Answers
Step-by-step explanation:
[tex]\bf L.H.S = \tt \dfrac{sec\: \theta + tan \: \theta - 1}{tan \: \theta - sec \: \theta + 1} \\ \\ [/tex]
[tex]: \implies \tt \dfrac{\frac{1}{cos \: \theta} + \frac{sin \: \theta}{cos \: \theta} - 1}{ \frac{sin \: \theta}{cos \: \theta} - \frac{1}{cos \: \theta} + 1 } \: = \dfrac{1 + sin \: \theta - cos \: \theta}{sin \: \theta + cos \: \theta} \\ \\ [/tex]
[tex]: \implies \tt\dfrac{ sin \: \theta - (cos \: \theta - 1)}{sin \: \theta + (cos \: \theta - 1)} \: \times \: \dfrac{ sin \: \theta - (cos \: \theta - 1)}{sin \: \theta - (cos \: \theta - 1)} \\ \\ [/tex]
[tex]: \implies \tt\dfrac{ sin^{2} \: \theta + cos^{2} \: \theta + 1 - 2 \: cos \: \theta - 2 \: sin \: \theta \: (cos \: \theta - 1)}{sin^{2} \: \theta - (cos \: \theta - 1)^{2} } \\ \\ [/tex]
[tex]: \implies \tt\dfrac{1 + 1 - 2 \: cos \: \theta - 2 \: sin \: \theta \: cos \: \theta + 2 \: sin \: \theta}{sin^{2} \: \theta + cos^{2} \: \theta - 1 + 2 \: cos \: \theta } \\ \\ [/tex]
[tex]: \implies \tt\dfrac{2 - 2 \: cos \: \theta - 2 \: sin \: \theta \: cos \: \theta + 2 \: sin \: \theta}{sin^{2} \: \theta + cos^{2} \: \theta - sin^{2} \: \theta - cos^{2} \: \theta + 2 \: cos \: \theta } \\ \\ [/tex]
[tex]: \implies \tt\dfrac{2 (1 - \: cos \: \theta )- 2 \: sin \: \theta (1 - \: cos \: \theta)}{ 2 \: cos \: \theta - 2 \: cos^{2} \: \theta} \\ \\[/tex]
[tex]: \implies \tt\dfrac{(2 + 2 \: sin \: \theta) \: \cancel{(1 - cos\: \theta)}}{2 \: cos \: \theta \: \cancel{(1 - cos \: \theta)}} \: = \: \dfrac{1 + sin \: \theta}{cos \: \theta} \\ \\[/tex]
[tex]: \implies\tt\dfrac{1 + sin \: \theta}{cos \: \theta} \: \times \: \dfrac{1 - sin \: \theta}{1 - sin \: \theta} \\ \\ [/tex]
[tex]: \implies\tt\dfrac{1 + sin^{2} \: \theta}{cos \: (1 - sin \: \theta)} \\ \\ [/tex]
[tex]: \implies\tt\dfrac{cos^{2} \: \theta}{cos \: \theta (1 - sin \: \theta)} \\ \\ [/tex]
[tex]: \implies\tt\dfrac{cos \: \theta}{1 - sin \: \theta} \: = \: \bf{ R.H.S}\\ \\ [/tex]
[tex]\huge\bigstar \:\underline{\red{\sf Hence, Proved}} \: \bigstar \\ [/tex]
Related Questions
Find a general term a, for the sequence whose first four terms are given.
6, 14, 22, 30,...
Answers
Answer:
an = 6 +8(n -1)
Step-by-step explanation:
Usually, you're asked for a general term when you're studying arithmetic and/or geometric sequences. One way to tell which kind of sequence you have is to look at the differences between adjacent terms. If they are all the same, the sequence is arithmetic, and the general term is ...
an = a1 +d(n -1)
where a1 is the first term, and d is the common difference.
Here, the differences are ...
