Answers
Answer:
The solutions of the equations are π/3 , 2π/3 , 4π/3 , 5π/3
Step-by-step explanation:
* Lets revise the four quadrant before solving the equation
# First quadrant the measure of all angles is between 0 and π/2
the measure of any angle is α
∴ All the angles are acute
∴ All the trigonometry functions of α are positive
# Second quadrant the measure of all angles is between π/2 and π
the measure of any angle is π - α
∴ All the angles are obtuse
∴ The value of sin(π - α) only is positive ⇒ sin(π - α) = sinα
# Third quadrant the measure of all angles is between π and 3π/2
the measure of any angle is π + α
∴ All the angles are reflex
∴ The value of tan(π + α) only is positive ⇒ tan(π + α) = tanα
# Fourth quadrant the measure of all angles is between 3π/2 and 2π
the measure of any angle is 2π - α
∴ All the angles are reflex
∴ The value of cos(2π - α) only is positive ⇒ cos(2π - α) = cosα
* Now lets solve the equation
∵ 4 sin²Ф - 3 = 0 ⇒ the domain is 0 ≤ Ф ≤ 2π
- Add 3 for both sides
∴ 4 sin²Ф = 3 ⇒ divide the both sides by 4
∴ sin²Ф = 3/4 ⇒ take square root for both sides
∴ √(sin²Ф) = √(3/4)
∴ sinФ = √3/2 OR sinФ = -√3/2
- When the value of sinФ is positive
∴ The angle Ф is on the first or second quadrant
- When the value of sinФ is negative
∴ The angle Ф is on the third or fourth quadrant
- We have four values of Ф because 0 ≤ Ф ≤ 2π
- Lets find the measure of the acute angle α
∵ sinα = √3/2
∴ α = sin^-1(√3/2) = π/3
- If Ф is on the first quadrant
∴ Ф = α = π/3
- If Ф is on the second quadrant
∴ Ф = π - α = π - π/3 = 2π/3
- If Ф is on the third quadrant
∴ Ф = π + α = π + π/3 = 4π/3
- If Ф is on the fourth quadrant
∴ Ф = 2π - α = 2π - π/3 = 5π/3
* The solutions of the equations are π/3 , 2π/3 , 4π/3 , 5π/3
Related Questions
3x+4y= -23. x=3y+1. X___. Y___
Answers
X=-5
Y=-2
Explanation:
Picture below, help fast please!
Answers
Answer:
[tex]x=21,y=25[/tex]
Step-by-step explanation:
The given equation is:
[tex]\frac{(5-3i)(x+iy)}{(4-5i)}=(2+i)^2-(3-4i)^2[/tex]
Apply difference of two squares on the RHS.
[tex]\frac{(5-3i)(x+iy)}{(4-5i)}=[(2+i)+(3-4i)][(2+i)-(3-4i)[/tex]
Simplify the RHS.
[tex]\frac{(5-3i)(x+iy)}{(4-5i)}=(5-3i)(5i-1)[/tex]
Expand the RHS
[tex]\frac{(5-3i)(x+iy)}{(4-5i)}=(10+28i)[/tex]
Cross multiply to get:
[tex](5-3i)(x+iy)=(10+28i)(4-5i)[/tex]
Expand both sides
[tex](5x+3y)+(5y-3x)i=180+62i[/tex]
Comparing the complex parts, we obtain:
[tex]5y-3x=62...(1)[/tex]
Comparing the real number parts we get;
[tex]5x+3y=180...(2)[/tex]
Solving equations (1) and (2) simultaneously; we get:
[tex]x=21,y=25[/tex]
What is the value of the expression....
Answers
The right answer is Nine.
Answer:
The answer is 9.
Step-by-step explanation:
If you substitute a and b with the numbers given, the equation you'll have to solve is: 2(5)+2-3.
2(5)=10 and 2-3=-1
Once you subtract 10-1, the answer would be 9.
How do you use the digits in a hundredths decimal to write a percent?
Answers
Explanation:
"Percent" literally means "per hundred" or "divided by 100". The percent symbol (%) is a shorthand way to write /100 ("divided by 100," or "hundredths"). So, hundredths and percent are essentially the same thing.
