Answers
Step-by-step explanation:
LHS = (tan β + Sec β)(1 - sin β)
= ((sin β / cos β) + (1/cos β))(1-sin β)
= ((1+ sin β)*(1- sin β))/cos β
= (1 - sin^2 β) / cos β
= cos^2 β / cos β
= cos β
= RHS
Hence proved
Related Questions
please help!!!!!!!!!!!!!!
Answers
Answer:
A
Step-by-step explanation:
By solving (x+6)(x-9), we get x^2 - 3x - 54. By looking at our y-intercept, we can see that only option A has the correct intercept.
Answer:
A
Step-by-step explanation:
Review the proof of de Moivre’s theorem (not in order).
Proof of de Moivre's Theorem
[cos(θ) + isin(θ)]k + 1
A = [cos(θ) + isin(θ)]k ∙ [cos(θ) + isin(θ)]1
B = cos(kθ + θ) + isin(kθ + θ)
C = cos(kθ)cos(θ) − sin(kθ)sin(θ) + i[sin(kθ)cos(θ) + cos(kθ)sin(θ)]
D = [cos(kθ) + isin(kθ)] ∙ [cos(θ) + isin(θ)]
E = cos[(k + 1)θ] + isin[(k + 1)θ]
Which steps must be switched to put the proof in order?
steps B and C
steps B and D
steps C and D
steps C and E
Answers
Answer:
steps B and D
Step-by-step explanation:
the correct chart is below :)
The steps which must be switched to put the proof in order are steps B and D
Since [cos(θ) + isin(θ)]k + 1
= [cos(θ) + isin(θ)]k ∙ [cos(θ) + isin(θ)]1
= [cos(kθ) + isin(kθ)] ∙ [cos(θ) + isin(θ)]
= cos(kθ)cos(θ) − sin(kθ)sin(θ) + i[sin(kθ)cos(θ) + cos(kθ)sin(θ)]
= cos(kθ + θ) + isin(kθ + θ)
= cos[(k + 1)θ] + isin[(k + 1)θ]
Since the step after A is [cos(kθ) + isin(kθ)] ∙ [cos(θ) + isin(θ)] = D, and the step after C is cos(kθ + θ) + isin(kθ + θ) = B.
So, steps B and D must be switched.
The steps which must be switched to put the proof in order are steps B and D.
Learn more about De Moivre's theorem here:
https://brainly.com/question/11889817
A criminologist developed a test to measure recidivism, where low scores indicated a lower probability of repeating the undesirable behavior. The test is normed so that it has a mean of 140 and a standard deviation of 40. Suppose an individual is in the 67th percentile in this exam.What is his or her corresponding recidivism score
Answers
Answer:
157.6
Step-by-step explanation:
The formula for calculating a z-score is is z = (x-μ)/σ,
where x is the raw score,
μ is the population mean, and
σ is the population standard deviation.
From the question:
Mean = 140
Standard deviation = 40
Recidivism score = x score = ??
z = z score of 67th percentile = 0.44
Hence,
0.44 = x - 140/40
Cross Multiply
0.44 × 40 = x - 140
17.6 = x - 140
x = 140 + 17.6
x = 157.6
Therefore, his corresponding recidivism score is 157.6
Enter the equivalent distance in km in the box.
1 km = 1000 m
1 m = 100 cm
35,000 cm =
km
Answers
Answer:
0.350 km
Step-by-step explanation:
Hi there !
35000 cm = 35000/100 m = 350 m
350 m = 350/1000 km = 0.350 km
Good luck !
Write 310,763,029 expanded form
Answers
Answer:
300,000,000
10,000,000
700,000
60,000
3,000
20
9
Step-by-step explanation:
Anya purchased $124.35 worth of home improvement items at the hardware store. If the sales tax rate in her city is 6.75%, what is the total cost of her purchase!
Answers
Answer:
124.35 X 6.75
Step-by-step explanation:
The total cost of Anya's purchase of home improvement hardware is 132.74 dollars.
What is percentage?
The percentage is the value per hundredth.
It is given that, the sales tax is 6.75% which is not there in the home improvement hardware which cost 124.35 dollars to Anya.
The total cost of purchase including the sales tax is ( 100 + 6.75)% = 106.75% of 124.35 dollars which is,
= (106.75/100)×124.35 dollars.
= 1.0675×124.35 dollars.
= 132.74 dollars.
learn more about percentage here :
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#SPJ5
please help meeeeeeeeeeeeee
Answers
There are (26)3⋅ 20 bacteria in a sample. What is the total number of bacteria in the sample? (1 point)
Answers
Answer: If we multiply then I guess it’s 26*3=78 and 78*20=1,560
Step-by-step explanation:
Suppose that you roll a die 8 times. What is the probability that you roll a six three or fewer times
Answers
Answer:
0.96
Step-by-step explanation:
Given that the a die is rolled 8 number of times.