14 -6 = 8
22 -14 = 8
30 -22 = 8
These are all the same, hence a "common" difference. The first term is 6, so the general term is ...
an = 6 +8(n -1)
20% of the gummy bears in a bag are blue. There are 12 blue gummy bears in the bag. Shade the grid to show the percent of gummy bears that are blue. How many gummy bears are in the bag?
Answers
Answer:
60 gummy bears in total
Step-by-step explanation:
20% of the gummy bears are blue.
12 gummy bears are blue
That means 6 gummy bears is 10% of the total.
6*10=60
100%=60 gummy bears.
Asher please $156 every six weeks for piano lessons what is the price per year for piano lessons
Answers
So you would multiply 52x156
Which equals 8112
Asher pays $8112 per year for piano lessons
I need help with this solving equations X + 9 = -16
Answers
Answer:
Step-by-step explanation:
x + 9 = -16
Subtract 9 form both sides
x + 9 - 9 = - 16 - 9
x = -25
Answer:
X= -25
Step-by-step explanation:
Subtract 9 from both sides.
The current value of a baseball card is 50 times its original value v (in dollars). The baseball card is worth $62. Write and solve an equation to find the original value of the baseball card
Answers
Answer:
50v
Step-by-step explanation:
The equation would be 50v, because $62 is the original value, or v, and we are trying to find the value of the card now. Which is now 50 times the original price, $62.
if bill payed 73.80 for 32 4/5 gallons of gas, how much did he pay per gallon
Answers
Answer:
$2.25
Step-by-step explanation:
73.80/32.8
A box can hold 9 books. There are only 5 books in the box. What percentage of the box is full? 56% 80% 1.8% 44%
Answers
Answer:
I do believe that the answer would be 56%
Step-by-step explanation:
Using estimation if the box is half full it would have 4.5 books in the box, if you add that extra book it would be around 56%
Round the following whole number to the nearest thousand.
9474
Answers
Answer:
9,000
Step-by-step explanation:
9474
Locate the thousands place:
9474
Check the number to the right:
9474
If the number is greater than or equal to 5, we round up. If the number is less than or equal to 4, we round down.
Since there is a '4', we round down.
9474 ≈ 9000
Hope this helps.
which segment is longer, please explain
Answers
Answer:
Blue, if you look, they both are close, but due to the pathagrium theory blue is longer.
Step-by-step explanation:
Answer:
Red is longer
Step-by-step explanation:
With the distance equation formula, you can find this. The distance equation formula is d=[tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2} } \\[/tex]. (x1,y1)(x2,y2) are the coordinates of each individual point.
If you turn the grid into a graph, red's points would be (0,0)(3,3)
Blue's points would be (0,3)(-1,-1). Using the distance formula blue is [tex]\sqrt{17}[/tex].
The red is [tex]\sqrt{18}[/tex], so red is longer.
a profit of 9$ integer
Answers
Answer:
+ or - $9
Step-by-step explanation:
answerrrrrrrrrrrrrrr pleaswe correctly.
Answers
Hey There!!
The answer to this is: A.
the line will cross the y intercept at 6 therefor the only option that has 6 is the first one the slope will be 1/2
Hope It Helped!~
Good Luck With Your Assignment!~
[tex]UsedLess[/tex]~
(^///^)
can you please simplify -2x-8x
Answers
Answer:
- 10x
Step-by-step explanation:
Step 1:
-2x - 8x
Answer:
- 10x
Hope This Helps :)
derive f=ma solve 9.1
Answers
Answer:
I hope it helped you and you understood it.
Answer:
we know that,
Force is directly proportional to rate of change of momentum.
→ F [tex]\propto[/tex] (Pv - pu)/t
→ F = k p (v - u)/t
→ F = k p a
Here, body must have some mass.
→ F = ma
Derived.
An airplane can fly at a rate of 600 miles per hour. How fast does an airplane travel per minute? Remember, there are 60 minutes in an hour.