Given a "hundredths decimal", move the decimal point 2 places to the right and add a % symbol. (Moving the decimal point multiplies the number by 100; adding the % symbol divides it by 100, so the end result is the same value written in a different form.)
Example:
19% = 19/100 = 0.19 . . . . (nineteen percent = nineteen hundredths)
and in the other direction, ...
0.53 = 53/100 = 53% . . . . (fifty-three hundredths = fifty-three percent)
Answer:
"Percent" literally means "per hundred" or "divided by 100". The percent symbol (%) is a shorthand way to write /100 ("divided by 100," or "hundredths"). So, hundredths and percent are essentially the same thing. Given a "hundredths decimal", move the decimal point 2 places to the right and add a % symbol.
20 Points PLEASE Hep .Factorize this
h(t) = -16x^+72x
( negative 16 squared plus 72x )
Answers
Answer:
-8x(2x - 9)
Step-by-step explanation:
-16x² + 72x
GCF = 8x
8x(16x² / 8x, -7x/8x)
-8x(2x - 9)
hope this helps!!
The answer would be -8x(2x-9)
Expand (x+3)^3 and simplify how to do this
Answers
Answer:
x^3 +9x^2 +27x +27
Step-by-step explanation:
The expansion of a power of a binomial looks like ...
(a +b)^n = nC0·a^n·b^0 + nC1·a^(n-1)·b^1 + nC2·a^(n-2)·b^2 + ... + nC(n-1)·a^1·b^(n-1) + nCn·a^0·b^n
Of course, nCk = n!/(k!·(n-k)!) and a^0 = b^0 = 1. The list of coefficients nCk corresponds to a row of Pascal's triangle (see attached).
For n=3, this is ...
(a +b)^3 = a^3 +3a^2b +3ab^2 +b^3
You have a=x and b=3, so the expansion is ...
(x +3)^3 = x^3 +3·x^2·3 +3·x·3^2 +3^3
= x^3 +9x^2 +27x +27
Please help and find what the value of x is
Answers
Answer:
x=30
Step-by-step explanation:
53+97+x=180
150+x=180
x=30
The sum of all the angles of a triangle is 180 degrees.
Add all the angles together and set it equal to 180, then solve for x
53 + 97 + x = 180
(150-150) + x = 180 -150
x = 30
Hope this helped!
HELP ME PLZZ This is a shape whose base is a circle and whose sides taper up to a point.
Answers
the shape of the above image is conical
The shape is a cone.
A vehicle factory manufactures cars. The unit cost c (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function c(x)=1.1x^2-660x+107,357. How many cars must be made to minimize the unit cost?
Do not round your answer.
Answers
Answer:
300
Step-by-step explanation:
The vertex of quadratic ax^2 +bx+c is on the line x=-b/(2a). This unit cost function defines a parabola opening upward, so its vertex is its minimum. The location of the vertex is ...
x = -(-660)/(2·1.1) = 660/2.2 = 300
300 cars must be made to minimize the unit cost.
_____
Note:
The unit cost at that production level will be $8357.
The dot plot shows the number of attempts each basketball player took to make a three-point shot.
Select from the drop-down menus to correctly complete the statement.
The distribution of data is (approximately normal-skewed left-skewed right) , with a mode of (#) , and a range of (#) .
Answers
Answer:
The distribution of data is (approximately normal-skewed left-skewed right) , with a mode of (7 ) , and a range of (8 )
Step-by-step explanation:
The data distribution is a normal skewed right with a range of (8) and a mode of (7).
What is the mode?Mode is the most frequently used number.
From the dot plot, it is observed that on the data 7th player took 6 attempts. Which is the greatest. The mode of the data distribution is 7.
The range of the data is the difference between the maximum and the minimum value.
Range = 9-1
Range=8
From the dot plot, it is observed that the maximum value is toward the right. So that it is right-skewed.
Hence, the data distribution is a normal skewed right) with a range of (8) and a mode of (7).
To learn more about the mode refer to:
https://brainly.com/question/17727138
#SPJ2
Do you know what this means? And how do I solve it?
Answers
a and b are matrices
Given: m∠EYL=72°
Find: mEHL , mLVE
Answers
Answer:
Part 1) The measure of arc EHL is [tex]108\°[/tex]
Part 2) The measure of angle LVE is [tex]54\°[/tex]
Step-by-step explanation:
step 1
Let
x-----> the measure of arc EHL
y----> the measure of arc EVL
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
so
[tex]m<EYL=\frac{1}{2}(y-x)[/tex]
we have
[tex]m<EYL=72\°[/tex]
substitute
[tex]72\°=\frac{1}{2}(y-x)[/tex]
[tex]144\°=(y-x)[/tex]
[tex]y=144\°+x[/tex] ------> equation A
Remember that
[tex]x+y=360\°[/tex] -----> equation B ( complete circle)
substitute equation A in equation B and solve for x
[tex]x+(144\°+x)=360\°[/tex]
[tex]2x=360\°-144\°[/tex]
[tex]x=216\°/2=108\°[/tex]
Find the value of y
[tex]y=144\°+x[/tex]
[tex]y=144\°+108\°=252\°[/tex]
therefore
The measure of arc EHL is [tex]108\°[/tex]
The measure of arc EVL is [tex]252\°[/tex]
step 2
Find the measure of angle LVE
we know that
The inscribed angle measures half that of the arc comprising
Let
x-----> the measure of arc EHL
[tex]m<LVE=\frac{1}{2}(x)[/tex]
we have
[tex]x=108\°[/tex]
substitute
[tex]m<LVE=\frac{1}{2}(108\°)=54\°[/tex]
A store sells shirts to the public at one pricing scale and wholesale at another pricing scale.
Answers
Answer:
Option B is correct.
Step-by-step explanation:
The slope for public sales:
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\[/tex]
here x₁ = 2 , x₂= 5 , y₁=24, y₂= 60
[tex]m= \frac{60-24}{5-2}\\ m= \frac{36}{3}\\ m=12[/tex]
The slope for Wholesale sales:
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \\[/tex]
here x₁ = 18 , x₂= 35 , y₁=162, y₂= 315
[tex]m= \frac{315-162}{35-18}\\ m= \frac{153}{17}\\ m=9[/tex]
Now, comparing slopes of wholesales sale and Public sales
9:12
0r
3:4
3:4 can be written as 3/4.
So, Option B The slope of wholesale table is 3/4 times of the slope of the Public table is correct.
Answer:
b
Step-by-step explanation:
took quiz on edge
A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree. Note that the two triangles are proportional to one another.
Answers
Answer:
30 ft
Step-by-step explanation:
Let the height of the tree be x ft. There are two right triangles:
1. Tree and its shadow are two legs of the first triangle;
2. Man and his shadow are two legs of the second triangle.
A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. This means these two triangle are similar. Similar triangles have proportional sides' lengths. Hence,
[tex]\dfrac{\text{tree}}{\text{tree shadow}}=\dfrac{\text{man}}{\text{man's shadow}}\\ \\\dfrac{x}{24}=\dfrac{5}{4}\\ \\4\cdot x=5\cdot 24\\ \\x=\dfrac{5\cdot 24}{4}=5\cdot 6=30\ ft[/tex]
Answer:
30 feet
Step-by-step explanation:
We are given that a tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet.
We are to find the height of the tree.
Using their proportions to compare the height of each object to the length of the shadow.
[tex]\frac{h}{24} =\frac{5}{4}[/tex]
[tex]h=\frac{5\times24}{4}[/tex]
[tex]h=30[/tex]
Therefore, the height of the tree is proportion comparing the height of each object to the length of the shadow 30 feet.
Please help me last question
Answers
Answer:
The letters in the word glacier can be arranged in 5040 different ways
Step-by-step explanation:
As there are 7 letters in the word glacier, that means that the number of ways would be 7!
This can also be written as
[tex]7*6*5*4*3*2*1=5040[/tex]
The letters in the word glacier can be arranged in 5040 different ways.
What is permutation?When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.
A permutation of a set exists, loosely articulating, an arrangement of its members into a sequence or linear order, or if the set exists already contained, a rearrangement of its elements.
Given,
As there are 7 letters in the word glacier, that means that the number of ways would be 7!
