{1}{2} \text{ or }d=4$

3.

In this question, we have to find the area of the cylinder and the sphere.

From the information given, we have

a = 5mm and d = 5mm, therefore the radius is 2.5 mm.

The volume of a cylinder:

V=\pi r^2h

V=\pi (2.5)^2 \cdot 5

V=31.25 \pi

V_{c} \approx 98.17 \text{ m}^3

The volume of the sphere:

$V=\frac{4}{3}  \pi r^2$

V_{s} \approx 65.4 \text{ m}^3

The volume of the capsule is approximately 163.57  \text{ m}^3

3 0
3 years ago
Other questions:
  • Name three common measurements that are expressed as a ratio of two units.
    5·1 answer
  • Elly buys 75 shares of stock in a mutual fund for a total investment of $450. She sells 50 shares of her stock for total proceed
    8·2 answers
  • The value of n is both 5 times as much as the value of m and 36 more than the value of m. What are the values of n and m? Explai
    6·1 answer
  • Suppose the two sinusoidal curves shown above are added together. which of the plots shown below best represents
    15·1 answer
  • What are the proceeds of a note for $10,500 at a discount rate of 5%, for 30 months?
    12·1 answer
  • Yunika downloaded three applications for $2.99 each to her cell phone. The remaining applications that Yunika purchased cost $1.
    6·2 answers
  • HELP ASAP, GIVING BRAINLIEST​
    9·1 answer
  • (-2,-5) on a graph. I really need to know.
    5·1 answer
  • Mother shared 60 sweets among her 2 daughters in the ratio 2:3. If Janice gets 20, how many do Kayla gets?​
    5·1 answer
  • A survey found that 52% of middle school students needed extra help in class.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!