Answers
We are asked to solve the integral:
[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dx}{\cos^{2}(x)-\tan (x)\cos^{2}(x)}}[/tex]
Re write as
[tex]{:\implies \quad \displaystyle \sf \int \dfrac{dx}{\cos^{2}(x)\{1-\tan (x)\}}}[/tex]
Using (1/cos x) = sec(x), we have
[tex]{:\implies \quad \displaystyle \sf \int \dfrac{\sec^{2}(x)dx}{1-\tan (x)}}[/tex]
Now, substitute 1 - tan (x) = t, so that -dt = sec²(x) dx
[tex]{:\implies \quad \displaystyle \sf -\int \dfrac{1}{t}dt}[/tex]
[tex]{:\implies \quad \sf log|t|+C}[/tex]
[tex]{:\implies \quad \boxed{\displaystyle \bf \int \dfrac{dx}{\cos^{2}(x)-\tan (x)\cos^{2}(x)}=-log|1-\tan (x)|+C}}[/tex]
Where, C is any Arbitrary Constant
Related Questions
A 400 pound metal star is hanging on two cables which are attached to the ceiling. The left hand cable makes a 18° angle with the ceiling while the right hand cable makes a 72° angle with the ceiling. What is the tension on each of the cables? (Round your answers to three decimal places.)
Answers
Answer:
left: 123.607 lbright: 380.423 lbStep-by-step explanation:
By balancing horizontal and vertical forces, we find the cable tensions to be ...
Ta = W·sin(b)/sin(a+b) . . . . . where W is the weight being held
Tb = W·sin(a)/sin(a+b)
Where Ta is the tension in the cable that makes an angle of 'a' with respect to the vertical, and Tb is the tension in the cable that makes an angle of 'b' with respect to the vertical.
__
The given angles are with respect to the ceiling, so the angles with respect to the vertical will be their compmements.
left cable (a)angle 'a' is 90° -18° = 72°
angle 'b' is 90° -72° = 18°
a+b = 72° +18° = 90°
Ta = (400 lb)sin(18°)/sin(90°) = 123.607 lb
right cable (b)Tb = (400 lb)sin(72°)/sin(90°) = 380.423 lb
_____
Additional comment
The nice expressions for cable tension come from the balance of forces.
vertical: Ta·cos(a) +Tb·cos(b) = W
horizontal: Ta·sin(a) = Tb·sin(b)
Solving the horizontal equation for Ta, we get ...
Ta = Tb·sin(b)/sin(a)
Substituting into the vertical equaiton gives ...
Tb·sin(b)cos(a)/sin(a) +Tb·cos(b) = W
Multiplying by sin(a) gives ...
Tb(sin(b)cos(a) +sin(a)cos(b)) = W·sin(a)
Using the trig identity for the sine of the sum of angles, we can rewrite this in the form shown above:
Tb = W·sin(a)/sin(a+b)
The problem is symmetrical with respect to 'a' and 'b', so the other tension is found by interchanging 'a' and 'b' in the equation:
Ta = W·sin(b)/sin(a+b)
What is the value of the expression 2.5 (j.k) j when je 6 and K = 4? OA) 6 OB) 8 OC) 10 OD) 12
help ASAP
Answers
Answer:
C
Step-by-step explanation:
substitute the given values for j and k into the expression
[tex]\frac{2.5(6)(4)}{6}[/tex]
= [tex]\frac{2.5(24)}{6}[/tex]
= [tex]\frac{60}{6}[/tex]
= 10
can someone help me pls
Answers
Part A
Multiply each age with its corresponding frequency
19*2 = 3820*3 = 6021*1 = 2122*4 = 8823*1 = 23Then add up those products
38+60+21+88+23 = 230
We divide that sum over the total frequency of 11 (since 2+3+1+4+1 = 11).
mean = 230/11 = 20.9 approximately
Answer: 20.9Nice work on getting the correct answer.
============================================================
Part B
x = age of the new player
Adding x to the sum of the products 230, and then dividing over 11+1 = 12 will get us the new mean of 22.
The 230 represents the sum of the ages of the original eleven people. The expression 230+x represents the sum of the twelve ages.
