Answer:
[tex]A.\ \tan(x) \to 2.\ \sin(x) \sec(x)[/tex]
[tex]B.\ \cos(x) \to 5. \sec(x) - \sec(x)\sin^2(x)[/tex]
[tex]C.\ \sec(x)csc(x) \to 3. \tan(x) + \cot(x)[/tex]
[tex]D. \frac{1 - (cos(x))^2}{cos(x)} \to 1. \sin(x) \tan(x)[/tex]
[tex]E.\ 2\sec(x) \to\ 4.\ \frac{\cos(x)}{1 - \sin(x)} +\frac{1-\sin(x)}{\cos(x)}[/tex]
Step-by-step explanation:
Given
[tex]A.\ \tan(x)[/tex]
[tex]B.\ \cos(x)[/tex]
[tex]C.\ \sec(x)csc(x)[/tex]
[tex]D.\ \frac{1 - (cos(x))^2}{cos(x)}[/tex]
[tex]E.\ 2\sec(x)[/tex]
Required
Match the above with the appropriate identity from
[tex]1.\ \sin(x) \tan(x)[/tex]
[tex]2.\ \sin(x) \sec(x)[/tex]
[tex]3.\ \tan(x) + \cot(x)[/tex]
[tex]4.\ \frac{cos(x)}{1 - sin(x)} + \frac{1 - \sin(x)}{cos(x)}[/tex]
[tex]5.\ \sec(x) - \sec(x)(\sin(x))^2[/tex]
Solving (A):
[tex]A.\ \tan(x)[/tex]
In trigonometry,
[tex]\frac{sin(x)}{\cos(x)} = \tan(x)[/tex]
So, we have:
[tex]\tan(x) = \frac{\sin(x)}{\cos(x)}[/tex]
Split
[tex]\tan(x) = \sin(x) * \frac{1}{\cos(x)}[/tex]
In trigonometry
[tex]\frac{1}{\cos(x)} =sec(x)[/tex]
So, we have:
[tex]\tan(x) = \sin(x) * \sec(x)[/tex]
[tex]\tan(x) = \sin(x) \sec(x)[/tex] --- proved
Solving (b):
[tex]B.\ \cos(x)[/tex]
Multiply by [tex]\frac{\cos(x)}{\cos(x)}[/tex] --- an equivalent of 1
So, we have:
[tex]\cos(x) = \cos(x) * \frac{\cos(x)}{\cos(x)}[/tex]
[tex]\cos(x) = \frac{\cos^2(x)}{\cos(x)}[/tex]
In trigonometry:
[tex]\cos^2(x) = 1 - \sin^2(x)[/tex]
So, we have:
[tex]\cos(x) = \frac{1 - \sin^2(x)}{\cos(x)}[/tex]
Split
[tex]\cos(x) = \frac{1}{\cos(x)} - \frac{\sin^2(x)}{\cos(x)}[/tex]
Rewrite as:
[tex]\cos(x) = \frac{1}{\cos(x)} - \frac{1}{\cos(x)}*\sin^2(x)[/tex]
Express [tex]\frac{1}{\cos(x)}\ as\ \sec(x)[/tex]
[tex]\cos(x) = \sec(x) - \sec(x) * \sin^2(x)[/tex]
[tex]\cos(x) = \sec(x) - \sec(x)\sin^2(x)[/tex] --- proved
Solving (C):
[tex]C.\ \sec(x)csc(x)[/tex]
In trigonometry
[tex]\sec(x)= \frac{1}{\cos(x)}[/tex]
and
[tex]\csc(x)= \frac{1}{\sin(x)}[/tex]
So, we have:
[tex]\sec(x)csc(x) = \frac{1}{\cos(x)}*\frac{1}{\sin(x)}[/tex]
Multiply by [tex]\frac{\cos(x)}{\cos(x)}[/tex] --- an equivalent of 1
[tex]\sec(x)csc(x) = \frac{1}{\cos(x)}*\frac{1}{\sin(x)} * \frac{\cos(x)}{\cos(x)}[/tex]
[tex]\sec(x)csc(x) = \frac{1}{\cos^2(x)}*\frac{\cos(x)}{\sin(x)}[/tex]
Express [tex]\frac{1}{\cos^2(x)}\ as\ \sec^2(x)[/tex] and [tex]\frac{\cos(x)}{\sin(x)}\ as\ \frac{1}{\tan(x)}[/tex]
[tex]\sec(x)csc(x) = \sec^2(x)*\frac{1}{\tan(x)}[/tex]
[tex]\sec(x)csc(x) = \frac{\sec^2(x)}{\tan(x)}[/tex]
In trigonometry:
[tex]tan^2(x) + 1 =\sec^2(x)[/tex]
So, we have:
[tex]\sec(x)csc(x) = \frac{\tan^2(x) + 1}{\tan(x)}[/tex]
Split
[tex]\sec(x)csc(x) = \frac{\tan^2(x)}{\tan(x)} + \frac{1}{\tan(x)}[/tex]
Simplify
