Simplify cot x – csc x cos x.1) cot x csc x – cot x cos x2) 03) 2 cot x4) 1
Answers
ANSWER
\(2)0\)EXPLANATION
We want to simplify the trigonometric expression:
\(\cot x-\csc x\cos x\)According to trigonometric ratios, we have that:
\(\begin{gathered} \cdot\cot x=\frac{1}{\tan x}=\frac{1}{\frac{\sin x}{\cos x}}=\frac{\cos x}{\sin x} \\ \cdot\csc x=\frac{1}{\sin x} \end{gathered}\)Substitute those into the expression given:
\(\begin{gathered} \frac{\cos x}{\sin x}-(\frac{1}{\sin x})\cos x \\ \Rightarrow\frac{\cos x}{\sin x}-\frac{\cos x}{\sin x} \\ \Rightarrow0 \end{gathered}\)The answer is option 2.
Related Questions
1. An airplane flies with a constant
speed of 740 miles per hour. How
far can it travel in 2 hours?
Answers
Answer:
740×2= 1480 in 2 hours
hope this helps :)
4x + 7 − 23
In this expression, the coefficient is 4.
True or False
Answers
Answer:
True
Step-by-step explanation:
Which of the following surfaces matches the level curves below?
Answers
Answer:
(a) z = x² -y² +6
Step-by-step explanation:
Each of the equations can be interpreted as describing a family of curves based on the value of z.
(a)The difference of squares will give rise to hyperbolic curves, matching the given diagram
(b)The sum of linear terms will give rise to straight lines.
(c)Squaring both sides gives ...
z² -6 = x² +y²
which gives rise to a family of circles.
(d)This is the same formula as (c), but with circles of a different radius.
__
Additional comment
The standard form equation for a hyperbola is ...
(x/a)² -(y/b)² = 1 . . . . . centered at the origin, with semi-axes 'a' and 'b'.
Here, we have a=b=√(z-6).
Observe that \(y=\pm x\) form a level curve for the surface in question. This means that if we substitute \(y=x\) or \(y=-x\) in to the equation for the surface, then \(z=f(x,y)=c\) is a constant.
This is only true for the surface in option A.
\(z = x^2 - y^2 + 6\)\(y = x \implies z = x^2 - x^2 + 6 \implies z = 6\)
\(y = -x \implies z = x^2 - (-x)^2 + 6 \implies z = 6\)
\(z\) is constant, so both of \(y=\pm x\) are level curves.
\(z^2 = x + y + 6\)\(y=x \implies z^2 = x + x + 6 \implies z = \pm\sqrt{2x + 6}\)
\(y=-x \implies z^2 = x + (-x) + 6 \implies z = \pm\sqrt6\)
\(y=x\) is not a level curve.
\(z = \sqrt{x^2 + y^2 + 6}\)\(y = x \implies z = \sqrt{x^2 + x^2 + 6} = \sqrt{2x^2 + 6}\)
\(y = -x \implies z = \sqrt{x^2 + (-x)^2 + 6} = \sqrt{2x^2 + 6}\)
Neither are level curves.
\(z = \sqrt{x^2 + y^2}\)\(y = x \implies z = \sqrt{x^2 + x^2} = \sqrt2 |x|\)
\(y=-x \implies z = \sqrt{x^2 + (-x)^2} = \sqrt2 |x|\)
Again, neither are level curves.
una persona tiene 6 chaquetas y 10 pantalones. de cuántas formas distintas puede combinar estas prendas?
Answers
The total number of combinations is given as follows:
60.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways for one experiment and n ways for another experiment, then there are m x n ways in which the two experiments can happen simultaneously.
This can be extended to more than two trials, where the number of ways in which all the trials can happen simultaneously is the product of the number of outcomes of each individual experiment, according to the equation presented as follows:
\(N = n_1 \times n_2 \times \cdots \times n_n\)
The parameters for this problem are given as follows:
\(n_1 = 6, n_2 = 10\)
Hence the total number of combinations is given as follows:
6 x 10 = 60.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/15878751
#SPJ1
how can you use pythagora's theorem to solve problems involving right-angled triangles
Answers
Using Pythagorean theorem, the length of the ladder is 10ft
What is Pythagorean Theorem?In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:
x² = y² + z²
In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.
To calculate the length of the ladder, we can write the formula as;
x² = 8² + 6²
x² = 64 + 36
x² = 100
x = √100
x = 10
The length of the ladder is 10 feet
Learn more on Pythagorean theorem here;
https://brainly.com/question/343682
#SPJ1
HELP AS SOON AS POSSIBLE
Answers
The coordinates of polygon A'B'C'D' after the rotation of 180º are given as follows:
A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).
What are the rotation rules?The five more known rotation rules are given as follows:
90° clockwise rotation: (x,y) -> (y,-x).90° counterclockwise rotation: (x,y) -> (-y,x).180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y).270° clockwise rotation: (x,y) -> (-y,x).270° counterclockwise rotation: (x,y) -> (y,-x).The original coordinates for this problem are given as follows:
A(0,0), B(5,2), C(5,-5), D(0,-3).
Exchanging the sign of each of the coordinates, the coordinates after the rotation are given as follows:
A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).
More can be learned about rotation rules at brainly.com/question/17042921
#SPJ1
Phillip is competing in a race car competition. He drives 218.4 miles in 2.4 hours.
(a) What unit rate may be of interest here?
Answers
If he drives the car 218.4 miles in 2.4 hours. Then the speed of the car will be 91 miles per hour.
How to find the speed of an object?If the object is going linearly, and at a constant speed, then the speed of that object is given by the distance it traveled to the time it took to travel that distance.
If the object traveled D distance in T units of time, then that object's speed will be given as
Speed = Distance traveled/Time taken
S = D/T
Phillip is competing in a race car competition.
He drives 218.4 miles in 2.4 hours.
Then the speed of the car will be
S = 218.4/2.4
S = 91 miles per hour
More about the speed link is given below.
https://brainly.com/question/7359669
#SPJ2
Which value of h makes the inequality 4h + 3 < 10 true? A: h = -2 B: h =2 C: h = 4 D: h = 7
Answers
Answer: A h = - 2
Step-by-step explanation:
Substitute -2 for h
4(-2) + 3 < 10
-8 + 3 < 10
-5 < 10 true
The sum of two numbers is -6.5 and their difference is 4. 5. What are the numbers? A. -1.25 and -5.25 B. 1.25 and -5.25 D. 1 and -7.5 C. -1 and -5.5
Answers
Answer:
C. -1 and -5.5 is the correct answer.
please help me 80% of what number is 16
What is the part?
What is the total?
What is the percent?
What is the answer?
Answers
Answer:
80 percent of 16 is 12.8 I'm sorry but that's all I know
What rigid motion maps the solid-line figure onto the dotted-line figure?
A. reflection
Brotation
Ctranslation
Answers
The rigid motion of the solid line figure is translated to the dotted line figure.
How to find the rigid motion maps a solid line?Translation describe a function that moves an object a certain distance.
In a translation, every point of the object must be moved in the same direction and for the same distance.
In translation, the object is not resized, rotated or reflected. The object usually remains the same but it moves a certain distance.
Therefore, the rigid motion maps the solid-line figure onto the dotted-line figure by translation
learn more on motion here:https://brainly.com/question/29166471
#SPJ1
What is the reference angle for the angle with measure −π4?
A 7π4
B π
C π4
D −7π4
Answers
Answer:
What is the reference angle for the angle with measure −π/4?
Answer: n/4
pie/4
Step-by-step explanation:
I just took the test lol the other answer is wrong.
Answer:
π/4
I took the quiz
Need ANSWER ASAP
Consider the following transformed function
y = −2 Sin [2( − 45°)] + 1
a) Graph the five key points of Parent function on the provided grid.
b) State the following for the transformed function
Amplitude=
period=
Horizontal Phase shift =
Equation of axis=
c) Graph at least two cycles of the transformed function by transforming the key points of the parent function. (Don’t forget to label the x-axis and y -axis)
Answers
Answer:
See explanation below.
