Mathematics High School

Verify the following identity:

[tex]\dfrac{1-\sin t}{\cos^2t}+\dfrac{1}{1-\sin t}=2\sec^2t[/tex]

Answers

Answer 1

We will simplify the left hand side of the equation to look like the right

[tex]\displaystyle \frac{1-sin(t)}{cos^{2}(t)} + \frac{1}{1 - sin(t)}[/tex]

taking the LCM

[tex]\displaystyle \frac{[1-sin(t)]^{2} + cos^{2}(t)}{[cos^{2}(t)][1 - sin(t)]}[/tex]

expanding the binomial in the numerator

[tex]\displaystyle \frac{[1 + sin^{2}(t) - 2sin(t) + cos^{2}(t)]}{[cos^{2}(t)][1 - sin(t)]}[/tex]

Since sin²x + cos²x = 1

[tex]\displaystyle \frac{[2 - 2sin(t)]}{[cos^{2}(t)][1 - sin(t)]}[/tex]

factoring out the 2 from the numerator

[tex]\displaystyle \frac{2[1 - sin(t)]}{[cos^{2}(t)][1 - sin(t)]}[/tex]

1-sin(t) will cancel out

[tex]\displaystyle \frac{2}{cos^{2}(t)}[/tex]

since cos²(t) = 1/(sec²(t))

[tex]2 sec^{2}(t)[/tex]

which is equal to the right hand side of our given equation.

So we verified the identity!

Answer 2

Answer:

[tex]\rm 2 \sec {}^{2} T[/tex](Verified identity)

Step-by-step explanation:

Please refer to the attachment for calculations.

I hope this helps!

Verify The Following Identity:[tex]\dfrac{1-\sin T}{\cos^2t}+\dfrac{1}{1-\sin T}=2\sec^2t[/tex]

Related Questions

Which point would be a solution to the system of linear inequalities shown below?

Y>2/3x-4
​
Y<−4x−6

Answers

2/3x-4 im not all the way sure


I need help completing this question.

Answers

Answer:

9.73556* 10^34

Step-by-step explanation:

A day and a half is 36 hours  ( 1 day is 24 hours)

1.5 days is 24 * 1.5 = 36 hours

P(t) = 300  ( 2) ^ 3t

t = 36

p(36) = 300 * 2^ (3*36)

         = 300  * 2^108

         =9.73556* 10^34

2. What is the equation of a line that has a slope of 3 and passes through the point(-1,4)?
y + 4 = 3(x - 1)
y - 1 = 3(x + 4)
y + 1 = 3(x – 4)
y – 4 = 3(x + 1)

Answers

Answer:

last one

Step-by-step explanation:

point slope form:

[tex](y - y1 )= m(x - x1)[/tex]

just plug in the numbers and you will get the answer:

[tex](y - 4) = 3(x + 1)[/tex]

If there are 18 boys and 54 gurls in a room,fill out a of the possible ratios of boys to girls that could be made

Answers

Answer:

2:6 and 1:3.

Step-by-step explanation:

18 divided by 9 = 2

54 divided by 9 = 6

18 divided by 18 = 1

54 divided by 18 = 3.

Hope that helps. x

Answer : 1:3, 2:6, 3:9, 4:12, 5:15, 6:18, 7:21, 8:24, 9:27, 10:30, etc . . .

Step - by - step explanation :

18:54 divided by 6/6 = 3:9

3:9 divided by 3/3 = 1:3 <-- simplest form :D

1
A line has a slope of -2 and a y-intercept of -2.

What is the x-intercept of the line?
A -4
B -1
C 1
D 4

Answers

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 2 and c = - 2 , then

y = - 2x - 2 ← is the equation of the line

To find the x- intercept let y = 0 in the equation and solve for x , that is

- 2x - 2 = 0 ( add 2 to both sides )

- 2x = 2 ( divide both sides by - 2 )

x = - 1

The x- intercept is - 1 → B

solve the inequality and graph its solution.

Answers

Answer:

D

Step-by-step explanation:

Hope this helped! :D

compare:
1. 4 3/8 (__) 4 7/10
2. 3/10 (__) 25/100
3. 5/8 (__) 3/5
4. 8/12 (__) 6/9
Help me please, and thx for the help

Answers

1. > 7/10 = 70% and is more than 3/8.
2.> 3/10 is equal to 30% which is more than 25%
3. > 5/8 is equal to 25/40 and 3/5 is equal to 24/40
4. = 8/12 is equal to 72/108 and 6/7 is equal to 72/ 108 too

1) 4 3/8 < 4 7/10

2) 3/10 > 25/100

3) 5/8 > 3/5

4) 8/12 = 6/9

hope this is helpful!

