[tex] \frac{(1 - \cos(a))(1 + \cos(a)) }{(1 - \sin(a) )(1 + \sin(a)) } = \\ [/tex]
[tex] \frac{1 - {cos}^{2}(a) }{1 - {sin}^{2}(a) } = \\ [/tex]
[tex] \frac{ {sin}^{2}(a) }{ {cos}^{2}(a) } = \\ [/tex]
[tex] {tan}^{2} (a)[/tex]
Help Me on this!!
[tex] \: \: \: [/tex]
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Here's the solution~
Standard equation of a circle is represented as :
[tex]\qquad \sf \dashrightarrow \:(x - h) {}^{2} + (y - k) {}^{2} = r {}^{2} [/tex]
where,
h = x - coordinate of center k = y - coordinate of centerradius = diameter/2 = [tex]4\sqrt{3}[/tex]Now, let's plug in the values to find the required equation of circle ~
[tex]\qquad \sf \dashrightarrow \:(x - 8) {}^{2} + (y - ( - 10)) {}^{2} = (4\sqrt{3} ) {}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:(x - 8) {}^{2} + (y + 10) {}^{2} = 16 \times 3[/tex]
[tex]\qquad \sf \dashrightarrow \:(x - 8) {}^{2} + (y + 10) {}^{2} = 48[/tex]
The equation of given circle with centre C ( 8 , - 10 ) and diameter ( 8√3 ) is x² + y² - 16x + 20y + 116 = 0
[tex]\quad\rule{300pt}{1pt}\quad [/tex]
Solution:The standard equation of Circle is given by :
[tex] {\pmb{\sf {\longrightarrow r^2 = (x-h)^2 +( y-k)^2}} }[/tex]
This is the standard form of the equation. Thus if we know the coordinates of center of the circle and it's radius, we can easily find its equation
Here, in this question we are given that the centre C is ( 8 , -10 ) and diameter 8√3.
[tex] \longrightarrow[/tex]h = 8
[tex] \longrightarrow[/tex] k = - 10
[tex] \longrightarrow[/tex] r = [tex] \sf{\dfrac{diameter}{2}}[/tex]
[tex] \longrightarrow[/tex] r = [tex] \sf 4\sqrt{3}[/tex]
[tex] \qquad\qquad\rule{250pt}{1pt}\qquad[/tex]
On putting the values in the formula :
[tex] \sf{:\implies \qquad r^2 = (x-h)^2+ ( y-k)^2 }[/tex]
[tex] \sf{:\implies \qquad (4\sqrt{3})^2 = ( x-8)^2 +(y-(-10))^2 }[/tex]
[tex] \sf{:\implies \qquad (4)^2.(\sqrt{3})^2=(x-8)^2+(y+10)^2}[/tex]
[tex] \sf{:\implies \qquad 16\times 3 =( x^2 + 8^2 -2\times x \times 8 ) + ( y^2 + 10^2 + 2\times y \times 10 )}[/tex]
[tex] \sf{:\implies \qquad 48 = x^2 + y^2 - 16x + y^2 + 100 + 20y }[/tex]
[tex] \sf{:\implies \qquad 48 = x^2 + y^2 -16 x + 20y + 100 + 64 }[/tex]
[tex] \sf{:\implies \qquad 48 = x^2 +y^2 -16x +20y +164}[/tex]
[tex] \sf{:\implies \qquad x^2 + y^2 -16x +20y +164 - 48 = 0}[/tex]
[tex] \sf{:\implies \qquad{\boxed{ \sf x^2 + y^2 -16x + 20y +116 = 0 }}}[/tex]
ㅤㅤㅤㅤ~Hence, the required equation of Circle is x² + y² - 10x + 20y + 116 = 0
¿Qué significa un punto en el diagrama de líneas?
un punto en un gráfico de líneas es un valor específico que normalmente es un valor de entrada y salida (x)
The graph shows the distance (d) in miles that an animal runs at a constant speed in (t) minutes. Which equation represents this situation.
Can you do number 1 for me
Answer:
c. 3/5
Step-by-step explanation:
CAN SOMEONE PLSSSSS ANSWER BOTH OF THESE QUESTIONS
I WILL MARK BRAINLIEST
Answer: B and C
Step-by-step explanation:
404 + 50 + 50 = 504
you are buying 144 magazines total
504/144 = cost of one magazine
cost of one = 3.50
you are paying $60 a year for 12 years
60 x 12 = 720
720/144 = 5
5 - 3.50 = 1.50
2.
