Answers
Answer:
[tex]\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)[/tex]
Step-by-step explanation:
[tex]\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}[/tex]
Apply formula:
[tex]\cos\left(A\right)-\cos\left(B\right)=-2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)[/tex] and
[tex]\sin\left(A\right)+\sin\left(B\right)=2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)[/tex]
We get:
[tex]=\frac{-2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\sin\left(\frac{2x-4x}{2}\right)}{2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\cos\left(\frac{2x-4x}{2}\right)}[/tex]
[tex]=\frac{-\sin\left(\frac{2x-4x}{2}\right)}{\cos\left(\frac{2x-4x}{2}\right)}[/tex]
[tex]=\frac{-\sin\left(\frac{-2x}{2}\right)}{\cos\left(\frac{-2x}{2}\right)}[/tex]
[tex]=\frac{-\sin\left(-x\right)}{\cos\left(-x\right)}[/tex]
[tex]=\frac{-\cdot-\sin\left(x\right)}{\cos\left(x\right)}[/tex]
[tex]=\frac{\sin\left(x\right)}{\cos\left(x\right)}[/tex]
[tex]=\tan\left(x\right)[/tex]
Hence final answer is
[tex]\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)[/tex]
Related Questions
You roll a number cube numbered from 1 to 6. What is the probability that the number is a composite number?
Answers
For the six numbers in the cube, we have.
1 is not prime nor composite2 is prime3 is prime4 is composite, because it can be written as [tex]2\cdot 2[/tex]5 is prime6 is composite, because it can be writte as [tex]2\cdot 3[/tex]So, only two of the numbers in the cube are composite. This means that you have a chance of
[tex]\dfrac{2}{6}=\dfrac{1}{3}[/tex] of rolling one of them.
Ther are 6 girls and 7 boys in a class. A team of 10 players is to be selected from the class. How many different combinations of players are possible
Answers
Answer:
[tex]13C10 =286[/tex]
Step-by-step explanation:
To solve this problem we must use the formula of combinations.
[tex]nCr =\frac{n!}{r!(n-r)!}[/tex]
Where n is the number of players that there are and elect r of them
In this case there are [tex]7 + 6 = 13[/tex] players and you choose 10 of them
Then we look for 13C10
[tex]13C10 =\frac{13!}{10!(13-10)!}[/tex]
[tex]13C10 =\frac{13!}{10!*3!}[/tex]
[tex]13C10 =286[/tex]
There are 286 possible combinations
For what value of x does 3^4x=27^x-3? a. –9 b. –3 c. 3 d. 9
Answers
[tex]\bf 3^{4x}=27^{x-3}\implies 3^{4x}=(3^3)^{x-3}\stackrel{~\hfill \textit{same base, the exponents must also be the same}}{\implies 3^{4x}=3^{3(x-3)}\implies 3^{4x}=3^{3x-9}\qquad } \\\\\\ 4x=3x-9\implies x=-9[/tex]
The midpoint of MN is point P at (–4, 6). If point M is at (8, –2), what are the coordinates of point N? (–16, 14) (–10, 5) (2, 2) (6, 2)
Answers
Answer is
(-16 , 14)
Answer:
-16, 14
Step-by-step explanation:
Which of the following equations of y = sin x has been transformed by a vertical shift down 3 units and stretch factor of 2?
A. y = sin 20
B. y = 2 sin +3
C. y = -2sin 8 - 3
D. y = 3 sin 0 - 2
E. y = 2sin 0-3
Answers
ANSWER
E.
[tex]y = 2 \sin( \theta) - 3[/tex]
EXPLANATION
The parent function
[tex]y = \sin( \theta) [/tex]
can be shifted down by 3 units to obtain
[tex]y = \sin( \theta) - 3[/tex]
Also, when the basic sine function is stretched vertically by a factor of 2, the equation becomes,
[tex]y = 2 \sin( \theta) [/tex]
Therefore, a vertical shift down 3 units and stretch factor of 2 gives the equation:
[tex]y = 2\sin( \theta) - 3[/tex]
The correct choice is E.
Which is the value of this expression when j=-2
Answers
Answer:
Step-by-step explanation:
(jk^-2/j^-1k^-3)^3
(-2)(-1)^-2
------------- ^3
(-2)^-1(-1)^-3
switch negative exponenst to other side
(-2)(-2)(-1)^3
__________
(-1)^2
4(-1)
-----
1
= -4
REMEMBER all to the 3rd power!
(-4)^3
-64
What is the mode of 4, 7, 7, 7, 4, 6, 6, 6, 7?
Answers
Answer: 7
Step-by-step explanation:
mode is the most replicated number
Answer:
The mode is 7.. :)
Step-by-step explanation:
The area of a circle is 81pie square feet. What is the length of the radius? What is the length of the diameter? Please show steps!
