-10 sin(x) = -4 csc(x) + 3
Recall that csc(x) = 1/sin(x) :
-10 sin(x) = -4/sin(x) + 3
Multiply both sides by sin(x) :
-10 sin²(x) = -4 + 3 sin(x)
Move everything to one side:
10 sin²(x) + 3 sin(x) - 4 = 0
Factorize the left side:
(2 sin(x) - 1) (5 sin(x) + 4) = 0
Then we have two cases,
2 sin(x) - 1 = 0 or 5 sin(x) + 4 = 0
Solve for sin(x) :
sin(x) = 1/2 or sin(x) = -4/5
Solve for x :
• if sin(x) = 1/2, then
x = arcsin(1/2) + 2nπ or x = π - arcsin(1/2) + 2nπ
x = π/6 + 2nπ or x = 5π/6 + 2nπ
• if sin(x) = -4/5, then
x = arcsin(-4/5) + 2nπ or x = π - arcsin(-4/5) + 2nπ
x = -arcsin(4/5) + 2nπ or x = π + arcsin(4/5) + 2nπ
(where n is any integer)
1. When two lines cross, the opposite angles are ___________ angles and are congruent. *
Straight Angle
Adjacent Angles
Angle Addition Postulate
Vertical Angles
2. Two angles that share a side and a vertex but do not overlap. *
Straight Angle
Adjacent Angles
Angle Addition Postulate
Vertical Angles
3. Two angles whose measures add up to 180 degrees. *
Angle Addition Postulate
Adjacent Angles
Supplementary Angles
Vertical Angles
Answer:
1. vertical angles
2. Adjacent angles
3. Supplementary angles
Step-by-step explanation:
Evaluate g(10) of g(x) =1/2x -4
Answer:
g(x)= 1
Step-by-step explanation:
[tex]g(x) = \frac{1}{2} x - 4 \\g(10) = \frac{1}{2} (10) = 5 \\ 5 - 4 = 1[/tex]
Help please!
Solve for x
Answer:
x=5
Step-by-step explanation:
What is the second number in the sequence?
Answer:
Step-by-step explanation:
Let "n" be the second odd number in the sequence
(n - 2) + n + (n + 2) + (n + 4) + (n + 6) = 135
5n + 10 = 135
5n = 125
n = 25
23 + 25 + 27 + 29 + 31 = 135
1498 x 99 I already know the answer is 148302
Answer:
148302
Step-by-step explanation:
Answer:
148302
Step-by-step explanation:
Because that's the answer
Maxden wanted to measure the length of the objects below.
For each one circle which unit of measurement he should use.
A. His puppy
Inches or Yards
B. A toy car
Yards or Centimeters
C. Width of his desk
Yards or Feet
D. His foot
Inches or Yards
Johnny has a box filled with 10 black marbles and 5 purple marbles.What are the odd he pulls two purple marbles in a row without replacemnet
Answer:
2/21
Step-by-step explanation:
The first purple is 5/15 and the second is 4/14. Multiply them together to get 2/21.
write an expression that is equivalent to 1/3(24p-33) -iready
Answer:
8p - 11
Step-by-step explanation:
Got the same I-Ready question lol
is (33,10), (35,8), and (36,10) a function
Answer: yes it’s a function because the x values aren’t repeating
1
1.
A random variable X has expected value
and probability distribution as
12
follows:
X
-3
-2
-1
0
1
N
3
f(x)
a
2a
1
1
1
b
сле
b b
2
5
10
5
(a)
(b)
Find the values of a and b.
Find E[X2 + 1].
(8 marks)
Answer:
huh
Step-by-step explanation:
\sqrt((x-(1)/(2))^(2))=3.5
Answer:
8
Step-by-step explanation:
sqrt((x-1)/2)^2))=3.5
square root and squared cancel out
(x-1)/2 = 3.5
x-1 = 7
x = 8
How would you find the average rate of change between two points
on a curve?
Answer:
For a function, it is the change in the y-value divided by the change in the x-value for two distinct points on the graph
Step-by-step explanation:
Answer:
i think that you can find the average rate of change between 2 points on a curve by dividi the change in the output value (Y) by the change in the input value (X)
Step-by-step explanation:
How to find the derivative???
Answer:
[tex]y'= \dfrac{2}{3}e^{2x + e^{2x}/3}[/tex]
Step-by-step explanation:
We have [tex]e^{2x} = \ln(y^3)[/tex] and we want the implicit differentiation [tex]\dfrac{dy}{dx}f(x) = y'[/tex]
Therefore, we want to separate the [tex]y[/tex] from the equation.