This can also be written as
7*6*5*4*3*2*1 = 5040
To know more about permutation refer to :
https://brainly.com/question/1216161
#SPJ2
What’s the value of y
Answers
Answer:
y = 60°
Step-by-step explanation:
The measure of angle y is half the measure of the subtended arc, so is ...
y = 120°/2 = 60°
You need 20 liters of 20% acid solution. You have jugs of 10% solution and 25% solution. How many liters of each should you combine to get the needed solution?
Answers
Answer:
6.(6) and 13.(3) liters.
Step-by-step explanation (this way is not the shortest one):
1. the basic rule is: the mas/volume of pure substance after and before combination is the same.
2. There is 4 liters of pure substance in 20*0.2 acid solution (20*0.2=4);
3. if 'x' is the volume of pure substance in 10%-solution; and if 'y' is the volume of pure substance in 20%-solution, then their sum of volumes is 4. It means, x+y=4 - this is the 1-st equation for system.
4. the volume of 10%-solution is x/0.1=10x; the volume of 20%-solution is y/0.25=4y; their sum is 20 litres. It means, 10x+4y=20 - this is the 2-d equation of the system.
5. to calculate the volumes of the pure substance:
[tex]\left \{ {{x+y=4} \atop {10x+4y=20}} \right. \ =>\ \left \{ {{x=\frac{2}{3} } \atop {y=\frac{10}{3} }} \right.[/tex]
6. to calculate the volume of 10%-solution: 2/3 *10=20/3≈6.(6) litres;
to calculate the volume of 25%-solution: 10/3 *4=40/3≈13.(3) litres.
Solve the equation for the interval
Answers
Answer:
x=0,3π/2,π
Step-by-step explanation:
Given
sin^2 x+sinx=0
sin x is a common factor
so,
sinx (sinx+1)=0
We can put both factors one by one equal to zero
sinx=0
x= sin^(-1)0
sinx is zero at 0 and π
x=0,π
sinx+1=0
sinx= -1
x= sin^(-1)(-1)
sin is -1 for 3π/2
So,
x=3π/2
So,
x=0,3π/2,π
12. What is the diameter of a circle when the circumference is 75.4 inches?
A. 12.0 inches
B. 24.0 inches
C. 27.3 inches
D. 37.7 inches
Show Your Work
Answers
Answer:
b
Step-by-step explanation:
24*pi=75.4
circumference is found when diameter is multiplied by pi
The diameter is 12 inches.
Option A is the correct answer.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
The area of a circle is πr².
The diameter of the circle is 2r.
The equation of a circle is also written as,
(x - h)² + (y - k)² = r²
Where r is the radius and (h, k) is the center of the circle.
We have,
Circumference of the circle = 75.4 in
This means,
2πr = 75.4
r = 75.4/(2 x 3.14)
r = 75.4 / 6.28
r = 12 in
Diameter of the circle.
= 2r
= 2 x 12
= 24 in
Thus,
The diameter is 12 inches.
Learn more about circle here:
https://brainly.com/question/11833983
#SPJ6
The difference between twice an angle's measure and it's supplement is 27. find the measure of the angle
Answers
x and y are supplementary angles
x - y = 27
x + y = 180
--------------------- We add the equations:
2x / = 207
2x = 207
x = 207/2
x = 103.5° = 103° : 30 miny = 180° - 103.5° = 76.5° = 76° : 30minFinal answer:
To find the angle measure, set up the equation 2x - (180 - x) = 27, simplify to 3x = 207, and solve to find that x = 69 degrees.
Explanation:
The question asks to find the measure of an angle where the difference between twice the angle's measure and its supplement is 27. To solve this, let's designate the measure of the angle as x. Since the angle's supplement will be 180° - x, we can set up the equation 2x - (180° - x) = 27. Simplifying this equation, we get 2x - 180° + x = 27, which simplifies further to 3x = 207°. Dividing both sides of the equation by 3, we find that x = 69°. Therefore, the measure of the angle is 69 degrees.
Garry is studying a square pyramid and wants to draw a net of the figure to help determine its surface area. Which net represents a square pyramid?please hurry than you
Answers
The net represents a square pyramid is a net with a square base and 4 triangular sides.
What is a square pyramid?A square pyramid is a pyramid with a square base in geometry. A right square pyramid is one with the tip perpendicular to the square's centre.
There will be five surfaces in the pyramid the base is square and the remaining four will be triangular.