Answers
[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=81\pi \end{cases}\implies 81\pi =\pi r^2\implies \cfrac{81\pi }{\pi }=r^2\implies 81=r^2 \\\\\\ \sqrt{81}=r\implies \boxed{9=r}~\hspace{10em}\stackrel{\textit{diameter = twice the radius}}{18}[/tex]
[tex]
A=81\pi \\
A=\pi r^2 \\
81\pi=\pi r^2\Longrightarrow r^2=81
radius=\sqrt{81}=\boxed{9} \\
diameter=2radius = 2\cdot9=\boxed{18}
[/tex]
About what percent of the village women took between 48 and 56 minutes to collect one container of water
Answers
Answer:
50%
Step-by-step explanation
Each quartile of a box plot contains 25% of the data.
45-48 minutes is 25%
48-53 minutes is 25%
53-56 minutes is 25%
56-64 minutes is 25%
The questions asks for the percentage from 48-56.
48-53 is 25% and 53-56 is 25%. If you add 25% + 25%, you get 50%
Therefore, the percentage of village women who took 48-56 minutes to collect one container of water if 50%.
Hope this helps!
Which of these sentences is always true for a parallelogram?
A.All sides are congruent.
B. All angles are congruent.
c.The diagonals are congruent.
D. Opposite angles are congruent.
Answers
Answer:
D. Opposite angles are congruent
With option A, we can see that it is clearly wrong, in a parallelogram, only the opposite sides are congruent, if all of the sides are congruent then the shape is more likely to be a square or a rhombus.
With option B, only the opposites angles are congruent. If all four angles are congruent, that will be more likely to be true when we consider a square or a rectangle.
With option C, it is also wrong, unless the shape is a rhombus, square or rectangle.
That leaves us with the last option which is D.
How is dividing mixed numbers related to dividing whole numbers
Answers
Answer:
Dividing mixed numbers is very similar to multiplying mixed numbers. You just add one step—after changing the divisor into an improper fraction, you then find its reciprocal and multiply. ... First step: Write the whole number and the mixed number as improper fractions.
Step-by-step explanation:
Dividing mixed numbers is essentially similar to dividing whole numbers, with an extra step of converting mixed numbers into improper fractions. The core concepts remain the same but it extends division into fractions.
Explanation:Dividing mixed numbers is related to dividing whole numbers because the fundamental concepts remain the same. In dividing whole numbers, we take a number (dividend) and distribute it into equal parts. For instance, dividing 6 by 2, we are distributing 6 into 2 equal parts, which will give us 3 in each part.
Similarly, when dividing mixed numbers, we proceed in the same manner. However, it adds an extra step of converting mixed numbers into improper fractions first before proceeding with the division. For example, when dividing 2 1/2 by 1 1/2, we would first convert these into improper fractions and then proceed with the division as we would do with whole numbers.
Therefore, the concept for dividing mixed numbers is essentially an extension of the concept for dividing whole numbers.
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Hiro has a stack of cards with one number from the set 1, 1, 2, 2, 3, 3, 3, 4 written on each card. What is the probability that he pulls out a 3 first and then pulls out a 2 without replacing them?
Answers
Answer:
3/28
Step-by-step explanation:
Given in the question that,
stack of cards have numbers (1, 1, 2, 2, 3, 3, 3, 4)
Total number of cards = 8
Number of card with 3 on them = 3
Number of card with 2 on them = 2
To find the probability that he pulls out a 3 first and then pulls out a 2, we will multiple the probability of having 3 with 2.
Probability of having 3 = 3/8
Probability of having 2 = 2/7 (without replacing)
3/8 x 2/7 = 3/28
Thus, the answer is 3/28
Answer:3/28
Step-by-step explanation:
Took test got it right
Which statement Is best represented by the inequality d<0.35? A. The pen cost less than $0.35. B. The pencil costs greater than $0.35. C. The toys cost more than $0.35. D. The stamps cost is equal to $0.35
Answers
Answer:
Option A, The pen cost less than $0.35.
Step-by-step explanation:
The given inequality is d ∠ 0.35
Now we have to define this inequality with the help of given options.
If d represents the cost of pen, then cost of pen should be less than 0.35.
Option A, The pen cost less than $0.35. is the answer.
Answer:
A
Step-by-step explanation:
Can someone please help me on this
Answers
Answer: no
Step-by-step explanation:
Because of the angles
On centimeter dot paper, draw all possible rectangles with a perimeter of 12 cm and sides whose lengths are whole numbers. Label the lengths of two adjacent sides of each rectangle.