Help!!
So I think that someone is tracking my truck with an apple airtag but I don't know for sure. The only apple product I have is an iPad and I don't know how to check if an airtag is near by!!

Answers

Answer:

well....

Step-by-step explanation:

trow the apple

is y=3/4x proportional or non proportional

Answers

Yes, it’s proportional. it’s proportional because when you graph the equation it’s a straight line the goes through the origin! brainliest is always appreciated :)

Find the midpoint of the segment with the following endpoints. (10,6) and (4,9)​

Answers

Answer:

(7,7.5)

Step-by-step explanation:

midpoint formula:

(10+4)/2=7

(6+9)/2=7.5

(7,7.5)

Trevor paid a total of $1.08 in fines for an overdue library book. If the penalty for overdue books is $0.09 per day, how many days late was the book?
2 days
8 days
12 days
20 days

Answers

Answer:

12

Step-by-step explanation:

You have to divide the total by the number per day to solve this problem.

1.08/0.09=12

I really really really need help with this

Answers

Answer:

404

Step-by-step explanation:

PEMDAS48 ÷ 6 + (5×6) × 13 + 6 =            → Parenthesis48 ÷ 6 + 30 × 13 + 6 =                → Multiplication, division8 + 390 + 6 =                              → Addition404

[tex]\huge \bf༆ Answer ༄[/tex]

Use PEDMAS/BODMAS rule for simplification !

Let's solve ~

[tex] \sf{48} \div 6 + (5 \times 6) \times 13 + 6[/tex]

[tex] \sf48 \div 6 + 30 \times 13 + 6[/tex]

[tex] \sf8 + 30 \times 13 + 6[/tex]

[tex] \sf8 + 390 + 6[/tex]

[tex] \sf404[/tex]

The equation 5y = 6 represents purchasing tubs of yogurt for $6. Which of these equations are equivalent to the equation 5y=6?
a 5y + 4 = 10
b 5y - 1 = 3
c 15y = 18
d 5y = 12

Answers

Answer:

blah blah

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

this question


please help please

m=n+4b

Answers

Answer:

m=n+4b:- b=m-n/4.........

Math problem (easy)
……………………………………..

Answers

PEMDAS multiply first
(-3/8 x 1/2)
= -3/16
3/4 - 3/16 multiply numerator and denominator to simplify

12/16 - 3/16

9/16

Hope this helps!
Brainliest and a like is much appreciated!
The answer would be 9/16 :))))))

2. Graph each inequality on a number line:

5x + 15 < 0

Answers

Answer:

x < -3

Step-by-step explanation:

1. To put this inequality on a number line, we first must solve it.

Step 1: Subtract 15 from both sides.

[tex]5x + 15 - 15 < 0 - 15[/tex] [tex]5x < -15[/tex]  

Step 2: Divide both sides by 5.

[tex]\frac{5x}{5} <\frac{-15}{5}[/tex] [tex]x < -3[/tex]

2. Now that we know x < -3, let's graph it!

Since it's less than, we make the number line point to the left, and we make the circle open.

I need help to find the radius

Answers

Answer:

Step-by-step explanation:

i think 0.6

which ratio is equivalent to the ratio 7:6

Answers

Answer:

B. 21:18

Step-by-step explanation:

7/6 x 3 = 21/18

This means they are equivalent.

Answer:

Option B is correct.

Step-by-step explanation:

Let's first turn 7:6 into a fraction:

=> 7:6 = 7/6

Now, let's simplify all the options to see which one is the correct answer.

Option A:

=> 14:18=> 14/18=> 7/9=> 7/9 ≠ 7/6

Therefore, Option A is incorrect.

Option B:

=> 21:18=> 21/18=> 7/6=> 7/6 = 7/6

Therefore, Option B is correct.

Option C:

=> 21:12=> 21/12=> 7/4=> 7/4 ≠ 7/6

Therefore, Option C is incorrect.

Option D:

=> 18:14=> 18/14=> 9/7=> 9/7 ≠ 7/6

Therefore, Option D is incorrect.

We can conclude that Option B is correct.

[tex]BrainiacUser1357[/tex]

ben's grandma gave him $75 in a new piggy bank. Ben will add $15 to his piggy bank each month. find x, the number of months Ben must add $15 until he has more than $225 in his piggy bank.

Answers

10 Months is the answer or it’ll be X=10

Pls Help T^T ASAP FIRT TO ANSWER GETS BRAINLIEST

Answers

Answer:

The answer would be the third one shaded circle at -1 arrow goes left.

PLLSSS HELP MEEEE!!

Is it possible for Bruce and Felicia to have used the same number of tiles? Use complete sentences to explain your reasoning.

Number of tiles Bruce used: 5x + 2
Number of tiles Felicia used: 5x + 5

Answers

Answer:

No it is not possible for Bruce and Felicia to have used the same number of tiles.