[tex]\sec(x)csc(x) = \tan(x) + \cot(x)[/tex] proved
Solving (D)
[tex]D.\ \frac{1 - (cos(x))^2}{cos(x)}[/tex]
Open bracket
[tex]\frac{1 - (cos(x))^2}{cos(x)} = \frac{1 - cos^2(x)}{cos(x)}[/tex]
[tex]1 - \cos^2(x) = \sin^2(x)[/tex]
So, we have:
[tex]\frac{1 - (cos(x))^2}{cos(x)} = \frac{sin^2(x)}{cos(x)}[/tex]
Split
[tex]\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) * \frac{sin(x)}{cos(x)}[/tex]
[tex]\frac{sin(x)}{\cos(x)} = \tan(x)[/tex]
So, we have:
[tex]\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) * \tan(x)[/tex]
[tex]\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) \tan(x)[/tex] --- proved
Solving (E):
[tex]E.\ 2\sec(x)[/tex]
In trigonometry
[tex]\sec(x)= \frac{1}{\cos(x)}[/tex]
So, we have:
[tex]2\sec(x) = 2 * \frac{1}{\cos(x)}[/tex]
[tex]2\sec(x) = \frac{2}{\cos(x)}[/tex]
Multiply by [tex]\frac{1 - \sin(x)}{1 - \sin(x)}[/tex] --- an equivalent of 1
[tex]2\sec(x) = \frac{2}{\cos(x)} * \frac{1 - \sin(x)}{1 - \sin(x)}[/tex]
[tex]2\sec(x) = \frac{2(1 - \sin(x))}{(1 - \sin(x))\cos(x)}[/tex]
Open bracket
[tex]2\sec(x) = \frac{2 - 2\sin(x)}{(1 - \sin(x))\cos(x)}[/tex]
Express 2 as 1 + 1
[tex]2\sec(x) = \frac{1+1 - 2\sin(x)}{(1 - \sin(x))\cos(x)}[/tex]
Express 1 as [tex]\sin^2(x) + \cos^2(x)[/tex]
[tex]2\sec(x) = \frac{\sin^2(x) + \cos^2(x)+1 - 2\sin(x)}{(1 - \sin(x))\cos(x)}[/tex]
Rewrite as:
[tex]2\sec(x) = \frac{\cos^2(x)+1 - 2\sin(x)+\sin^2(x)}{(1 - \sin(x))\cos(x)}[/tex]
Expand
[tex]2\sec(x) = \frac{\cos^2(x)+1 - \sin(x)- \sin(x)+\sin^2(x)}{(1 - \sin(x))\cos(x)}[/tex]
Factorize
[tex]2\sec(x) = \frac{\cos^2(x)+1(1 - \sin(x))- \sin(x)(1-\sin(x))}{(1 - \sin(x))\cos(x)}[/tex]
Factor out 1 - sin(x)
[tex]2\sec(x) = \frac{\cos^2(x)+(1- \sin(x))(1-\sin(x))}{(1 - \sin(x))\cos(x)}[/tex]
Express as squares
[tex]2\sec(x) = \frac{\cos^2(x)+(1-\sin(x))^2}{(1 - \sin(x))\cos(x)}[/tex]
Split
[tex]2\sec(x) = \frac{\cos^2(x)}{(1 - \sin(x))\cos(x)} +\frac{(1-\sin(x))^2}{(1 - \sin(x))\cos(x)}[/tex]
Cancel out like factors
[tex]2\sec(x) = \frac{\cos(x)}{1 - \sin(x)} +\frac{1-\sin(x)}{\cos(x)}[/tex] --- proved
An economics professor is interested in seeing if the mean hours worked by ISU students in a week at part time or full time jobs (including work study) is greater than 10. To accomplish this, the professor randomly selected 50 students from the university. It was found that the distribution was right skewed and unimodal. The sample mean was 11 hours with a sample standard deviation of 3. The professor then did a hypothesis test. Please find the test statistic for this hypothesis test Group of answer choices
Answer:
2.3574
Step-by-step explanation:
This question requires us to find the t test statistic given the data in the question.