120x + 180x = 1080
300x = 1080
x = 1080/300
x = 3.6
3.6 x 60 = 216
HURRY PLS WILL MARK BRAINLIEST, Find an equation in slope intercept form of the line that has two slope and passes through points A [9, -2 ]
Answer:
D
Step-by-step explanation:
sub in the x value and if its equal to -2 its on that line
66 is 8-% of what number?
4
Simplify the expression.
Answer:
the answer is
[tex] \frac{12 {c}^{8} }{ {d}^{2} } [/tex]
Step-by-step explanation:
[tex] \frac{12}{ {c}^{ - 8} {d}^{2} } [/tex]
Evaluate [tex]\frac{1}{2^{-2}x^{-3}y^{5} }[/tex] for x=2 and y=-4.
A)-16
b)-4
c)[tex]-\frac{1}{32}[/tex]
d)16
Answer:
[tex]\bf C)\: -\cfrac{1}{32}[/tex]
Step-by-step explanation:
[tex]\tt \cfrac{1}{2^{-2}x^{-3}y^5}[/tex]
[tex]\tt x=2\\y=-4[/tex]
~
Substitute ''x'' with '2' & 'y' with "-4":-
[tex]\tt \cfrac{1}{2^{-2}\times \:2^{-3}\left(-4\right)^5}[/tex]
First let's solve [tex]\tt 2^{-2}\times \:\:2^{-3}\left(-4\right)^5[/tex]
[tex]\tt 2^{-2}\times \:2^{-3}=\boxed{\cfrac{1}{32} }[/tex]
[tex]\tt \cfrac{1}{32}\left(-4\right)^5[/tex]
Calculate exponents:- -4^5= -1024
[tex]\tt \cfrac{1}{32}\left(-1024\right)[/tex]
Remove parentheses, apply rule:- [tex]\tt a\left(-b\right)=-ab[/tex]
[tex]\tt-\frac{1}{32}\times \:1024[/tex]
[tex]\tt \cfrac{1}{32}\times \cfrac{1024}{1}[/tex]
Apply fraction rule:-
[tex]\tt -\cfrac{1\times \:1024}{32\times \:1}[/tex]
[tex]\tt \cfrac{1024}{32}[/tex]
Divide numbers:-
[tex]\tt -32[/tex]
Now that we're done factoring the denominator let's bring down the numerator which is ' 1 ':-
[tex]\tt -\cfrac{1}{32}\;\; \bf Answer[/tex]
☆-------☆-------☆-------☆
[tex]\dfrac 1{2^{-2}\cdot x^{-3}\cdot y^5}\\\\=\dfrac 1{2^{-2} \cdot2^{-3} \cdot (-4)^5}\\\\=-\dfrac 1{2^{-2} \cdot 2^{-3} \cdot (2^2)^5}\\\\=-\dfrac{1}{2^{-2} \cdot 2^{-3} \cdot 2^{10}}\\\\=-\dfrac{1}{2^{-2-3+10}}\\\\=-\dfrac 1{2^{5}}\\\\=-\dfrac 1{32}[/tex]
if i make 8.50 an hr and i work 30 hours a week 5 days a week how much would i make in a month?
help pplease i need help
Answer:
15/2 min/m
Step-by-step explanation:
Minuters per meter = min/m
4.5 min/(3/5) m
4.5 x 5/3 = 7.5
7.5 = 15/2
Hope this helps!
The average gas mileage (mpg) for vehicles produced by a particular automotive company is 26 mpg, with a standard deviation of 2 mpg. What percentage of the vehicles produced by the automotive company have a gas mileage greater than 24?
Note: Assume that a Normal model is appropriate for the distribution of the gas mileages for the vehicles.
Answer:
above 84°/. of the vehicles have a gas mileage greater then 24 mpg
[tex]\frac{-65}{100} - \frac{12}{7}[/tex]
Answer:
-331/140
Step-by-step explanation:
I’m so confused by this:( Could someone please explain how to do this thoroughly?
