Find all solutions to the equation
in the interval [0, 21). Enter the
solutions in increasing order.
sin 2x = 2 sin x
x = [?],[1]
TT
Remember: sin 20 = 2 sin 0 cos 0
Answers
Answer:
[tex]x=0, \\x=\pi[/tex]
Step-by-step explanation:
Recall the trigonometric identity [tex]\sin 2x=2\sin x\cos x[/tex].
Therefore, given [tex]\sin 2x=2\sin x[/tex], rewrite the left side of the equation:
[tex]2\sin x\cos x=2\sin x[/tex]
Subtract [tex]\sin x[/tex] from both sides:
[tex]2\sin x\cos x-2\sin x=0[/tex]
Factor out [tex]2\sin x[/tex] from both terms on the left:
[tex]2\sin x(\cos x-1)=0[/tex]
We now have two cases:
[tex]\begin{cases}2\sin x=0, x=k\pi\text{ for }k\in \mathbb{Z}\\\cos x-1=0,x=k2\pi\text{ for }k\in \mathbb{Z}\end{cases}[/tex]
Since the problem stipulates that [tex]x[/tex] is in the interval [tex][0, 2\pi)[/tex], we have:
[tex]\text{For }x\in [0, 2\pi):\\\sin x=0\rightarrow \boxed{x=0, x=\pi}\\\cos x-1=0\rightarrow \boxed{x=0}[/tex]
Recall that square brackets mean inclusive and parentheses mean exclusive. Therefore, [tex]2\pi \notin [0, 2\pi)[/tex].
Related Questions
According to a survey of 1000 families of any town in 2010 A.D.,794 families have radio and 187 families have television.lf 63 families do not have any one of them,then how many families will have both radio and television?Find it.
Answers
Answer:
Number of families will have both radio and television = 44
Step-by-step explanation:
Given:
Number of family have radio = 794
Number of family have TV = 187
Number of family haven't both = 63
Find:
Number of families will have both radio and television
Computation:
Number of families will have Tv or radio = 1,000 - 63
Number of families will have Tv or radio = 937
Number of family have one of them = 794 + 187
Number of family have one of them = 981
Number of families will have both radio and television = 981 - 937
Number of families will have both radio and television = 44
does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
Answers
Step-by-step explanation:
The solution and answer are well written in the Pic above.
Given equation of the Circle is ,
[tex]\sf\implies x^2 + y^2 = 25 [/tex]
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]
Here we can see that the distance of point from centre is less than the radius.
Hence the point lies within the circle .
Write the following phrase as an expression c less than 27
A C +27
B C -27
C c/27
D 27 - C
Answers
Answer:
(D) 27 - C
Step-by-step explanation:
The "less than" means we are subtracting C from 27, so 27 - C.
Hope it helps (●'◡'●)
Which expression has a value of 15 when n = 7?
1: 43 minus 5 n
2: 3 n minus 5
3: 6 n minus 28
4: 19 minus StartFraction 28 Over n EndFraction
Answers
Answer:
[tex]19-\frac{28}{n}[/tex] is the expression with the value of 15 when n = 7
Step-by-step explanation:
To find the expression whose value is 15, substitute the value of n = 7 in each given expression.
Expression 1:
[tex]43-5n[/tex]
Substitute the value of n & simplify,
[tex]43-5(7)[/tex]
[tex]43-35=8[/tex]
Since the value of the expression is 8 which is not equal 15.
Hence expression [tex]43-5n[/tex] does not have value of 15 when n = 7.
Expression 2:
[tex]3n-5[/tex]
Substituting the value of n & simplify,
[tex]3(7)-5[/tex]
[tex]21-5=16[/tex]
Since the value of the expression is 16 which is not equal 15.
Hence expression [tex]3n-5[/tex] does not have value of 15 when n = 7.
Expression 3:
[tex]6n-28[/tex]
Substituting the value of n & simplify,
[tex]6(7)-28[/tex]
[tex]42-28=14[/tex]
Since the value of the expression is 14 which is not equal 15.
Hence expression [tex]6n-28[/tex] does not have value of 15 when n = 7.
Expression 4:
[tex]19-\frac{28}{n}[/tex]
Substituting the value of n & simplify,
[tex]19-\frac{28}{7}[/tex]
[tex]19-4=15[/tex]
Since the value of the expression is 15 which is equal 15.
