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
IceJOKER [234]
3 years ago
5

URGENT HELP PLEASE!

Mathematics
1 answer:
Vaselesa [24]3 years ago
5 0

Answer:

(a) x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}

(b) x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}

Step-by-step explanation:

It is given that 0\leq x\leq 2\pi.

(a)

\sqrt{2}\sin 2x=1

\sin 2x=\dfrac{1}{\sqrt{2}}

\sin 2x=\dfrac{\pi}{4}

2x=\dfrac{\pi}{4},\dfrac{3\pi}{4},\dfrac{9\pi}{4},\dfrac{11\pi}{4}     [\because \sin x=\sin y\Rightarrow x=n\pi+(-1)^ny]

x=\dfrac{\pi}{8},\dfrac{3\pi}{8},\dfrac{9\pi}{8},\dfrac{11\pi}{8}

(b)

\csc^2 x-\csc x-2=0

\csc^2 x-2\csc x+\csc x-2=0

\csc x(\csc x-2)+1(\csc x-2)=0

(\csc x+1)(\csc x-2)=0

\csc x=-1\text{ or }\csc x=2

\sin x=-1\text{ or }\sin x=\dfrac{1}{2}         [\because \sin x=\dfrac{1}{\csc x}]

x=\dfrac{3\pi}{2}\text{ or }x=\dfrac{\pi}{6},\dfrac{5\pi}{6}

Therefore, x=\dfrac{3\pi}{2},\dfrac{\pi}{6},\dfrac{5\pi}{6}.

You might be interested in
Write an equation of a line that has a slope of –5 and a y-intercept of 2.
Bingel [31]

Answer:

y-2 = -5x

5x+y = 2 is the required equation of a line.

4 0
3 years ago
A culture started with 5000 bacteria after 5 hours it grew to 6500 bacteria predict how many bacteria will be present after 16 h
postnew [5]

Answer:

After 16 hours bacterial count will be 11600.

Step-by-step explanation:

Bacterial growth is always an exponential growth in a given culture.So the formula for the growth will be

Final counts of bacteria = Initial counts × (rate of growth)^{time}

Given from first part Initial counts = 5000

Final counts= 6500 and time of growth = 5 hours

Then we will get the value of rate of growth of bacteria from the bacteria

⇒ 6500 = 5000×(rate)^{5}

(rate)^{5}= \frac{6500}{5000} = 1.3

Rate = \sqrt[5]{1.3} = 1.05

Now again to get the value of bacteria after 16 hours

Final Count = 5000×(1.05)^{16}

                   = 5000×2.32

                   = 11600


7 0
3 years ago
PLS PLS PLS HELP ME ILL GIVE 20 points.
lisov135 [29]

Answer:

if you want to know the x is.

Step-by-step explanation:

(180°-4x)+(180°-6x)+2x=180°

x=22.5°

8 0
3 years ago
PLZ ANSWER APSP IM IN THE TEST RN!!!
olchik [2.2K]

Answer:

x = 38

y = 25

Step-by-step explanation:

To find x, you do

(2x + 5) = (3x - 33)

Subtract 2x from both sides to isolate x on one side, you get:

5 = (x - 33)

Add 33 to both sides to separate the normal number from the x, you get:

38 = x

From there, you plug x into one of the equations

2(38) + 5

The answer's 81, meaning that angle is 81 degrees. Using supplementary angles, you can find that angle ACD = 99, which you can use to find angle BCE. You'll get this equation:

(4y - 1) = 99

Add one to both sides to get rid of it, you get:

4y = 100

Divide by four, to get the y all alone:

y = 25

I hope this helped!

8 0
3 years ago
Read 2 more answers
A group of workers can plant at a rate of 12 acres per day.
Rashid [163]

Answer:

36

Step-by-step explanation: if they do 12 acres per day.. it would be 36 for three days. 12x3=36

4 0
3 years ago
Read 2 more answers
Other questions:
  • -2 2/3, -5 1/3, -10 2/3, -21 1/3, -42 2/3. which formula can be used to describe the sequence?
    6·1 answer
  • Find the possible value or values of y in the quadratic equation z^2 - 4z+ 4 =0
    9·1 answer
  • Hanna puts $4,383 in a savings account with an annual interest rate of 5.2 percent for 3 years. Into which variable should she s
    11·1 answer
  • What is the product 5/10 x 10/3 ​
    13·2 answers
  • If 8 students have to split 5 pieces of cake how much did each student get?
    6·2 answers
  • Nate solve the equation 3 times 5 equals 15 by writing and solving 15 divided by 5 is 3 x plane why Nate's method works
    7·1 answer
  • Select all the correct answers.
    13·1 answer
  • Write the equation of the line given the slope and the point that it passes through.
    6·1 answer
  • I need help ASAP I wasn’t paying attention and lowkey forgot all of this
    9·1 answer
  • Help i don't know what to do please help
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!