if cos7x-cos8x/1+2cos5x=cos(ax)-cos(bx),where a,b are positive integers, then a²+b²=??

pls help! :(​

Answers

Answer 1

Step-by-step explanation:

[tex]hope \: its \: helful[/tex]

If Cos7x-cos8x/1+2cos5x=cos(ax)-cos(bx),where A,b Are Positive Integers, Then A+b=??pls Help! :(
If Cos7x-cos8x/1+2cos5x=cos(ax)-cos(bx),where A,b Are Positive Integers, Then A+b=??pls Help! :(
Answer 2

if cos7x - cos8x/1 + 2cos5x = cos(ax) - cos(bx), where a, b are positive integers, then a²+b²= 100.

The given equation is:

cos7x - cos8x/1 + 2cos5x = cos(ax) - cos(bx)

The LHS can be expanded as follows:

cos7x - cos8x/1 + 2cos5x = (2*cos4x*sin3x)/(2*cos2x) = sin3x

The RHS can be expanded as follows:

cos(ax) - cos(bx) = -2sin((a + b)/2)*sin((a - b)/2)

For the given equation to be true, the following must be true:

sin3x = -2sin((a + b)/2)*sin((a - b)/2)

3x = 180(a + b)/2

3x = 180(a - b)/2

Solving for a and b, we get a=6 and b=3.

Therefore, a² + b² = 6² + 3²=100.

To learn more about positive integers, here

https://brainly.com/question/26051073

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Related Questions

HELPPP!!
Rate the following bank accounts from most to least liquid: CD, savings account, checking account, money market
account
a. CD, savings account, checking account, money market account
b. Savings account, checking account, CD, money market account
C. CD, money market account, savings account, checking account
d. Checking account, savings account, money market account, CD
Please select the best answer from the choices provided
OA
OB
О С
OD

Answers

Answer:

C

Step-by-step explanation:

There isn’t one

I need help make sure to round it to the nearest 10th

Answers

Answer:

10.52

Step-by-step explanation

Answer: x= 10.5

Step by step explanation: in order to find the missing side you need to use sin=opposite/hypotenuse, which gets you sin26*=x/24, multiply both sides by 24 which will get you 24(sin26*)=x once rounded to the nearest tenth will give you the result of 10.5

What is the slope of the line shown below?
10+
5
(9, 1)
o A. -
OB.
OC
10
15
(-3,-7) 5
10
O
D.
WIN

Answers

Answer:

D 2/3

Step-by-step explanation:

Rise over run. The x values is -3 and 9 which is the distance or run between the dots. Find the distance by finding which number is between then so -3+x=9 where x is 12. The y values are -7 and 1. Find y where -7+y=1 where y is 8. That is the rise. So the rise is 8 and that is over the run, 12, gives you 8/12 which can be simplified to 2/3.

Round off all these
1) 378811,
2) 267988,
3) 250260,
4) 196596,
5) 193171
to the nearest ten thousand

Answers

Answer:

1. 380,0002. 270,0003. 250,0004. 200,0005. 190,000

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

378811=380000267988=270000250260=250000196596=200000193171=200000

If give 7 billions for 7 millions people. What is total?

Answers

Answer:

this is a very big number

Step-by-step explanation:

(7000000000)⁷⁰⁰⁰⁰⁰⁰

Determine the rule of a quadratic function in factored
form given the following information:
.
the zeros are (-2,0) and (4,0)
it passes through the point (5,14)
.

Answers

Answer:

[tex]y=2(x+2)(x-4)[/tex]

Step-by-step explanation:

Hi there!

Factored form: [tex]y=a(x-r)(x-s)[/tex] where r and s are two zeros

Given that the zeros are (-2,0) and (4,0), we know that -2 and 4 are r and s in the above equation. Plug these in:

[tex]y=a(x-(-2))(x-(4))\\y=a(x+2)(x-4)[/tex]

Now, to solve for a, plug in the given point (5,14) as (x,y):

[tex]14=a(5+2)(5-4)\\14=a(7)(1)\\14=7a\\a=2[/tex]

Therefore, a=2. Plug this back into the original equation:

[tex]y=2(x+2)(x-4)[/tex]

I hope this helps!

PLEASE HELP!!!PLEASE HELP!!!PLEASE HELP!!!PLEASE HELP!!!PLEASE HELP!!!PLEASE HELP!!!

Answers

So here, for basically any quadratic function, the domain is: [tex]x \in \mathbb{R}[/tex].

Now right off the bat, that means C and D are out.

