Answers
Answer:
Step-by-step explanation:
Use the formulas supplied in the picture attached. There's nothing to really learn here, it is just a plug-and-chug formula:
[tex]sin(3x)sin(2x)=\frac{1}{2} [cos(3x-2x)-cos(3x+2x)][/tex]
[tex]sin(3x)sin(2x)=\frac{1}{2} [cos(x)-cos(5x)][/tex]
Moving on to the second problem:
[tex]cos(a)sin(b)=\frac{1}{2}[ sin(a+b)-sin(a-b)][/tex]
Therefore:
[tex]2cos(a)sin(b)=sin(a+b)-sin(a-b)[/tex]
Where:
[tex]a+b=5x[/tex]
[tex]a-b=3x[/tex]
Solve for 'a' using the second equation to get:
[tex]a=3x+b[/tex]
Plug this into the first equation to get:
[tex]3x+b+b=5x[/tex]
[tex]3x+2b=5x[/tex]
[tex]2b=2x[/tex]
[tex]b=x[/tex]
Therefore:
[tex]a+x=5x[/tex]
[tex]a=4x[/tex]
Finally:
[tex]sin(a+b)-sin(a-b)=2cos(4x)sin(x)[/tex]
Related Questions
B. Study the figure on the right.
1. Name the points on it
2 Name any three segments from the figure,
3. Which segments have B as one endpoint?
4. Which points are endpoints of only two segments?
5. Which points are endpoints of three segments?
6. Which point is the endpoint of six segments?
7. Name the lines with A as one of the points on them.
8. Name any three rays from the figure, 9. How many segments are there in the figure?
10. How many rays can be named from the figure?
Answers
Answer:
can you clear more I don't understand
A pillar is fixed in the centre of a circular meadow with diameter of 60 metres. The angle of elevation of its top was found to be 60%, when observed from a point of the circumference of circular meadow. Find the height of the pillar from the ground.
Answers
Answer:
17 meters
Step-by-step explanation:
|\ angle = 60 degrees here of triangle
| \ <-- digitaly drawn triangle
|___\
cirlcle diameter is 60 meters, since pillar is at the center then the distance of the pillar to the edge of the circlular meadow is (60/2) 30 meters.
30 meters is opposite of the angle.
The height of the pillar is adjacent to the angle so use tangent to solve
Tan(60) = 30/x
Tan(60) = 1.7; make sure that calculator is in degrees and not in radians to not get an incorrect value
1.7 = 30/x --> 1.7x = 30
x = 30/1.7
x = 17.3205 meters
using 2 significant figures gives us 17 meters
It is known that
the pair of values x = –3 and y =8 is a solution to the equation
5x +by =17. Find the value of the coefficient b.
Answers
[tex] \huge\boxed { \frak{Answer : }}[/tex]
Given :
[tex] \: \: \: [/tex]
[tex] \rm \large \: x = - 3 \: , \: y= 8[/tex][tex] \: \: \: [/tex]
We Have To Find The Value Of " b ".
[tex] \: \: \: [/tex]
[tex] \sf \large \: 5x + by = 17 \: \: \: \: \: -- eqn( 1 )[/tex][tex] \: \: [/tex]
Now , Put the given value of x & y in the above eqn ~.
[tex] \: \: [/tex]
[tex] \sf \large \: \: \: \: ⇝5x + by = 17[/tex]
[tex] \: \: [/tex]
[tex]\sf \large \: \: \: \: ⇝5( - 3) + b(8) = 17[/tex]
[tex] \: \: [/tex]
[tex]\sf \large \: \: \: \: ⇝ - 15 + 8b = 17[/tex]
[tex] \: \: [/tex]
[tex]\sf \large \: \: \: \: ⇝8b = 17 + 15[/tex]
[tex] \: \: [/tex]
[tex]\sf \large \: \: \: \: ⇝8b = 32[/tex]
[tex] \: \: [/tex]
[tex]\sf \large \: \: \: \: ⇝b = \cancel\frac{32}{8} [/tex]
[tex] \: \: [/tex]
[tex] \boxed{\sf \large \: \: \: \: \underline{ \: \: ⇝b = 4 \: \: \: \: }}[/tex]
[tex] \: \: [/tex]
Hope Helps!:)
The value of the coefficient b in the linear equation 5x +by =17 is -4
How to determine the equation solutions?The pair of values are given as:
(x,y) = (-3,-8)
The equation is given as:
5x +by =17
Substitute values for x and y in the equation
-5 * 3 - 8 * b =17
Evaluate the product
-15 - 8b =17
Add 15 to both sides
-8b = 32
Divide both sides by -8
b = -4
Hence, the value of the coefficient b is -4
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A town has a population of 75,000 and is growing every year at a rate of 3.5%. What will the population be in 15 years?
