Mathematics College

simplify sin(2x+7y)+sin(2x-7y)

Answers

Answer 1
sin(a+b)=sin a * cos b + sin b cos a
sin(a-b)=sin a * cos b - sin b cos a

Related Questions

“the sum of eight and twice w”

Answers

8+2w
Sum is +
twice w=2w
Sum of 8 and 2w
8+2w
hope this helps:)
please mark thanks and brainliest:)

Answer:

the expression is [tex]8+2w[/tex]

Step-by-step explanation:

WE need to write the expression for the given statement

“the sum of eight and twice w”

Expression represents the terms that contains variables and operations. the variable we use for the expression is 'w'

Difference represents the subtraction operation.

Sum represents the addition operation.

twice 'w' means 2 times w that is 2w

the sum of 8 and 2w

For sum we use '+'

so ,the expression becomes [tex]8+2w[/tex]

Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?

Answers

inequation 1: 

[tex] \frac{2}{3}x-3 \geq y[/tex]

to plot the pairs (x, y) for which the inequation holds, draw the line [tex]y=\frac{2}{3}x-3[/tex]

then pick a point in either side of the line. If that point is a solution of the inequation, than color that region of the line, if that point is not a solution, then color the other part of the line.

we do the same for the second inequation. Then the solution, is the region of the x-y axes colored in both cases.

inequation 2: 

[tex]y+ \frac{2}{3}x\ \textless \ 4 [/tex]

[tex]y\ \textless \ - \frac{2}{3} x+ 4 [/tex]


draw the lines 

i)  [tex]y=\frac{2}{3}x-3[/tex]          use points (0, -3),  (3, -1)

ii)[tex]y=- \frac{2}{3} x+ 4 [/tex]       use points ( 0, 4),   (3, 2)


let's use the point P(3, 3) to see what region of the lines need to be coloured:

[tex]\frac{2}{3}x-3 \geq y[/tex]  ; 
[tex]\frac{2}{3}(3)-3 \geq 3[/tex]
[tex]2-3 \geq 3[/tex], not true so we color the region not containing this point


[tex]y+ \frac{2}{3}x\ \textless \ 4 [/tex]
[tex](3)+ \frac{2}{3}(3)\ \textless \ 4 [/tex]
[tex]3+ 5\ \textless \ 4 [/tex] not true, so we color the region not containing the point (3, 3)

The graph representing the system of inequalities is the region colored both red and blue, with the blue line not dashed, and the red line dashed.



Answer:

in other words b

Step-by-step explanation:

Pamela is 13 years older than Jiri. The sum of their ages is 53 what is Jiri's age?

Answers

You are first told that Pamela is 13 years older than Jiri so:

p=j+13

Then you are told that the sum of their ages is 53 so:

p+j=53

We already know from the first statement that p=j+13, this makes p+j=53 become:

(j+13)+j=53  so we combine the two j's on the left side

2j+13=53  subtract 13 from both sides

2j=40  divide both sides by 2

j=20

So Jiri is 20 years old.

The solution is: Jiri is 20 years old.

What is addition?

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

Pamela is 13 years older than Jiri so:

p=j+13

Then you are told that the sum of their ages is 53 so:

p+j=53

We already know from the first statement that p=j+13, this makes p+j=53 become:

(j+13)+j=53  so we combine the two j's on the left side

2j+13=53  subtract 13 from both sides

2j=40  divide both sides by 2

j=20

So Jiri is 20 years old.

Hence, The solution is: Jiri is 20 years old.

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A student was asked to use the formula for the perimeter of a rectangle, P = 2l + 2w, to solve for l. The student came up with an answer, P -2w=2l. What error did The student make? Explain. Then solve for l

Answers

The student solved for 2l, not l. Dividing P -2w=2l by 2, we get l=P/2-w

2^-1 ∙ 2^-4 is what?

Answers

1/2 . 1/16 = 1/32

When the power is minus just flip the number and make it denominator and make the power positive
The rule for multiplying similar bases with exponents...

(a^b)(a^c)=a^(b+c)

In this case:

(2^-1)(2^-4)  

2^(-1-4)

2^-5  which is equal to:

1/(2^5)

1/32

what is the product x 2-16/2 x+8 . x3-2x2+x/x2+3x-4

Answers

   x^2 - 16      x^3 - 2x^2+x
------------- * ---------------------
    2x+8          x^2 + 3x -4

      (x+4)(x-4)        x (x - 1)(x - 1)
= ----------------- * ----------------------
       2(x+4)             (x + 4)(x - 1)

     x(x- 4) (x - 1)
= ----------------- 
       2 (x + 4)

Answer:

A on Edge 2021

[tex] \frac{x(x - 4)(x - 1)}{2(x + 4)} [/tex]

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. suppose a sample of 100 major league players was taken. find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.

Answers

Final answer:

The probability is approximately 0.267.

Explanation:

To find the approximate probability that the mean salary of the 100 players exceeded $4.0 million, we can use the Central Limit Theorem and the Z-score formula. The Z-score formula is:

Z = (x - μ) / (σ / sqrt(n))

where x is the value we want to find the probability for (in this case $4.0 million), μ is the mean of the population ($3.26 million), σ is the standard deviation of the population ($1.2 million), and n is the sample size (100).

We calculate the Z-score as follows:

Z = (4.0 - 3.26) / (1.2 / sqrt(100)) = 0.617

We then use a Z-table or a calculator to find the probability corresponding to a Z-score of 0.617. The probability is approximately 0.267.

Find the surface area of a regular pentagonal prism with side length 8, altitude 20, and apothem approximately 5.5

Answers

Final answer:

The surface area of a regular pentagonal prism can be found by calculating the area of the pentagonal bases and the area of the rectangular sides and then summing those areas together.

Explanation:

Calculating the Surface Area of a Regular Pentagonal Prism

To find the surface area of a regular pentagonal prism with given dimensions, we need to calculate the area of two components: the area of the pentagonal bases and the area of the rectangular sides (also called the lateral faces). We are given that the side length (s) of the pentagon is 8 units, the prism's altitude (h), or height, is 20 units, and the apothem (a) is approximately 5.5 units.

Firstly, the area of a pentagon (Apentagon) is calculated using the formula Apentagon = ½ * perimeter * apothem, where the perimeter (P) of a regular pentagon is the side length multiplied by 5. Thus, the area of one pentagonal base is ½ * 5 * 8 * 5.5. Next, to find the entire area of the two pentagonal bases, we multiply this result by 2.

The area of each of the rectangular sides can be found by multiplying the side length by the prism's altitude. Since there are 5 identical rectangular sides in a regular pentagonal prism, their total area is 5 * 8 * 20.

Adding these two results together gives us the total surface area of the prism. So, the formula for the surface area is Total Surface Area = (2 * ½ * 5 * 8 * 5.5) + (5 * 8 * 20).

this box can be packed with 48 unit cubes the edge length each unit cube is 1 meter what is the voume of the box

Answers

Since each cube has a volume of 1 cubic meter and the box and fit 48 unit cubes the volume of the box is 48  cubic meters.

Answer:

48  cubic meters.

Step-by-step explanation:

48x1

unit meter is cubic meters

The formula can be used to find the velocity v in feet per second of an object that has fallen h feet. Find the velocity of an object that has fallen 25 feet. Round your answer to the nearest tenth.

Answers

I assume you are looking for the formula, and the velocity.

The formula:
v1^2-v0^2=2aS

where
v0=initial velocity (0 if object falls from rest), ft/s
v1=velocity reached after falling a distance S, ft/s
S=distance from initial position, positive downwards (for falling objects), ft
a=acceleration due to gravity, 32.2 ft/s^2 in imperial units

So substituting numbers, assuming initial velocity is zero (from rest), then
S=25 ft
v1^2-0^2=2*32.2*25
v1^2=1610
v1=sqrt(1610)
=40.1 ft/s

Write the quadratic function in the form g(x)= a (x-h)^2 +k . Then, give the vertex of its graph. g(x)=3x^2+30x+72
Writing in the form specified: g(x)= ___
Vertex:___

Answers

so hmmm as you may know by now...   [tex]\bf \begin{array}{cccccllllll} {{ a}}^2& + &2{{ a}}{{ b}}&+&{{ b}}^2\\ \downarrow && &&\downarrow \\ {{ a}}&& &&{{ b}}\\ &\to &({{ a}} + {{ b}})^2&\leftarrow \end{array}\qquad % perfect square trinomial, negative middle term \begin{array}{cccccllllll} {{ a}}^2& - &2{{ a}}{{ b}}&+&{{ b}}^2\\ \downarrow && &&\downarrow \\ {{ a}}&& &&{{ b}}\\ &\to &({{ a}} - {{ b}})^2&\leftarrow \end{array}[/tex]

is a perfect square trinomial

now, let's take a closer look at the middle guy
is just 2 * guy on the left * guy on the right
so the middle term is just the product of the  two terms of the binomial, without the exponent, or square rooted, and 2

alrite... that said.... now let's do some grouping

[tex]\bf g(x)=3x^2+30x+72\implies g(x)=(3x^2+30x)+72 \\\\\\ g(x)=3(x^2+10x)+72\implies g(x)=3(x^2+10x+\boxed{?}^2)+72[/tex]

so hmm we're missing the guy on the right there... who may that be?

well, we know the middle term is 10x, wait a minute, 10x is just 2 * 5 * x

so, if the guy on the left is "x", the other guy must be "5", 2*5*x = 10x

now, what we do is, we add 5²

however, bear in mind that, all we're doing is, borrowing from our very good friend Mr Zero, 0

so, if we add 5², we also have to subtract 5², so +5² - 5²

let's do so

[tex]\bf g(x)=3(x^2+10x)+72\implies g(x)=3(x^2+10x\boxed{+5^2-5^2})+72 \\\\\\ \textit{let's take out the negative from the group} \\\\\\ g(x)=3(x^2+10x+5^2)+\boxed{3(-5^2)}+72 \\\\\\ g(x)=3(x^2+10x+5^2)-75+72\implies g(x)=3(x+5)^2-3 \\\\\\ g(x)=3[x-(-5)]^2-3[/tex]

[tex]\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} y=a(x-{{ h}})^2+{{ k}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ \begin{array}{lcclll} g(x)=3[x-&(-5)]^2&-3\\ &\uparrow &\uparrow \\ &h&k \end{array}[/tex]

What is the next number of 2 7 8 3 12 9

Answers

6 would be the next number in pattern

Answer with Step-by-step explanation:

We are given a pattern  

2 7 8 3 12 9

and we are asked to find the next term of this pattern

2+1=3

7+5=12

and 8+1=9

We can view this pattern in the set of three numbers and then, the next three are formed by  adding one, five & one, respectively.

See these COLUMNS of groups of three:

2  3   4

7 12 17

8  9  10

Hence, next number in the pattern is:

4

Differentiate
1/√x^2-1

Answers

the function is [tex]f(x)= \frac{1}{ \sqrt{ x^{2} -1}} [/tex]

write f again as [tex]f(x)= (x^{2} -1)^{- \frac{1}{2} } [/tex] 

(the power -1 takes the expression to the denominator, and the power 1/2 is square root)

writing rational expressions as power expressions, generally makes differentiation more practical.

In [tex]f(x)= (x^{2} -1)^{- \frac{1}{2} } [/tex] we notice 2 functions:

the outer function [tex]u^{ -\frac{1}{2} } [/tex], where [tex]u=x^{2} -1[/tex], and the inner, u itself , which is a function of x.

So we differentiate by using the chain rule:

[tex]f'(x)= -\frac{1}{2}u^{- \frac{1}{2}-1 }*u'= -\frac{1}{2}u^{- \frac{3}{2} }*(2x)=- \frac{x}{ \sqrt{ u^{3} } } =- \frac{x}{ \sqrt{ (x^{2} -1)^{3} } }[/tex]


Answer: [tex]- \frac{x}{ \sqrt{ (x^{2} -1)^{3} } }[/tex]

A triangle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of the remaining board?

Answers

you must first subrtact 4 -6 to get 42 then add 99 

Based on the historical record what is the empirical probability that the city will be hit by a tornado

Answers

25.875% Chance of the city being hit by a tornado.

In a glide reflection, what comes first and what comes second?
first the glide, and second another glide
first the glide, and second a reflection
first the reflection, and second another reflection
first the reflection, and second a glide

Answers

First the glide, and second a reflection
Final answer:

In a glide reflection, the reflection comes first and the glide comes second.

Explanation:

In a glide reflection, first the reflection is applied, and second a glide is performed. The reflection is a transformation that flips the shape across a line of reflection, while the glide is a transformation that slides the shape along a vector. The combination of the reflection and glide creates a glide reflection.

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Write 935.97 in expanded form

Answers

 935.97 = 900 + 30 + 5 + 0.9 + 0.07

hope it helps

What are the spherical coordinates of the point whose rectangular coordinates are (4,1,4)?

Answers

Final answer:

The spherical coordinates for the given rectangular coordinates (4,1,4) can be calculated using formulas for the transformation. They approximately yield (sqrt(33), 0.505, 1.540).

Explanation:

In mathematics, we can convert rectangular coordinates to spherical coordinates using given formulas. Here, we have the rectangular coordinates (4,1,4). The transformation from rectangular to spherical involves three-step calculations:

First, calculate the radial coordinate, r, which is the distance from the origin to the point. It is given by r = sqrt(x^2 + y^2 + z^2).Second, find the polar angle, theta, measured relative to the vertical z-axis. It is given by cos(theta) = z/r.Lastly, find the azimuthal angle, phi, measured relative to the x-axis. It is given by cos(phi) = x/(r*sin(theta)).

Applying the formulas, we get: r = sqrt(4^2 + 1^2 + 4^2) = sqrt(33), theta = cos^-1(4/sqrt(33)) which is approximately 0.505, and phi = cos^-1(4/sqrt(33)*sin(0.505)) which is approximately 1.540.

So, the spherical coordinates of the point whose rectangular coordinates are (4,1,4) are approximately (sqrt(33), 0.505, 1.540).

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Write 337,060 in expanded form using exponents

Answers

3x10^5 \\ +3x10^4 \\ +7x10^3 \\ + 0x10^2 \\ +6x10^1 \\ +0x10^0

A cylinder has a base area of 169π cm2 . Its height is 4 cm more than the radius. Identify the volume of the cylinder. Round to the nearest tenth, if necessary.

Answers

check the picture below.

Answer:

V = 9025.8 cm3

Step-by-step explanation:

What is a ratio equivalent to 8/10 with lower terms

Answers

You divide both the top and bottom by the GCF (Greatest common factor)

In this case the gcf is 2 so you divide both 8 and 10 by 2, and you get 4/5.

The length of the hypotenuse is:
0.
1.
2.
4.

Answers

divide the base by the sin of the opposite angle

 base = 2

opposite angle = 30 degrees

2/sin(30) = 4

 x = 4

Assume the Poisson distribution applies. Use the given mean to find the indicated probability.

Find ​P(4​) when μ = 8.

Answers

For given Poisson distribution, μ=8.

P(k)=μ^k*e^(-μ)/k!
so
P(4)=8^4*e^(-8)/4!=0.05725 approx.

Final answer:

Using the Poisson distribution formula, substitute the given mean and the number of occurrences into the formula to find the probability. Hence P(4; 8)= e^-8 * 8^4 / 4!. The answer will be in decimal form, signifying the probability.

Explanation:

The probability in a Poisson distribution that an event happens exactly k times when the mean occurrence rate (μ or Lambda) is given is determined using the following formula:

P(k; μ) = (e^-μ * μ^k) / k!

Where e is Euler's number (approximately equal to 2.71828), k is the number of occurrences (in this case, it is 4) and μ is the mean number of occurrences (in this case, it is 8).

Applying the values into the formula, we have:

P(4;8) = (e^-8 * 8^4) / 4!

You can calculate the above expression using a calculator to find the probability. Remember, the answer will be in decimal form, representing the probability of the event occurring 4 times when the average rate of occurrence is 8.

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A line passes through the point (6−6) and has a slope of 3/2 . Write an equation in point-slope form for this line.

Answers

y= (3/2)x-15 is the equation 

Preston goes on a camel safari in Africa. They travel 5 km north, then 3km east and then 1 km north again. What distance did he cover? What was his displacement?

Answers

what distance did he cover? well, he went 5km first, then 3km, then 1km, 5 + 3 + 1, is how much he covered.

what was his displacement? well, he has a north displacement of 6, 5 + 1, and a horizontal displacement of 3, check picture below.

so, his total displacement is "c" northeast.

The total distance Preston covered on his camel safari is 9 km, and his displacement is 6.71 km toward the northeast.

Determining Distance and Displacement

To answer the student's question about Preston's journey during his camel safari, we need to consider the definitions of distance and displacement.

Distance is the total length of the path traveled regardless of direction. In Preston's case, he traveled 5 km north, then 3 km east, and then 1 km north again. Therefore, the total distance covered is the sum of these individual distances

Displacement, on the other hand, measures the change in position from the starting point to the final point and is direction-dependent. It is a vector quantity with both magnitude and direction. To find the displacement, we can represent Preston's movement on a coordinate system with north being the positive y-direction and east being the positive x-direction.

From the starting point, moving 5 km north and then 1 km north results in a total of 6 km in the positive y-direction.

The magnitude of the displacement can be calculated using the Pythagorean theorem:

√((6 km)² + (3 km)²) = √(36 km² + 9 km²) = √(45 km²) = 6.71 km (rounded to two decimal places)The direction of the displacement would be to the northeast. Therefore, Preston's displacement is 6.71 km toward the northeast.

A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)=52t-16t^2 . What is the maximum height that the ball will reach? Do not round your answer.
Height: ________Feet

Answers

A quick way to do this problem is to use the vertex formula as if you were trying to graph the parabolic function. 
We know that in this case the vertex is at a maximum height because the leading coefficient is negative. If it were positive, then the vertex would be at the lowest point, in other words, they would ask you to solve for the lowest point. In this case we are solving for the highest point. 
Primarily, we can use the axis of symmetry formula to solve for the x-coordinate of the vertex which demonstrates the time the object takes to reach its apex. Once we find the t or the x-coordinate, we can plug it back into the equation to solve for the h or height. 
Axis of symmetry formula: -b/ 2a

(b) is 52 in this case. (a) is -16 in this case. Just plug the numbers in but be mindful of the signs included in the formula. 
-(52)/ 2(-16) = -52/-32
The quotient would be a terminating decimal: 1.625

Therefore, the time it takes for the ball to reach its highest point would be 1.625 seconds. Now you can plug this number back in as a substitution for the variable t and you can solve for h. 

h = -16(1.625)^2 + 52(1.625)
h = -16(2.640625) + 84.5
h= -42.25 + 84.5
h = 42.25 
Therefore, the maximum height that the ball will reach in 1.625 seconds is 42.25 feet. 

The maximum height would be 42.25 feet that the ball will reach.

What is the velocity?

Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.

A vertical upward throwing of a ball Its height h after t seconds (in feet) is given by the function h(t) = 52t - 16t²

Here h(t) = 52t - 16t²

Differentiate with respect to t to get maximum height

h'(t) = 52 - 2 × 16t

h'(t) = 52 - 32t

In this position, the acceleration would be zero,

So 0 = 52 - 32t

32t = 52

t = 52/ 32

t = 1.625

Substitute the value of t = 1.625 in the given function,

⇒ h = 52(1.625) - 16(1.625)²

⇒ h = 84.5 - 42.25

⇒ h = 42.25

Therefore, the maximum height would be 42.25 feet that the ball will reach.

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Ricky is filling an 8 inch by 4 inch by 4 1/2 inch rectangular box with packing peanuts. The peanuts are cubes that come in two different sizes ,1 cubic inch and 1/8 inch .How many peanuts of each size are needed to fill the box?

Answers

First find the volume of the box: 8•4•4.5=144 cubic inches.
8 of the 1/8 inch=1 of the 1 cubic inch
He could do 144 and 0
143 and 8
142 or 16
Or just keep following the pattern... Hope that helped

A pilot can travel 540 miles with the wind in the same amount of time as 380 miles against the wind. Find the speed of the wind if the pilots speed in still air is 230 miles per hour.

Answers

t=d/v

540/(230+w)=380/(230-w)

540(230-w)=380(230+w)

124200-540w=87400+380w

124200-920w=87400

-920w=-36800

w=40

So the wind speed is 40 miles per hour.

Rewrite the equation in standard form and identify a, b, and c. 2x^2 + 6x - 9 = 3x^2 - 11x - 7

Answers

[tex]2x^2 + 6x - 9 = 3x^2 - 11x - 7\\ x^2-17x+2=0\\ a=1\\ b=-17\\ c=2[/tex]
2x^2 + 6x - 9 = 3x^2 - 11x - 7

Subtract 2x^2 from both sides
6x - 9 = x^2 - 11x - 7

Substract 6x from both sides
-9 = x^2 - 17x - 7

Add 9 to both sides
0 = x^2 - 17x + 2

a = 1
b = -17
c = 2

A collection of quarters and nickels is worth ​$3.75. There are 27 coins in all. Find how many of each there are.

Answers

Q +N =27

Q=27-N

0.25Q + 0.05N =3.75

0.25(27-N) + 0.05 =3.75

6.75-0.25N+0.05N=3.75

6.75-0.2N=3.75

-0.2N=-3

N=-3/-0.2 = 15

15 nickels

27-15 = 12

12 quarters

15x0.05 = 0.75

12 x 0.25 = 3.00

3.00 + 0.75 = 3.75


 12 quarters & 15 nickels

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