![[Pre-Calc] Please Help! I Dont Know Where To Start. How Do I Do This?](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/w97MEBN5ZpqXjT1Evg2IlafVKWWswJJW.png)
Answers
Answer:
See Below.
Step-by-step explanation:
Problem A)
We have:
[tex]\displaystyle \csc^2\theta \tan^2\theta -1=\tan^2\theta[/tex]
When in doubt, convert all reciprocal trig functions and tangent into terms of sine and cosine.
So, let cscθ = 1/sinθ and tanθ = sinθ/cosθ. Hence:
[tex]\displaystyle \left(\frac{1}{\sin^2\theta}\right)\left(\frac{\sin^2\theta}{\cos^2\theta}\right)-1=\tan^2\theta[/tex]
Cancel:
[tex]\displaystyle \frac{1}{\cos^2\theta}-1=\tan^2\theta[/tex]
Let 1/cosθ = secθ:
[tex]\sec^2\theta -1=\tan^2\theta[/tex]
From the Pythagorean Identity, we know that tan²θ + 1 = sec²θ. Hence, sec²θ - 1 = tan²θ:
[tex]\tan^2\theta =\tan^2\theta[/tex]
Problem B)
We have:
[tex]\sin^3x=\sin x-\sin x \cos^2 x[/tex]
Factor out a sine:
[tex]\sin x(\sin^2 x)=\sin x-\sin x\cos^2 x[/tex]
From the Pythagorean Identity, sin²θ + cos²θ = 1. Hence, sin²θ = 1 - cos²θ:
[tex]\sin x(1-\cos^2 x)=\sin x-\sin x\cos^2x[/tex]
Distribute:
[tex]\sin x- \sin x \cos^2 x=\sin x-\sin x\cos^2 x[/tex]
Problem C)
We have:
[tex]\displaystyle \frac{\cos 2x+1}{\sin 2x}=\cot x[/tex]
Recall that cos2θ = cos²θ - sin²θ and that sin2θ = 2sinθcosθ. Hence:
[tex]\displaystyle \frac{\cos^2 x-\sin^2 x+1}{2\sin x\cos x}=\cot x[/tex]
From the Pythagorean Identity, sin²θ + cos²θ = 1 so cos²θ = 1 - sin²θ:
[tex]\displaystyle \frac{2\cos^2 x}{2\sin x\cos x}=\cot x[/tex]
Cancel:
[tex]\displaystyle \frac{\cos x}{\sin x}=\cot x[/tex]
By definition:
[tex]\cot x = \cot x[/tex]
Related Questions
A jazz concert brought in $167,000 on the sale of 8,100 tickets. If the tickets sold for $15 and $25 each, how many of each type of ticket were sold?
Answers
Answer:
3,550 $15 tixkets and 4,550 $25 tickets were sold.
Step-by-step explanation:
15 × 3550=53250
25 × 4550=113750
53250+113750=167000
An object has a mass of 630 kg and a volume of 7 m cube.
Find the density of the object in kg/m cube.
Answers
Step-by-step explanation:
Hey there!
According to the question;
Mass of an object (m) = 630 kg
Volume of an object (v) = 7m³
We know that;
[tex]density = \frac{mass(kg) \: }{volume( {m}^{3} )} [/tex]
or, density = (630/7) kg/m³
Therefore, density of the substance is 90kg/m².
Hope it helps!
what is the missing angle
Answers
Answer:
the answer is 67 like the other angle because they are vertical from each other which make them the same
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
x = 67 degrees
Step-by-step explanation:
Use opposite angles! The angle opposite from x is 67, therefore x is also 67. Hope this helps! :)
Maya is riding on a bike course that is 35 miles long. So far, she has ridden 14 miles of the course. What percentage of the course has Maya ridden so far
Answers
Answer:
40%
Step-by-step explanation:
Find the percentage she has ridden so far by dividing 14 by 35:
14/35
= 0.4
So, Maya has ridden 40% of the course
Answer: 40%
Step-by-step explanation: i went to a percentage calculator and found out what it was
The financial analysis component of a business plan is to describe
a. how your business will be organized and what type of management or department structure
your business will have
b. the big picture? behind your business, what your business has to offer the consumer, and
why your business will be successful
C. the size of the market, how your business will fit into the market, and how your business will
stand out from other businesses in the market
d. where the funds to start and operate your business will come from, when you expect to see
profit, and how much profit you expect to see
Answers
Answer:
The correct answer is D. The financial analysis component of a business plan is to describe where the funds to start and operate your business will come from, when you expect to see profit, and how much profit you expect to see.
Step-by-step explanation:
Financial analysis is a type of economic analysis associated with the study of the financial results and financial condition of an organization. With the help of the analysis of the financial condition, it is possible to determine the strengths and weaknesses of the enterprise, the optimal management decision, forecasting individual indicators of the enterprise and financial activities in general, which, in turn, allows you to control the efficiency of the movement of financial flows, check the compliance with the norms and standards for the expenditure of financial and material resources and the feasibility of the costs incurred.
The purpose of the analysis of financial statements is an assessment of past activities according to the data of the report and the situation at the time of analysis, as well as an assessment of the future potential of the enterprise, that is, the forecast of the further development of the enterprise.
Malik, who is 5 feet tall, stands 15 feet from a mirror. In the mirror, he can see the reflection of the top of a tree, which he measures to be 92 feet away from the mirror. Determine the height of the tree pictured in the diagram above. Round your answer to the nearest foot if applicable. Use mathematics to explain how you determine your answer.
Answers
Find csc 0, tan 0, and cos 0, where 0 is the angle shown in the figure. Give exact values, not decimal approximations. (marking BRAINLEST)
Answers
Answer:
sqrt = square root of
Cosecant of 0 = (sqrt 41) / 5
Cos of 0 = 4/(sqrt41)
Tan of 0 = 5/4
Step-by-step explanation:
In this case, the opposite is 5, the adjacent is 4 and the hypotenuse is C in 5^2+4^2 = C^2 (pythagorean theorem)
5^2 = 25, 4^2 = 16
25+16 = 41
sqrt 41 is the hypotenuse
cosecant is hypotenuse/opposite
cos is adjacent/hypotenuse
and
tan is opposite/adjacent
A bag contains exactly 50 coins. The coins are either worth 10 cents, 20 cents or 50 cents and there is Atleast one of each. The total value of the coins is $10. How many different ways can this occur?
Answers
Answer:
This can happen in two ways:
1) 42 20-cent coins, 6 10-cent coins and 2 50-cent coins.
2) 30 10-cent coins, 10 20-cent coins and 10 50-cent coins.
Step-by-step explanation:
Given that a bag contains exactly 50 coins, and the coins are either worth 10 cents, 20 cents or 50 cents and there is at least one of each, and the total value of the coins is $ 10, to determine how many different ways can this occur, the following calculation must be performed:
48 x 0.5 + 1 x 0.2 + 1 x 0.1 = 24.30
48 x 0.1 + 1 x 0.2 + 1 x 0.5 = 5.5
48 x 0.2 + 1 x 0.1 + 1 x 0.5 = 10.3
45 x 0.2 + 4 x 0.1 + 1 x 0.5 = 9.9
44 x 0.2 + 5 x 0.1 + 1 x 0.5 = 9.8
42 x 0.2 + 6 x 0.1 + 2 x 0.5 = 10
30 x 0.1 + 10 x 0.2 + 10 x 0.5 = 10
Therefore, this can happen in two ways:
1) 42 20-cent coins, 6 10-cent coins and 2 50-cent coins.
2) 30 10-cent coins, 10 20-cent coins and 10 50-cent coins.
Derive the first three (non-zero) terms of Taylor's series expansion for the function
(a) f(x)=sin(x)f(x)=sin(x) about the origin and thereby estimate sin(0.2)=
Answers
Answer:
We want to find the first 3 terms of the Taylor's series expansion for f(x) = sin(x) around x = 0.
Remember that a Taylor's series expansion of a function f(x) around the point x₀ is given by:
[tex]f(x) = f(x_0) + \frac{1}{2!}f'(x_0)*(x - x_0) + \frac{1}{3!}*f''(x_0)*(x - x0)^2 + ...[/tex]
Where in the formula we have the first 3 terms of the expansion (but there are a lot more).
So, if:
f(x) = sin(x)
x₀ = 0
The terms are:
[tex]f(x_0) = sin(0) = 0[/tex]
[tex]\frac{1}{2!}*f(x_0)'*(x - x_0) = \frac{1}{2} cos(0)*(x - 0) = x/2[/tex]
[tex]\frac{1}{3!}*f(x_0)''*(x - x_0)^2 = \frac{1}{6}*-sin(0)*(x - 0)^2 = 0[/tex]
[tex]\frac{1}{4!}*f(x_0)'''*(x - x_0)^3 = \frac{1}{24}*-cos(0)*(x- 0)^3 = -\frac{x^3}{24}[/tex]
We already can see that the next term is zero (because when we derive the cos part, we will get a sin() that is zero when evaluated in x = 0), then the next non zero term is:
[tex]\frac{1}{6!}*f(x_0)''''*(x - x_0)^5 = \frac{1}{2*3*4*5*6} *(x - 0)^5 = \frac{x^5}{720}[/tex]
Then we can write:
[tex]sin(x) = \frac{x}{2} - \frac{x^3}{24} + \frac{x^5}{720}[/tex]
Evaluating this in x = 0.2, we get:
[tex]sin(0.2) = \frac{0.2}{2} - \frac{0.2^3}{24} + \frac{0.2^5}{720} = 0.099667[/tex]
Can someone help me out?
Which of the following set of side lengths could not be used to create a triangle? Provide your explanation.
a. 2 cm, 6 cm, 7 cm
b. 3 cm, 3 cm, 3 cm
c. 4 cm, 5 cm, 8 cm
D. 5 cm, 7 cm, 12 cm
Answers
9514 1404 393
Answer:
D. 5, 7, 12 cm
Step-by-step explanation:
In order for sides lengths to be able to form a triangle, the sum of the shortest two must exceed the longest. That is the case for all except D.
5 cm + 7 cm = 12 cm . . . . . is not greater than 12 cm
Joseph earns $10,000 a month working at a law firm. His monthly living expenses like food and gasoline amount to $3,500. He pays $2,700 for his mortgage. He also has $900 in credit card debt and pays $1,200 toward his auto loan each month. What is Joseph's debt-to-income ratio
Answers
To rent an instrument from the school it costs a $50 insurance fee and then $350 per day of use. If Sally rents her instrument for 25 days before she buys her own, how much did she have to pay to rent one?
Answers
Answer:
$2,500
Step-by-step explanation:
$350 per day for 25 days
350*25=2450
Add the 50 for insurance and that makes it 2500
If its wrong im sorry
Answer:
8800 is the amount before she buys her own instrument
Step-by-step explanation:
350 x 25 = 8750
8750 + 50 = 8800
Help? Plz and thank u
Answers
Answer:
147
Step-by-step explanation:
GIVING OUT BRAINLIEST ANSWER HELP ME OUT PLEASE
Answers
Answer:
x = 11.67
Step-by-step explanation:
3(x + 3) = 4(4 + 7)
3x + 9 = 44
3x = 35
x = 11.67
I’ll give brainliest
Answers
Answer:
Hello! answer: -12
Step-by-step explanation:
-36 ÷ 3 = -12
-72 ÷ 6 = -12
-108 ÷ 9 = -12
answer is -12
Answer:
-12
Step-by-step explanation:
To do this, you have to divide the x and y, to find the scale factor.
-36 ÷ 3 = -12
So the answer is -12.
Factor using sum and product:
Answers
Answer:
[tex]x^4 - 1 = (x- 1)(x + 1)(x^2 + 1)[/tex]
[tex]2x^2 - 4x - 240 = 2(x + 10) (x - 12)[/tex]
Step-by-step explanation:
Given
[tex]1.\ x^4 - 1[/tex]
[tex]2.\ 2x^2 - 4x - 240[/tex]
Required
Factor
[tex]1.\ x^4 - 1[/tex]
Express as difference of two squares
[tex]x^4 - 1 = (x^2 - 1)(x^2 + 1)[/tex]
Express [tex]x^2 - 1[/tex] as difference of two squares
[tex]x^4 - 1 = (x- 1)(x + 1)(x^2 + 1)[/tex]
[tex]2.\ 2x^2 - 4x - 240[/tex]
Expand
[tex]2x^2 - 4x - 240 = 2x^2 -24x + 20x - 240[/tex]
Factorize
[tex]2x^2 - 4x - 240 = 2x(x -12) + 20(x - 12)[/tex]
Factor out x - 12
[tex]2x^2 - 4x - 240 = (2x + 20) (x - 12)[/tex]
Factor out 2
[tex]2x^2 - 4x - 240 = 2(x + 10) (x - 12)[/tex]
x + 4 < 8 HELP please
Answers
Answer:
x + 4 < 8
- 4 -4
x < 4
Step-by-step explanation:
So, Basically anything less than 4 is a solution for this equation.
A quadrilateral is graphed in the coordinate plane below. Which classification best describes the quadrilateral (parallelogram, rhombus, etc.)?
Answer in complete sentences and include all relevant calculations to support your conclusion.
Answers
9514 1404 393
Answer:
trapezoid
Step-by-step explanation:
One pair of sides is parallel, so the figure is a trapezoid.
__
The upper right and lower left line segments both have slopes of -2/3. Since their slopes are the same, they are parallel. The slope is found by counting grid squares between points where the lines cross grid intersections. Those crossings occur down 2 and right 3 grid squares apart, so the slope is ...
m = rise/run = -2/3
Using the following image-solve the problems below given that M the midpoint of LN.
Answers
Hello,
[tex]11x-21=8x+15\\\\3x=36\\\\x=12\\\\LM=11*12-21=111\\\\MN=8*12+15=111\\\\LN=2*111=222\\\\[/tex]
Find the missing dimension of the prism
Answers
X = 2 cm
Volume = Bh= 8×5×1/2×X= 80
X = 80/20 = 4
Which Variable Is Most Important To The Following Problem?
A company has 95,000 shares of stock to sell.
A stockbroker decides to buy
equal shares of the stock for each of her 250 clients.
If the company has 75,000 shares of stock remaining after she makes her purchase,
how many shares did each client receive?
A. The price of one share
B. The number of shares remaining to be sold for the company
C. The number of shares bought for each customer
NO LINKS
Answers
Answer:
b
Step-by-step explanation:
this equation can be derived from the question :
95,000 - 250x = 75,000
where x is the equal amount of shares purchased for each client
given the amount of shares that remains after the shares has been purchased, we can determine the amount of shares bought by dividing the difference between 95,000 and 75,000 by 250
the price of each share was not made reference to in the question, thus it is not an important variable
y - 4x = -2
2y - 8x = -4
Answers
Answer:
Using substitution method
First make y in equation 1 the subject of formula
Y=4x-2
Sub in equation 2
2(4x-2)-8x=4
8x-4-8=4
8x=4+12
8x=16
X=2
Sub in any of equation to get y
Step-by-step explanation:
Y =4(2)-2=6
Answer:
(x, -2+4x)
Step-by-step explanation:
See The image below:)
1. 7/18 * 1 ⅐ + 2/3.
2. 3x + 1 ⅐ = 2
Answers
Answer:
Step-by-step explanation:
for first one's answer visit;
https://answers.everydaycalculation.com/subtract-fractions/2-3-minus-7-18
for sencond one;
3x=2+1
3x=3
x=1
for more info visit;
https://www.cymath.com/answer?q=3x-1%3D2
how many unique triangles can be formed with two side lengths of 10 centimeters and one 40 angel?
Answers
Answer:
2 unique types
Step-by-step explanation:
we can form 2 isosceles triangles
A recent study indicated that the average cost of living for a family of four in various cities across the US was $65,351 with a standard deviation of $7712. A company is thinking about relocating to a city with a lower cost of living. They would like to choose a city in the bottom 30% of those surveyed. What is the cutoff for the cost of living that would make a city eligible for relocation by this company
Answers
Answer:
The correct answer is "57408".
Step-by-step explanation:
Given:
[tex]\mu=65351[/tex]
[tex]\sigma=7712[/tex]
[tex]p=0.15[/tex]
As per the standard table, we know,
[tex]z=-1.03[/tex]
Now,
⇒ [tex]z=\frac{x-\mu}{\sigma}[/tex]
By putting the values, we get
[tex]-1.03=\frac{x-65351}{7712}[/tex]
[tex]x=57407.64[/tex]
or,
[tex]=57408[/tex]
Factor x^2 + 29x - 30. Type your answer in the space provided. Do not type spaces in your answer. Use only lowercase letters and include all necessary parentheses, variables and operation signs. For example, if the answer is (x +1)(x+2), type (x+1)(x+2).
Answers
Answer:
(x-1)(x+30)
..............
find the y intercept of the line on the graph
Answers
Answer:
Step-by-step explanation:
y-intercept is -4
Simplify the expression:
7–3p+4p
Answers
Answer:
7 + p
Step-by-step explanation:
Solve:
7 - 3p + 4p
Simplify using like terms
Wrote problem using addition
7 + ( -3p + 4p)
7 + 1p or 7 + p
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer and Step-by-step explanation:
The simplified expression is:
7 + p
because we subtract 3p from 4p.
#teamtrees #PAW (Plant And Water)
AYUDAAAAAAAA POR FAVORRRRR
Answers
so sorry not sure how to do this ! :c
Solve for x. Assume that lines which appear tangent are tangent. Help!!!
Answers
Answer:
x = 0
Step-by-step explanation:
From the intersecting secants theorem, If from an exterior point, we draw two secant segments to a circle, then the product of the length of one secant segment and its external secant part will be equal to the product of the length of the other secant segment and its external secant portion.
Thus, applying it to this question;
(x + 27 + 48) × (x + 27) = (x + 45)²
(x + 75)(x + 27) = x² + 90x + 2025
x² + 102x + 2025 = x² + 90x + 2025
Like terms will cancel put to give;
102x - 90x = 0
12x = 0
x = 0/12
x = 0