Also, since this graph has a negative sign in front of the x^2, that means it is facing downwards and so it has a maximum. The only option that leaves us with is A.

what's the answer for this? ​

Answers

Answer:

A

Step-by-step explanation:

Observe the coordinates of C, it's (5,2). Now observe C' which is (2, - 5). Hence the rule is (x, y) -> (y, - x)

Find the perimeter of the sector of a circle of radius 14cm with an angle of 72 degree

Answers

Answer:

the area sector is 123.2

Its awpicture please help if you can

Answers

Someone help me... please

geometry translations help!!

Answers

Answer:

A' (7,-8)

B' (8,-11)

C' (4,-10)

Answered by GAUTHMATH

Answer:

Step-by-step explanation:

A will be 7,-8

B will be 8,-11

C will be 4,-10

How?

add 3 to the x coordinate of the original points and -7 to the y coordinate of the original points, Example: 4+3 = 7 and -1+-7 = -8

How to do this???????

Answers

Answer:

x=14

Step-by-step explanation:

Form an equation; since the two sides are the same length set them equal to each other. 2x-9=x+5 the solve

2x=x+14

x=14

then you can plug it back in to check if you want

2(14)-9 = 19

14+5 = 19

Answer:

14

Step-by-step explanation:

2x-9=x+5 (being isosceles triange)

2x-x=5+9

x=14

hope u understood

Have to finish these by the 23rd :(

Answers

Answer:

5/6

Step-by-step explanation:

x²- 3x + 7 / x + 4

when [x = 2]

Putting the value of x,

2² - 3(2) + 7 / 2 + 4

= 4 - 6 + 7 / 6

=5 / 6

One of the factors of x² + y² + 2xy - z² is ?​

Answers

Answer:

x + y + z.

Step-by-step explanation:

x² + y² + 2xy - z²

= (x + y)^2 - z^2

This is the difference between 2 squares so the factors are:

(x + y + z) and (a + y - z).

Answer: The factors are (x+y+z) and (x+y-z)

In other words, it factors to (x+y+z)*(x+y-z)

=====================================================

Work Shown:

[tex]x^2 + y^2 + 2xy - z^2\\\\(x^2 + 2xy + y^2) - z^2\\\\(x+y)^2 - z^2\\\\(x+y+z)(x+y-z)\\\\[/tex]

Notes:

In the third step, I used the rule (A+B)^2 = A^2+2AB+B^2. For this, A = x and B = y.In the last step, I used the difference of squares factoring rule A^2-B^2 = (A+B)(A-B). In this case, A = x+y and B = z.

Triangle LMN is dilated by a factor of 1.25 to create triangle PQR what is the length of PQ A 20 cm B 18.75 cm C 17 cm di 12 cm

Answers

Answer:

See explanation

Step-by-step explanation:

Given

[tex]\triangle LMN \to \triangle PQR[/tex]

[tex]k = 1.25[/tex]

Required

The length of PQ

[tex]\triangle LMN \to \triangle PQR[/tex] means that the side lengths of LMN are multiplied by 1.25 to get the side lengths of PQR

And it implies that the following sides are corresponding

[tex]LM \to PQ[/tex]

[tex]MN \to QR[/tex]

[tex]LN \to PR[/tex]

So, we have:

[tex]PQ = k * LM[/tex]

[tex]PQ = 1.25* LM[/tex]

The question is incomplete.

Assume LM = 16, then:

[tex]PQ = 1.25* 16[/tex]

[tex]PQ = 20[/tex]


In parallelogram ABCD, what is BDC?

Answers

Answer:

25

Step-by-step explanation:

<ABD=<BDC

Check it out

Answer:

∠ BDC = 25°

Step-by-step explanation:

Since ABCD is a parallelogram , then

AB and DC are parallel , so

∠ BDC = ∠ ABD = 25° ( alternate angles )

Which of the following is an example of exponential growth?
A. Investing $1,000 at an annual interest rate of 3%, compounded monthly
B. A bacterial culture increases by 1,000 bacteria per day
C. The height of a tree increases by 2 feet each year
D. Water drips into a bucket at a rate of 2 pints each minute

Answers

An example of an exponential function is given as follows:

A. Investing $1,000 at an annual interest rate of 3%, compounded monthly.

What is an exponential function?

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

A(0) is the initial value.r is the growth rate, as a decimal.

As we saw above, the rate of change is a percent, and in this problem, only option A has a rate of change as a percent, hence it is an exponential function.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of y = 2x2 – 12x + 6.

Answers

Step-by-step explanation:

The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non-trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011. The Riemann hypothesis, a famous conjecture, says that all non-trivial zeros of the zeta function lie along the critical line.

s

SO, LAST IS CORRECT

?ARK ME AS BRAILIEST

5. Find the measure of x and and the angle measure.
(3x - 15)
(2x + 7)

Answers

Answer:

here's the answer to your question

A pole that is 2.7 m tall casts a shadow that is 1.56 m long. At the same time , a nearby building casts a shadow that is 38.25 m long. How tall is the building ? Round your answer to the nearest meter.

Answers

Set up a ratio of height/ shadow

2.7/1.56 = x/38.25

Cross multiply:

1.56x = 103.275

Divide both sides by 1.56

X = 66.2

Round to nearest meter = 66

Answer: 66 meters

Solve the system of equations and choose the correct ordered pair.
4x - 2y = -2
6x + 3y = 27
A. (2,5)
B. (3,7)
C. (0, -1)
D. (0,9)

Answers

Answer:

(2,5)

Step-by-step explanation:

4x - 2y = -2

6x + 3y = 27

Divide the first equation by 2 and the second equation by 3

2x - y = -1

2x + y = 9

Add the equations together

2x - y = -1

2x + y = 9

-------------------

4x = 8

Divide by 4

4x/4 = 8/2

x =2

2x+y = 9

2(2) +y = 9

4+u = 9

y = 9-4

y=5

(2,5)

The Oxy coordinate plane for two parallel lines a and a' has the equations 2x - 3y-1 = 0 and 2x - 3y + 5 = 0. respectively. Which vector translation to convert a to a'

Answers

Answer:

Remember that a vector translation can be written as:

T(a, b)

And if we apply this to a random point, (x, y), the translation gives:

T(a, b)(x, y) = (x + a, y + b)

now, remember that a general line can be written as:

y = m*x + s

Then a point of that line can be written as: (x, m*x + s)

Then if we apply the translation to a point in the line, we get:

T(a, b)(x, m*x + s) = (x + a, m*x + s + b)

Here we have two lines:

2x - 3y - 1 = 0

2x - 3y + 5 = 0

First, let's rewrite both of these in the slope-intercept form:

y = (2/3)*x - 1/3

y = (2/3)*x + 5/3

Now let's assume that we apply a translation to the first line, that has points of the form (x,  (2/3)*x - 1/3), such that we want to get points of the form:

(x, (2/3)*x + 5/3).

Then we must have:

T(a, b)(x,  (2/3)*x - 1/3) = (x + a,  (2/3)*x - 1/3 + b) = (x, (2/3)*x + 5/3).

Then we need to solve:

(x + a,  (2/3)*x - 1/3 + b) = (x, (2/3)*x + 5/3).

This means that:

x + a = x

(2/3)*x - 1/3 + b = (2/3)*x + 5/3

From the first equation, we can see that a = 0

Now we can solve the second one to find the value of b.

(2/3)*x - 1/3 + b = (2/3)*x + 5/3

subtracting (2/3)*x in both sides, we get:

-1/3 + b = 5/3

b = 5/3 + 1/3

b = 6/3 = 2

b = 2

Then the vector translation is:

T(0, 2)

So it moves the whole line 2 units upwards.

10^12 X (5.0 x 10^8) X (3.33 x 10^0) =

Answers

Answer:

1.665e+21

Step-by-step explanation:

hope it help

make it as brininst

Answer:

[tex]10^{12}\left(5\cdot \:10^8\right)\left(3.33\cdot \:10^0\right)[/tex]

Exponent rule:  [tex]a^b\cdot \:a^c=a^{b+c}[/tex]

[tex]10^{12}\cdot \:10^8\cdot \:10^0=\:10^{12+8+0}[/tex]

[tex]5\cdot \:3.33\cdot \:10^{12+8+0}[/tex]

Now, add 12 + 8 + 0 =20

[tex]=5\cdot \:3.33\cdot \:10^{20}[/tex]

Multiply 5 × 3.33=16.65

[tex]=10^{20}\cdot \:16.65[/tex]

Convert to decimal form

[tex]10^{20}=1.0E20[/tex]

Multiply

[tex]16.65\cdot \:1.0E20=1.665E21[/tex]

OAmalOHopeO

A blueprint for a lighthouse uses a scale of 1 in.:5 ft. The lighthouse in the blue print is 6 in. tall. How tall is the actual lighthouse?

Answers

it would be 30ft tall, because each inch = 5 ft, therefore, 6 x 5 = 30.

Answer:

30 ft

Step-by-step explanation:

5 X

— = —

1 6


5•6=30

30/1= 30


therefore the answer is 30 ft

8.

The table shows the estimated number of deer living in a forest over a five-year period. Are the data best represented by a linear, exponential, or quadratic model? Write an equation to model the data.


A. quadratic; y = 0.79x2 + 98

B. linear; y = 0.79x + 98

C. quadratic; y = 98x2 + 0.79

D. exponential; y = 98 • 0.79x

Answers

Answer:

D. exponential; y = 98 • 0.79x

Step-by-step explanation:

Answer:

Option D is correct.

Exponential model are the data best represented.

Equation:  

Step-by-step explanation:

An exponential function is in the form of   .....[1] where a is the initial value and b≠0 , b > 1.

Consider any two points from the table;

(0, 98) and ( 1, 77)

Then substitute these in [1];

For (0, 98)

x = 0 and y = 98 substitute in [1] we get;

98 = a

Similarly, For (1, 77)

we have;

77 = ab

Substitute the value of a =98 we get;

Divide both sides by 98 we get;

⇒ b = 0.79

We get an equation;  

Therefore, the data represent here is, Exponential function.

also, an equation to model the data is;  

...............................................................................................................................................

All the functions grow with x except B that decreases when x grows. That i your function. Also check that when you divide the population of two consecutive years, the ratio remains 0.79 approx

The solution is D

...............................................................................................................................................

Exponential would be the correct answer I believe...

...............................................................................................................................................

For a better understanding of the explanation provided here please find the attachment.

The solution will employ the use of the trial and error method and basic math.

As can be see from the given data, the deer population keeps on falling from the year zero. Thus, we can safely conclude that the quadratic and the linear models will not represent the situation at all.

We are left with the exponential model and since we have  in it we can see that the deer population will fall as the years pass.

We have checked it in the table that has been provided and we have concluded that the data is best represented by the exponential model because when the exponential formula is applied it is almost equal to the actual number of deers.

Please check the attached table for a better understanding.

Amy is biking to school from her father's house and Jeremy is biking to school from his aunt's house. Suppose Amy is moving at a rate 10 miles per hour and Jeremy is moving at a rate of 8 miles per hour. Can you assume that Amy will get to school first?

Answers

Answer:

No, more information is needed to prove that Amy will get to school first.

Step-by-step explanation:

Even though Amy is traveling at a faster rate than Jeremy, the problem does not say how far away Amy's father's or Jeremy's aunt's houses are from the school.  

Answer:

Step-by-step explanation:

No, the rate with the greater positive rate of change will not necessarily reach the output with the smallest input. The initial value will also affect the outcome. Although Amy is biking at a faster rate of change, Jeremy might get to school before her if his aunt lives closer to the school than her father does.

Explanation: Edge. said so.

If 12(x - a)(x - b) = 12x² - 7x - 12 , then ab =

Answer choices :

1
-1
7
12
-12​

Answers

Answer: -1

Step-by-step explanation:

12x^2-7x-12 = (4x+3)(3x-4)

4x+3=0. X = -3/4

3x-4=0. X = 4/3

(-3/4) (4/3) = -1

I rlly need help like pleasee

The parallelogram in Quadrant III is the image of the parallelogram in Quadrant II after a counterclockwise rotation about the origin. What is the angle of rotation?

A.) 90 B.) 180 C.) 270 D.) 360​

Answers

Answer:

A. 90

Step-by-step explanation:

Correct on EDGE

Answer:

maybe 90

Step-by-step explanation:

calculate the speed, in ms-¹ of vehicle A and of vehicle B​

Answers

9514 1404 393

Answer:

A: 0.32 m/sB: 0.56 m/s

Step-by-step explanation:

The speed is the ratio of the change in distance to the corresponding change in time.

Vehicle A moves from a position of 12 m to one of 28 m in 50 seconds, so its speed is ...

  A = (28 -12)/50 m/s = 16/50 m/s = 0.32 m/s

Vehicle B moves from 0 to 28 m in 50 seconds, so its speed is ...

  B = (28 m)/(50 s) = 0.56 m/s

Can someone help thanks.

Answers

Answer:

1/144

Step-by-step explanation: I presume..

And recall something from Algebra...

I hope it helps...

Square it

And reverse it because of the negative

It is a fraction

Answer:

[tex] = { \sf{ \frac{1}{ 144 } }}[/tex]

Step-by-step explanation:

[tex] = { \tt{ \frac{1}{ {12}^{2} } }} = \frac{1}{144} [/tex]

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