Answer:
A. Complementary and Adjacent
B. ∠KLM = 22° and ∠MLN = 68°
Step-by-step explanation:
Question A
As ∠KLN is a right angle, ∠KLN = 90°
⇒ ∠KLM + ∠MLN = 90°
When the sum of two angles is 90°, they are called complementary angles.
∠KLM and ∠MLN have a common side of ML and a common vertex (corner point) L.
When two angles have a common side and a common vertex but do not overlap in any way, the are called adjacent angles.
Question B
First find n:
∠KLM + ∠MLN = ∠KLN
⇒ 2n + (6n + 2) = 90
⇒ 2n + 6n + 2 = 90
Combine like terms:
⇒ 8n + 2 = 90
Subtract 2 from both sides:
⇒ 8n = 88
Divide both sides by 8:
⇒ n = 11
Now substitute the found value of n into the expressions for the two angles:
⇒ ∠KLM = 2(11) = 22°
⇒ ∠MLN = 6(11) + 2 = 68°
Order of Operations
40 + (1 + 2) - 2
3[16 - (2 + 5)]^2
100-50/100-3(2+3)^2
Answer:
41, 243, 2
Step-by-step explanation:
40 + (1 + 2) - 2
=41
3[16 - (2 + 5)]^2
=243
100-50/100-3(2+3)^2
=2
1 message What is the graph of the solution set of b - 4 ≥ -1?
Answer:
Hope the picture will help you!!
PLEASE HELP ILL GIVE FIVE STARS AND MARK BRAINLIEST
Ray is x years old. His brother Ron is y years older than Ray.
How old was Ray 3 years ago?
Ray is [tex]x[/tex] years old.
Ron is [tex]y[/tex] years old.
In 2 years, Ron will be two years older than now, so [tex]x+y+2[/tex] years old.
Find the value of x.
45°
96°
Answer:
39
Step-by-step explanation:
all angles of a triangle equal to 180, so you just have to subtract those two known angles from 180, and you will get the answer.
Find the value of angle x .
Given : -First angle = 45°Second angle = 96°Third angle = x°To Find : -We have to find the value of x .Concept : -The concept of this question belongs to angles of triangle . We know that the sum of all the three angles of triangle is 180°.
So let's get started : -As we know that all the angles of triangle is equal to 180° . So :
1st angle + 2nd Angle + 3rd Angle = 180°45° + 96° + x° = 180°141° + x° = 180°x° = 180° - 141°x° = 39°Therefore , angle x is of 39° .
Verifying : -45° + 96° + 39° = 180°141° + 39° = 180°180° = 180°L.H.S = R.H.SHence, Verified .Thus, our answer is valid .#[tex] \sf \bold{Keep \: Learning}[/tex]Since the sample size is always smaller than the size of the population, the sample mean a. must be larger than the population mean b. can be smaller, larger, or equal to the population mean c. must be equal to the population mean d. must always be smaller than the population mean
Using the mean concept, it is found that the correct option regarding the sample mean is given by:
b. can be smaller, larger, or equal to the population mean.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
No matter the population mean, the sample mean is calculated as stated above, having no restrictions about it's value, hence option b is correct.
More can be learned about the mean concept at https://brainly.com/question/24628525
#SPJ1
Solve the linear differential equation 2xy' + y = 2√x
Answer:
Step-by-step explanation:
General form of the linear differential equation can be written as:
[tex]\frac{dy}{dx}+P(x)y=Q(x)[/tex]
For this case, we can rewrite the equation as:
[tex]\frac{dy}{dx}+\frac{1}{2x}y=\frac{\sqrt{x}}{x}[/tex]
Here [tex]P(x) =\frac{1}{2x}; Q(x)=\frac{\sqrt{x}}{x}[/tex]
To find the solution (y(x)), we can use the integration factor method:
[tex]Fy(x)=\int Q(x)Fdx+C \rightarrow F=e^{\int P(x)dx[/tex]
Then [tex]F=e^{\int \frac{1}{2x}dx}=e^{\frac{1}{2}\ln|x|\right}=\sqrt{|x|}[/tex]
So, we can find:
[tex]y\sqrt{|x|}=\int \frac{\sqrt{x}\sqrt{|x|}}{x}dx+C[/tex]
Suppose that [tex]x\in \double R[/tex], then [tex]\sqrt{|x|}=\sqrt{x}[/tex] , and we find:
[tex]y\sqrt{x}=x+C \rightarrow y(x)=\sqrt{x}+\frac{C\sqrt{x}}{x}[/tex]
To check our solution is right or not, put your y(x) back to the ODE:
[tex]y' = \frac{1}{2\sqrt{x}}-\frac{C}{2\sqrt{x^{3}}}[/tex]
[tex]2xy'=\frac{x-C}{\sqrt{x}}[/tex]
[tex]2xy'+y=\frac{x-C}{\sqrt{x}}+\sqrt{x}+\frac{C\sqrt{x}}{x}=2\sqrt{x}[/tex]
(it means your solution is right)
Which statement is a TRUE statement about rectangles?