So,
(230+x)/12 = 22
230+x = 12*22
230+x = 264
x = 264-230
x = 34
Answer: 34NESESITO LA RESPUETA URGENTEEEEEE
[tex]\frac{(6)}{(3)}[/tex]
Answers
Will give BRAINLIEST this is the full question please show work. Easy
Answers
Answer:
[tex]4x-y-11=0[/tex]
or
[tex]y = 4x -11[/tex]
Step-by-step explanation:
Equation of given line is: y = 4x - 7Comparing it with: y = mx + b, we find: slope (m) = 4Required line is parallel to the line y = 4x - 7SLopes of parallel lines are equal.-> slope of required line (m) = 4Required line passes through the point (3, 1) [tex]\implies x_1= 3,\: y_1= 1[/tex]Equation of line in point slope form is [tex] y-y_1= m(x-x_1)[/tex]Plugging the values of m, [tex]x_1,\: and\: y_1[/tex] in the above equation, we find:[tex] y-1= 4(x-3)[/tex]
[tex] y-1= 4x-12[/tex]
[tex] \implies -1+12= 4x-y[/tex]
[tex] \implies \red{\bold{ 4x-y-11=0}}[/tex]
or
[tex]\purple{\bold{y = 4x -11}}[/tex]
Answer:
[tex]y = 4x - 11[/tex]
Step-by-step explanation:
Parallel lines have the same slope.
[tex]1 = 4(3) + b[/tex]
[tex]1 = 12 + b[/tex]
[tex]b = - 11[/tex]
[tex]y = 4x - 11[/tex]
Jaylon has 20 math problems for homework. He has completed 60% of the
problems so far. How many problems has he completed?
Answers
Answer:
Jaylon has completed 12 problems.
Step-by-step explanation:
(This is how I learned it- I'm not sure if you have been taught this way..)
Step 1. Set up a proportion
[tex]\frac{60}{100} = \frac{x}{20}[/tex]
Step 2. Do 200x 60 to get 1200
Step 3. Get this equation
[tex]\frac{1200}{100} = x[/tex]
Step 4. Get the answer of 12
I hope this helps! :)
Answer:
Jaylon has completed 12 problems so far
Step-by-step explanation:
Step 1: Determine the amount of problems that were completed
(Total number of problems) * (Percent of completed problems)
(20) * (60% / 100%)
(20) * (0.6)
12
Answer: Jaylon has completed 12 problems so far
5 I think of a number x. If I subtract the number 7 from it, I get the same answer as if I double it and add 3. Find the value of x.
Answers
Answer:
x = -10
Step-by-step explanation:
the equation will be;
x - 7 = 2x + 3
- 7 - 3 = 2x - x
- 10 = 1x
x = -10
describe the following polynomial by degree and number of terms x^4-3x^2+2
Answers
Answer:
Option c
Step-by-step explanation:
Three terms and the degree is four
Hence Three terms,fourth Degree is your required answer
I hope it helped you
Tyler and Gabe went to the arcade and played the same two games. Tyler played 5 rounds of one game and two rounds of the other for $24. Gabe played 4 rounds of each game for $30. Write two equations for the amounts the two boys spent. Then find the cost for one round of each game.
Answers
Answer:
Tyler: 5x + 2y = 24
Gabe = 4x + 4y = 30
x = 3
y = 4.5
Step-by-step explanation:
4y = 30 - 4x
y = 7.5 - x
5x + 2(7.5 - x) = 24
3x + 15 = 24
x = 3
y = 7.5 - 3
y = 4.5
A town has a population of 14000 and grows at 5% every year. What will be the population after 14 years, to the nearest whole number?
Answers
Answer:
I got 27,719.
Step-by-step explanation:
I Did the long route and multiplied 14,000 by .05 and adding that and doing that to my answer 14 times. so 14,000-14,700-15,435-16,206.75,17,017 so on and on. Tbh I would know tho
solvr 5 3/4 = z- 6 3/8
Answers
Answer:
x=12 1/8
hope this helps
can i get brainliest
How many solutions does the equation y + 12 = y + 10 + 2 have?
Zero
One
Two
Infinitely many
Answers
Answer:
Infinitely many
Step-by-step explanation:
1. Subtract y from both sides:
y-y + 12 = y-y + 10 + 2
12 = 10 + 2
2. Simplify:
12 = 12
Because the left and right side are equal, then there are infinitely many solutions.
hope this helps!
beinggreat78, you're looking for this
Answers
Answer:
z = 6
9 followed by a lowercase number, whether it's x, y, or z usually always means add 1 or multiply by an unknown number. In this case, we are multiplying.
[tex]9 * 45 = 405(wrong)\\\\9 * 63 = 567(wrong)\\\\9 * 7 = 63(wrong)\\\\9 * 6 = 54(correct)[/tex]
That said, the answer is six.
Which expression is equivalent to 6x² - 7x-20 ?