[tex]n[/tex] = 8
Probability of getting a 6 on roll of a die, [tex]p=\frac{1}{6}[/tex]
Probability of not getting a 6 on roll of a die, [tex]q=1-p=1-\frac{1}{6}=\frac{5}{6}[/tex]
Probability of getting 6 three or fewer times:
[tex]P(r \le 3)=P(r=0)+P(r=1)+P(r=2)+P(r=3)[/tex]
Formula:
[tex]P(r=k)=_nC_k.p^k.q^{n-k}[/tex]
Putting the values using this formula:
[tex]P(r \le 3)=_8C_0.\frac{1}{6}^0.\frac{5}{6}^{8-0}+_8C_1.\frac{1}{6}^1.\frac{5}{6}^{8-1}+_8C_2.\frac{1}{6}^2.\frac{5}{6}^{8-2}+_8C_3.\frac{1}{6}^3.\frac{5}{6}^{8-3}\\\Rightarrow P(r \le 3)=1.\frac{5}{6}^{8}+8.\frac{1}{6}.\frac{5}{6}^{7}+28.\frac{1}{36}^2.\frac{5}{6}^{6}+56.\frac{1}{216}.\frac{5}{6}^{5}\\\Rightarrow P(r \le 3)=0.23+0.37+0.26+0.1=\bold{0.96}[/tex]
What is 86.929 rounded to the nearest tenth ?
Answers
Answer:
86.9
Step-by-step explanation:
This is because after the decimal point, it goes to the tenths place and then the thousands place, therefore, if you round it, it would be 86.9.
Labor costs. Labor costs for a farmer are $55 per acre for corn and $45 per acre for soybeans. How many acres of each crop should the farmer plant if he wants to spend no more than $6,900 on labor?
Answers
Answer:
392984
Step-by-step explanation:
A florist must make 5 identical
bridesmaid bouquets for a wedding. The budget is
$160, and each bouquet must have 12 flowers. Roses
cost $2.50 each, lilies cost $4 each, and irises cost
$2 each. The florist wants twice as many roses as the
other two types of flowers combined.
Answers
Answer:
A. 40x + 10y + 10z = $160
B. 8 Roses, 2 lilies and 2 irises
C.
1. 20x + 5y + 5z = $80
2. 4x + y + z = $16
3. 8x + 2y + 2z = $32
Step-by-step explanation:
Cost for each flower = $160/5 = $32
So we have $32 for each bouquet consisting of 12 flowers each.
Roses = x = $2.50 each
lilies = y = $4 each
irises = z = $2 each
8x + 2y + 2z = $32
8($2.50) + 2($4) + 2($2) = $32
$20 + $8 + $4 = $32
$32 = $32
a. Maximum budget is $160
40x + 10y + 10z = $160
40($2.50) + 10($4) + 10($2) = $160
$100 + $40 + $20 = $160
$160 = $160
b. From above
8x + 2y + 2z = $32
8 Roses, 2 lilies and 2 irises
c. No. There are other solutions If total cost is not limited
1. 20x + 5y + 5z
20($2.50) + 5($4) + 5($2)
$50 + $20 + $10
= $80
2. 4x + y + z
4($2.50) + $4 + $2
$10 + $4 + $2
= $16
3. 8x + 2y + 2z
8($2.50) + 2($4) + 2($2)
$20 + $8 + $4
= $32
I WILL BRAINLIST ITS ONLY ONE PROBLEM !!!!!!!!!!!!!!!
Answers
Answer:
11/200
Step-by-step explanation:
This is the correct answer boo
show that: (1-sin x)/(cos x)=(sec x - tan x)
Answers
This is the step-by-step explanation
Find the values of x and y.
x=
Answers
y = 6
hope this helps!
when writing fraction from a graph does the x axis number go on top or bottom
Answers
Answer:
x ax-s can be horizontal and top
y axis is bottom
Step-by-step explanation:
what is the rate of change for the liner relationship modeled in the table?
Answers
i'm sorry wheres the picture?
Mary used 1/2 of a can of paint to cover 1/8 of the outside of her house. How many cans of paint will Mary need to cover the entire outside of her house?
Answers
Answer:
4 cans of paint
Step-by-step explanation:
Half of a can = 1/8 of the outside of the house.
2 halves = whole can of paint
8/2=4
4 cans of paint
in exercises 15-20 find the vector component of u along a and the vecomponent of u orthogonal to a u=(2,1,1,2) a=(4,-4,2,-2)
Answers
Answer:
The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].