H0: u = 10
H1: u > 10
Population variance is not known
T = (barX - u)/(s/√n)
u = 10 hours
BarX = 11 hours
Sd = 3 hours
n = 50
(11-10)/(3/√50)
t test = 1/(3/√50)
= 1/0.4242
Test statistic = 2.3574
please help i’ll give brainliest
Answer: D
Step-by-step explanation:
Substitute values for x until they all work.
A. y = 2 x 2 + 5 = 9 fail
B. y = 2 x 2 - 6 = -2 fail
C. y = -2 x 2 - 5 = -9 fail
D. y = -0.5 x 2 - 5 = -6 ok
y = -0.5 x 5 - 5 = -7.5 ok
y = -0.5 x 6 - 5 = -8 ok
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer: option b), option c), and option e) are correct options.
Step-by-step explanation:
Given:
The area of a rectangular room= 750 square feet
The width of the room = 5 feet less than the length of the room
The length of the room = Y
To find:
Equations that can be used to solve the value of Y i.e. the length of the rectangular room.
Solution:
The equation can be derived from using the following formula:
Area of rectangle = length * width
According to the question,
Length of the rectangular room = Y
Width of the rectangular room = 5 feet less than the length of the room
= (Y-5)
Since, Area of rectangle = length * width
Area of the rectangular field = length of the room* width of the room
750 = Y (Y – 5) ………..eqn. (1)
Or, the above equation can be solved a step further and written as
750 = Y2 – 5Y ………..eqn. (2)
750- Y2 + 5Y= 0 ………..eqn. (3)
750-Y (Y- 5) =0 ………..eqn. (4)
Apart from the above equations, if we solve eqn. (2) we get the following equation:
750 = Y2 – 5Y
Y2 – 5Y- 750= 0
Y2 – 30Y + 25Y- 750 = 0
Y (Y- 30) + 25 (Y- 30) = 0
take Y- 30 common from L.H.S.
(Y -30) (Y+ 25) = 0 …………….eqn. (5)
Hence, the correct options are option b), option c), and option e).
Fill in the blanks to write the solutions to the quadratic equation.Fill in the blanks to write the solutions to the quadratic equation.Fill in the blanks to write the solutions to the quadratic equation.Fill in the blanks to write the solutions to the quadratic equation.x^2+2x+10 = 0
The solution to the given quadratic equation is x = -1 + 3i OR x = -1 - 3i
Solving Quadratic equationsFrom the question, we are to solve the given quadratic equation
From the given information,
The quadratic equation is
x² + 2x + 10 = 0
Using the Quadratic formula,
x = [-b ± √(b² - 4ac)] / 2a
From the equation,
a = 1, b = 2, and c = 10
Then,
x = [-b ± √(b² - 4ac)] / 2a
x = [-(2) ± √((2)² - 4(1)(10))] / 2(1)
x = [-2 ± √(4 - 40)] / 2
x = [-2 ± √(-36)] / 2
x = [-2 ± -6i] / 2
x = -1 ± 3i
x = -1 + 3i OR x = -1 - 3i
Hence, the solution is x = -1 + 3i OR x = -1 - 3i
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An airplane in flight needed to make an emergency landing so it descended at
an angle of depression of 15 degrees for 50000 feet until it landed. How many
feet is the vertical drop from when the plane initially began it's descent to
when it reached the ground? Round to the nearest whole number. (Hint:
draw a picture)
Answer:
13,397 ft
Step-by-step explanation:
tan 15 = height/50,000
0.2679(50,000) = 13,397 ft
i need help please! Much appreciated
Answer:
From SOHCAHTOA
Sin60 = 9/y
y= 9/sin60
y=10.39 ~ 10.4
Again
From SOCAHTOA
Tan60= 9/x
x= 9/tan60
x=5.19 ~ 5.2.
6) Create your own word
problem using the
format in the example
on the page above.
Format in the example are Surds on the page above in own word is [tex]36z^{15} ,\ 100,\ 9^7,\ and \ 6r^3\\[/tex]
How do indices and Surds differ from one another?Surds are the root values for which there is no whole number representation. Indices represent the exponent or power of a value. For instance, the base is 3 and the index is 2 for the number 32. the index being 3/2.