Answers
Answer:
10 miles per hour I'm not sure tho just trying to help :)
Step-by-step explanation:
try to divide
Answer:
10
Step-by-step explanation:
600mph= 10miles/min
Solve for X X - 24 = 73 Question 6 options: 49 97 47 95
Answers
Answer:
x = 97
Step-by-step explanation:
X - 24 = 73
Add 24 to each side
X - 24+24 = 73+24
x = 97
[tex]\text{Hello! :D}[/tex]
[tex]\large\boxed{x = 97}[/tex]
[tex]\text{x - 24 = 73}[/tex]
[tex]\text{Solve for x by adding 24 to both sides:}[/tex]
[tex]x- 24 + 24 = 73 + 24\\\\x = 97[/tex]
how do i solve this? 12x÷100+35000minus 14x ÷100
Answers
Answer:
-2x/100 + 35
Step-by-step explanation:
Step 1:
12x ÷ 100 + 35,000 - 14x ÷ 100
Step 2:
- 2x ÷ 100 + 35,000 ÷ 100
Step 3:
- 2x ÷ 100 + 35
Answer:
- 2x/100 + 35
Hope This Helps :)
The price of an item has been reduced by 55%. The original price was $53. what is the price now
Answers
Answer:
$29.15
Step-by-step explanation:
Step 1:
$53 × 55%
Step 2:
53 × 0.53
Answer:
29.15
Hope This Helps :)
Show your work. Find the length of SU. (~Brainiliest will be awarded):)
Answers
Answer:
SU= 14
Step-by-step explanation:
if QU= 24 and RU= 19 then you can subtract 24-19=5. and if QR=RS=ST then you subtract 19-5=14
A baker needs 2 pounds of flour and 3 sticks of butter to
make 64 cupcakes. At these rates, how many pounds of
flour and how many sticks of butter would the baker
need to make 352 cupcakes?
Answers
Answer:
11 pounds of flour and 16.5 sticks of butter
Step-by-step explanation:
2/64 = 0.03125
3/64 = 0.046875
0.03125 * 352 = 11
0.046875 * 352 = 16.5
Answer:
15 1/2 sticks of butter, and 11 pounds of flower, hoped this helped.
Step-by-step explanation:
PLEASE HELP I W WILL MARK YOU BRAINLIEST
Answers
Answer:
200 students
Step-by-step explanation:
Since there are 7 buses and 6 of them are full you would multiply 30•6. Then you would multiply 2/3 with 30 to find how many are on the 7th bus, which is 20. So you would add 180 and 20 to get the answer
What is the answer to this question?
Answers
Answer:
(-6,300)
Step-by-step explanation:
Answer:
(-6,300)
Step-by-step explanation:
(x,y)
then:
x = -6
y = 300
then:
(-6 , 300)
2a + 2b = c for b
Solve for b
Answers
2a + 2b = c
Subtract 2a from both sides
2b = -2a + c
Divide both sides by 2
b = -a + (c/2)
Ken’s prediction for December was –5°C. The actual low temperature was 3 degrees higher than his prediction. The actual low temperature in December was
Answers
Answer:
-2°C
Step-by-step explanation:
Add 3 to -5:
-5 + 3
= -2
So, the actual low temperature in December was -2°C
Answer:
-2
Step-by-step explanation:
i took the assignment
The price of a tv is rs3000.if the discount is rs1560,find the percent of discount.
Answers
Answer:
price of tv = 3000
discount =1560
discount % = 1560/3000 * 100% = 52%
Step-by-step explanation:
Answer:
52
Step-by-step explanation:
Formula =discount ×100÷original price
1560×100÷3000=52%
Help? =/
I'm not sure what's it's about.
Answers
Answer:
the answer is the 2nd one
Step-by-step explanation:
Write 0.2 repeating as a fraction in simplest form.
Answers
Answer:
[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
We require to create 2 fractions with the repeating 2 after the decimal point.
let x = 0.22.... → (1) ← multiply both sides by 10
10x = 2.22....... → (2)
Subtract (1) from (2) thus eliminating the repeating decimal
9x = 2 ( divide both sides by 9 )
x = [tex]\frac{2}{9}[/tex]
Thus
0.22..... = [tex]\frac{2}{9}[/tex]
Answer:
2/9
Step-by-step explanation:
We require to create 2 fractions with the repeating 2 after the decimal point.
let x = 0.22.... → (1) ← multiply both sides by 10
10x = 2.22....... → (2)
Subtract (1) from (2) thus eliminating the repeating decimal
9x = 2 ( divide both sides by 9 )
x =
Thus
0.22..... =
Emily is thinking of a number, which she calls n. She finds 1/4 of the number and subtracts 3. Write an expression that represents Emily’s number.