Answers
The growth of the town is an illustration of exponential growth function
The population of the town in 15 years is 125651
How to determine the population in 15 years?The given parameters are:
Initial value, a = 75000Rate, r = 3.5%An exponential growth function is represented as:
y = a * (1 + r)^t
So, we have:
y =75000 * (1 + 3.5%)^15
Evaluate
y =125651
Hence, the population in 15 years is 125651
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A square pyramid is shown. What is the surface area of the pyramid? Enter your answer in the box. 100 points
Answers
Answer:
33 cm²
Step-by-step explanation:
Formula
Surface Area = 4 x Area (triangle) + Area (square)S.A. = 4 x 1/2 x bh + b²Solving
Given that h = 4 cm and b = 3 cmS.A. = 2 x 4 x 3 + 3²S.A. = 24 + 9 = 33 cm²Answer:
33 cm²
Step-by-step explanation:
Since the pyramid has a square base, the area of each of the triangular sides will be the same.
Therefore, to calculate the total surface area, find the area of one triangle, multiply it by 4, then add it to the area of the square base.
Formulae
Area of a square = x³ (where x is the side length)
Area of a triangle = 1/2 × base × height
Calculation
area of the square base = 3² = 3 × 3 = 9 cm²
area of one triangle = 1/2 × 3 × 4 = 6 cm²
Solution
Total area = area of the square base + 4 × area of one triangle
= 9 + (4 × 6)
= 9 + 24
= 33 cm²
30 POINTS! Explanation too, please!
Point A' prime is the image of point A under a rotation about point P. Determine the angles of rotation. Choose all answers that apply: (Choice A) 90 degrees clockwise (Choice B) 90 degrees counterclockwise (Choice C) 180 degrees (Choice D) 270 degrees clockwise (Choice E) 270 degrees counterclockwise
Answers
Please help what is the product?
Answers
Answer: It's A bro
Step-by-step explanation: if you get the brainly app on your phone you can take pics and use that to solve it that's what I did
1/17의 십진법 확장에서 반복되는 자릿수 블록의 최대 자릿수는 얼마입니까? 나눗셈을 하여 답을 확인하세요.
what can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? perform the division to check your answer.
Answers
Ayudaa no le entiendoo.
Answers
[tex]3 {x}^{5} + 2 {x}^{3} + x + {x}^{2} - 2x + 5 = [/tex]
[tex]3 {x}^{5} + 2 {x}^{3} + {x}^{2} - x + 5[/tex]
Answer:
3x⁵ + 2x³ + x² -x + 5
Step-by-step explanation:
(3x⁵ + 2x³ + x) - (-x² + 2x - 5) <== multiply to remove the parenthesis
1(3x⁵ + 2x³ + x) - 1(-x² + 2x - 5)
1(3x⁵) + 1(2x³) + 1(x) + -1(-x²) + -1(2x) + -1(-5) <== remember multiplying 2 negatives, makes a positive
3x⁵ + 2x³ + x + x² - 2x + 5 <== combine any like terms
3x⁵ + 2x³ + x² -x + 5 <== make sure that your answer is in Standard form (in decreasing degrees)
Hope this helps!
if 15% of a class of 20 students were boys, how many boys and girls?
Answers
Answer:
15 percent of 20 is 3. so there are 3 boys and 17 girls in the class.
Step-by-step explanation:
Please help nowww thxx
Answers
The water of the cylinder cannot fill the container, since the cylinder has less volume. Lastly, there is no apparent mistakes.
How to determine if two volumes are equivalent?The rectangular container ([tex]V_{R}[/tex]), in cubic inches, is full whether its volume is equal to the volume of the cylinder ([tex]V_{C}[/tex]), in cubic inches. The volume formulae for both containers are described below:
Rectangular container[tex]V_{R} = w\cdot l \cdot h[/tex] (1)
Where:
[tex]w[/tex] - Width, in inches[tex]l[/tex] - Length, in inches[tex]h[/tex] - Height, in inchesCylinder[tex]V_{C} = \pi\cdot r^{2}\cdot h[/tex] (2)
Where:
[tex]r[/tex] - Radius, in inches[tex]h[/tex] - Height, in inchesNow we proceed to determine the volume of each figure:
Rectangular container (w = 3.6 in, l = 3.6 in, h = 5.3 in)[tex]V_{R} = (3.6\,in)\cdot (3.6\,in)\cdot (5.3\,in)[/tex]
[tex]V_{R} = 68.688\,in^{3}[/tex]
Cylinder (r = 1.8 in, h = 5.3 in)[tex]V_{C} = \pi\cdot (1.8\,in)^{2}\cdot (5.3\,in)[/tex]
[tex]V_{C} \approx 53.947\,in^{3}[/tex]
The volume of the water in the cylinder is approximately 53.947 cubic inches. The water of the cylinder cannot fill the container, since the cylinder has less volume. Lastly, there is no apparent mistakes. [tex]\blacksquare[/tex]
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You are working for the company Trinity Mathematical Concepts are
asked for create the following logo for the company. If each vertices of the triangle are the centers of the circles, what is the area of the shaded region?
Your answer will be in terms of "x", where "x" is the radius of the circles.
Answers
Answer:
[tex](2\pi -3\sqrt{3})x^2/4[/tex]Step-by-step explanation:
The sides of the triangle in the middle are equal to x so tis is equilateral triangle.
Its interior angle is 60°.
Each shaded part is the area of 60° segment of circle with the radius x.
The area of each segment is the difference between 60° sector and the area of triangle.
[tex]A_{segment}=A_{sector}-A_{triangle}[/tex]Area of sector
[tex]A_{sector} = (60/360)*\pi r^2=(1/6)\pi x^2[/tex]Area of triangle
[tex]A_{triangle}=(\sqrt{3}/4)a^2= (\sqrt{3}/4)x^2[/tex]The shaded area is
[tex]A = 3((1/6)\pi x^2 - (\sqrt{3} /4)x^2)=((1/2)\pi -3\sqrt{3} /4)x^2=(2\pi -3\sqrt{3})x^2/4[/tex]At the beginning of the year, Alyssa had $100 in savings and saved an additional $7 each week thereafter. Colton started the year with $55 and saved $10 every week. Let AA represent the amount of money Alyssa has saved tt weeks after the beginning of the year and let CC represent the amount of money Colton has saved tt weeks after the beginning of the year. Write an equation for each situation, in terms of t,t, and determine the amount of money Alyssa and Colton have saved in the week that they have the same amount of money saved.
Answers
The equation that represents the amount saved by Alyssa after tt weeks is AA = 100 + $7tt
The equation that represents the amount saved by Colton after tt weeks is CC = $55 + $10tt
The amount they would have when they have same amount of money is $205.
What equation represents the total amount saved?The total amount saved: inital amount + (amount saved per week x total number of weeks
AA = 100 + $7tt
CC = $55 + $10tt
What would be the amount when they have the same amount of money?$55 + $10tt = 100 + $7tt
Combine similar terms and solve for tt
100 - 55 = 10tt - 7tt
45 = 3tt
tt = 15 weeks
100 + $7(15) = $205
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PLEASE HELP ME I REALLY NEED IT
Answers
Answer: 170
Step-by-step explanation: Angle G and Angle H are consecutive angles, meaning they both add up to 180 degrees. Thus, if 10 is the value of Angle G, Angle H must be 170.
Write the equation of the circle with the given information: Center: (3,-3) Radius: 2sqrt{6}
Answers
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{2\sqrt{6}}{ r} \\\\[-0.35em] ~\dotfill\\\\\ [x-3]^2~~ + ~~[y-(-3)]^2~~ = ~~(2\sqrt{6})^2\implies (x-3)^2+(y+3)^2=24[/tex]
#36
You look up at a drone at an angle of elevation of 23º. Your eyes are 5 feet above the ground, and the distance to
the drone is 210 feet. What is the altitude of the drone? Round your answer to the nnearest tenth.
Altitude: about ___
feet
Answers
Using the slope concept, it is found that the height of the drone is of about 94 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem:
The vertical change is of h - 5, in which h is the altitude of the drone.The horizontal change is of 210 ft.The angle is of 23º.Hence:
[tex]\tan{23^\circ} = \frac{h - 5}{210}[/tex]
[tex]h - 5 = 89[/tex]
[tex]h = 94[/tex]
The height of the drone is of about 94 feet.
More can be learned about the slope concept at https://brainly.com/question/18090623
If the volume of a sphere is 83.5cm3 (cubed) what is the radius??
Answers
Answer:
2.71
Step-by-step explanation:
Using this formula: Volume= 4 over 3 * π * r cubed.
then do R=(3V4π)⅓=(3·83.54·π)⅓≈2.71144
2.71144 rounded to the nearest 10 is 2.71
Use the diagram below to answer the
following questions.
2x - 1
x + 7
B
X-4
What is the value of x?
X =
=
What is the perimeter of triangle ABC?
The perimeter is
units.
Answers
Answer:
34
Step-by-step explanation:
Since this an isosceles triangle we can say the length of AB = AC
2x - 1 = x + 7
2x - x = 7 + 1
x = 8
The perimeter is calculated by adding all side lengths
2x - 1 + x + 7 + x - 4 = Area add like terms
4x + 2 = Area replace x with the value we found
4*8+2 = 34 units square
what is the perimeter ?
Answers
Answer:
53
Step-by-step explanation:
You get the perimeter by adding up all of the sides. I added them up and got 53
peaches cost 1.79 per pound what equation is used to find c the total cost for p pounds of peaches
Answers
Answer:
[tex]\huge{\boxed{\bf\:1.79 * p}[/tex]
Step-by-step explanation:
Given,
Cost of 1 pound of peaches = 1.79If pounds of peaches = p, then,
Cost of p pounds of peaches
= Cost of 1 pound × p pounds of peaches (p)
= 1.79 × p
[tex]\rule{150pt}{2pt}[/tex]
Q: Ribbon cost $1.44 for 3 m.
(1) What is the cost per meter?
(2) How much would 5 m of ribbon cost?
(3) How much ribbon could you buy for $12?
Answers
Answer:
1.44 divided by 3m will give $0.48/5 times 0.48 gives 2.412 times three divided by 1.44 gives$.25Can someone help me understand this?? I ended up getting 594 and that’s not even an option!
Answers
Answer:
Option D
Step-by-step explanation:
I am taking a guess here, but since the volume of the rectangle part is 594, and it is sort of a similar size as the top part, then I assume it is D.
Let me know how it goes.
Express the function graphed on the axes below as a piecewise function.
Answers
Answer:
f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}
Step-by-step explanation:
To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.
__
Left PieceThe domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.
The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.
The first piece can be written ...
f(x) = x-3 for x ≤ -1
__
Right PieceThe domain is shown as 5 to ∞, with 5 not included.
The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...
y -(-1) = -3(x -5)
y = -3x +15 -1 = -3x +14
The second piece can be written ...
f(x) = -3x +14 for x > 5
__
Whole functionPutting these pieces together, we have ...
[tex]\boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}[/tex]
_____
Additional comment
Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, x > 5.
The measure of an angle is 88 degrees. FInd the measure of its complement and the measure of its supplement.
Answers
Answer:
Step-by-step explanation:
Complementary angles add to 90 degrees, so the measure of its complement is 90-88=2 degrees.
Supplementary angles add to 180 degrees, so the measure of its supplement is 180-88=92 degrees.
find the m < VXW of the parallelogram
Answers
Answer: A
Step-by-step explanation:
Find the lateral surface area of the cylinder. use 3.14 for π, and round your answer to the nearest hundredth. refer to your staar 8th grade math reference sheet for the appropriate formula. question 10 options: 376.99 cm2 362.16 cm2 367.59 cm2 354.18 cm2
Answers
The lateral surface area of the given cylinder of radius 10cm and height of 5cm is 314cm sq.
What is the lateral surface area of the cylinder?For a right circular cylinder of radius r and height h, the lateral surface area is the product of diameter to the height and pie.
The lateral surface area of the cylinder = 2πrh
Let assume Radius, r = 10
Height, h = 5.
The lateral surface area of the cylinder = 2πrh
= 2 × 3.14 × 10 × 5
= 314cm sq.
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I NEED HELP ASAP !!!!!!!
Answers
Answer:
$42,782.40
Step-by-step explanation:
You want to know how much more Glados paid than Shaq on a 30-year mortgage if their monthly payments were $755.99 and $637.15, respectively.
Added amountEach month, Glados paid this amount more:
$755.99 -637.15 = $118.84
Over the 360-month life of the 30-year loan, this excess amount adds up to ...
360 × $118.84 = $42,782.40
Glados pays $42,782.40 more than Shaq for the same loan amount.
<95141404393>
On the same coordinate plane, mark all points (x, y) that satisfy each rule.
y = -3 -X
Answers
The rule y = -3 - x is an illustration of a linear equation
The points on the coordinate plane with the rule y = -3 - x are (0,-3), (1,-4) and (2,-5)
How to determine the points?The rule of the points is given as:
y = -3 - x
When x = 0, we have:
y = -3 - 0
y = -3
When x = 1, we have:
y = -3 - 1
y = -4
When x = 2, we have:
y = -3 - 2
y = -5
From the above computation, we have the following points
(0,-3), (1,-4) and (2,-5)
Hence, the points on the coordinate plane with the rule y = -3 - x are (0,-3), (1,-4) and (2,-5)
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The perimeter of a triangle is 29cm. The length of side 2 is double the length of side 1 the length of side 3 is 5 more than side 1. Find the side length of the triangle
Answers
Answer: 6 cm, 11 cm, 12 cm
Step-by-step explanation:
How many ways can 8 books be arranged on a shelf? Show all of your work for full credit.
Answers
There are 40,320 ways, in which 8 books can be arranged on a shelf.
Solution:Here, we are to find the number of ways in which 8 books can be arranged on a shelf. The total number of books is 8 and the way of arranging books is also 8.
If one book is placed in the first place, then 7 books will be placed in front of it. If 2 books are placed in the 2nd place, then only 6 books can be placed after that book. This sequence will continue till 1 .Permutations :
A permutation is an arrangement of objects in a definite order.➲ P ( n, r )= n ! / ( n - r ) !
n = total number of objectsr = number of objects selectedThe number of ways to arrange 8 books on a shelf will be :
➝ P ( n, r ) = n ! / ( n - r ) !
➝ P ( n, r ) = 8 ! / ( 8 - 8 ) !
➝ P ( n, r ) = 8 ! / 0 !
➝ P ( n, r ) = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / 1
➝ P ( n, r ) = 40, 320
ㅤㅤㅤㅤㅤㅤ~ Hence, there are 40,320 ways in which 8 books can be arranged on a shelf !
If the 3 books can't be together (but any 2 of the 3 can be) then it's 36,000 ways. If any one of the 3 books can't touch either of the other 2, it's 15,840 ways.
Explanation:I'm not sure if the question is saying that all three books can't be together in a group (and so biology and history can be together, but biology, history and programming can't), or if the books in that group can't sit next to other books in the group (and so biology and history can't be together). Let's do it both ways - case 1 will be all three together and case 2 will be any 2 together.
Before we work this, let's first see the number of ways we can have all 8 books arranged. Order matters and so we can approach this using a permutation equation. Moreover, since we're using all the books, we'll end up with the total number being:
8 ! = 40 , 320 .