Answers
Answer:
(3x+4)(2x−5)
Step-by-step explanation:
The first term is, 6x2 its coefficient is 6 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is -20
Step-1 : Multiply the coefficient of the first term by the constant 6 • -20 = -120
Step-2 : Find two factors of -120 whose sum equals the coefficient of the middle term, which is -7 .
-120 + 1 = -119
-60 + 2 = -58
-40 + 3 = -37
-30 + 4 = -26
-24 + 5 = -19
-20 + 6 = -14
-15 + 8 = -7 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 8
6x2 - 15x + 8x - 20
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (2x-5)
Add up the last 2 terms, pulling out common factors :
4 • (2x-5)
Step-5 : Add up the four terms of step 4 :
(3x+4) • (2x-5)
Which is the desired factorization
I need help with a question.
Some students are playing a game. they roll a number cube and spin the arrow on a spinner on each turn.
-The number cube has sides numbered 1 through 6.
-The spinner has 3 equal-sized sections colored red(r), yellow(y), and blue(b).
This tree diagram shows the sample space for the possible outcomes of rolling a number cube one time and then spinning the arrow on the spinner once.(I'll put the diagram on the bottom)
What is the probability that, on a student's turn, the number cube will land with an even number on the top face and the arrow on the spinner will stop on the blue(b) section?
A. 1/3
B. 3/6
C. 3/18
D. 9/16
Answers
Answer:
option c
Step-by-step explanation:
3/6probability of number cube lands on an even number
1/3 probability that it will land on the spinner
multiply 1/3 x 3/6 =3/18
let me know if i get it correct
The probability that on a student's turn, the number cube will land with an even number on the top face and the arrow on the spinner will stop on the blue(b) section is P = 3/18
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
The probability of the number cube landing with an even number on the top face is 3/6 or 1/2 since there are three even numbers (2, 4, and 6) out of the six possible outcomes (1, 2, 3, 4, 5, and 6)
The probability of the arrow on the spinner stopping on the blue section is 1/3 since there is only one blue section out of the three possible outcomes
To find the probability of both events occurring together, we multiply the probabilities of each event:
P(even number and blue section) = P(even number) × P(blue section)
P(even number and blue section) = 1/2 × 1/3
P(even number and blue section) = 1/6
P = 3/18
Therefore, the probability that, on a student's turn, the number cube will land with an even number on the top face and the arrow on the spinner will stop on the blue section is 1/6.
Hence , the probability is P = 3/18
To learn more about probability click :
https://brainly.com/question/17089724
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What would the quadratic equation be in standard form?
Answers
Answer:
ax^2 + bx + c = 0
Step-by-step explanation:
This is the standard form of the quadrartic equation. "a" is the leading coefficient and a non-zero real number.
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
x = 3√2
Step-by-step explanation:
This is a special triangle known as the 45-45-90 triangle. It has special rules that I will detail below:
a = xb = xc = x√2Since we known that x = 3 plug in this value to find b and c, or the hypotenuse:
a = x = 3
b = x = 3
c = x√2 = 3√2
BRAINLIEST please if this helped!
Solve x2 − 20 = 0. If necessary, round to the nearest hundredth.
±4.47
400
±40
There is no solution as you cannot take the square root of a negative number.
Answers
Answer:
Option A, [tex]x =[/tex] ± [tex]4.47[/tex]
Step-by-step explanation:
Step 1: Add 20 to both sides
[tex]x^2 - 20 = 0[/tex]
[tex]x^2 - 20 + 20 = 0 + 20[/tex]
[tex]x^2 = 20[/tex]
Step 2: Square root both sides
[tex]\sqrt{x^2} = \sqrt{20}[/tex]
[tex]x =[/tex] ± [tex]4.47[/tex]
Answer: Option A, [tex]x =[/tex] ± [tex]4.47[/tex]
Kyle needs 4 feet of ribbon for an art project. He has 20 inches of ribbon. How many
more inches does Kyle need for the project?
1 foot = 12 inches
Answers
Answer:
28 Inches more
Step-by-step explanation:
1 ft = 12 in
He needs 4ft
12x4=48
So he needs 48 inches
He has 20 inches
48-20=28
He needs 28 inches
What is the volume of this right prism?
96 in³
60 in³
48 in³
44 in³
Answers
Answer:
48
Step-by-step explanation:
find the value of each variable. 3x 2y 34
Answers
X= 30
Y=28
Step-by-step explanation:
It's a right-angle triangle. So, 3 x 30 will give you a 90 degree angle.
180-90=90
That means the next 2 angles should add to 90.
2x28=56
56+34=90
Hope this helps!