Answers
Answer nica me ayudan a mi pliss...oh mana nose
Step-by-step explanation:
In the picture below, what is the approximate area that is shaded blue?
A.
38 in2
B.
77 in2
C.
79 in2
D.
157 in2
Answers
Answer:
it is not C i did that so it might be B
Step-by-step explanation:
The approximate area that is shaded blue 77 in².
What area is a circle?A circle's area is equal to pi times the radius squared (A = r2).The following formulas can be used to determine a circle's area: Area is equal to r2, where r stands for radius.What is area of rectangle?When calculating the area of a rectangle, we multiply its length by its breadth.A = lw, where l and w are the length and width of the rectangle (rectangle)
In this question we simply calculate area of circle where r=5 , and area of rectangle l = 2 and b = 1.
Area of circle = πr²
= [tex]\frac{22 *5*5}{7}[/tex] = 78.57
Area of rectangle = l * b
2 * 1 = 2
Then simply subtract area of rectangle to area of circle .
Area of shaded blue = 78.57 - 2
= 76.57 ⇒ 77 in²
Therefore, The approximate area that is shaded blue 77 in².
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pllllllzzz help me look at the picture
Answers
Answer:
the correct option is option c.
Step-by-step explanation:
We have the expression: (160*243)^1/5
First, we know that 160 = 5(2^5)
And, 243 = 3^5
Then we have: (160*243)^1/5 = [5(2^5)(3^5)]^1/5 = 6(5)^1/5
So the correct option is option c.
Factorise x^2/4-y^2/4
Answers
Answer:
[tex]\large\boxed{\left(\dfrac{x}{2}-\dfrac{y}{2}\right)\left(\dfrac{x}{2}+\dfrac{y}{2}\right)=\dfrac{x-y}{2}\cdot\dfrac{x+y}{2}}[/tex]
Step-by-step explanation:
[tex]\dfrac{x^2}{4}-\dfrac{y^2}{4}=\dfrac{x^2}{2^2}-\dfrac{y^2}{2^2}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\=\left(\dfrac{x}{2}\right)^2-\left(\dfrac{y}{2}\right)^2\qquad\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\left(\dfrac{x}{2}-\dfrac{y}{2}\right)\left(\dfrac{x}{2}+\dfrac{y}{2}\right)=\dfrac{x-y}{2}\cdot\dfrac{x+y}{2}[/tex]
Rectangle we're prison has a length of 3 and 1/2 meters a with of 4 and 1/2 meters and a height of 2 m. Which expression can be used to find the volume of the prism?
Answers
Answer:
volume = 3.5 m * 4.5 m * 2 m
Step-by-step explanation:
The volume of a rectangular prism is
volume = length * width * height
volume = 3.5 m * 4.5 m * 2 m
Find the measure of ∠M.
Answers
Measure of an angle is usually in degrees or radians. The measure of angle M is [tex]36^\circ[/tex]. Thus, [tex]m\angle M = 36^\circ[/tex]
How to find measure of missing third angle in a triangle?It is a theorem in mathematics that sum of internal angles of a triangle equate to [tex]180^\circ[/tex].
Suppose that two angles are given as [tex]a^\circ[/tex] and [tex]b^\circ[/tex] and let there is one angle missing. Let its measure be [tex]x^\circ[/tex]
Then, by the aforesaid theorem, we get:
[tex]a^\circ + b^\circ + x^\circ = 180^\circ\\\\ \text{Subtracting a + b degrees from both sides} \\\\x^\circ = 180^\circ - (a^\circ + b^\circ)[/tex]
For the given case, we have:
[tex]m\angle S = 84^circ\\\\m\angle A = 60^\circ\\\\m\angle M = x^\circ \text{ (say)}[/tex]
Thus,
[tex]x^\circ = 180^\circ - (60+84)^\circ\\\\x^\circ = 36^\circ[/tex]
Thus,
The measure of angle M is [tex]36^\circ[/tex]. Thus, [tex]m\angle M = 36^\circ[/tex]
Learn more about triangle's angles here:
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Find the equation of the line that is perpendicular to the line 4x + 2y = 1 and passes through the point (−4, 3).
Answers
Answer:
[tex]\large\boxed{y=\dfrac{1}{2}x+5}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ 4x+2y=1.\ \text{Convert to the slope-intercept form y = mx + b:}\\\\4x+2y=1\qquad\text{subtract 4x from both sides}\\\\2y=-4x+1\qquad\text{divide both sides by 2}\\\\y=-2x+\dfrac{1}{2}\to m_1=-2.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-2}=\dfrac{1}{2}.\\\\\text{The equation of the searched line:}\ y=\dfrac{1}{2}x+b.\\\\\text{The line passes through }(-4,\ 3).[/tex]
[tex]\text{Put the coordinates of the point to the equation.}\ x=-4,\ y=3:\\\\3=\dfrac{1}{2}(-4)+b\\\\3=-2+b\qquad\text{add 2 to both sides}\\\\b=5[/tex]
A customer wants you to enlarge a photo to 2 3/4 its current height. The photo’s current height is 3 /14 inches. What should its enlarged height be, in inches?