What are the Surds rules?These are the surds rules:
Rule 1: = √(r*s) = √r*√s.Rule 2: √(r/s) = √r/√s.Rule 3: r/√s = (r/√s) X (√s/√s)Rule 4: p√r ± q√r.Rule 5: r / (p+q√n)Rule 6: r / (p-q√n)1) [tex](2z^3)^5=32^{15}[/tex]
2) [tex]\sqrt[3]{1000*1000}=100[/tex]
3) [tex]\frac{9^{3} }{9^{-4} } = 9^7[/tex]
4) [tex](6r^{-3}) ^{-1} = 6r^3[/tex]
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Can anyone help me!! Thank you
:)
Answer:
23
Step-by-step explanation:
Select all ratios that are in their simplest form,
A=21:7
B=25:19
C=23:7
D=16:4
E=24:26
Answer:
B and C
Just see if there is any number that can divide both top and bottom
If there isnt, its in simplest form
What is the measure of the x?
DO NOT ANSWER IF YOU DO NOT THE ANSWER! Whoever answers correctly will get Brainliest! :)
Answer:
A
Step-by-step explanation:
The sum of the two angles is 180 degrees
x + 138 = 180
x = 42 degrees
If a store advertises a package of 22 stickers for
$4.57, what is the unit rate, or price per sticker?
Write an equation using a variable and solve.
Can y’all help me on question 32??!
Answer:
(B)
Step-by-step explanation:
It is 1.9 miles from a house to a restaurant and 1.2
miles to a pier, as shown at the right. The angle
between the two lines of sight is 87°. How far is it from
the pier across the water to the restaurant.
9514 1404 393
Answer:
2.2 miles
Step-by-step explanation:
The Law of Cosines can be used to figure this.
c² = a² +b² -2ab·cos(C)
c² = 1.2² +1.9² -2(1.2)(1.9)cos(87°) ≈ 4.811348
c ≈ √4.811348 ≈ 2.193
It is about 2.2 miles across the water from the pier to the restaurant.
What the heck is this??
Please help with this and thank u brother and sisters
Answer:
Equivalent
Step-by-step explanation:
Two fractions are equivalent if the value, proportion, or quantity they represent is the same. Equivalent fractions can have different numerators and denominators.
If you multiply the first one by 4/4 then you will have 8s/20s, which is the same as the second one
Answer:
I dont know if the letters are there to confuse me but if not yes there equivalent I cross multiplied 2 × 20 = 40 and 8 × 5 = 40 as well meaning there equivalent cause they equal the same when cross multiplying hope that helps!
Erika sells bicycles at a store. She is paid a monthly salary plus a bonus on each bike she sells. Her monthly pay is modeled in the table. Choose the linear equation below that best represents this data.
Answer: Show the table
Step-by-step explanation:
SHow the table
If you work for an airline need to sit a passenger every 30 seconds. If the doors open at 9:35 am, what time does the last passenger sit if there are 110?
Answer: 10:30 am
Step-by-step explanation: If you need to seat a passenger every 30 seconds, (half of a minute, which is 60 seconds), for every minute, 2 passengers will be seated. So, if you seat 2 passengers for a min each until you have seated 110 people, you will have taken up 55 minutes in total. (110 divided by 2 passengers a min). And finally, 55 minutes past 9:35 am would be 10:30 am. Hope this helps!
Please help with this
Answer:
I would say 109 if you were to plot this
How much fencing is required to enclose a circular garden whose radius is 14m? Use 22/7 for π.
Answer:
The fencing required to enclose a circular garden whose radius is 22m is 138.16m
Answer:
[tex]\boxed {\boxed {\sf 88 \ meters}}[/tex]
Step-by-step explanation:
We want to find the amount of fencing required to enclose the garden. The fencing goes around the garden, which is a circle. Essentially, we are finding the perimeter or circumference of the circle.
The formula for circumference is:
[tex]c=\pi \times d[/tex]
We are given the radius, so we need to find the diameter. The radius goes from the center to the edge of the circle, while the diameter goes from edge to edge through the center. So, the diameter is twice the radius of 14 meters.
d=2 ×r d= 2 × 14 m d= 28 mNow we know the diameter is 28 meters. We also know 22/7 is being used for pi. Substitute these values into the formula.
[tex]c= \frac{22}{7} \times 28 \ m[/tex]
[tex]c=88 \ m[/tex]
The circumference is 88 meters, so 88 meters of fencing is requires to enclose the garden.
is 4.97 a terminating decimal
or a repeating decimal?