[tex]\ln(y^3) =e^{2x} \implies 3 \ln(y) = e^{2x} \implies \ln(y) = \dfrac{e^{2x} }{3}[/tex]
[tex]\implies e^{\ln(y)} = e^{e^{2x}/3} \implies \boxed{y = e^{e^{2x}/3}}[/tex]
Now we can calculate the derivative. By the chain rule,
[tex]y' = \dfrac{d}{dx}\left(e^{e^{2x}/3}\right) = e^{e^{2x}/3}\dfrac{d}{dx}\left(\dfrac{e^{2x}}{3}\right)[/tex]
Now
[tex]\dfrac{d}{dx}\left(\dfrac{e^{2x}}{3}\right) =\dfrac{1}{3}\dfrac{d}{dx}\left(e^{2x}\right) = \dfrac{2}{3}e^{2x}[/tex]
Therefore
[tex]y' = e^{e^{2x}/3}\cdot \dfrac{2}{3}e^{2x} = \dfrac{2}{3}e^{2x + e^{2x}/3}[/tex]
pls help me . Eleven family members are going on a trip together. They have cars that fit only 4
people. How many cars will they need to take? help
Answer:
3.
Step-by-step explanation:
Since there are 11 family members and only 4 people fit in a car, they will have to take 3 cars.
4 x 3 = 12,
Also, even though there is going to be 1 seat extra you cannot squeeze 3 people in. Ps. (Just a safety note) In real life it is illegal to drive with extra passengers in a vehicle.
Hope that helps. x
Answer:
3
Step-by-step explanation:
3×4=12 so will still have one vacant seat on one of the cars
You visit two banks to determine their interest rates. Bank A offers you 6.2% annual
interest compounded monthly, and Bank B offers you 6.3% compounded quarterly.
Determine which bank is offering the best deal.
Answer:
6.3% quarterly
Step-by-step explanation:
The monthly compounded rate is equivalent to a quarterly compounded rate of ...
(1 +0.062/12)^3 -1 = 1.558%
The quarterly compounded rate is ...
6.3%/4 = 1.575%
The 6.3% rate compounded quarterly is the better deal.
_____
Additional comment
An annual rate r compounded n times per year for m compounding periods is equivalent to a rate of
(1 +r/n)^m -1 . . . per m/n of a year
Then an annual rate of r compounded 12 times per year for 3 months is equivalent to a quarterly (3/12 year = 1/4 year) of ...
(1 +r/12)^3 -1
__
An annual rate of r compounded 4 times per year for 1 quarter is equivalent to ...
(1 +r/4)^1 -1 = r/4
which graph shows the Same and behaviour as the Graph of F(x) = 2X^6=2x²2-5
Given function:-
f(x) = 2x6 – 2x2 – 5.In order to find the end behavior of the graph, we need to find the degree of the given function and the leading coefficent.Degree of the given function is the highest power of the variable.
We have variable x there.
Highest power of x is 6.So, we can say:
Degree = 6 ( an even degree)
And leading coefficent is the coefficent of highest power term.
We have highest power term is 2x^6.
So, the leading coefficent is : 2 (Positive number)
For even degree and positive leading coefficent, end behaviour is
x --> ∞ f(x) = +∞
x-->-∞ f(x) = +∞
2. What conclusion can you make from each pair of true statements? State which law
logic you used.
a. If an animal is an omnivore, then it eats both plants and animals. Orangutans are omnivo
b. If an animal is a female mammal, then it produces milk. If an animal produces milk, it
nurse its young.
mammary gland
c. If a species is endangered, then it is likely to become extinct. Giant panda bears are
endangered
Answer:
tried my best!!!!!
Step-by-step explanation:
a) they eat both meat and palnts
b) it nurses its young,and feeds us beings
c) yes it is
Expression:
Simplify 2s - s + 6s
Please explain step by step how I get the answer to get marked as brainliest
Answer:
7s.
Step-by-step explanation:
2s - s + 6s (Given)
Rembember that - s is the same as - 1s because there is an invisible 1.
So, 2s - 1s = 1s or s.
1s + 6s = 7s.
2s - s + 6s (Given)
7s (Combine like terms)
A line has a slope of and passes through the point (4, 7). What is its equation in
slope-intercept form?
Answer:
y = (7/4)x + 0
Step-by-step explanation:
yeah-ya....... right?
Ellie and Isaiah are helping their friend Nora move. If Ellie can move 4 boxes for
every 16 boxes that Isaiah moves, then how many boxes can Isaiah move for every
box that Ellie moves?