Hence expression [tex]19-\frac{28}{n}[/tex] has the value of 15 when n = 7.
simplify (-81)÷9 pls ans
Answers
Answer:
[tex] \frac{ - 81}{9} [/tex]
[tex] - 9[/tex]
true or false? A circle could be circumscribed about the quadrilateral below.
Answers
Answer: the answer is true
Answer:
false
Step-by-step explanation:
here the opposite angle of quadrilateral aren't supplematary the circle have no chance to be circumscribed
is (-3,-5) a solution of the graphed inequality
Choose 1 answer:
Yes
No
Answers
Answer:
No
General Formulas and Concepts:
Algebra I
Reading a coordinate planeCoordinates (x, y)Solving inequalitiesStep-by-step explanation:
When we plot (-3, -5) on the coordinate plane, we can see that it is not in the shaded region.
∴ (-3, -5) is not a solution.
F(x)=sqrt x -4.find the inverse of f(x) and it’s domain
Answers
Answer:
B
Step-by-step explanation:
[tex]y = \sqrt{x } - 4 \\ \sqrt{x} = y + 4 \\ x = (y + 4) {}^{2} \\ [/tex]
Domain of inverse = Range of f = x>-4
Hence B
The correct option is B which is f⁻¹(x) = ( x + 4 )² and x ≥ -4.
What is an inverse function?The inverse function of a function f in mathematics is a function that reverses the operation of f. If and only if f is bijective, the inverse of f is true.
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
The given function is f(x) = √x - 4. The inverse function will be calculated as:-
y = √x - 4
√x = y + 4
Squaring on both sides.
x = ( y + 4 )²
Replace x with y.
y = ( x + 4 )²
The range of the function is x ≥ -4.
Therefore, the correct option is B which is f⁻¹(x) = ( x + 4 )² and x ≥ -4.
To know more about an inverse function follow
https://brainly.com/question/3831584
#SPJ5
which point is a solution to y>2x-1?
Answers
Answer:
B) (0,2)
Step-by-step explanation:
We substitute the values of x and y into this inequality:
2 ≥ 2(0)-1
2 ≥ 0-1
2 ≥ -1
This is true, so this is the correct point
hope this helps have a good day
Answer:
there it is
Step-by-step explanation:
Translate this sentence into an equation. 144 is the product of Diego's age and 9.
Answers
Step-by-step explanation:
Represent Diego's age by d. Then 9d=144.
f(x)=2x+3/4x+5 find f(-9)
pls solve it
Answers
Answer:
15/31
Step-by-step explanation:
substitute -9 were there's x in the function
f(-9)=2(-9)+3/4(-9)+5
=-18+3/-36+5
=-15/-31
the negatives cancel giving you
15/31
Which expressions are in simplest form? Check all that apply.
Answers
Because you can simplify the rest the answers
PLEASE HELP I'LL MARK BRANLIEST!
Activity Gina is playing dominoes with her family. She and her brother, Greg, are playing as a team (team A) against their parents (team B). The table shows how many points the two teams have scored in each round. Gina is keeping track of the scores and wants to know which measures of center and spread best represent each team’s data.
Team A: 15 20 15 5 10 15 10 15 5 20
Team B: 20 15 25 30 20 25 0 15 25 30
Part B What is the mean score for team A? Show your calculation.
Answers
Answer:
Mean of team A is 13
Step-by-step explanation:
I hope it helps:)
What is the explicit formula for this sequence?
7, 2, -3, -8...
Answers
Answer:
The explicit formula of that sequence is T - 5
Step-by-step explanation:
Let T represent each term in the sequence. So now try replacing T with each term in the sequence. Like this ;
7 - 5 = 2
2 - 5 = -3
-3 - 5 = -8
hope this helps
Find the slope of the line that passes through (1, 2) and (8, 8).
Answers
Answer:
slope = [tex]\frac{6}{7}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (8, 8)
m = [tex]\frac{8-2}{8-1}[/tex] = [tex]\frac{6}{7}[/tex]
The measure of two supplementary angles are (6x+28)° and (7x+87)°. Find the value of x.