Answers
Answer:
1/4n - 3
Step-by-step explanation:
1/4 of a number means multiplying 1/4 to n. So we can write 1/4n. Now we write the subtract 3 portion. 1/4n - 3.
The expression n = 1/4n - 3 shows that Emily's number can be obtained by adding 3 to one-fourth of her number.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
Emily's number can be represented as:
n
One-fourth of Emily's number can be represented as:
1/4n
Subtracting 3 from one-fourth of Emily's number gives us:
1/4n - 3
Therefore, the expression that represents Emily's number is:
n = 1/4n - 3
This expression shows that Emily's number can be obtained by adding 3 to one-fourth of her number.
Learn more about the algebraic expression here :
brainly.com/question/21751419
#SPJ7
A diesel train traveled to Las Vegas and back. The trip there took ten hours and the trip back took 14 hours. It averaged 60 mph on the return trip. Find the average speed of the trip there.
Answers
A golf ball is hit with a club from the ground on a flat surface. The height of the ball, h(t), in feet, t seconds after it was hit can be modeled by the function h(t)=40t-16t^2.
Move the number to the blanks to describe the path of the ball.
When the ball is hit at 0 seconds, it has a height of _____ feet. The ball's height increases until it reaches its maximum height of _____ feet after ____ seconds. The ball's height then decreases until it reaches the ground _____ seconds after it was hit.
Fill in the blanks with these numbers: 0, 0.4, 1.25, 2, 2.5, 4, 16, 25, 40
Answers
Answer:
The correct numbers are;
1) 0
2) 25
3) 1.25
4) 2.5
When the ball is hit at 0 seconds, it has a height of 0 feet. The ball's height increases until it reaches its maximum height of 25 feet after 1.25 seconds. The ball's height then decreases until it reaches the ground 2.5 seconds after it was hit
Step-by-step explanation:
The given equation for the height of the ball, h(t), in feet, is given as follows
h(t) = 40·t - 16·t²
Therefore;
1) When the ball is hit at 0 seconds, it has a height of h(0) = 40×0 - 16×0² = 0 feet
2) The time to reach maximum height by the ball is found by taking the derivative (slope) of the function for the height of the ball and noting that at maximum height, the derivative (slope) = 0
Therefore;
h'(t) = 40 - 2 × 16·t = 0
40 - 32·t = 0
t = 40/32 = 5/4 seconds = 1.25 seconds
3) The maximum height is then found from the value of the function at t = 5/4 seconds as follows;
h(5/4) = 40×5/4 - 16×(5/4)² = 50 - 25 = 25 feet
4) The time in which the ball reaches the ground where h(t) = 0 is given from the formula for the height of the gulf ball as follows;
h(t) = 0 = 40·t - 16·t²
40·t - 16·t² = 0
(40 - 16·t)·t = 0
Therefore;
t = 0 seconds or t = 40/16 = 2.5 seconds
(40 - 16·t) = 0/t = 0
t = 40/16 = 2.5 seconds
Therefore, the filling the blanks with the correct numbers gives;
When the ball is hit at 0 seconds, it has a height of 0 feet. The ball's height increases until it reaches its maximum height of 25 feet after 1.25 seconds. The ball's height then decreases until it reaches the ground 2.5 seconds after it was hit
need help on question 4??
Answers
HK consists of two part, HJ and JK
HK = HJ + JK
We know that:
HK = 12.2ft
JK = 3.1ft
HJ = ?
Let's plug our values into the equation above.
12.2ft = HJ + 3.1ft
Subtract 3.1ft from both sides.
9.1ft = HJ