Step-by-step explanation:
Let [tex]\vec u[/tex] and [tex]\vec a[/tex], from Linear Algebra we get that component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] by using this formula:
[tex]\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a[/tex] (Eq. 1)
Where [tex]\|\vec a\|[/tex] is the norm of [tex]\vec a[/tex], which is equal to [tex]\|\vec a\| = \sqrt{\vec a\bullet \vec a}[/tex]. (Eq. 2)
If we know that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec a=(4,-4,2,-2)[/tex], then we get that vector component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] is:
[tex]\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)[/tex]
[tex]\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)[/tex]
[tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]
Lastly, we find the vector component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] by applying this vector sum identity:
[tex]\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}[/tex] (Eq. 3)
If we get that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex], the vector component of [tex]\vec u[/tex] is:
[tex]\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]
[tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex]
The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].
I will give brainliest :D
Which equation matches this scenario?
A family buys 8 tickets to a show. They also pay a $5
parking fee. They spend $61 to see the show.
• 5x+8=61
• 61+8x=5
• 8+5x=61
• 8x+5=61
Answers
Answer: 8x + 5= 61
Step-by-step explanation: x represents the cost of one ticket for the show, 8 is the amount of tickets, 5 is the extra fee, 61 is the total.
An airplane pilot over the Pacific sights a ship wreck at an angle of depression of 5°. At this time, the horizontal distance from the airplane to the wreck is 4629 meters. What is the height of the plane to the nearest meter?
405 m
Answers
Answer:
The height of the plane is 405 meters
Step-by-step explanation:
Trigonometric Ratios
The situation can be represented as shown in the image below. The ground, the height H, and the direct distance to the plane to the shipwreck form a right triangle, where the trigonometric ratios stand.
Since the known distance is adjacent to the angle, and the required height is opposite to the given angle, we use the tangent ratio, defined as:
[tex]\displaystyle \tan\ x=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
[tex]\displaystyle \tan 5^\circ=\frac{H}{4629}[/tex]
We need to find H, so we solve for H:
[tex]H=4629\cdot\tan5^\circ[/tex]
H=405 m
The height of the plane is 405 meters
Hi guys I’m bored can someone talk to me please? :)
Answers
Answer:
sure
Step-by-step explanation:
Answer:
hello
Step-by-step explanation:
fplzz ans my question
factorize p^4+4
Answers
Answer:
Step-by-step explanation:
(p²)²+2²
(p²+2)²-2p²2
(p²+2)²-4p²
(p²+2)²-(2p)²
(p²+2-2p)(p²+2+2p)
If A is the least common multiple of 12, 24, and 36, and B
is the lowest prime number, what is the sum of A and B ?
F.
3
G.
4
H.
73
J.
74
K.
145
Answers
Answer:
74
Step-by-step explanation:
A= Least common multiple of 12,24,36
Factors of 12 = 2*2*3
Factors of 24 = 2*2*2*3
Factors of 36 = 2*2*3*3
A = 2*2*2*3*3 = 72
B = Lowest prime number = 2
A+B = 72+2 = 74
Linearize the data. Then find the least squares regression equation
Answers
Answer:
C
Step-by-step explanation:
adult men weights mean of 190 30 3 random men mean weight
Answers
Answer:
is this the question ?
Step-by-step explanation:
Text a friend and write a clear set of instructions on how to find a ratios amount
Answers
Answer:
Hi ___
A ratio is created from two numbers it can also be a fraction.
To find a ratio you have to have 2 numbers
You can take these 2 numbers and divide them so they are a unit ratio
For example 3:6 can be reduced to 1:3
Step-by-step explanation:
Hope this helps please give brainliest
Explain how you would solve -5/8 divided by 2/3 and what the solution is?
Answers
Answer:
-15/16
Step-by-step explanation:
-5/8 ÷ 2/3
Copy dot flip
-5/8 * 3/2
Multiply the numerators
-5*3 = -15
Multiply the denominators
8*2 =16
Put the numerator over the denominator
-15/16
6 TH grade math
On a hot day, Myra poured 4 1/8 buckets of water into a plastic wading pool. A few minutes later she added another 3 5/8 buckets. How much water did Myra pour into the pool?
Answers
Answer:
7 3/4
Step-by-step explanation:
4 1/8 + 3 5/8
Add the whole numbers, 4 + 3 = 7.
Add the fractions, 1/8 + 5/8 = 6/8.
You get 7 6/8. Simplify 6/8 to get 3/4.
Your answer is 7 3/4.
Your brother asked you to help him build a bookcase for your next-door neighbor. Since he is doing most of the work, you get 3 dollars for every 5 dollars he makes. He got paid 67 dollars. How much did you get paid?
Answers
Answer:
So, friend Let me solve the question for you :
let's use disturbutive property
67 x 5 - 67 × 3
67 × (5-3)
67 ×2 = 134
Step-by-step explanation:
Hope it. helps PISas Markbrainliest
Answer:
You got paid $40.20
Step-by-step explanation:
First let's find out how many 5's they gave him:
$67 (brother's money) ÷ 5 = 13.4 (how many times they paid him)
Now we find out how much money they gave you:
$3 (how much they give you) x 13.4 = $40.20 (your total money)