Answer:
it's a terminating decimal
4 glasses cost £24 in total how much do seven glasses cost
Using simple unitary method process in the given problem with the provided values, The answer is £42 .
What is unitary method?The unitary method is a method of solving mathematical problems in which the relationship between a quantity and its unit of measurement is used to find an unknown quantity. It involves expressing the given quantity in terms of a unit, then solving for the unknown quantity in terms of the same unit.
What are arithmetic operators?Arithmetic operators are used to perform basic mathematical operations, such as addition (+), subtraction (-), multiplication (*), division (/), and modulus (%). They take numerical values (either literals or variables) as their operands and return a single numerical value. These are widely used in mathematical computations, like in programming languages, spreadsheets and calculator apps.
4 glasses cost £24.
1 glass cost £24/4 = £6
7 glasses cost = £6 * 7 = £42
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PLS HELP FOR 10 POINTS PLEASE (SHOW YOUR WORK)
Question: Find the measure of the missing angle
IF YOUR A BOT AND IS JUST SAYING “PLEASE CHECK THE LINK BELOW FOR ANSWERS” I WILL REPORT
THANK YOU (-:
Answer:
The answer is 90 degrees
Step-by-step explanation:
It is a right angle and a right angle is equal to 90 degrees
The box in a triangle always represents a right angle
Answer:
The missing angle is 65 degrees
Step-by-step explanation:
Answer: 65 degrees
First, you can make the conclusion that a right angle is 90 degreesNext, you can add 90 to 25 to get 115You then subtract 115 from 180.You are left with 65, which is the measure of the missing angleRemember that a triangle equals 180 degrees! :)determine the area of the rectangle below
Answer:
A=10.75
Step-by-step explanation:
Formula; A=wl
Plug in values; 2.5·4.3
Area ; 10.75
Answer:
Formula: bh
Plug in Values: 4.33 and 2.5
Area: 10.825 inches squared
Step-by-step explanation:
Before anything, when you converted 4 1/3 to 4.3, I recommend doing 4.33. ‘Ight, let’s begin.
The formula is base times height, therefore, you multiply the base (2.5) times the height (4.33).
2.5x4.33=10.825
please help me please i really need help please help me please
9514 1404 393
Answer:
26.2 in³
Step-by-step explanation:
The formula for the volume of a cone uses the radius of the cone as one of its variables. Here, the diameter is given, so we need to divide it by 2 to find the radius.
r = d/2 = (5 in)/2 = 2.5 in
The volume is ...
V = 1/3πr²h
V = (1/3)π(2.5 in)²(4 in) = 25π/3 in³ ≈ 26.2 in³
The volume of the cone is about 26.2 in³.
Simplify 3.5m(3m + 1.8) using the distributive property.
10.5m + 6.3m
10.5m + 1.8
10.5m2 + 6.3m
10.5m2 + 1.8
Answer:
3.5m(3m + 1.8)
10.5m^2+6.3m
Step-by-step explanation:
What is a possible value of sin(x) if the cos(2x) = 0.42
Answer:
The answer is 0.54 have a great day
What is the volume of the following triangular prism?
Answer:
37.8
Step-by-step explanation:
Change 12 mm to 1.2 cm
Then apply the volume rule
Area * height
A = 1.2*7=8.4
H=4.5
Volume 8.4*4.5 =37.8
How many possible triangles can be created if measure of angle A equals pi over 6 comma c = 18, and a = 9?
0 triangles
1 triangle
2 triangles
Cannot be determined based on the given information
If the measure of angle A equals pi over 6, the angle c equals 18, and the angle an equals 9, triangles may be formed.
When do three lines join to make a triangle?You only need to apply the Triangle Inequality Theorem, which asserts that the sum of a triangle's two side lengths is always greater than the third side. A triangle will exist if this holds true for each of the three possible added side length combinations.
From the given information, we have that:
m<B = pi/6 = 30 degres
c = 10
b = 5
This shows that we can use the cosine rule to find the third side b of the triangle. Since all the sides are complete, hence we can use the information given to find just 1 triangle
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Solve ^4√5x - 4 =1
A) x = 625
B) x = 81∕5
C) x = 25
D) x = 125
x=125
...............
Find the missing side length of the right triangle. If needed, round to the nearest tenth
10 cm.
126 cm.
Answer:
24 Is the answer. (I used 26, not 126 as 26 is what was in the picture)
Step-by-step explanation:
A^2 + b^2 = c^2
10^2 + b^2 = 26^2
100 + b^2 = 676
B^2=576
B=24