For the sale of a $ 10 item with a discount of 30 % has a sales tax of $ 0.35.
How much money should we pay in sales tax?
In this question we must determine the amount of money needed to pay in taxes by the purchase of an item with a discount. Sales taxes are an example of indirect taxes, this kind of indirect tax is usually calculated on the basis of total costs, including discounts. The amount of money need for the sales tax is described below:
t = (r / 100) · (1 - d / 100) · c (1)
Where:
d - Discount rater - Sales tax ratec - Item pricet - Sales tax totalIf we know that d = 30, r = 5 and c = 10, then the sales tax total is:
t = (5/ 100) · (1 - 30 / 100) · 10
t = 0.35
For the sale of a $ 10 item with a discount of 30 % has a sales tax of $ 0.35.
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The length of the diagonal of a wooden cube is 24 cm. The cube is cut into the cylinder of the
biggest volume possible. The volume of the cylinder is:
The volume of the cylinder is [tex]384\pi \sqrt{3cm }^{2}[/tex].
What is the diagonal of the cube?The diagonal that runs through the middle of a cube is it's main diagonal; the diagonal that runs along one of its faces is not. Any cube's major diagonal can be calculated by multiplying one side's length by the square root of three.Cos-1(2/3) is the angle formed between a cube's diagonal and the diagonal of one of its faces.Body of the diagonal=24cm.
Assume the length of the side= a.
[tex]a^{2} +(a^{2} +a^{2} )=24^{2}[/tex]
[tex]a=\sqrt[8]{3} cm[/tex]
The area of the cylinder base=[tex]\pi R^{2}[/tex]
=[tex]\pi (\frac{1}{2} \sqrt[8]{3} )^{2}[/tex]
=[tex]48cm^{2}[/tex]
The high of the cylinder is[tex]\sqrt[8]{3}cm[/tex]
The volume of the cylinder:
=s*h
=[tex]48\pi *\sqrt[8]{3}[/tex]
=[tex]384\pi \sqrt{3} cm^{3}[/tex]
The volume of the cylinder is [tex]384\pi \sqrt{3cm }^{2}[/tex].
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The biggest possible volume of the cylinder will be [tex]2089.497\hspace{1mm}\text{cm}^3[/tex].
What will be the diameter and height of the cylinder obtained from a cube and what are the formulas for the diagonal of a cube and the volume of a cylinder?If a cylinder with the biggest possible volume is cut inside the cube, the height of the cylinder and the diameter of the cylinder will be equal to the side length of the cube.For example, consider the following figure in which the cylinder is cut inside of the cube and since the side length of the cube is [tex]x[/tex], the diameter and the height of the cylinder are also [tex]x[/tex]If the side length of a cube is [tex]x[/tex] unit, then its diagonal will be [tex]x\sqrt{3}[/tex] unit.The formula for the volume of a cylinder is [tex]V=\pi r^2h[/tex], where [tex]r[/tex] is the radius and [tex]h[/tex] is the height of the cylinder. If [tex]d[/tex] is the diameter, then [tex]r=\frac{d}{2}[/tex].Now, given that the diagonal of the cube is [tex]24[/tex] cm. So, if the side length of the cube is [tex]x[/tex] cm, then we must have
[tex]x\sqrt{3}=24\\\Longrightarrow x=\frac{24}{\sqrt{3}}\\\Longrightarrow x=8\sqrt{3}[/tex]
Thus, the side length of the cube is [tex]8\sqrt{3}[/tex] cm.
So, the height of the cylinder with maximum volume will be [tex]h=8\sqrt{3}[/tex] cm and the diameter will be [tex]d=8\sqrt{3}[/tex]cm i.e. the radius will be [tex]r=\frac{d}{2}=\frac{8\sqrt{3}}{2}=4\sqrt{3}[/tex] cm.
So, using the above formula for the volume of a cylinder, we get
[tex]V=\pi r^{2}h=\pi\times (4\sqrt{3})^2\times 8\sqrt{3}=2089.497\hspace{1mm}\text{cm}^3[/tex].
Therefore, the biggest possible volume of the cylinder will be [tex]2089.497\hspace{1mm}\text{cm}^3[/tex].