2. Which of the following is equivalent to (g+h)(p+q-r)?
Ogp+gq+gr + hp + hq + hr
Ogp+hq-hr
Ogp+hq-r
Ogp+gq-gr + hp +hq - hr
Answers
Answer:
[tex]\boxed{D)\;gp+gq-gr+hp+hq-hr}[/tex]
Step-by-step explanation:
[tex]\left(g+h\right)\left(p+q-r\right)[/tex]
[tex]gp+gq+g\left(-r\right)+hp+hq+h\left(-r\right)[/tex]
[tex]gp+gq-gr+hp+hq-hr[/tex]
Hope it helps!
Answer:
D. gp + gq - gr + hp + hq - hr
Step-by-step explanation:
I got it right on my test.
A local gym charges a flat monthly fee plus a fee for each day the gym is used. The total cost in dollars, y, to use the gym for x days can be found by the equation; y=6x+81. What is the daily cost of using the gym and why?
Answers
Answer:
The daily cost is $6 because that is being multiplied by the x which represents days. The 81 represents the flat fee.
Step-by-step explanation:
I hope this I better than the blurry photo I took '-'
Answers
Answer:The fourth option
decreases by 1 minute every 2 hours trained
Step-by-step explanation:
If y is how much it decreses its negative, and if the slope is -1/2 then they decrease by one for every 2 hours since the two represents x.
Select the correct answer.
Which value of x makes the equation true?
Answers
Answer:
letter po
3(-11)-6 -33-6 -39
---------- = ---------- = ---------- = 13
3 3 3
7(-11)-6 -77-6 -83
---------- = ---------- = ---------- = 13
3 3 6
What is the range of the relation below?
Answers
Answer:
a
Step-by-step explanation:
you can see on y in which range the line goes, I hope its correct
Answer:
Step-by-step explanation:
None of them its:
-3.2 ≤ y ≤ 4.
Mrs. Vanwhy made a two-way table to show which students made honor roll and which students study a foreign language. Which is the best two-way table for Mrs. Vanwhy to organize her data?
A 4-column table with 3 rows. Column 1 has entries honor roll, no foreign language, total. Column 2 is labeled foreign language. Column 3 is labeled not on honor roll. Column 4 is labeled total.
A 4-column table with 3 rows. Column 1 has entries honor roll, not on honor roll, total. Column 2 is labeled foreign language. Column 3 is labeled no foreign language. Column 4 is labeled total.
A 4-column table with 3 rows. Column 1 has entries honor roll, no foreign language, total. Column 2 is labeled not on honor roll. Column 3 is labeled no foreign language. Column 4 is labeled total.
A 4-column table with 3 rows. Column 1 has entries foreign language, honor roll, total. Column 2 is labeled no foreign language. Column 3 is labeled not on honor roll. Column 4 is labeled total.
Answers
The most appropriate chart for Mrs. Vanwhy is the one where the columns are foreign language and honor roll, no foreign language, honor roll, and total (option D).
How to identify the relevant table for Mrs. Vanwhy?To identify the most appropriate table for Mrs. Vanwhy we must identify what data she wants to include in the table.
Taking the above information into account, it can be inferred that the most appropriate table for Mrs. Vanwhy is option D because it includes all the data that she wants to tabulate.
Honor roll.Foreign language.Learn more about tables in: https://brainly.com/question/10670417
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Answer:
D.) The last table is the answer
Step-by-step explanation:
I finished the test.
The sum of the digits of a three digit number is 19. The second digit is one more than the first digit. The third
digit is two more than the second digit. Find the number.
A. 890
B. 124
C. 345
D. 568
Answers
Answer:
D. 568Step-by-step explanation:
Let the number is in the form of xyz
We haveSum of the digits is 19
x + y + z = 19The second digit is one more than the first digit
y = x + 1The third digit is two more than the second digit
z = y + 2 = x + 1 + 2 = x + 3Substitute the values of y and z into the first equation and solve for x
x + x + 1 + x + 3 = 193x + 4 = 193x = 15x = 5Find the value of y and z
y = 5 + 1 = 6z = 5 + 3 = 8The number is 568
Please help meeeee!!
Answers
1/9
[tex]\bold{EXPLANATIONS:}[/tex]
Figure ABCD is similar to figure WXYZ. Which proportion must be true for these figures?
Answers
Answer:
Polygon WXYZ is the same shape and size as polygon ABCD. Each side of WXYZ is double the length of ABCD. The ratio of the length of each side of WXYZ to its corresponding side of ABCD is 2. A characteristic of figures that have the same shape is that ratios of corresponding sides are equal.
Step-by-step explanation: