Answers
[tex]\dfrac{\sin \alpha}{\cos \alpha + \sin \alpha} - \dfrac{\cos \alpha}{\cos \alpha - \sin \alpha}\\\\\\=\dfrac{\sin \alpha(\cos \alpha - \sin \alpha) - \cos \alpha(\cos \alpha + \sin \alpha)}{(\cos \alpha + \sin \alpha)(\cos \alpha -\sin \alpha)}\\\\\\=\dfrac{\sin \alpha \cos \alpha - \sin^2 \alpha - \cos^2 \alpha - \cos \alpha \sin \alpha}{\cos^2 \alpha - \sin^2 \alpha}\\\\\\=\dfrac{-(\sin^2 \alpha + \cos^2 \alpha)}{\cos 2 \alpha}\\\\\\=-\dfrac{1}{\cos 2 \alpha}\\[/tex]
[tex]=-\left(\dfrac{1}{\tfrac{1- \tan^2 \alpha}{1 + \tan^2 \alpha}} \right)~~~~~~~~~~~~~~~~~~; \left[\cos 2\theta = \dfrac{1 - \tan^2 \theta}{1+ \tan^2 \theta} \right]\\\\\\\ = -\left(\dfrac{1+ \tan^2 \alpha}{1- \tan^2 \alpha}\right)\\\\\\= \dfrac{1+\tan^2 \alpha}{\tan^2 \alpha -1}[/tex]
Related Questions
Caroline leaves her apartment and walks 45° north of west for 1000 feet and then walks 200 feet due north to go to the grocery store. How far and at what north of west
quadrant is Caroline from being at her apartment?
Answers
Answer:
1150 ft W 52° N
Step-by-step explanation:
There are several ways a problem like this can be solved. Perhaps the easiest is to make use of a suitable vector calculator.
Using West as the reference for angles measured clockwise (toward north), the final position is ...
1000∠45° +200∠90° = 1150.149∠52.063°
__
You can also figure this using the Law of Cosines. It will tell you the resultant distance (c) in terms of the individual distances (a, b) and the angle between them (135°).
c² = a² +b² -2ab·cos(C)
c² = 1000² +200² -2·1000·200·cos(135°) ≈ 1,322,842.7
c ≈ √1322842.7 ≈ 1150.149
The angle difference from 45°N can be found using the Law of Sines.
sin(B)/b = sin(C)/c
B = arcsin(b/c·sin(C)) = arcsin(200/1140.149·sin(135°)) ≈ 7.063°
This means Caroline's bearing from home is 45° +7.063° ≈ 52° north of west.
Caroline's final position is 1150 W 52° N in relation to her home.
Nick sketches the graph of y = 0.5' for x 20 y 0.5 of Make one criticism of his sketch.
Answers
Answer:
the graph would just be a straight line going up at points (0, 0.5)
Step-by-step explanation:
This would have no slope
h=19+3.5w. What could the number 3.5 represent in the equation?
Answers
Answer:
the slope of the equation
Step-by-step explanation:
Solve pls brainliest
Answers
Answer:
a is 0.085 b is 19.6%
Step-by-step explanation:
1% = 0.01 so 8.5 = 0.085
0.20 = 20% so 0.196 = 19.6%
simplify: -4(x - 6) + 3(a - 7)
A. -4x + 3a - 3
B. -4x + 3a + 3
C. -4x + 3a + 45
D. -4x + 3a - 45
Answers
We have -4(x - 6) + 3(a - 7) = -4x + 24 + 3a - 21 = -4a + 3a + 3
so the answer is B
ok done. Thank to me :>
One theme in “Thank You, Ma’am” is that respectful treatment encourages mutual respect. Which passages from the story support this theme?
Select all that apply.
Thank You, Ma’am
He did not trust the woman not to trust him. And he did not want to be mistrusted now.
He did not trust the woman , not, to trust him. And he did not want to be mistrusted now.
The woman did not ask the boy anything about where he lived, or his folks, or anything else that would embarrass him.
The woman did not ask the boy anything about where he lived, or his folks, or anything else that would embarrass him.
The water dripping from his face, the boy looked at her. There was a long pause. A very long pause. After he had dried his face and not knowing what else to do dried it again, the boy turned around, wondering what next.
The water dripping from his face, the boy looked at her. There was a long pause. A very long pause. After he had dried his face and not knowing what else to do dried it again, the boy turned around, wondering what next.
“Then, Roger, you go to that sink and wash your face,” said the woman, whereupon she turned him loose—at last. Roger looked at the door—looked at the woman—looked at the door—and went to the sink.
Answers
Answer:
Either B. 'The woman did not ask the boy anything about where he lived, or his folks, or anything else that would embarrass him' or A. 'He did not trust the woman not to trust him. And he did not want to be mistrusted now.'.
Step-by-step explanation:
Brainliest Please!The passages from the story "Thank You, Ma'am" that support the theme that respectful treatment encourages mutual respect are: "The woman did not ask the boy anything about where he lived, or his folks, or anything else that would embarrass him." "The water dripping from his face, the boy looked at her. There was a long pause. A very long pause. After he had dried his face and not knowing what else to do dried it again, the boy turned around, wondering what next." and "Then, Roger, you go to that sink and wash your face,” said the woman, whereupon she turned him loose—at last. Roger looked at the door—looked at the woman—looked at the door—and went to the sink." Correct options are 2, 3 and 4.
These passages highlight how the woman treats the boy, Roger, with kindness and respect despite his attempt to steal her purse. Her understanding and respectful treatment lead Roger to reflect on his actions and ultimately decide to follow her guidance. This illustrates how respectful treatment encourages mutual respect between the characters.
To know more about respectful treatment :
https://brainly.com/question/28730771
#SPJ3
Rose spent 124 on 10 cars & 4 cats what is the cost for 1 car & 1 cat.
Answers
Answer:
$6 per cat, $10 per car
Step-by-step explanation:
I guess and checked my work.
What is an equation of the line that passes through the points (-6, -4)
and (-4, 0)?
Answers
Answer:
y=2x+8
Step-by-step explanation:
Hi there!
We want to find the equation of the line that passes through the points (-6, -4) and (-4, 0).
There are 3 ways to write the equation of the line:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the y interceptPoint-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a pointStandard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be equal to zero, and a cannot be negativeLet's write the equation in slope-intercept form, which is the most common way to do it.
We'll need to start by finding the slope of the line
The formula for the slope calculated from two points is [tex]\frac{y_2- y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
Even though we are already given two points, let's label their values in order to avoid any confusion and mistakes for later:
[tex]x_1=-6\\y_1=-4\\x_2=-4\\y_2=0[/tex]
Substitute these equations into the formula to find the slope (m):
m=[tex]\frac{y_2- y_1}{x_2-x_1}[/tex]
Substitute (remember: we have NEGATIVE numbers and SUBTRACTION, so we'll end up subtracting a negative):
m=[tex]\frac{0- -4}{-4--6}[/tex]
Simplify
m=[tex]\frac{0+4}{-4+6}[/tex]
Add the numbers together
m=[tex]\frac{4}{2}[/tex]
Divide
m=2
The slope of the line is 2
We can immediately plug it into the formula for slope-intercept form as m:
y=2x+b
Now we need to find b
As the equation passes through both (-6, -4) and (-4, 0), we can use either one of them to solve for b
Taking (-4, 0) for example:
Substitute -4 as x and 0 as y:
0=2(-4)+b
Multiply
0=-8+b
Add 8 to both sides
8=b
Substitute 8 as b into the equation
y=2x+8
Hope this helps!
3. A floor is 5 m long and 4 m wide. A square carpet of sides 3 m is laid on the floor. Find the area of the floor that is not carpeted.