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For the first 150 miles of a trip, an car drives at v mph. For the next 200 miles, the car drives at (v
+25) mph. The average speed of the whole trip is 35 mph. Find the value of v.
(A) 20
(B) 25
(C) 30
(D) 35
If for the first 150 miles of a trip, an car drives at v mph, for the next 200 miles, the car drives at (v+25) mph and the average speed of the whole trip is 35 mph, then the value of v will be 20mph (A).
Given Information:
Average speed = 35 mph
Total distance = 150 + 200 = 350 miles
For the first 150 miles of a trip, an car drives at v mph speed
⇒ Time, t1 = 150/v hrs
For the next 200 miles, the car drives at (v+25) mph speed
⇒ Time, t1 = 200 / (v+25) hrs
Now, the formula for average speed is given as,
Total distance / Total time
= [tex]\frac{350}{\frac{150}{v}+\frac{200}{(v+25)} }[/tex]
⇒ [tex]\frac{350}{\frac{150}{v}+\frac{200}{(v+25)} }[/tex] = 35 mph
[tex]\frac{350 v (v+25)}{150(v+25) + 200v}[/tex] = 35
[tex]\frac{350v^{2} + 8750v}{150v +3750 + 200v}[/tex] = 35
350v² + 8750v = 35 (350v + 3750)
v² + 25v = 35v + 375
v² - 10v = 375
v² - 10v - 375 = 0
Now, the above equation for speed can be written as,
v² - 20v + 15v - 375 = 0
v(v-20) + 15(v-20) = 0
(v-20) (v+15) = 0
v = 20
or v = -15
Since, speed is a scalar quantity, it can't be negative. Thus, v = 20 mph
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Which of these expressions demonstrates the identity property? 25(0) = 25 25(1) = 25 25 + 0 = 25 25 + 1 = 25
The expressions which demonstrates the identity property of multiplication is; 25(1) = 25 option B
Identity Property
Identity Property of Multiplication states that any number multiplied by 1 does not change, that is, it is constant or remains the same
Check all options
25(0) = 25
0 = 25
Not true
25(1) = 25
25 = 25
True (identity property of multiplication holds)
25 + 0 = 25
25 = 25
True (Not identity property of multiplication)
25 + 1 = 25
26 = 25
Not true
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3. Bob has 8 pieces of square index cards that each measures 8 inches per side. Using a pair of scissors, he cuts each piece in half (so the resulting size is 8” x 4”) and then places all the resulting card pieces in a new stack. If he repeats this procedure 4 more times, how many pieces of card stock will he have and what will be the measure of each piece? (Note: All cuts will be made along the longer edge of the piece if the piece of index card is not square.)
The number of pieces of card stock which would result upon the process repetition is; 256 pieces.
What is the number of card stock pieces resulting from the cutting process?According to the task content, it follows that since, there are 8 pieces of the 8 inches per side cards initially, the resulting number of cards after carrying out the process of cutting cards into half five, 5 times is;
No of cards = 8 (2)⁵
No. of cards = 256 pieces.
The size of each of the cards in discuss provided that all cuts will be made along and not across the longer edge is; 8 by 1/4 inches.
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Use the ratio test to determine whether the series is convergent or divergent. 2 4/2^2 8/3^2 16/4^2 ......
I assume the given series is
[tex]\displaystyle 2 + \frac4{2^2} + \frac8{3^2} + \frac{16}{4^2} + \cdots = \frac{2^1}{1^2} + \frac{2^2}{2^2} + \frac{2^3}{3^2} + \frac{2^4}{4^2} + \cdots = \sum_{n=1}^\infty \frac{2^n}{n^2}[/tex]
By the ratio test, the series diverges, since
[tex]\displaystyle \lim_{n\to\infty} \left|\frac{2^{n+1}}{(n+1)^2} \cdot \frac{n^2}{2^n}\right| = 2 \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = 2 > 1[/tex]
Mike wants to find the confidence interval for a set of data. he knows the sample size and the sample proportion. which other piece of information does he need to determine the confidence interval?