Answers
Answer:
[tex]x = - 59[/tex]
Step-by-step explanation:
[tex](6x + 28) = (7x + 87)[/tex]
[tex]6x + 28 = 7x + 87[/tex]
[tex]6x - 7x = 87 - 28[/tex]
[tex]1x = - 59[/tex]
[tex]x = \frac{ - 59}{1} [/tex][tex]x = - 59[/tex]
Hope it is helpful....Two exponential functions are shown in the table.
х
f(x)=2*
g(x)=
1
2
2
4
1
4
Which conclusion about f(x) and g(x) can be drawn from
the table?
O The functions f(x) and g(x) are reflections over the x-
axis.
O The functions f(x) and g(x) are reflections over the y-
axis.
O The function f(x) is a decreasing function, and g(x) is
an increasing function.
O The function f(x) has a greater initial value than g(x).
1
2
OT
1
2
1
2
1
1
2
1
4
-2.
4
Answers
The true statement about the exponential functions is (b) the functions f(x) and g(x) are reflections over the y-axis.
The functions are given as:
[tex]f(x) = 2^x[/tex]
[tex]g(x) = (\frac 12)^x[/tex]
Reflect function over the y-axis.
The rule of this transformation is:
[tex](x,y)\to (-x,y)[/tex]
So, we have:
[tex]f(x) = 2^x[/tex]
[tex]f'(x) = 2^{-x}[/tex]
Apply power rule of indices
[tex]f'(x) = (\frac{1}{2})^x[/tex]
By comparison:
[tex]g(x) = f'(x) = (\frac{1}{2})^x[/tex]
Hence, the functions f(x) and g(x) are reflections over the y-axis.
Read more about function transformation at:
https://brainly.com/question/1548871
In ΔCDE, the measure of ∠E=90°, ED = 28, CE = 45, and DC = 53. What ratio represents the tangent of ∠C?
Answers
Explanation:
Angle E is 90 degrees. The segment DC = 53 is opposite this angle. Note how "DC" does not contain the letter "E". Furthermore, note how this is the largest side. So it's the hypotenuse.
The side ED = 28 is the opposite side of reference angle C, because "C" is nowhere to be found in the sequence "ED".
The side CE = 45 is the adjacent side because "E" is found in "CE".
The tangent ratio is...
tan(angle) = opposite/adjacent
tan(C) = ED/CE
tan(C) = 28/45
the maximum mark of 30 student is 100. if its range is 75, find the minimum mark and coefficient of range.
Answers
Answer:
3000 ................,...
Help me please ASAP thank you
Answers
Answer:
The first one: 3x+4=-2x-1
Step-by-step explanation:
3(-1)+4=1
-2(-1)-1=1
Pipe A can fill 3 tanks in 8 minutes. Pipe B can fill 5 tanks in 10 minutes. How long will it take for them to fill a single tank if they work together?
Answers
Answer:
8/7 min = [tex]1 \frac{1}{7} minutes[/tex]
Step-by-step explanation:
A rate 2 2/3 = 8/3 min per tank
B rate 2 min per tank
thus:
A rate = 3/8 tank per min
B rate = 1/2 tank per min
A+ B = 3/8 + 4/8 = 7/8 tank per min
7/8 x = 1
x = 8/7 min
5 times the complement of an angle is 15 more than two times the supplement of the angle. Find the angle,
the complement, and the supplement.
Answers
Answer:
The angle measures 25°; the complement measures 65°; the supplement measures 155°.
Step-by-step explanation:
The sum of the measures of two complementary angles is 90.
If the angles measure x and y, then x + y = 90.
Given angle x, then y = 90 - x.
The sum of the measures of two supplementary angles is 180.
If the angles measure x and y, then x + y = 180.
Given angle x, then y = 180 - x.
Let the angle be x.
Its complement is 90 - x.
Its supplement is 180 - x.
5(90 - x) = 2(180 - x) + 15
450 - 5x = 360 - 2x + 15
-3x = -75
Angle: x = 25
Complement: 90 - x = 90 - 25 = 65
Supplement: 180 - x = 180 - 25 = 155
Answer: The angle measures 25°.;, the complement measures 65°; the supplement measures 155°.
Find the area of this parallelogram.