Answer:
Isaiah can move 4 boxes for every box Ellie moves.
Pls give brainliest. :D
100 points ‼️ (I would give more but that’s the limit)
if g(x)=x^2-x then what is g(2)-2
Answer:
0Step-by-step explanation:
[tex]g(x) = {x}^{2} - 2[/tex]
To find g(2) - 2 first find g(2) by substituting the value of x that's 2 into the original expression after that subtract 2 from the final answer obtained.
We have
[tex]g(2) = {2}^{2} - 2 \: \: \: \: \: \: \: \: \: \: \\ = 4 - 2 = 2 \\ \\ \\ g(2) - 2 = 2 - 2 = 0[/tex]
We have the final answer as
0Hope this helps you
Does anyone know how to add fractions? Please explain step by step to get marked!
Answer:
To add fractions there are Three Simple Steps:
Step 1: Make sure the bottom numbers (the denominators) are the same.
Step 2: Add the top numbers (the numerators), put that answer over the denominator.
Step 3: Simplify the fraction (if possible)
How do I rewrite the improper fractions as a mixture number? Please explain step by step to get marked as brainliest
Answer:
1) Divide the numerator by the denominator.
2) Write down the whole number result.
3) Use the remainder as the new numerator over the denominator. This is the fraction part of the mixed number.
Step-by-step explanation:
not sure of this will help... but hope it does!
Answer:
Explained below :)
I tried my best to explain, sorry if it doesn't make sense
Step-by-step explanation:
Example problem: 11/4 (Mixed number)
1: 11 divided by 4 = 2 (whole number) with a remainder of 3
( Numerator divided by denominator) (Don't turn the number into a decimal leave the remainder)
2: Take the remainder and put it over the denominator 3/4
3: Whole number beside the remainder over the denominator
Your answer would be 2 3/4
help now plsssssssssssssssssssssssss
cheater bro wyd ur doing a diagnostic try ur best lol
*WILL GIVE BRAINLIEST FOR BEST ANSWER*
Jasper won the raffle at the zoo and gets to feed the dolphins! The dolphin trainer gives Jasper a bucket of fish to divide evenly among 4 dolphins. Each dolphin gets 3 fish.
Which equation can you use to find the number of fish f in the bucket before Jasper feeds the dolphins?
Solve this equation for f to find the number of fish in the bucket before Jasper feeds the dolphins.
fish
The number of fish in the bucket before Jasper feeds the dolphins was 12.
Since Jasper won the raffle at the zoo and gets to feed the dolphins, and the dolphin trainer gives Jasper a bucket of fish to divide evenly among 4 dolphins, and each dolphin gets 3 fish, to find the number of fish F in the bucket Before Jasper feeds the dolphins, the following equation must be performed:
Number of dolphins = D Fish for each dolphin = E Total fish = F D x E = F 4 x 3 = F 12 = F
Therefore, the number of fish in the bucket before Jasper feeds the dolphins was 12.
Learn more about maths in https://brainly.com/question/25843658
Describe how to find all the points on a baseball field that are equidistant from second base and third base.
In the figure, m∠DBE=50. Find each of the following.
m∠BEDm angle b e d
m∠BEAm angle b e eh
x
y
BE
BC
From the given diagram, the following statements are true:
AB = BC
3y = 5y - 22
3y - 5y = -22
-2y = -22
y = 11
Similarly, m<DBE = 50 degrees
m<BED = 90 - m<DBE
m<BED = 90 - 50
m<BED = 40 degrees
Since BE = BC = 3y
BE = BC = 3(11) = 33
Also, 7x - 2 = 40
7x = 40 + 2
7x = 42
x = 6
Get the measure of m<BEA
m<BEA = 7x - 2
m<BEA = 7(6) - 2
m<BEA = 40 degrees
Learn more on angles here: https://brainly.com/question/16281260
find the value of x.
Answer:
25
Step-by-step explanation:
x+7 = 32 (similar triangles)
x = 25
1x10,000 + 6x1,000 + 3x100+ 7x10 + 8x 1/10 + 9/100 in a standed form
a- 163,789
b- 163,700.89
c- 16,378.9
d- 1,637.89
e- 16,370.89
Answer:
C
Step-by-step explanation:
because write in standard form hope it helps to you
Henry used his GPS to measure the distances from his house to two locations to the thousandth mile. Then, he rounded both values to the nearest hundredth. Which pair of distances could be the actual distances Henry measured?
school: 3.26 miles
piano lessons: 5.84 miles