Using the formula for a z-distribution confidence interval of proportions, he also needs to know the confidence level.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.Of these 3 itens, the problem states that he knows the sample size and the sample proportion, hence he needs to know z to determine the confidence interval. z depends on the confidence level, which is the remaining parameter.
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List the sides in order from the smallest to the largest.
L
K
27°
OA. LJ, KL, JK
OB. LJ, JK, KL
OC. KL, LJ, JK
D. JK, LJ, KL
Reset Selection
78°
75°
Answer:
A
Step-by-step explanation:
the side opposite of the angle is related to the size of this angle. Smaller angles have less space for the line to "spread out," so it will be shorter. Vice versa, bigger angles will have opposite sides longer because of more space.
Measure of angle TRV?
Answer:
130 degrees
Step-by-step explanation:
We know (x-10)+(2x+10) is 180 degrees.
So first we need to find x. (x-10)+(2x+10)=3x
3x=180
x=60
Angle TRV is 2x+10.
If we input 60 in the place of x, it is 2(60)+10=120+10=130.
The answer is 130 degrees.
PLEASE HELP IM STUCK PLS
Answer:
y is equal to -16
Answer:
y = 8
Step-by-step explanation:
We can use proportions for this question since y varies directly with x. This means that if x changes, y changes along with the x, and vice versa.
When y = -8, x = 4, so the proportion will be -8 : 4.
We need to find the y when x is 4, so our equation will be:
-8 : 4 = y : -4
Since the proportion will be the same.
Next, we multiply the inner two numbers, and the outer two numbers, saying that the values are the same.
4y = 32
y = 8
So y = 8 will be our answer!
Find the value of x
a. 13 b. 14/5 c. 5 d. 8
Using the chord theorem, option C is the best solution since x = 5.
The four line segments that are created by two intersecting chords inside of a circle are explained by the chord theorem, sometimes referred to as the intersecting chords theorem, a statement in fundamental geometry. The products of the line segment lengths on each chord are equal, according to this assertion.
The value of x must be determined in order to answer the question.
We may determine the following using the chord property:
8*x = 4*10,
or, 8x = 40,
or, x = 40/8,
or x = 5.
Given that x = 5, option C is the best option according to the chord theorem.
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When the dollar price of pounds rises, for example, from $1 = 1 pound to $2 = 1 pound, the dollar has ______ relative to the pound.
The dollar gains depreciated relative to the pound when the price of pounds in dollars increases, for instance, from $1 = 1 pound to $2 = 1 pound.
What is Depreciated relative?Devaluation of a currency can take place in both absolute and relative terms. When the value of one currency declines in relation to the values of other currencies, this is referred to as a relative devaluation. For instance, the British pound sterling may be worth more today than it did yesterday in terms of US dollars.
A currency's value declines when compared to other currencies, which is known as currency depreciation. Political unrest, interest rate differences, weak economic fundamentals, and investor risk aversion are a few examples of the causes of currency devaluation.
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To gain a pass a student needs to achieve a mean of at least 60% in eight tests. In the first seven
tests the student achieved a mean of 54%. What percentage must the student achieve in test eight
if they are to pass the course?
Step-by-step explanation:
the mean value is the sum of all data points divided by the number of data points.
first we have 7 tests and their mean value :
(t1 + t2 + t3 + t4 + t5 + t6 + t7) / 7 = 54
that means
(t1 + t2 + t3 + t4 + t5 + t6 + t7) = 54 × 7 = 378
in order for the mean value to be at least 60% after 8 tests, we need to add a t8, so that
(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) = 60 × 8 = 480
because only then we have
(t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8) / 8 = 60
and the student passes.
so,
(t1 + t2 + t3 + t4 + t5 + t6 + t7) + t8 = 480
378 + t8 = 480
t8 = 480 - 378 = 102%
the student would have to achieve 102% on the 8th test.
which would be normally impossible, but maybe the tests involve some bonus points.
how to solve problem in the document
The number of views on a viral video can be modeled by the function p(t)=590(5)^3t . Write an equivalent function of the form p(t)=ab^t
Answer:
p(t) = 2950^3t
Step-by-step explanation:
I’m not sure if this is exactly what you wanted or not. Please let me know more info and I’ll write any more answers for this question in the comments. Have a great day!!
