Given that
Sin θ = a/b
LHS = Sec θ + Tan θ
⇛(1/Cos θ) + (Sin θ/ Cos θ)
⇛(1+Sin θ)/Cos θ
We know that
Sin² A + Cos² A = 1
⇛Cos² A = 1-Sin² A
⇛Cos A =√(1-Sin² A)
LHS = (1+Sin θ)/√(1- Sin² θ)
⇛ LHS = {1+(a/b)}/√{1-(a/b)²}
= {(b+a)/b}/√(1-(a²/b²))
= {(b+a)/b}/√{(b²-a²)/b²}
= {(b+a)/b}/√{(b²-a²)/b}
= (b+a)/√(b²-a²)
= √{(b+a)(b+a)/(b²-a²)}
⇛ LHS = √{(b+a)(b+a)/(b+a)(b-a)}
Now, (x+y)(x-y) = x²-y²
Where ,
x = b and y = aOn cancelling (b+a) then
⇛LHS = √{(b+a)/(b-a)}
⇛RHS
⇛ LHS = RHS
Sec θ + Tan θ = √{(b+a)/(b-a)}
Hence, Proved.
Answer: If Sinθ=a/b then Secθ+Tanθ=√{(b+a)/(b-a)}.
also read similar questions:- i) sin^2 A sec^2 B + tan^2 B cos^2 A = sin^2A + tan²B..
https://brainly.com/question/12997785?referrer
Sec x -tan x sin x =1/secx Help me prove it..
https://brainly.com/question/20791199?referrer
About how many years ago did Jesus live
A.10,000
B. 5,000
C. 2,000
D. 1,000
Jesus was born in 4 BC (more or less) and live to be 33 years old, which means His death was around 29 AD (more or less). That was precisely, 1992 years ago
It costs $4.00 for 25 fl. oz. of detergent or $3.40 for 20 oz. Which is a better buy?
A dog runs 100 meters in 4 seconds. A lion runs 250 meters in 10 seconds.
What is the difference in their speeds?
Answer:
C their speeds are equal
Answer: C) Their speeds are equal
Step-by-step explanation:
Use the speed-distance equation
Dog - s=d/t = 100/4 = 25m/s
Lion - s=d/t = 250/4 = 25m/s
The sequence -1, 1, -1, 1 and so on is
Answer:
-1 is the next one ithink
Anyone know how to work this problem? I need to find the domain and range
Answer:
Step-by-step explanation:
Domain : [-9,-3]
Range: [2,6]
Answer:
um I think it's the range is 30
Please confirm my answer to be correct
Answer:
Actually, Corresponding angles are congruent.
Step-by-step explanation:
They are only supplementary in the special case where they are both 90°
Answer:
Option D
Step-by-step explanation:
Since we know that measure of corresponding angles are equal. So, corresponding angle are congruent to each other
What is 5,783 divided by 6 ?
2v-3(v+5) simplify answer
Answer:
-v-15
Step-by-step explanation:
This is the answer.
Have a good day.
Let me know if you need an explanation.
Marcus has hired 3 people to help him with his lawn business. He pays all the same, and he pays them every day. He paid $360 to his 3 workers today. How much did each worker get. In complete sentence
Hi!
If they each got the same, then they each got 1/3 of the total $360. Therefore, we can divide 360 by 3. We can do this by dividing 36 by 3, 36/3, and that's 12. Then add the 0! 120.
Your sentence could be: "The amount of money each worker got can be represented by 360/3, which is $120."
Hope this helps! :D
Answer: Since Marcus hired 3 people and paid them $360 altogether, it should be easy to figure this out through dividing. 360/3 or 360 divided by 3 = 120. You can put three into 360 one-hundred and twenty times. So, your answer would be that each worker got $120.
0.1/0.5=X/10 what is x
0.1/0.5 is the same as 1/5
1/5 = X/10
we times both sides by 10 to get x on its own
1/5 x 10 = 10/5 = 2 ( which equals X/10 x 10)
X/10 x 10 = X
2 = X
Compare the linear equation 2x-y=4 to the function graphed below.
Answer:
The answer is be the intercept
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Finding missing sides- similar triangles Algebraic practice )
Answer:
k=6
?=24
Step-by-step explanation:
[tex] \frac{ln}{xz} = \frac{nm}{zy} = \frac{lm}{xy} [/tex]
[tex] \frac{36}{k + 3} = \frac{44}{k + 5} [/tex]
Now we just cross multiply
44(k+3)=36(k+5)
44k+132=36k+180
Take k-values to one side
44k-36k=180-132
8k=48
k=6
Now we can use k to find ?
[tex] \frac{44}{6 + 5} = \frac{36}{6 + 3} = \frac{?}{6} [/tex]
once simplified we get:
[tex] \frac{44}{11} = \frac{36}{9} = \frac{?}{6} [/tex]
[tex]4 = 4 = \frac{?}{6} [/tex]
in essence we know that:
[tex] \frac{4}{1} = \frac{?}{6} [/tex]
so we can cross multiply:
?=24
A 2-gallon bottle of fabric softener costs $16.64. What is the price per cup?
Answer:
each cup would cost $0.52
Step-by-step explanation:
there are 16 cups in 1 gallon so you multiply that by two. Then you have 32 so you divide 16.64 by 32 and you end up with 0.52. hope this helped :))
Tell me I got this wrong
3x+4y+6z=15
Solve for x.
Answer:
[tex]x = 5 - \frac{4}{3} y - 2z [/tex]Step-by-step explanation:
Question:-To solve for xEquation:-3x + 4y + 6z = 15Solution:-=> 3x + 4y + 6z = 15
[On subtracting both sides with 4y]=> 3x + 4y + 6z - 4y = 15 - 4y
[On Simplification]=> 3x + 6z = 15 - 4y
[On subtracting both sides with 6z]=> 3x + 6z - 6z = 15 - 4y - 6z
[On Simplification]=> 3x = 15 - 4y - 6z
[On dividing both sides with 3][tex] = > \frac{3x}{3} = \frac{15 - 4y - 6z}{3} [/tex]
[On Simplification][tex] = > x = 5 - \frac{4}{3} y - 2z \: (ans)[/tex]
[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\huge\bold\orange{QUESTIONS:}[/tex]
3x+4y+6z=15 Solve for x.[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\huge\bold\orange{ANSWER:}[/tex]
[tex]x = 5 - \frac{4}{3} y - 2z[/tex]
[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\huge\bold\orange{SOLUTION:}[/tex]
[tex]3 \orange{+ 4y + 6z = 15}[/tex]
Move the variables to the right-hand side and change their signs.
[tex]3x = 15 \orange{ - 4 - 6z}[/tex]
Divide both sides of the equation by 3
[tex]\orange{3x = 15 - 4 - 6z}[/tex]
[tex]↓[/tex]
[tex]\orange{x = 5 - \frac{4}{3} y - 2z}[/tex]
The x-intercepts of 3x+4y+6z=15 is
[tex]x = 5 - \frac{4}{3} y - 2z[/tex]
[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
#CarryOnlearning
A bottle rocket takes off with a speed of 13 m/s and is angled 55 degrees above the horizon. What is the Y component of the velocity ?
Step-by-step explanation:
Let the speed of bottle rocket be u and angle with horizon be A.
Then,
u= 13m/s
A= 55°
Now,
we know that,
x- component,
X= 13 cosA
Y-component,
Y = 13 sinA
=13×0.81915
=10.649 m/s ANS
An undersea explorer descends from the surface at a rate of 36 feet per minute.
What is the position of the undersea explorer relative to the surface after descending for 4 minutes?
Enter your answer in the box.
Answer:
-144 feet from the surface in 4 minutes
Step-by-step explanation:
-36 x 4
With the same rate, the position of the undersea after 4 minutes will be -144.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
Rate of descends = 36 feet per minute
After 4 minutes,
36 x 4 = 144
Since it is descending so it can be said to be -144.
Hence "After 4 minutes at the same rate, the position of the undersea will be -144".
To learn more about the rate of change here,
brainly.com/question/12786410
#SPJ2
solve for x where xe(0,2pi). state exact answers.
b)
[tex] \frac{1}{ \sqrt{3} } \sin(2x) + \cos(x) = 0[/tex]
e)
[tex]3 \cos(x) + \tan(x) = 0[/tex]
Note: for question e, get this equation to a point ready for factoring or to use the quadratic formula, then stop. make sure its in standard form.
Answer:
that's the correct answer
Divide £121 in the ratio 2:9.
is this one of your answer choice?
help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast help fast
Answer:
4
Step-by-step explanation:
The number in from of sin is the frequency
Answer:
4
Step-by-step explanation:
Full explanation and answers on these 2 questions please. Also only answer if u know what ur doing.
Step-by-step explanation:
Q3
25 - (x-8)²/4 = [100 - (x-8)²]/4
[100 - (x²- 16x + 64)]/4
(100 - x² + 16x - 64)/4 = (-x² + 16x + 36)/4
(36 + 16x - x²)/4 = (36 - 2x + 18x - x²)/4
[2(18 - x) + x(18 - x)]/4 = [(2 + x)(18 - x)]/4
....proved
Q4
3(ax + 7) - 2(x + b) = 4x + 29
expanding,
3ax + 21 - 2x - 2b = 4x + 29
3ax - 2x + 21 - 2b = 4x + 29
Comparing terms; x terms,
3ax - 2x = 4x
3a - 2 = 4
3a = 6
a = 6/3
a = 2
constant terms,
21 - 2b = 29
21 - 29 = 2b
2b = -8
b = -8/2
b = -4
.... proved
how do you write this expression in word form?
Answer:
d-7 divided by 2 or over 2
MCQS:
Solve for X: X-3 = 27/64
A. 42
B. 43
C. 34
D. 14
Answer:
219/64
Step-by-step explanation:
x - 3 = 27/64
64(x - 3) = 27
64x - 192 = 27
64x = 27 + 192
64x = 219
x = 219/64
Answer:
[tex]x = 3.4218[/tex]
Step-by-step explanation:
[tex]x -3=\frac{27}{64}[/tex]
[tex]64(x-3)=27[/tex]
[tex]64x-192=27[/tex]
[tex]64x=27+192[/tex]
[tex]64x=219[/tex]
[tex]\frac{64x}{64} =\frac{219}{64}[/tex]
[tex]x = 3.4218[/tex]
Hope this helps you :-)
Let me know if you have any other questions :-)
A sequence begins with-3. Each term is calculated by multiplying the previous term by -4, then subtracting 1.
Which option correctly represents the sequence described?
A -3, 11, -45, 179, ...
B {-3, -13, -53, -213, ...}
C. {-3, 11, -45, 179, ...}
D -3, -13, -53, -213,...
Answer:
C
Step-by-step explanation:
[tex]a_{1}=-3\\a_{2}=(-3)(-4)-1=12-1=11\\a_{3}=11(-4)-1=-44-1=-45\\a_{4}=-45(-4)-1=180-1=179\\................................................\\[/tex]
Answer: Choice A) -3, 11, -45, 179, ...
=====================================================
Explanation:
1st term = -3
new term = -4*(previous term) - 1
2nd term = -4*(1st term) - 1
2nd term = -4*(-3) - 1
2nd term = 12 - 1
2nd term = 11
The answer is between choice A and C since both involve "-3, 11" as the first two terms in that order. The only difference between A and C are the outer surrounding curly braces. These braces tell the reader that we have a set of numbers.
When it comes to a set, the order does not matter. Something like {1,2,3} is identical to {3,2,1}. Because of this, we rule out choice C.
On the other hand, order does matter in a sequence. The sequence 1,2,3 is different from 3,2,1.
how to fix my calculator please help meee i cuold not fix it plsss what to do
so, you must have some kind of device for you to make a question on brainly. if you are using your phone, there is probably an already installed calculater app on there. if you don't have one, go to app store or play store and download it. if you are using computer, simply search it. of course, you can also use your phone and just search it on the web.
Answer:
by a new one?????
Step-by-step explanation:
4x+6<-6 how to solve
Answer:
The answer is below.
Step-by-step explanation:
4x<-6-6
4x<-12
x= -3
Inequality form:
x< -3
Interval Notion:
(-8,-3)
Note: Turn the -8 on the sideways on the right, because its not 8.
Answer: x < -3
Step-by-step explanation: 4x+6=-6
-6 -6
4x/4 -12/4
x<-3
Multiply and write in standard form:
(2x + 1)(5x - 2)
Show all work for full credit.
Answer:
10x^2+x-2
Step-by-step explanation:
(2x+1)(5x-2)
10x^2+5x-4x-2
10x^2+x-2
pls help anyone know dis
Answer:
1st one:5≥x>-infinity
2nd one :5<x<+infinity
3rd one :5>x>- infinity
what is the answer to this question?
posted a picture for better understanding:)
Answer:
5
Step-by-step explanation:
Usually, the sequence is [tex]a_{1}, a_{2}, a_{3}, a_{4}, ..., a_{n}[/tex] where n is a postive number.
From the question,
[tex]a_{n} = a_{n-1} - 5[/tex]
if n = 2 ;
[tex]a_{2} = a_{1} - 5[/tex]
[tex]a_{2} = 20 - 5 = 15\\[/tex]
Thus, we got [tex]a_{2} = 20[/tex].
if n = 3 ;
[tex]a_{3} = a_{2} - 5[/tex]
[tex]a_{3} = 15 - 5 = 10[/tex]
Thus, we got [tex]a_{3} = 10[/tex].
if n = 4 ;
[tex]a_{4} = a_{3} - 5[/tex]
[tex]a_{4} = 10 - 5 = 5[/tex]
Thus, we got [tex]a_{4} = 5[/tex].
***There are many ways to solve this question
example:
[tex]a_{n} = a_{n-1} - 5[/tex]
[tex]a_{n} - a_{n-1} = - 5[/tex]
Substitute n with 2, 3, 4
Then, we will get 3 equations.
Sum them up;
We will get
[tex]a_{4}-a_{3}+a_{3}-a_{2}+a_{2}-a_{1} = -15\\a_{4}-a_{1} = -15\\a_{4} = -15+20 = 5[/tex]
It costs a man 75 dollars to buy the things that he needs to make hot dogs. The city allows him to sell his hot dog somewhere near the city hall. However, the city hall charges him 1 dollar for each hot dog sold
Calculate how many hotdogs he will have to sell in order to make a profit if the price he charges for 1 hot dog is $1.50.
Factor w2 + 3w+w + 3 by grouping,
Answer:
(w+3)(w+1)
Step-by-step explanation:
In w^2 + 3w+w + 3,
we group it so that it looks like (w^2+w) + (3w+3)
Then we factor so that is w(w+1) + 3(w+1).
Distributive property(converse) allows us to simplify to (w+3)(w+1)