13 cm
15cm
h
20cm
Answers
Answer:
260 square centimeters
Step-by-step explanation:
The formula for the area of a parallelogram is:
b x h
Where the base (b) is multiplied by the height (h) perpendicular to it.
The base here is 20 cm
The height perpendicular to the base is 13 cm
20 x 13 = 260
Or you can decompose and rearrange it into a rectangle. You will get 20 cm as the length and 13 cm as the width. The answer will be just the same!
Hope this helps!
Answer: 260 cm²
Step-by-step explanation: A parallelogram is a
quadrilateral with two pairs of parallel sides.
The formula for the area of a parallelogram is A = bh.
Since the base of the parallelogram is 20 cm and the height
of the parallelogram is 13 cm, we can plug this information into the formula
to get (20 cm)(13 cm) which gives us 260 cm².
So the area of the parallelogram shown is 260 cm².
Evaluate the expression. 37
Answers
Answer:
[tex]2187[/tex]
Step-by-step explanation:
[tex] {3}^{7} \\ = (3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3) \\ = 2187[/tex]
Hope it is helpful....Answer:
2187
Step-by-step explanation:
3*3=9
9*3=27
27*3=81
81*3=243
243*3=729
729*3=2189
Find the measure of the indicated angle
Answers
Answer:
73 degrees
Step-by-step explanation:
The line on the two sides of the triangle indicates that the triangles is isosceles. This means that the base angles are congruent.
Someone please help me
Answers
[tex]( {9x}^{2} - 4)( {9x}^{2} + 4) \\ (3x - 2)(3x + 2)( {9x}^{2} + 4)[/tex]
Hi i need help please
Find the volume of this sphere.
Use 3 for TT.
V
11 in
V ~ [?]in3
V= inr3
Answers
Answer:
So the volume of a sphere is calculated using the formula: [tex]\frac{4}{3} \pi r^{3}[/tex]
r = the radius = 11 inchesπ = 3.14Substitute in the value of r and solve:
[tex]\frac{4}{3} \pi 11^{3}\\\\=\frac{4}{3} \pi *1331\\\\=\frac{4*3.14*1331}{3}\\\\=5,575.28[/tex]
After the increase the price of a rail season ticket from brighton to london was 2828.80 work out the price before this increase
Answers
Answer:
2720
Step-by-step explanation:
Given that,
Price of the ticket = 2828.80
To find,
The price before the increase = ?
Procedure:
Let the price before the increase be x
so,
x(100% + 4%) = 2828.80
⇒ 1.04x = 2828.80
⇒ x = 2828.80 ÷ 1.04
∵ x = 2720
Thus, the price before the increase was 2720.
In the diagram, what is AC?
Answers
find the DB =[tex]\displaystyle\bf \sqrt{17^2-8^2} =15[/tex] ; now find AD=AB-DB=21-15=6 .Then AC=[tex]\displaystyle\bf \sqrt{AD^2+CD^2} =\sqrt{6^2+8^2} =10[/tex]
Answer:
C
Step-by-step explanation:
Using Pythagoras' identity in both right triangles
To find BD
BD² + CD² = BC²
BD² + 8² = 17²
BD² + 64 = 289 ( subtract 64 from both sides )
BD² = 225 ( take the square root of both sides )
BD = [tex]\sqrt{225}[/tex] = 15
Then
AD = AB - BD = 21 - 15 = 6
To find AC
AC² = AD² + CD²
AC² = 6² + 8² = 36 + 64 = 100 ( take the square root of both sides )
AC = [tex]\sqrt{100}[/tex] = 10 → C
After substituting, what is the first step when evaluating vegy 4 2 when x 6?
O Multiply 3 by 5
O Add 5 and 3
Subtract 4.2 from 5
Add 3 and 4.2 hurry I'm being timedd!!!
Answers
Answer:
Multiply 3 by 5
Step-by-step explanation:
After substituting, what is the first step when evaluating x+3x-4.2 when x=5
Given:
x + 3x - 4.2
when x = 5
Substitute x = 5 into the expression
x + 3x - 4.2
= 5 + 3(5) - 4.2
= 5 + 15 - 4.2
= 20 - 4.2
= 16.8
x + 3x - 4.2, when x = 5 is 16.8
After substituting, the first step when evaluating x + 3x - 4.2 when x = 5 is Multiply 3 by 5