Hence net represents a square pyramid is a net with a square base and 4 triangular sides.
To know more about the Square pyramid follow
https://brainly.com/question/3688277
#SPJ2
Someone explain to me how to do this
Answers
Answer:
14.9 cm
Step-by-step explanation:
The side of interest is opposite an angle that is not marked. You find the value of that angle by making use of the fact that the sum of angles of a triangle is 180°.
C = 180° -150° -12° = 18°
Now, fill in the available information in the given formula for the Law of Sines and solve for c:
sin(B)/b = sin(C)/c
sin(12°)/(10 cm) = sin(18°)/c
Cross multiply:
c·sin(12°) = (10 cm)·sin(18°)
Divide by the coefficient of c:
c = (10 cm)·sin(18°)/sin(12°) ≈ 14.9 cm
If $75 is invested at an interest rate of 8% per year and is compounded monthly, how much money is in the account in 15 years?
Answers
Answer:
$248.03
Step-by-step explanation:
The formula you use for this is as follows:
[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]
where A(t) is the amount after the compounding is done, P is the initial amount invested, r is the interest rate in decimal form, n is the number of times the compounding is done per year, and t is the time in years. Using that information and filling in our equation gives us this:
[tex]A(t)=75(1+\frac{.08}{12})^{(12)(15)}[/tex]
which simplifies down to
[tex]A(t)=75(1+.0066667)^{180}[/tex]
which simplifies further to
[tex]A(t)=75(3.307118585)[/tex]
which multiplies to $248.0338938. Round to the nearest cent to get your answer.
The amount of money is $248.02.
Principal amount = P=75
Interest rate = r = 8% = 0.08
Number of years = t = 15
Number of times compounded in a year = n = 12
A = Amount after t years.
After 15 years there will be:
[tex]A=P\left(1+\frac{r}{n}\right)^{nt}\\ A=75\left(1+\frac{0.08}{12}\right)^{\left(12\cdot15\right)}\\ A=248.019110806\\ A \approx 248.02[/tex]
Learn more: https://brainly.com/question/10241002
Elanor paints this figure on her wall. Find the area of the figure.
Answers
Answer: Your answer would be 59.5
if line m bisects ab at point p, and if ap= 1/2y and PB = y - 2, then find ab
Answers
Answer:
AB = 4
Step-by-step explanation:
Since point P bisects AB, we have ...
AP = PB
y/2 = y - 2
0 = y/2 - 2 . . . . subtract y/2
0 = y - 4 . . . . . . multiply by 2
4 = y . . . . . . . . . add 4
Now, we can find AB:
AB = 2(AP) = 2(1/2y) = y
AB = 4
How many hours will it take to complete a 76km bike ride if you go bike ride if you go 14km per hour the whole time?
Answers
To find the number of hours, divide the total distance by the speed.
Hours = 76 km / 14 km per hour
Hours = 4.529
Round the answer as needed.
Angles of elevation and depression-SOMEONE HELP ME
Answers
If the angle of depression is 28° the complementary angle in the triangle is 62°. With this you can use soh-cah-toa to find the x value.
cos62 = 350/x; multiply both sides by x
cos62 x = 350; divide both sides by cos62
x = 350 / cos62
x = 745.519
x = 746 ft
Hope this helps you!
Find the measure of AED
Answers
Answer:
D) 155°
Step-by-step explanation:
The marked vertical angles are equal in measure, so ...
5x = 3x+10
2x = 10
x = 5
5x = 25 . . . . measure of angle AEB
Angle AED is the supplement of angle AEB, so is ...
180° -25° = 155°
Which equation has a solution of all real numbers
Answers
Answer:
There is few equation that has a solution of all real numbers like this picture
,
Jay on started off his penny collection with 1 penny. He then adds 5 pennies to his collection each day. How could you change the above scenario to make it a geometric series rather than an arithmetic series?
Answers
Answer:
By doubling each day
Step-by-step explanation:
Jay is increasing daily a fixed amount of pennies to his collection. That's an arithmetic series, because to obtain the next term you have to do an addition.
To get a geometric series or progression you have to find the next term through multiplication.
So, if he wants to convert his series into a geometric series, he'd have to double his contribution to his collection each day (as an example).