Answers
Answer:
Length of floor = 5 m and breadth of floor = 4 m
Area of floor = length x breadth
= 5 m x 4 m = 20 m.sq
Now, Side of square carpet = 3 m
Area of square carpet = side x side = 3 x 3 = 9 m.sq
Area of floor that is not carpeted = 20 m – 9 m = 11 m.sq
Answer:
[tex]11 {m}^{2} [/tex]Step-by-step explanation:
First Condition:Given ,
Length of a floor = 5 m
Width of the floor = 4 m
Therefore,
Area of the floor
= l × b
= 5m × 4m
[tex] = 20 {m}^{2} [/tex]
Second Condition:Given,
Sides of a square carpet = 3 m
Therefore,
Area of the carpet
= s × s
= 3m × 3m
[tex] = {9m}^{2} [/tex]
At last:Now,
Area of the floor that is not carpeted is
= Area of the floor - Area of the carpet
[tex] = {20m}^{2} - {9m}^{2} [/tex]
[tex] = 11 {m}^{2} (ans)[/tex]
Write 2549 correct to the nearest 10
Answers
Answer:
2550
Step-by-step explanation:
7.90×10^−2/1.0×10^−5
Answers
Answer:
[tex] \frac{7.90 \times {10}^{ - 2} }{1.0 \times {10}^{ - 5} } \\ = 7.9 \times {10}^{5 - 2} \\ = 7.9 \times {10}^{3} [/tex]
The sum of a two-digit number and the number obtained by reversing its digits is 121. Find the number if it’s unit place digit is 5.
Answers
Answer:
65+56=121
Let no. be t5
reverse will be 5t
t*10 + 5 + 5*10 + t = 11t + 55 = 121 => 11t = 66 => t = 6
So no. = 65
Step-by-step explanation:
A line's y-intercept is –9, and its slope is 1/6 .What is its equation in slope-intercept form?
Answers
Answer:
y = 1/6x - 9
Step-by-step explanation:
The slope-form intercept formula is y = mx + b
What is y=6-2x-4x^2+5x^3 in standard form?
Answers
In standard form is……
Y=5x^3-4x^2-2x+6
The new iPhone 13 Pro Max cost p dollars. T-Mobile is running a promotion that gives you a 45% discount. Write an expression to represent the cost after discount.
The expression that represents the cost after discount is ?
Answers
Answer:
0.55p
Step-by-step explanation:
Iphone before discount = 100%p
Iphone after discount = 55%p
Expression = (1 - 0.45)p
Expression = 0.55p
-Chetan K
Which equation matches the graph shown?
Answers
Answer:
Vertex form: y = -2(x - 1)²
Standard form: y = -2x² + 4x - 2
Step-by-step explanation:
Given the x-intercept as the vertex, (1, 0), and the y-intercept, (0, -2) as the two points on the graph of a parabola:
We can determine the equation by substituting these given values into the vertex form of the quadratic equation:
y = a(x - h)² + k
where:
a = determines the direction of where the graph opens, and the wideness or narrowness of the parabola.
(h, k) = vertex
Solve for the value of a:Use vertex: (1, 0) and y-intercept, (0, -2):
y = a(x - h)² + k
-2 = a(0 - 1)² + 0
-2 = a(-1)²
-2 = a(1)
-2 = a
Quadratic Equation:Vertex form:The quadratic equation in vertex form that matches the graph is:
y = -2(x - 1)² + 0 or y = -2(x - 1)² ⇒ This is the quadratic equation in vertex form.
Standard form:To transform the vertex form into the standard form, y = ax² + bx + c:
Simply expand the perfect square, (x - 1)², through FOIL method before distributing -2:
y = -2(x - 1)²
y = -2(x - 1)(x - 1)
y = -2(x² -2x + 1)
y = -2x² + 4x - 2 ⇒ This is the quadratic equation in standard form.
Hello, ive been having issues with a quite easy topic. Slopes of lines? I dont really know how to solve this.
Answers
8. The sum of two numbers is 52. Find the larger number if their ratio is 1: 3.
Answers
Answer:
39
Step-by-step explanation:
Lets solve for x:
We know the ratio is 1:3
1x+3x = 52
4x = 52
x = 13
Since the ratio is 1:3:
13(3) = 39
13:39
Which makes 39 the larger number
ANSWER ASAP PLEASE!!!!!
What is the domain of the square root function graphed below?
A. x is less than or equal to -1
B. x is greater than or equal to -1
C. x is less than or equal to 0
D. x is greater than or equal to 0
Answers
Answer:
Step-by-step explanation:
A. If you need proof message me.
Answer:
D
Step-by-step explanation:
its correct
What is the value of x?
Answers
explanation it is a straight angle which means it adds up to 180.
180-72=108
3x=108
x=36
Answer:
AC is straight line.
72°+3x=180°[linear pair]
3x=180°-72°
3x=108°
x=108°/3
x=36°
option c.
Write an equation of a line
that passes through the
points
(-6,0) and (0,-24).
Answers
Answer:
y= -4x-24
Step-by-step explanation:
change in y/change in x = 0- -24/-6-0 = 24/-6 = -4
gradient is -4
then you put a set of coradinates into the formular y-y=m(x-x)
y - 0= -4 (x+6)
y-0=-4x-24
y=-4x-24
Answer:
4x +y = -24
Step-by-step explanation:
The given points are the x- and y-intercepts. It is convenient to write the equation in intercept form:
x/a +y/b = 1 . . . . . . x-intercept 'a', y-intercept 'b'
x/-6 +y/-24 = 1 . . . . . equation in intercept form
4x +y = -24 . . . . . . . equation in standard form (multiply by -24)
Work out the percentage change to 2 decimal places when a price of £189 is decreased to £150.
Answers
Answer:
20.63%
Step-by-step explanation:
189-20.63%=150,0093
Answer:
20.63%
Step-by-step explanation:
% change = (New Value - Initial Value)/(Initial Value) * 100
= (150-189)/189 * 100
= -20.63%
Though the value comes as negative but it only indicates that it is a percentage decrease. As the question mentioned that the value is decreased, the final answer would be only 20.63%.
Hopefully this helps!!
Which expression is equivalent to this expression?
34(4h – 6)
A. 3h – 92
B. 4h + 92
C. 3h – 6
D. 4h + 6
Answers
Answer:
the answer is d
Step-by-step explanation:
Can someone help me with this?
Answers
Answer:
y = 3x + 7.
Step-by-step explanation:
The slope = 6/2 = 3
y-intercept = 7.
Answer:
y = 3x + 7
Step-by-step explanation:
y-intercept = 7 {where the line intersect at y-axis (0,7)}
Plot a point: (-1 ,4 )
Slope intercept form: y = mx + b
y = mx + 7
4 = m*(-1) + 7
4 = -m + 7
4 - 7 = -m
-m = -3
m = 3
y = 3x + 7
the sum of two rational numbers is 17/18 If one of the numbers is 5/24 find the other number
Answers
Step-by-step explanation:
x + y = 17/18
x = 5/24
5/24 + y = 17/18
to bring both fractions to the same denominator (I see it is 72, but let's do it formally correct for you to learn), we look for the LCM, the lowest common multiple of both.
for this we split both numbers into their prime factors and then build the the combination of the longest chains per prime factor :
24 = 2×2×2×3
18 = 2×3×3
the LCM (and the new denominator) is then
2×2×2×3×3 = 8×9 = 72
so,
15/72 + y = 68/72
y = 53/72
53 is a prime number, so the fraction cannot be further refined.
20 points! :D
Help is much appreciated. :D
Answers
Answer:
I think it's 32x
Step-by-step explanation:
hope I got it right Im not to good at this
You have 64 coins, consisting of pennies, nickels, and quarters. The value of the coins is $4.60. You also know that you have three times as many nickels as quarters. Find the quantity of each type of coins
Number of pennies =
Number of nickels =
Number of quarters =
Answers
Answer:
There are 20 pennies, 33 nickels and 11 quarts.
Step-by-step explanation:
Total number of coins = 64 Amount of money = $4.60 = 460 cents
x = pennies y = nickels x = quarters
y x 3 = x
x + y + z = 64 coins
x + 5y + 25z
x + 4z = 64
x + 40z = 460
x = 20 z = 11
y = 3z = 33
Tell whether the given value is a solution of the inequality.
Answers
Answer:
Step-by-step explanation:
8p < -3
if p = -2
8* -2 < -3
-16 < -3 TRUE so p= -2 is a solution to the inequality 8p < -3
Dan is buying turkey cutlets for $2.69 per pound. The package weighs 4 pounds, 8 ounces.
How much will the cutlets cost?
Answers
if I did it right then it's $32.38.
ANSWER FAST PLEASE !!
Use synthetic division and the remainder theorem to find P(a).
P(x) = x^3 + 5x^2 - 6x +6; a = 4
P(a) =
Simplify your answer
Answers
Answer:
[tex]1 + 2 = [/tex]
answer