The sides in a rectangle are not parallel.
The angles in a rectangle are all different.
The opposite sides in a rectangle are equal.
All the sides in a rectangle are equal.
Answer:
The opposite sides in a rectangle are equal.
Step-by-step explanation:
If all sides were equal, you would have a square.
If the opposite sides were not parallel, you would not have 4 sides that meet at 90 degrees.
All angles in a rectangle are 90 degrees.
Answer:
The opposite sides in a rectangle are equal.
Step-by-step explanation:
hope this helps hope you get it correct
A local restaurant uses a computer to randomly select an appetizer and accompanying sauce. The table below shows all the
possible outcomes when ordering
What is the probability of receiving chicken or ribs and getting a red sauce?
Answer:
B 1/5
Step-by-step explanation:
there is 20 combinations
4 of the twenty are ribs or chicken with a red sauce
4/20 = 1/5
Four identical circles are lined up in a row with no
gaps between them such that the diameters for a
segment that is 68 centimeters long. What is the
combined area of all the circles to the nearest
hundredth? Use 3.14 for Pi
Answer: 907.46
Step-by-step explanation:
Tory is going to the fair with four of her friends. The entrance fee per person is $7.50. They plan to go together on all the rides. The cost of each ride is $3.00. Write an expression to represent the cost of the group to go to the fair for any number of rides.
Answer:
$37.5+$3r
Step-by-step explanation:
We can assume that the number of rides is r. Since each ride is $3.00, all rides are $3r ($3xr).
We also know that there are FIVE people going to the fair, with Tory being one and each of her friends. Since the entrance fee is 7.50, we can do 7.50x5 which is $37.5.
Then, you can add it which is $37.5+$3r
Which expression is not equivalent to 2\3 x 4?
Answer:
8/3
Step-by-step explanation:
convert radians to degrees
Answer:
135 degrees
Step-by-step explanation:
The image shows how i had my answer please
What is the equation
of the line that passes through the point (-2, -3) and has a
slope of -1?
Answer:
Step-by-step explanation:
Hello:
an equation for the line is : y =mx +b (m: is a slope )
given : m = -1
the equation is : y = -x+b
through the point (-2,-3) :-3 =-(-2)+b....... b=-5
the equation is : y = -x-5
Would appreciate some help
Answer:
e) 36x² - 32y³ = (4)(9x² - 8y³)
f) 45a⁴ - 54a³ = (9a³)(5a - 6)
Step-by-step explanation:
e) 36x² - 32y³ = (4)(9x² - 8y³) becuase 4*9 = 36 and 4*8 = 32
f) 45a⁴ - 54a³ = (9a³)(5a - 6) becuase 9*5 = 45 and 9*6 = 54 and when a is multiplied by a³ you get a⁴
(the exponent are added)
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
X²
cm
1
cm
3x
**2 cm
1. Write an expression that represents the perimeter of the figure and simplify.
3x2 +7X+7
A.
3x?
O
7x? +7x +7
B.
3x?
O
x2+2x +7
C.
x²
3x2 + 7x +21
D.
3x?
Answer:
The answer is D
Step-by-step explanation:
(7/x² × x²)+(1/3×x²)+(x+2/x × x²)
(7 + x/3 + x²+2x) times 3 to eliminate the 3 under x/3
so u will get 21+x+3x²+6x
Final answer = 3x²+7x+21
I dont know how to answer this
Answer:
sorry the image isnt clear
Answer:
Can you post it again but clearer