Step-by-step explanation:

Bruce would have used 10x of tiles and Felicia used 7x of tiles.

No, it is not possible that Bruce and Felicia to have used the same number of tiles

The expression which shows the difference is (n² - 2)/2n, the correct option is B.

What is an Expression?

An expression is a mathematical statement which consists of variables, constants and mathematical operators.

Number of tiles Bruce used: 5x + 2

Number of tiles Felicia used: 5x + 5

On equating the two expressions

5x+2 = 5x+5

There is no solution

At any value of x, Bruce would have always used 3 tiles less than Felicia.

To know more about Expression

https://brainly.com/question/14083225

#SPJ2

Write a two- column proof.

Given: 3x = x + 12
Prove: x =5​

Answers

3x-x=12
2x=12
x=12/2
x=6

A recursive rule for an arithmetic sequence is a1 = −4; an = an−1 + 11

a. What is a1?

b. What is d?

c. What is the iterative rule for the arithmetic sequence above? You do NOT need to simplify.

d. Find a10

Answers

It’s a for sure I really think it’s A i don’t know

Solve for y. 4/7 y + 2/7 = 6

A) y = 20
B) y = -10
C) y = 10

Answers

Answer:

C) y = 10

Step-by-step explanation:

Subtract 2/7 from each side

4/7y = 40/7

Divide both sides by 4/7 (Multiply by 7/4)

y = 10

Answer:

C) y=10

Step-by-step explanation:

4/7y+2/7=6

7(4/7y+2/7)=7(6)

4y+2=42

4y=42-2

4y=40

y=40/4

y=10

Malcolm took 18 minutes to do 15 math problems. Diedra took 17 minutes to do 16 math problems. Which student did more problems per minute?

Answers

The student that did more maths problems per minute is Diedra.

In order to determine which student did more maths problems per minute, the rate of each student has to be determined. Rate is the total questions solved divided by the time.

Rate = total questions / total time

Malcolm = 15 / 18 = 0.833 problems per minute

Diedra = 16/ 17 = 0.941 problems per minute

To learn more about rate, please check: brainly.com/question/9834403

Use the diagonals to determine whether a parallelogram with vertices A(2, 7), B(7, 9), C(5, 4), and D(0, 2) is a rectangle, rhombus, or square. Give all the names that apply.

Answers

Step-by-step explanation:

A and B have among each other the same distance relation as D and C : +5 in x, and +2 in y direction

and D and A have among each other the same distance relation as C and B : +2 in x, and +5 in y direction.

that means the slope of the first pair of sides is 2/5, and the slope of the second pair of sides is 5/2.

and that means that these 2 pairs of lines are not perpendicular (for this not only would we need to have the ratio upside down but also the sign would need to be flipped). there are no 90° angles.

so, there is no rectangle or square.

but because the sums of x and y coordinate differences are the same, we have the same distances between neighboring points.

and that makes it a rhombus.

If 12 candy canes cost $318, what will be the cost of 4 candy canes?​

Answers

Answer:

4 candy canes = $ 106

Step-by-step explanation:

Using unitary method to solve this question.

Given that:

12 candy canes = $ 318

Divide both sides by 12

1 candy cane = $318/12

1 candy cane = $26.5

Now, Multiply both sides by 4

4 candy canes = $ 26.5 * 4

4 candy canes = $ 106

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807

what is 3/7-7/14 as a fraction

Answers

-1/14
hope this is helpful!

Answer:

-1/14or-0.07

Step-by-step explanation:

3/7-1/2=(2x3)/(2x7)-(7x1)/(7x2)=6/14-7/14=(6-7)/14=-1/14or0.07

12. Fancy goldfish x cost $3 each and
common goldfish y cost $1 each. Graph
the function y
20
3x to determine
how many
of each type of goldfish Tasha
can buy for $20.

Answers

Answer:

x (Fancy Gold fish) = 3

y (Common goldfish) = 29

Step-by-step explanation:

Fancy goldfish x cost $3 each

common goldfish y cost $1 each

Graph: y  = 20 +  3x (I'm hoping this is the correct line equation, please do leave a comment below if it's not)

Thus, we graph it by subtitude either the x or y values. (Or you can use just X = 1,2,3).

Now, to find how many of each type of goldfish Tasha can buy. We subtitude the line equation by either using x = 3 or y = 1

Using either values to solve the equation, we get:

x = 3

y = 29

Hope this helps!

1. 6(12+4)
2. 10+4(2+20)
3. 7(4+19)

Answers

Answer:

1. 6 x 16 = 96

2. 10 + 4 x 22 = 10 + 88 = 98

3. 7 x 23 = 161

Step-by-step explanation:

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