When you send out a resume, the probability of being called for an interview is 0. 40. what is the probability that the first interview occurs on the fifth resume that you send out?
The probability that the first interview occurs on the fifth resume that you sent is 0.2592.
According to the given question.
The probability of being called for an interview, p = 0.40.
So, the probability of not being called for an interview, q = 1 - 0.40 = 0.60
As we know that binomial distribution summarizes the number of trials, or observations when each trial has the same probability of attaining one particular value. The binomial distribution determines the probability of observing a specified number of successful outcomes in a specified number of trials.
Therefore, the probability that the first interview occurs on the fifth resume that you send out
= [tex]^{5} C_{1} (0.40)^{1} (0.60)^{4}[/tex]
= 5(0.40)(0.1296)
= 0.2592
Hence, the probability that the first interview occurs on the fifth resume that you sent is 0.2592.
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3. Use the image to answer the following questions.
will brainiest if correct. try ur best!
(a) The angle pitch of a roof is safest when measuring between 18° – 27°. According to these guidelines, is the roof pictured in the image safe? (Note:
(b) What is length of the roof line (segment PR)? Round answer to the nearest tenth of a foot and show all your work.
Answer:
Answer:
Step-by-step explanation:
For missing hypotenuse: [tex]\sqrt({a^{2} + b^{2})[/tex]
Plug in the side lengths that are known to find the hypotenuse.
1. No, the angle is less than 18 degrees (closer to 15), so it is not safe
2. The length rounded to the nearest tenth is approximately 15.5 feet.
Which of the x values are solutions to the inequality 4(2 – x) > –2x – 3(4x 1)? check all that apply.
The solution for the inequality given exists x > -11/10. The inequality contains an infinite number of solutions as long as it is greater than -11/10.
How to determine the value of x?
Given: 4(2 – x) > –2x – 3(4x + 1)
The inequality can be simplified to
8 - 4x > -14x - 3
subtract 8 from both sides of the equation, and we get
8 - 4x - 8 > -14x - 3 - 8
- 4x > -14x - 11
Add 14x from both sides
- 4x + 14x > -14x - 11 + 14x
10x > - 11
x > - 11/10
The solution for the inequality given exists x > -11/10. This means that any number greater than -11/10 exists as a solution to the inequality given. The inequality contains an infinite number of solutions as long as it is greater than -11/10.
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Answer: C,E
Step-by-step explanation:
you did the work
(3x^{4} +3x^{3}+5x^{2})-(x^{4}-6x^{3}+5x^{2} )
Answer: x^{3}(2x+9)
Step-by-step explanation:
Eliminate redundant parentheses:
(3x^{4}+3x^{3}+5x^{2})-1(x^{4}-6x^{3}+5x^{2})
3x^{4}+3x^{3}+5x^{2}-1(x^{4}-6x^{3}+5x^{2})
Distribute:
^{4}+3x^{3}+5x^{2}{-1(x^{4}-6x^{3}+5x^{2})}
3x^{4}+3x^{3}+5x^{2}
Combine like terms UNTIL YOU FIND ONE FACTOR
A soccer team won only 10 of their first 30 games. How many of their remaining 20 games will they have to win to have a .500 record??
Answer: 5 games
Step-by-step explanation: A .500 record means that the soccer team won half of their games ( that's how I interpret it). Since they are going to play 30 games, they need to win half of 30 or 15 games to have that record. 15-10 = 5. So, they need to win 5 more games to have a .500 record.
greatest common factor of 24,36, and 96
Answer:
12
Step-by-step explanation:
[tex]24=2^{3} \times 3 \\ \\ 36=2^{2} \times 3^{2} \\ \\ 96=2^{5} \times 3[/tex]
Hey there!
What is GCF (Greatest Common Factor)?
Basically, the GCF is the biggest number in a data set that all of your numbers share.
What are the factors of the numbers?
24:1, 2, 3, 4, 6, 8, 12, and 24
36: 1, 2, 3, 4, 6, 9, 12, 18, and 36
96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96
What are the like terms that the numbers share?
1, 2, 3, 4, 6, 8, and 12
What is the biggest number out of the like terms?
12
What is your number?
12
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
If p(x,3) Q(7,1) and pQ(15) unit find the possible value of x
Answer:
Step-by-step explanation: P(x 3), Q(7, -1) and PQ= 5 .
To Find :
The possible value of x.
Solution :
We know, distance between two points in coordinate plane is given by :
Therefore, the possible value of x are 10 and 4.
Find the value of the indicated variable.
102 degrees
Step-by-step explanation:
Angles in a quadrilateral add to 360 degrees.
y = 360 - (120 + 85 + 53)
y = 360 - 258
y = 102 degrees
Ann and Tom want to establish a fund for their grandson's college education. What lump sum must they deposit at 12 % annual interest rate, compounded quarterly , in order to have 20,000$ in the fund at the end of 10 years?
The principal amount that must be deposited as a lump sum amount is = $16,666.7
Calculation of principal amountThe simple interest amount = $20,000
The interest rate = 12%
The time that is given= 10 years
Therefore the principle amount =?
Using the simple interest formula;
SI= P×T×R/100
Make P the subject of formula,
P = SI ×100/T×R
P= 20,000×100/10×12
P= 2,000,000/120
P= $16,666.7
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Help for a brianlest at show your work
Quick algebra 1 question for 25 points!
Only answer if you know the answer, Tysm!
Using a quadratic regression equation, it is found that the prediction of volunteers in year 10 is of:
A. 47.
How to find the equation of quadratic regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, we have that the function initially increases, then it decreases, which means that it is a quadratic function. The points (x,y) to be inserted into the calculator are given as follows:
(1, 20), (2,17), (3, 16), (4,16), (5,18), (6,21), (7,25), (8,31)
Inserting these points into the calculator, the prediction of y for a value of x is given as follows:
y = 0.702x^2 - 4.726x + 23.857
Hence, when x = 10, the prediction is:
y = 0.702 x 10² - 4.726 x 10 + 23.857
y = 47.
Hence option A is correct.
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Please gimme a hand I appreciate it in advance!!!
Answer:
30 degrees
Step-by-step explanation:
They are corresponding angles.
Answer: 30 degrees
Step-by-step explanation:
mangle8 and mangle 4 are corresponding angles meaning the angles are both the same.
Apyrotechnician plans for two fireworks to explode together at the same
height in the air. They travel at speeds shown below. Firework B is launched
0.25 s before Firework A. How many seconds after Firework B launches will
both fireworks explode?
Firework A Firework B
320 fts
240 fuis
Both fireworks will explode _?seconds after Firework B launches.
50 points!!!
Someone help pls, I can’t understand it and it’s due tomorrow :c
[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 1 :}}}}}}[/tex]
[tex]\star\:{\underline{\underline{\sf{\purple{Solution:}}}}}[/tex]
❍ Arrange the given data in order either in ascending order or descending order.
2, 3, 4, 7, 9, 11
❍ Number of terms in data [n] = 6 which is even.
As we know,
[tex]\star \: \sf Median_{(when \: n \: is \: even)} = {\underline{\boxed{\sf{\purple{ \dfrac{ { \bigg (\dfrac{n}{2} \bigg)}^{th}term +{ \bigg( \dfrac{n}{2} + 1 \bigg)}^{th} term } {2} }}}}}[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ { \bigg (\dfrac{6}{2} \bigg)}^{th}term +{ \bigg( \dfrac{6}{2} + 1 \bigg)}^{th} term } {2} }[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \dfrac{6 + 2}{2} \bigg)}^{th} term } {2} }[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \cancel{ \dfrac{8}{2}} \bigg)}^{th} term } {2} }[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ 4}^{th} term } {2} }[/tex]
• Putting,
3rd term as 4 and the 4th term as 7.
[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 4 + 7 } {2} }[/tex]
[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 11} {2} }[/tex]
[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: even)} = \purple{5.5}[/tex]
[tex]\\[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 2 :}}}}}}[/tex]
[tex]\star\:{\underline{\underline{\sf{\red{Solution:}}}}}[/tex]
❍ Arrange the given data in order either in ascending order or descending order.
1, 2, 3, 4, 5, 6, 7
❍ Number of terms in data [n] = 7 which is odd.
As we know,
[tex]\star \: \sf Median_{(when \: n \: is \: odd)} = {\underline{\boxed{\sf{\red{ { \bigg( \frac{n + 1}{2} \bigg)}^{th} term}}}}}[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: odd)} = {{ \bigg(\dfrac{ 7 + 1 } {2} \bigg) }}^{th} term[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: odd)} = { \bigg(\cancel{\dfrac{8}{2}} \bigg)}^{th} term[/tex]
[tex]\\[/tex]
[tex] \sf Median_{(when \: n \: is \: odd)} ={ 4}^{th} term[/tex]
• Putting,
4th term as 4.
[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: odd)} = \red{ 4}[/tex]
[tex]\\[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 3 :}}}}}}[/tex]
[tex]\star\:{\underline{\underline{\sf{\green{Solution:}}}}}[/tex]
The frequency distribution table for calculations of mean :
[tex]\begin{gathered}\begin{array}{|c|c|c|c|c|c|c|} \hline \rm x_{i} &\rm 3&\rm 1&\rm 7&\rm 4&\rm 6&\rm 2 \rm \\ \hline\rm f_{i} &\rm 4&\rm 6&\rm 2&\rm 2 & \rm 1&\rm 1 \\ \hline \rm f_{i}x_{i} &\rm 12&\rm 6&\rm 14&\rm 8&\rm 6&\rm \rm 2 \\ \hline \end{array} \\ \end{gathered} [/tex]
☆ Calculating the [tex]\sum f_{i}[/tex]
[tex] \implies 4 + 6 + 2 + 2 + 1 + 1[/tex]
[tex] \implies 16[/tex]
☆ Calculating the [tex]\sum f_{i}x_{i}[/tex]
[tex] \implies 12 + 6 + 14 + 8 + 6 + 2[/tex]
[tex]\implies 48[/tex]
As we know,
Mean by direct method :
[tex] \: \: \boxed{\green{{ { \overline{x} \: = \sf \dfrac{ \sum \: f_{i}x_{i}}{ \sum \: f_{i}}}}}}[/tex]
here,
• [tex]\sum f_{i}[/tex] = 16
• [tex]\sum f_{i}x_{i}[/tex] = 48
By putting the values we get,
[tex]\sf \longrightarrow \overline{x} \: = \: \dfrac{48}{16}[/tex]
[tex]\sf \longrightarrow \overline{x} \: = \green{3}[/tex]
[tex]{\large{\textsf{\textbf{\underline{\underline{Note\: :}}}}}}[/tex]
• Swipe to see the full answer.
[tex]\begin{gathered} {\underline{\rule{290pt}{3pt}}} \end{gathered}[/tex]
Please help me
Prove the following identity. Include a complete proof in proper form
1/1-sin x-1/1+sin x=2 tan x/COS X
By using algebra properties and trigonometric formulas we find that the trigonometric expression [tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex] is equivalent to the trigonometric expression [tex]\frac{2\cdot \tan x}{\cos x}[/tex].
How to prove a trigonometric equivalence by algebraic and trigonometric proceduresIn this question we have trigonometric expression whose equivalence to another expression has to be proved by using algebra properties and trigonometric formulas, including the fundamental trigonometric formula, that is, cos² x + sin² x = 1. Now we present in detail all steps to prove the equivalence:
[tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex] Given.
[tex]\frac{1 + \sin x - 1 + \sin x}{1 - \sin^{2}x}[/tex] Subtraction between fractions with different denominator / (- 1) · a = - a.
[tex]\frac{2\cdot \sin x}{\cos^{2}x}[/tex] Definitions of addition and subtraction / Fundamental trigonometric formula (cos² x + sin² x = 1)
[tex]\frac{2\cdot \tan x}{\cos x}[/tex] Definition of tangent / Result
By using algebra properties and trigonometric formulas we conclude that the trigonometric expression [tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex] is equal to the trigonometric expression [tex]\frac{2\cdot \tan x}{\cos x}[/tex]. Hence, the former expression is equivalent to the latter one.
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If 2 = x3, then x equals
A 05
B 01
C | 1
D 5
Answer:
D.
Step-by-step explanation:
