Working with the right side,
(1 + sin(θ))/(1 - sin(θ)) - (1 - sin(θ))/(1 + sin(θ))
multiply the first term by (1 + sin(θ))/(1 + sin(θ)) and the second one by (1 - sin(θ))/(1 - sin(θ)). This gives
(1 + sin(θ))/(1 - sin(θ)) • (1 + sin(θ))/(1 + sin(θ)) = (1 + sin(θ))^2 / (1 - sin^2(θ))
… = (1 + sin(θ))^2 / cos^2(θ)
and
(1 - sin(θ))/(1 + sin(θ)) • (1 - sin(θ))/(1 - sin(θ)) = (1 - sin(θ))^2 / (1 - sin^2(θ))
… = (1 - sin(θ))^2 / cos^2(θ)
Now combine the fractions, expand the numerator, and simplify:
(1 + sin(θ))^2 / cos^2(θ) - (1 - sin(θ))^2 / cos^2(θ) = ((1 + sin(θ))^2 - (1 - sin(θ))^2) / cos^2(θ)
… = ((1 + 2 sin(θ) + sin^2(θ)) - (1 - 2 sin(θ) + sin^2(θ))) / cos^2(θ)
… = 4 sin(θ) / cos^2(θ)
… = 4 • sin(θ)/cos(θ) • 1/cos(θ)
… = 4 tan(θ) sec(θ)
find lim h->0 f(9+h)-f(9)/h if f(x)=x^4 a. 23 b. -2916 c. 2916 d. 2925
[tex]\displaystyle\lim_{h\to0}\frac{f(9+h)-f(9)}h = \lim_{h\to0}\frac{(9+h)^4-9^4}h[/tex]
Carry out the binomial expansion in the numerator:
[tex](9+h)^4 = 9^4+4\times9^3h+6\times9^2h^2+4\times9h^3+h^4[/tex]
Then the 9⁴ terms cancel each other, so in the limit we have
[tex]\displaystyle \lim_{h\to0}\frac{4\times9^3h+6\times9^2h^2+4\times9h^3+h^4}h[/tex]
Since h is approaching 0, that means h ≠ 0, so we can cancel the common factor of h in both numerator and denominator:
[tex]\displaystyle \lim_{h\to0}(4\times9^3+6\times9^2h+4\times9h^2+h^3)[/tex]
Then when h converges to 0, each remaining term containing h goes to 0, leaving you with
[tex]\displaystyle\lim_{h\to0}\frac{f(9+h)-f(9)}h = 4\times9^3 = \boxed{2916}[/tex]
or choice C.
Alternatively, you can recognize the given limit as the derivative of f(x) at x = 9:
[tex]f'(x) = \displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h \implies f'(9) = \lim_{h\to0}\frac{f(9+h)-f(9)}h[/tex]
We have f(x) = x ⁴, so f '(x) = 4x ³, and evaluating this at x = 9 gives the same result, 2916.
What is the value of [ 3 × ( 8 − 2 ) ] + 5 ?
what's the standard equation of the circle with the general equation x2 + y2 + 4x - 2y - 20 = 0
Answer:
(x+2)2+(y-1)2=25
Step-by-step explanation:
x2+y2+4x-2y+4+1=20+4+1
The price of a ticket to attend a show is $28.50. In addition to the ticket price, Laurence had to pay a service fee of 10% and a sales tax
of 6%. The service fee and sales tax are each applied to the original price of the ticket
How much did Laurence pay in total?
Enter your answer in the box.
Answer:
HI!!
Step-by-step explanation:
Ryan has homework in six subjects. He is deciding what order to complete them in
Is 6.584 a rational number
What's your numerator and denominator value?
How many 5-digit numbers can be formed if each one uses all the digits 0,1,2,3,4
without repetition?
Answer:
{0, 1, 2, 3, 4} --> 96 5-digit numbers possible with this set.
Step-by-step explanation:
i dunno, i kinda just searched it up
link: https://gmatclub.com/forum/how-many-five-digit-numbers-can-be-formed-using-digits-91597.html#:~:text=If%200%20is%20included%3A,numbers%20possible%20with%20this%20set.
Answer:
120
Step-by-step explanation:
using the equation 5P5, you find that the total number of ways these 5 digits can be arranged to form 5 digit numbers if each is only used ONCE.
simplify 0.75 : 2 5/16
To start this is a ratio, and the goal is to get at least 1 to be a whole number so first lets get the number below 1 to 1.
0.75 : 2 5/16 ---> (x1.3333 on both sides) ---> 1 : 3 1/12.
Next, if needed for your answer, lets get the other number to be a whole number as well. We can do this my multiplying both sides by 12 since the fraction on 3 1/12 is 1/12.
1 : 3 1/12 --> (x12 on both sides) ---> 12 : 37
Your final answer will either be 1 : 3 1/12 or 12 : 37, depending on the formatting expected for your homework assignment.
HOW DO YOU SOLVE IT PLEASE 20/3 = 10/9 x
Answer:
!! , ' !!!
Step-by-step explanation:
ꜰɪʀꜱᴛ! ᴄᴏᴍʙɪɴᴇ ᴍᴜʟᴛɪᴘʟɪᴇᴅ ᴛᴇʀᴍꜱ ɪɴᴛᴏ ᴀ ꜱɪɴɢʟᴇ ꜰʀᴀᴄᴛɪᴏɴ:
/ = /
/ = / ᴊᴜꜱᴛ ʟɪᴋᴇ ᴛʜᴀᴛ!
ꜱᴇᴄᴏɴᴅ! ᴍᴜʟᴛɪᴘʟʏ ᴀʟʟ ᴛᴇʀᴍꜱ ʙʏ ᴛʜᴇ ꜱᴀᴍᴇ ᴠᴀʟᴜᴇ ᴛᴏ ᴇʟɪᴍɪɴᴀᴛᴇ ꜰʀᴀᴄᴛɪᴏɴ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀꜱ!! ᴇᴀꜱʏ ᴘᴇᴀꜱʏ:
/ = /
9⋅/= 9⋅/ ꜱᴇᴇ ᴇᴀꜱʏ ᴘᴇᴀꜱʏ!!
! :
9⋅/=!!!
ᴀʟᴍᴏꜱᴛ ᴅᴏɴᴇ!!
ꜰᴏᴜʀᴛʜʟʏ!! ᴍᴜʟᴛɪᴘʟʏ ᴛʜᴇ ɴᴜᴍʙᴇʀꜱ (ᴊᴜꜱᴛ ᴛʜᴀᴛ ꜱɪᴍᴘʟᴇ!):
9⋅/
˜”*°•.˜”*°• Which Would equal 60=10x!! •°*”˜.•°*”˜
ꜰɪꜰᴛʜ!! ᴅɪᴠɪᴅᴇ ʙᴏᴛʜ ꜱɪᴅᴇꜱ ᴏꜰ ᴛʜᴇ ᴇQᴜᴀᴛɪᴏɴ ʙʏ ᴛʜᴇ ꜱᴀᴍᴇ ᴛᴇʀᴍ:
60/10 = 10x/10
ʟᴀꜱᴛʟʏ!!! ꜱɪᴍᴘʟɪꜰʏʏ:
=6
ᴛʜᴇɴ ʏᴏᴜ ɢᴇᴛ ʏᴏᴜʀ ᴀɴꜱᴡᴇʀʀ!!
x=6 ʕ ˵• ₒ •˵ ʔ
ᴀɴʏᴡᴀʏꜱ ᴛᴏᴏᴅʟᴇꜱ!!
ʜᴀᴠᴇ ᴀɴ ᴀᴍᴀᴢɪɴɢ ɴɪɢʜᴛ ᴏʀ ᴅᴀʏ!
ꜰʀᴏᴍ ʏᴏᴜʀ ᴏɴᴇ ᴀɴᴅ ᴏɴʟʏ ᴘɪɴᴋʏ ʕ ﾟ ● ﾟʔ
A rectangular prism has a 192 cubic inches.
Answer:
6
Step-by-step explanation:
Volume of Rectangular Prism: (l)(w)(h)
8 x 4 x ? = 192
32 x ? = 192
/32 /32
height = 6
To check work:
(8)(4)(6) = 192
What is the probability of a coin landing on heads 3 times?
Answer:
50%
Step-by-step explanation:
Suppose you have a fair coin; this means it has a 50% chance of landing heads up. Suppose you dip it three times, these flips are independent. What is the probability that it lands heads up, then tails up and then heads up again. so the answer is 1/8 or 12.5%
(hope I wasnt late!!)
Researchers wish to examine the effectiveness of a new weight-loss pill. A total of 200 obese adults are randomly assigned to one of four conditions: weight-loss pill alone, weight-loss pill with a low-fat diet, placebo pill alone, or placebo pill with a low-fat diet. The weight loss after six months of treatment is recorded in pounds for each subject. To analyze this data, you would use __________.
a. a z-test
b. a t-test
c. an ANOVA F test
d. a Chi-square test
Answer:b
Step-by-step explanation:
To analyze this data, you would use An ANOVA F test.
What is a normal distribution?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range, while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center
The study involves comparing the weight loss of four groups of participants (weight-loss pill alone, weight-loss pill with a low-fat diet, placebo pill alone, or placebo pill with a low-fat diet) after six months of treatment. ANOVA (Analysis of Variance) is a statistical method used to analyze the differences among means of two or more groups.
In this case, ANOVA can be used to determine if there are significant differences in weight loss among the four treatment conditions.
A t-test or z-test would be appropriate if there were only two groups being compared.
A chi-square test is used to analyze categorical data, which is not applicable in this scenario where the data is continuous.
Therefore, an ANOVA F test would be used.
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Find the degree of the polynomial 7x⁴– 25x + 3x⁷
Answer:
The degree of the polynomial is equal to 7.
Step-by-step explanation:
The given polynomial is :
7x⁴– 25x + 3x⁷
We need to find the degree of the polynomial.
We know that,
Degree of the polynomial = The highest sum of exponents for anyone monomial.
In this case, the powers of x are 4,1 and 7.
Out of these three, the exponent of x is 7 which is highest.
Hence, the degree of the polynomial is equal to 7.
please help me!!!!!!! find the surface area of this figure ?
show your work.
Answer:
[tex] 93 \: {in}^{2} [/tex]
Step-by-step explanation:
Surface area of the figure
[tex] = \frac{1}{2} \times 6 \times 7 + 3 \times \frac{1}{2} \times 6 \times 8 \\ \\ = 3 \times 7 + 3 \times 3 \times 8 \\ \\ = 21 + 72 \\ \\ = 93 \: {in}^{2} [/tex]
Identify the constant of proportionality in the graph.
A) 60
B) 120
C) 180
D) 240
Answer:
A) 60
Step-by-step explanation:
Find two points that intersect with the grid.
(0,0) and (1, 60)
Subtract the second y value from the first y value. Do the same to the X-values.
Write this as a fraction with the y values over the x-values.
60-0= 60
-------------
1 - 0 = 1
60/1 = 60
What is the solution to the equation below round your answer to two decimal decimal places 5+6•log2 x=14
A. x=1.62
B. x=2.83
C. x=2.42
D. x=2.25
Answer:
x=2.83
Step-by-step explanation:
The solution to the equation, rounded to two decimal places, is x = 2.83.
The correct answer is option B: x = 2.83.
To solve the equation 5 + 6·log2(x) = 14 and round the answer to two decimal places, we can follow these steps:
1. Subtract 5 from both sides of the equation: 6·log2(x) = 9.
2. Divide both sides of the equation by 6: log2(x) = 9/6.
3. Simplify the right side: log2(x) = 1.5.
To find the value of x, we need to rewrite the equation in exponential form.
Remember that log2(x) = y is equivalent to [tex]2^y= x[/tex].
4. Rewrite the equation in exponential form: [tex]2^{1.5} = x[/tex].
5. Calculate the value of [tex]2^{1.5}[/tex] using a calculator or by approximating: x ≈ 2.83.
To learn more about the equation;
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Benny has two small fish tanks with one fish in each tank. One tank has 3 1/2 quarts of water. The other tank has 6 pints of water. Benny combines the water into one large fish tank with both fish in the large tank. How many pints of water are in the large tank?
Answer:
6 1/2 quarts I think
Step-by-step explanation:
So sorry if I'm wrong! Have a nice day! Owa Owa!
Find the GCD of 36,72 and 576
Answer:
36
Step-by-step explanation:
1×36
36×2
36×16
aaaaaaaaaaaaaaaaaaaaaa
I am doing this fr a meme so whoever responds is cool and I will mark brailiest
Answer:
Step-by-step explanation:
yesssss
Help look at picture no links!!!
Answer:
B
Step-by-step explanation:
Angle 1 is an exterior angle, while angle 6 is an interior angle and so they are not congruent
Which type of function is shown in the table below ?
X Y
0 1
1 4
2 16
3 64
Answer:
The answer is linear.
Step-by-step explanation:
The x int is being added by 1 while the y int is subtracting 1
Find the median of each set of data
Answer:
sorry, I think u got yr question incomplete.
stay safe healthy and happy.To find the median:
- Arrange the data points from smallest to largest.
- If the number of data points is odd, the median is the middle data point in the list.
- If the number of data points is even, the median is the average of the two middle data points in the list.
What is the volume (in cubic units) of a cylinder with a radius of 3 units and a height of 12 units?
1 point
Which exponential statement is equivalent to log I = 3?
A
10% = 3
B
103 = 1
С
310 = 1
D
34 = 10
A
B
оооо
С
D
Answer:
10³ = l
Step-by-step explanation:
Help me please I need help
Answer:
They have 11 inches of rope left.
Step-by-step explanation:
First we do the 6 foot rope minus the 4 foot cut. That leaves us with 2 feet, or 24 inches.
24-13 = 11
6)
Which polynomial is in standard form?
A)
3m3 + 2m? - m + 2
B)
8m3 + 6m2 + 2 - m
C)
-m” + 2m - m
– m2 + 1
D)
mº + 6m3 - 3m4 - 8
Answer:
D is the answer of this question
Find the indicated values. Geometry.
Answer:
1. x=16
2. x=35
3. x=10
4. x=30
5. x=3
Step-by-step explanation:
intercepted arcs are 2* the angle measure
1. x= 1/2( 32)=16 x=16
2. the intercepted arc is 360-110-180=70
1/2(70)= 35
3. 2x=x+10 subtract x from both sides
x=10
4. 2(x+30)=4x
2x+60=4x
60=2x
30=x
5. 2(3x)=12x-18
6x=12x-18
-6x=-18
x=m
Which rule defines Sn for a Subscript n Baseline = 5 (three-fourths) Superscript n? S Subscript n Baseline = 15 (three-fourths) Superscript n S Subscript n Baseline = 5 (three-fourths) Superscript n S Subscript n Baseline = 15 (1 minus (three-fourths) Superscript n) S Subscript n Baseline = 5 (1 minus (three-fourths) Superscript n)
ANSWER: C
Answer:
C
Step-by-step explanation:
Answering your question so it will not get removed.
The correct option for the question is C. [tex]S_{n}[/tex] = 15 [ 1 - [tex](3/4)^{n}[/tex] ]
What is a Geometric progression?If in a sequence of terms, each succeeding term is generated by multiplying each preceding term with a constant value, then the series is referred to as a geometric progression. (GP), while the constant value is called the common ratio.
Conclusion: The nth term from the end of the GP with the last term l and common ratio r = l/ [r(n – 1)]. The sum of infinite, i.e. the sum of a GP with infinite terms is S∞= a/(1 – r) such that 0 < r < 1.
[tex]a_{n}[/tex] = 5[tex](3/4)^{n}[/tex]
[tex]S_{n}[/tex]= Σ[tex]a_{n}[/tex]
[tex]S_{n}[/tex] = ∑5[tex](3/4)^{n}[/tex]
= 5∑[tex](3/4)^{n}[/tex]
= 5 [ 3/4 + [tex](3/4)^{2}[/tex] + ......+ [tex](3/4)^{n}[/tex]]
=5 [ 3/4 * { 1- [tex](3/4)^{n}[/tex]} / 1 - 3/4 ]
[tex]S_{n}[/tex] = 15 [ 1 - [tex](3/4)^{n}[/tex] ]
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Plz help me well mark brainliest if you are correct!!...
Answer:
2/B
Step-by-step explanation:
The base is 9 and the height is 4.
3. 8.F.1.3
Which of the following equations represents
a linear function?
A. y = 3x2
B. y = 2-
C. y = 4x+6
D. y = -x + 3