Answers
Answer:
33/56 inches
Step-by-step explanation:
2.75(3/14)=33/56
Answer:
[tex] 8\frac { 1 5 } { 1 6 } [/tex] inches or 8.94 inches
Step-by-step explanation:
We know that the current height of the photo is [tex]3\frac{1}{4}[/tex] inches and the customer wants it to be enlarged by a factor of [tex]2\frac{3}{4}[/tex] its current height.
[tex] 3\frac { 1 } { 4 } = 3.25 [/tex]
[tex] 2 \frac { 3 } { 4 } = 2.75 [/tex]
Multiplying this scale factor with the current height of photo to find the enlarged height.
Enlarged height = [tex]3.25 \times 2.75 = 8\frac{15}{16}[/tex] inches or 8.94 inches
lynn and dawn tossed a coin 30 times and got heads 12 times. what is the experimental probability of tossing heads using lynn and dawn's results
Answers
Answer:
So, the experimental probability of tossing heads using lynn and dawn's results is 2/5
Step-by-step explanation:
No of times the coin is tossed = 30
No of times head came = 12
Probability of tossing heads = No of times head came / No of times the coin is tossed
= 12/30
= 4/10
= 2/5
So, the experimental probability of tossing heads using lynn and dawn's results is 2/5
what is the area of a circle with radius 10 units
Answers
Answer is provided in the image attached.
priya has a recipe for banana bread she uses 7 1/2
Answers
This is an incomplete question.
Answer:
Step-by-step explanation:
This is incomplete
if f(x) = 4 x^2 and g(x) = x+1, find (f•g)(x)
Answers
Answer:
D assuming the black dot means multiplied
Step-by-step explanation:
Solve -t/5 > 15 A. t < -75 B. t > -75 C. t < -3 D. t > -3
Answers
For this case we must solve the following inequality:
[tex]- \frac {t} {5}> 15[/tex]
We follow the steps below:
We multiply by 5 on both sides of the inequality:
[tex]-t> 15 * 5\\-t> 75[/tex]
We multiply by -1 on both sides of the inequality. We must bear in mind, that when multiplying by -1, the sense of the inequality changes.
[tex]t <-75[/tex]
Answer:
Option A
You buy two ads in a newspaper. One ad takes up
5
8
58
of a page, and the other ad takes up
1
8
18
of a page. How much space did you buy for ads?
Answers
The total space bought for the two ads in the newspaper is 3/4 of a page. This is determined by adding the fractions representing the size of each ad together: 5/8 + 1/8 = 6/8, which simplifies to 3/4.
Explanation:You are dealing with fractions in this mathematics problem. If you bought two ads, one taking 5/8 of a page and the other taking 1/8 of a page, you need to add these fractions together to find out how much space you bought for ads overall.
Adding the fractions 5/8 and 1/8 would give you:
5/8 + 1/8 = 6/8
The fraction 6/8 can be simplified further by dividing both numbers by their greatest common divisor (which is 2), resulting in:
6/8 = 3/4
Therefore, the ads took up 3/4 of a page in total.
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you bought a total of 3/4 of a page for ads.
To calculate the total space bought for ads in a newspaper, simply add the proportions of the page that each ad takes up. The first ad covers 5/8 of a page, while the second ad occupies 1/8 of a page. Adding these together:
5/8 + 1/8 of a page
This can be calculated by adding the numerators and keeping the denominator the same since both fractions have the same denominator.
Add the numerators: 5 + 1 = 6
Keep the denominator the same: 8
Combine them to get the new fraction: 6/8 of a page
However, notice that 6/8 can be simplified to 3/4, because both the numerator and the denominator can be divided by 2.
Therefore, you bought a total of 3/4 of a page for ads.
Which equation can be used to determine Kim’s age, x, from the information about Bob and Paul?
Answers
Answer:
where is the information about bob and paul?
Step-by-step explanation:
Answer:
2x + 4 = 3x + (–1)
Step-by-step explanation:
I just did it so i hope this helped
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (0,0); y=3/7x+ 7
Answers
Answer:
y=3/7x
Step-by-step explanation:
Parallel means same slope.
y-y1=m(x-x1)
y-0=3/7(x-0)
y=3/7(x)+0
y=3/7x
Answer: The answer is y=3/7x