Answer:
See below
Step-by-step explanation:
We want to prove that
[tex]\sin(x)\tan(x) = \dfrac{1}{\cos(x)} - \cos(x), \forall x \in\mathbb{R}[/tex]
Taking the RHS, note
[tex]\dfrac{1}{\cos(x)} - \cos(x) = \dfrac{1}{\cos(x)} - \dfrac{\cos(x) \cos(x)}{\cos(x)} = \dfrac{1-\cos^2(x)}{\cos(x)}[/tex]
Remember that
[tex]\sin^2(x) + \cos^2(x) =1 \implies 1- \cos^2(x) =\sin^2(x)[/tex]
Therefore,
[tex]\dfrac{1-\cos^2(x)}{\cos(x)} = \dfrac{\sin^2(x)}{\cos(x)} = \dfrac{\sin(x)\sin(x)}{\cos(x)}[/tex]
Once
[tex]\dfrac{\sin(x)}{\cos(x)} = \tan(x)[/tex]
Then,
[tex]\dfrac{\sin(x)\sin(x)}{\cos(x)} = \sin(x)\tan(x)[/tex]
Hence, it is proved
An American tourist visits South Africa with $3000. The exchange rate when she arrives is
$1 = 12.90. She changes all her dollars into rands and then spends R900 per day for seven
days. She changes the rands she has left back into dollars at a rate of $1 = R12.93. How much
does she get in dollars? show your working.
9514 1404 393
Answer:
$2505.80
Step-by-step explanation:
After the first exchange, the tourist has ...
$3000(12.90 R/$) = R38,700
After 7 days, she has ...
R38,700 -7(R900) = R32,400
After the second exchange, she has ...
R32,400 × ($1/R12.93) = $2505.80
She gets $2505.80 at the second exchange.
The measure of the vertex angle of an isosceles triangle is (a + 30)°. The base angles each measure (2a - 15)º. What is the measure in degrees of one of the base angles?
1. Find the length of X (in the picture) plssss I need help.
Step-by-step explanation:
[tex] \frac{5}{4} = \frac{x}{6} \\ 4x = 30 \\ x = 7.5[/tex]
Find the coefficient of the t4
term in the expansion of
(4t – 375
a
9514 1404 393
Answer:
-3840t^4
Step-by-step explanation:
The k-th term, counting from k=0, is ...
C(5, k)·(4t)^(5-k)·(-3)^k
Here, we want k=1, so the term is ...
C(5, 1)·(4t)^4·(-3)^1 = 5·256t^4·(-3) = -3840t^4
__
The program used in the attachment likes to list polynomials with the highest-degree term last. The t^4 term is next to last.
If y= 5x- 2 were changed to y = x-2, how would the graph of the new
function compare with the first one?
O A. It would be less steep.
O B. It would be steeper.
O C. It would be shifted down.
OD. It would be shifted left.
Equation of lines acellus pls help ofooehhenxkdoke
Answer:
Firstly you must find the slope of two point
Step-by-step explanation:
m=(y2-y1)/(x2-x1) m=-8/4 = -2 after this step you should choose one point. I want to choose (3,1) y-1=2*(x-3). our equation y=2x-7
What are the x-coordinates for the maximum points in the function f(x) = 4 cos(2x − π) from x = 0 to x = 2π? (1 point) Select one: a. x = 3 pi over 2 , x = π b. x = pi over 2 , x = 3 pi over 2 c. x = 0, x = 2π d. x = 0, x = π
9514 1404 393
Answer:
b. x = π/2, x = 3π/2
Step-by-step explanation:
The maximum is found where the argument of the cosine function is a multiple of 2π.
2x -π = 2nπ
2x = (2n+1)π . . . . . . . add π
x = (2n+1) · π/2 . . . . . divide by 2
x = {π/2, 3π/2}
Find the 3rd term in the expansion of (a + b)^7 in simplest form.
9514 1404 393Answer:
21·a^5·b^2
Step-by-step explanation:
The k-th term is ...
C(7, k)·a^(7-k)·b^k . . . . . where k counts from 0 to n
Then k=2 for the third term. The coefficient of it is ...
C(7, 2) = 7!/(2!(7-2)!) = 7·6/(2·1) = 21
The third term is ...
21·a^5·b^2
What is ratio 1 hour and 15 minutes to 50 minutes in lowest terms?
Answer:
First, convert the hour to minutes.
1 hr = 60 mins
15 mins: 60 mins
1:4
Oh wait I read the question wrong, give me 5 minutes lol. Edit: Nvm, I read it right :). This is the answer.
Answer:
3:2
Step-by-step explanation:
1 hour and 15 minutes can be seen as 75 minutes so it would be
75:50
The highest common mutiple of 75 and 50 are 25. Divide both (75&50) by 25.
The answer would be 3:2
Convert the following equation into slope-intercept form.
x-26y=52
The pie chart below shows the percentage of total revenue that a publisher receives from various types of publications. Use this chart to answer the questions
below.
Answer:
a. Cookbooks
b. 50%
c. 30%
Step-by-step explanation:
According To the Question,
We have a total revenue of a publisher describe in a circle (360°).a. Now, Approximately Cookbooks & Textbooks revenue Form 180°, but textbook revenue is more than cookbooks as clearly visible in the diagram
Thus, cookbooks are less than 90°.
Now, we have to find 1/5th of total publisher revenue which is 360°/5= 72°. & the Cookbooks is nearest to 72° ( less than 90°)
So, Answer For (a) is Cookbooks
b. Here in Diagram Clearly Visible that The Cookbooks & Textbooks Revenue Form 180° which is Approximately 50% of total Publisher's Revenue.
So, the Total Revenue Comes From Textbooks & Cookbooks is 50%.
c. Now We know the Cookbooks + Textbooks Revenue form 180° Approximately & Cookbook is approximately equal to 72° (as we solve above)
So, textbooks are 180°-72° = 108°, which is 30% of 360° ∴ 30% Revenue Come From Textbooks.
which number line represents the solution set for the inequality ? HELP PLEASE
Step-by-step explanation:
if you need any explanation you can ask
5 is subtracted from the sum of 8 and 7.
Answer:
10
Step-by-step explanation:
Sum of 8 and 7 = 8 + 7 = 15
5 subtracted from sum of 8 and 7 = 15 - 5 = 10
The answer to this question = 10
What do you mean by a sum?The sum is the result of the addition of two or more numbers.
What do you mean by subtraction?The difference between the two numbers is called subtraction.
How do we evaluate the given question?First, we find the sum of 8 and 7
8 + 7 = 15
Now, we subtract 5 from 15
15 - 5 = 10
∴ The result to the given question = 10
Learn more about the Addition/Subtraction at
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Use the formula below to find the relative pressure inside the can in psi
Answer:
b
Step-by-step explanation:
you have to have psi to have p-e-n-i-s sand you get a jack hammer
the area of a tennis court is 2000m2 . a rugby pitch has a legnth of 45m and width of 45m . which has the biggest area?
Answer:
The area of a rugby pitch is more as compared to the area of the tennis court.
Step-by-step explanation:
Given that,
The area of a tennis court is 2000 m².
The length and width of a rugby pitch are 45 m and 45 m.
The area of a rugby pitch is given by :
A = lb
So,
A = 45×45
A = 2025 m²
So, it is clear that the area of a rugby pitch is more as compared to the area of the tennis court.
The rate of inflation measures the percentage increase in the price of consumer goods. The rate of inflation in the year 2014 was 2% per year. To get a sense of what this rate would mean in the long run, let's suppose that it persists through 2034.
What would be the cost in 2034 of an item that costs $100 in 2014? (Round your answer to the nearest cent.)
$
Answer:
148.59
Step-by-step explanation:
Inflation is kind of similar to interest and with that bieng said we can (kind of ) use the same formula
the time between 2034 and 2014 is 2034-2014= 20
100(1.02)²⁰=148.5947396
which we can round to 148.59
148.5 is the cost in 2034 of an item that costs $100 in 2014
What is Simple Interest?Simple interest is a quick and easy method of calculating the interest charge on a loan
[tex]A=P(1+r)^{t}[/tex]
where A is the Actual amount
P is Initial amount
t is time period
r is rate of interest
Given,
The rate of inflation measures the percentage increase in the price of consumer goods
The rate of inflation in the year 2014 was 2% per year.
2% is converted to decimal by dividing with 100
2/100=0.02
The time gap between 2014 and 2034 is
2034-2014=20 years
The initial amount is 100
A=100(1+0.02)²⁰
A=100(1.02)²⁰
A=100×1.485
A=148.5
Hence 148.5 is the cost in 2034 of an item that costs $100 in 2014.
To learn more on Simple interest click:
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Suppose one network executive is selected at random. find the indicated probabilities
Answer:
na answer ran nyo na po
Step-by-step explanation:
Find x
x³ + 3x - 14 = 0
x³ + x² - x² - x + 4x + 4 = 18
x²(x + 1) - x(x + 1) + 4(x + 1) = 18
(x + 1)(x² - x + 4) = 18
x² - x + 4 = 18/(x + 1)
x² - x + 4 - 6 = 18/(x + 1) - 6
x² - x - 2 = 18/(x + 1) - 6
(x - 2)(x + 1) = (18 - 6(x + 1))/(x + 1)
(x - 2)(x + 1) = (18 - 6x - 6)/(x + 1)
(x - 2)(x + 1) = (12 - 6x)/(x + 1)
(x - 2)(x + 1) = (-6(x - 2))/(x + 1)
x + 1 = (-6(x - 2))/(x + 1)(x - 2)
x + 1 = -6/(x + 1)
(x + 1)² = -6
x² + 2x + 8 = 0
x = (-b +- √(b² - 4ac))/2a
x = (-2 +- √(4 - 32))/2
x = (-2 +- √(-28)/2
x = (-2 +- i√28)/2
Something's wrong.
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = - 1 \: + \: i \sqrt{6} \:(or) \: \: x = - 1 \: -\: i \sqrt{6} }}}}}}[/tex]
And[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\:2}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \: {x}^{3} + 3x - 14 = 0[/tex]
➺[tex] \: {x}^{2} (x + 1) - x(x + 1) + 4(x + 1) = 18[/tex]
➺[tex] \: (x + 1)( {x}^{2} - x + 4) = 18[/tex]
➺[tex] \: {x}^{2} - x + 4 = \frac{18}{(x + 1)} [/tex]
➺[tex] \: {x}^{2} - x + 4 - 6 = \frac{18}{(x + 1)} - 6[/tex]
➺[tex] \: (x - 2)(x + 1) = \frac{18 - 6(x + 1)}{(x + 1)} [/tex]
➺[tex] \: (x - 2)(x + 1) = \frac{18 - 6x - 6}{(x + 1)} [/tex]
➺[tex] \: (x - 2)(x + 1) = \frac{12 - 6x}{(x + 1)} [/tex]
➺[tex] \: (x - 2)(x + 1) = \frac{ - 6(x - 2)}{(x + 1)} [/tex]
➺[tex] \: (x + 1 )² = \frac{ - 6(x - 2)}{(x + 1)(x - 2)} [/tex]
➺[tex] \: (x + 1)² = \frac{ - 6}{(x + 1)} [/tex]
[tex]\sf\pink{Error\:corrected\:here. }[/tex]
➺[tex] \: {x}^{2} + 2x + 1 = - 6[/tex]
➺[tex] \: {x}^{2} + 2x + 7 = 0[/tex]
By quadratic formula, we have
➺[tex] \: x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
➺[tex] \: x = \frac{ - 2± \sqrt{ {2}^{2} - 4.1.7} }{2 \times 1} [/tex]
➺[tex]x = \frac{ - 2± \sqrt{ - 24} }{2 } [/tex]
➺[tex] \: x = \frac{ - 2± \sqrt{ - 1 \times 4 \times 6} }{2} [/tex]
➺[tex] \: x = \frac{ - 2± \sqrt{ - 1} \times \sqrt{4} \times \sqrt{6} }{2} [/tex]
➺[tex] \: x = \frac{ - 2 \: ± \: i \times 2 \times \sqrt{6} }{2} [/tex]
➺[tex] \: x = \frac{ - 2 \: ± \:i \: 2 \sqrt{6} }{2} [/tex]
➺[tex] \: x = \frac{ 2 \: ( - 1 \: ± \: i \: \sqrt{6}) }{2} [/tex]
➺[tex] \: x = - 1 \: ± \: i \sqrt{6} [/tex]
Therefore, the two values of [tex]x[/tex] are ([tex] \: - 1 \: + \: i \sqrt{6}[/tex]) and ([tex] \: - 1 \: -\: i \sqrt{6}[/tex]).
Let us look at another method.[tex]x[/tex]³ + 3 [tex]x[/tex] - 14 = 0
➼ [tex]x[/tex]³ + 3 [tex]x[/tex] = 14
➼ [tex]x[/tex] ( [tex]x[/tex]² + 3 ) = 14
Factors of 14 = 1, 2, 7 and 14.
a) Substituting [tex]x\:=\:1[/tex], we have
➼ 1 ( 1 + 3 ) ≠ 14
➼ 1 x 4 ≠ 14
➼ [tex]\boxed{ 4\: ≠ \:14 }[/tex]
b) Substituting [tex]x\:=\:2[/tex], we have
➼ 2 ( 2² + 3 ) = 14
➼ 2 ( 4 + 3 ) = 14
➼ 2 x 7 = 14
➼ [tex]\boxed{ 14 \:= \:14 }[/tex]
c) Substituting [tex]x\:=\:7[/tex], we have
➼ 7 ( 7² + 3 ) ≠ 14
➼ 7 ( 49 + 3 ) ≠ 14
➼ 7 x 52 ≠ 14
➼ [tex]\boxed{ 364\: ≠ \:14 }[/tex]
d) Substituting [tex]x\:=\:14[/tex], we have
➼ 14 ( 14² + 3 ) ≠ 14
➼ 14 x 199 ≠ 14
➼ [tex]\boxed{ 2786\: ≠ \:14 }[/tex]
Hence, our only real solution is 2.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
please help meeeeeeeeeeeeeeeeee
pt 1
Answer:
Completing the square
Step-by-step explanation:
The proof is lengthy, and I don't think you came here to see that whole proof. Here it is anyway to show you the process of completing the square.
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:more-on-completing-square/a/quadratic-formula-proof-review
A video store charges $8 per movie, and the fifth movie is free. How much do you actually pay per movie?
Answer:
$6.40 per movie
Step-by-step explanation:
Since the fifth movie is free, find the total cost by multiplying 8 by 4:
8(4)
= 32
Find how much you actually pay per movie by dividing this by 5:
32/5
= 6.4
So, you are actually paying $6.40 per movie
Answer:
$6.40
Step-by-step explanation:
If you buy five movies, but only pay for the first four, then that is the first amount we need to find. Paying $8 for four movies means you are paying $32. If you are paying $32 for five movies, then you are paying $6.40 per movie.
Math:
8 + 8 + 8 + 8 + 0 = 32
32/5 = 6.4
The radius of a cylindrical water tank is 4.5 ft, and its height is 10 ft. What is the volume of the tank?
Answer:
636.3 cubic meters
Step-by-step explanation:
Volume of cylinder= pi × radius² × height
3.142 × 20.25 × 10 = 636.255 rounded to the nearest one decimal place is 636.3
Have a nice day.
The Home Cleaning Company charges $312 to power-wash the siding of a house plus
$12 for each window. Power Clean charges $36 per window, and the price includes
power-washing the siding. How many windows must a house have to make the total
cost from The Home Cleaning Company less expensive than Power Clean?
Answer:
14
Step-by-step explanation:
take 312 + 12×14 then take 36×14
2^5 + 10=?????????????
Answer:
Answer is 42
Step-by-step explanation:
2^5 + 10
2*2*2*2*2 + 10
32 + 10
42
What is the distance between the points (2, 1) and(6, 7)?
Answer:
[tex]\displaystyle d = 2\sqrt{13}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (2, 1)
Point (6, 7)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(6 - 2)^2 + (7 - 1)^2}[/tex][√Radical] (Parenthesis) Subtract: [tex]\displaystyle d = \sqrt{4^2 + 6^2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{16 + 36}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{52}[/tex][√Radical] Simplify: [tex]\displaystyle d = 2\sqrt{13}[/tex]Katy spent $2834 on a washing machine and a dryer. The dryer cost $875 less than the washing machine. How much did the dryer cost ?
Answer:
the answer is 1959
Step-by-step explanation:
2834-875=1959
In the last six months, Sonia's family used 529, 499, 651, 652, 1,163, and 310 minutes on their cell phone plan. To save money, Sonia's family wants to keep their mean cell phone usage below 600 minutes per month.
By how many minutes did they go over their goal in the last six months?
Answer:
They went over their goal for the last six months by 34 minutes per month.
Step-by-step explanation:
Mean of a data-set:
The mean of a data-set is the sum of all values in the data-set divided by the size of the data-set.
529, 499, 651, 652, 1,163, and 310 minutes on their cell phone plan.
The mean is:
[tex]M = \frac{529+499+651+652+1163+310}{6} = 634[/tex]
By how many minutes did they go over their goal in the last six months?
The mean was of 634 minutes, and they wanted to keep it below 600. So
634 - 600 = 34
They went over their goal for the last six months by 34 minutes per month.
you arrive in Mexico City with $360 how many pesos can you buy?
Answer:
7 442,84
Step-by-step explanation:
PLEASE HURRY!! I WILL MARK BRAINIEST!
The pentagons JKLMN and PQRST are similar.
Find the length x of QR.
Answer:
x=2.8
Step-by-step explanation:
If JKLMN and PQRST are similar then you can look the to other sides to find the ratio that relates the two. For this specific one you are able to fin 0.4 is the relationship.
NJ is related to TP by a factor of 1.4. -> NJ*1.4=TP -> 4*1.4=5.6
The rest can be said to relate all the other sides together.
Solve the equation by completing the square. Round to the nearest hundredth x^2 + 2x = 15
Answer:
x = 3, x = -5
Step-by-step explanation:
A perfect square trinomial is represented in the form a^2 + 2ab + b^2. We are already given the a^2 term, x^2, and the 2ab term, 2x. From this we can say:
a^2 = x^2
a = x
Now, we can substitute x for a in the other expression to create the equation:
2ab = 2x
2(x)b=2x
b = 1
From this, b^2 is one, so, to get our trinomial all on one side, we add 1 to both sides:
x^2 + 2x = 15
x^2 + 2x + 1 = 16
Now, we can factor. The perfect square trinomial factors into (a + b)^2. In this case, a is x, and b is one. We can factor and get:
(x + 1)^2 = 16
Now, we take the square root of both sides:
x + 1 = ± 4
We can separate this into two equations and solve:
x + 1 = 4
x = 3
x + 1 = -4
x = -5
Answer:
Step-by-step explanation:
x^2 + 2x = 15
x^2 + 2x + [1/2(2)]^2 = 15 + [1/2(2)]^2
(x + 1/2(2) )^2 = 15 + [(1/2)(2)]^2
(x + 1)^2 = 15 + 1^2
(x + 1)^2 = 15 + 1
(x+1)^2 = 16 Take the square root of both sides.
sqrt( (x + 1)^2 ) = sqrt(16)
x + 1 = +/- 4
x + 1 = 4
x = 4 - 1 = 3
x + 1 = -4
x = -4 - 1
x = - 5
So the roots are 3 and - 5
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