Step-by-step explanation:
Given transformed function:
\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)
Part (a)The parent function of the given function is: y = sin(x)
The five key points for graphing the parent function are:
3 x-intercepts → (0°, 0) (180°, 0) (360°, 0)maximum point → (90°, 1)minimum point → (270°, -1)(See attachment 1)
Part (b)Standard form of a sine function:
\(\text{f}(x)=\text{A} \sin\left[\text{B}(x+\text{C})\right]+\text{D}\)
where:
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shift (axis of symmetry: y = D)Therefore, for the given transformed function:
\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)
Amplitude = -2Period = 2π/2 = πPhase shift = 45° to the rightEquation of axis of symmetry: y = 1Part (c)See attachment 2.
![Need ANSWER ASAPConsider the following transformed functiony = 2 Sin [2( 45)] + 1a) Graph the five key](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/rHmvQCSFzLuN7xkVIxhNC3hToKfYa2ZX.png)
![Need ANSWER ASAPConsider the following transformed functiony = 2 Sin [2( 45)] + 1a) Graph the five key](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/RTeQ1nKnPwOJZpxZH6e5ecn6PqRfr3g0.png)
In a recent survey of 36 people, 18 said that their favorite color of car was blue.
What percent of the people surveyed liked blue cars? Explain your answer with every step you took to get to it.
Answers
Answer: The percentage of people surveyed who liked blue cars is 50%.
Step-by-step explanation:
Total number of people partaking in survey= 36
number of people who like blue cars= 18
therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)
hence, percentage of people who liked blue cars= (18/36)*100 %
= 50%
To learn more about percentages visit the link below:
https://brainly.com/question/30399396
Answer:
Percentage of people who like blue-coloured cars is 50%
Number of people who were surveyed=36
Number of people who like blue-colored cars=18
Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100
=(18/36)*100
=50%
Read more about percentage
https://brainly.in/question/21062337#:~:text=Answer%3A,has%20no%20unit%20of%20measurement.
3
Which is longer, 2 feet or 18 inches?
Answers
Answer:
2 feet
Step-by-step explanation:
1 foot = 12 inches
2 x 12 = 24 inches
24 inches > 18 inches
Hope it helps :)
An item has a listed price of $70. If the sales tax rate is 3%, how much is the sales tax (in dollars)?
Answers
3% of 70 means "0.03 x 70" which is 2.1.
The sales tax is $2.10.
A marine biologist measured one dish that was 1 1/4 of a foot and a second fish that was 3/4 of a foot long. How much longer was the first fish
Answers
Answer:
1/3 foot longer
Step-by-step explanation:
2/3-1/3=1/3
A cone and a cylinder have the same radius and height What would you need to do to the volume of the cone to find the volume of the cylinder? Multiply by 3 Divide by 3?
Answers
Is 12 ounces greater than 400 grams
Answers
Answer:
No it is less than 400 :))
Answer:
No
Step-by-step explanation:
12 ounces is 340.194.
estimate 7271 divided by 12= ?
Answers
Answer:
B
Step-by-step explanation:
Because i used a calculator
Answer:
C 700
Step-by-step explanation:
7271 is close to 7000
12 is close to 10
So 7000/10 = 700
A soda factory makes 9 flavours of soda. Each case of soda has 7 cans of each flavour. How many cans of soda does the factory put in 7 cases?
Answers
The factory will put 441 cans of soda in 7 cases.
If each case of soda contains 7 cans of each flavor, and the factory is putting 7 cases, we can calculate the total number of cans by multiplying the number of flavors, cans per flavor, and cases.
Given:
Number of flavors = 9
Cans per flavor = 7
Number of cases = 7
To calculate the total number of cans, we can multiply these values:
Total cans = Number of flavors × Cans per flavor × Number of cases
Total cans = 9 × 7 × 7
Total cans = 441
To arrive at this answer, we multiplied the number of flavors (9) by the number of cans per flavor (7) to get the number of cans per case (63). Then, we multiplied the cans per case (63) by the number of cases (7) to obtain the total number of cans (441).
Hence, the factory will put 441 cans of soda in 7 cases.
For more such questions on soda
https://brainly.com/question/29111121
#SPJ8
3. If (5,5) is the endpoint of a line with the midpoint at (0,0), where is the
other endpoint?
Answers
I need help I need help
Answers
Explanation:
a = 72°, alternate interior angle to the one marked 72°, so congruent
b = d = j = 180° -2(72°) = 36°; twice angle 'a' is supplementary to b; all the acute angles where parallel lines are crossed are the same measure
c = e = h = 2(72°) = 144°; the obtuse angles where parallel lines are all the same measure
f = (180° -e)/2 = 18°, base angle of isosceles triangle
g = 180° -f = 162° . . . supplementary to the base angle
k = 54°, complementary to b
m = 126°, supplementary to the base angle of the triangle containing 'a'.
_____
Additional comment
The base angles of an isosceles triangle with third angle A are ...
B = C = (180° -A)/2
Angles that together make a straight line have a total of 180°.
Complete this puzzle using each of these numbers only once : 2, 4, 5, 7, 8, 11, 13, 14, 16 Put the even numbers in the squares and the odd nurmbers in the circles. Each row of three numbers must add up to 26.
Answers
Here is one solution to the puzzle:
Squares: 2, 8, 16
Circles: 5, 7, 14
Total: 26
You can verify that each row of three numbers adds up to 26: 2 + 8 + 16 = 26, 5 + 7 + 14 = 26.
What are even and odd numbers?An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Odd numbers end in 1, 3, 5, 7, 9.
Therefore, the correct answer is as given above
learn more about odd and even numbers: https://brainly.com/question/2263958
#SPJ1
Find the value of the power.
2400
The value of the power is
Answers
0
This graph represents the flight path of a model rocket launched in a park.
What do the key features of the curve represent in terms of the flight path of the rocket?
Chose from the drop-down to match each situation.
ill give brainlyest to the first to correctly answer this
Answers
The drop down menu is used to match each situation as below.
1. The rocket reached its maximum the x-value of the vertex
height in 5 s.
2. ground level the y-intercept
3. The rocket launcher was the y-value of the point containing
on the ground. the x-intercept on the right
4. The rocket was in the air 10 the x-intercept on the right
5. The maximum height of the the y-value of the vertex
rocket is 50 ft.
6. the time the rocket was the x-value of the point containing the
launched y-intercept
What is the key feature of the curveThe key features of the curve such as the x intercept is the point the launcher and the rocket were on ground.
The vertex is the point the rocket had the maximum and height.
Generally, the curve traces a parabolic path
Learn more about parabolic equation at
https://brainly.com/question/4061870
#SPJ1
Selling Price = $ 504 and Gain % = 12%
Answers
Answer:
Step-by-step explanation:
sp = 504
gain = 12%
in this case
sp =100%+12%=504
112%=504
1%=504/112 =4.5
100%=450
so cost =$450
Hope im correct, if i am im glad to be of service.
factor this problem:
42x^2+25x+3
Answers
Answer: (6x+1)(7x+3)
Step-by-step explanation:
Step-by-step explanation:
a quadratic
use sum factor pattern
42x^2+25x+3
=42x^2+18x+7x+3
common factor
6x(7x+3)+7x+3
rewrite in factored form
(6x+1)(7x+3)
Devon’s bike has wheels that are 26 inches in diameter. After the front wheel picks up
a tack, Devon rolls another 100 feet (1200 inches) and stops. How far above the ground in inches is the tack?
Answers
To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.
First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:
C = π × 26
C ≈ 81.64 inches
This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.
Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:
1200 / 81.64 ≈ 14.68 revolutions
Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.
Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.
Therefore, the tack is located 13 inches above the ground.
For more such questions on distance
https://brainly.com/question/26550516
#SPJ8
A cylindrical-shaped hole is 42 feet deep and has a diameter of 5 feet.
Approximately how large is the hole?
A. 210 ft
B. 630 ft
C. 825 ft
D. 3,300 ft