Fifteen years from now, Atli’s age will be 4 times his current age. What is his current age?

It looks like your equation (it's not an identity) is

2 cos(5x) cos(3x) + sin(x) = cos(8x)

Recall that

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

==>   2 cos(x) cos(y) = cos(x + y) + cos(x - y)

so that

2 cos(5x) cos(3x) = cos(8x) + cos(2x)

Then the equation simplifies to

cos(8x) + cos(2x) + sin(x) = cos(8x)

cos(2x) + sin(x) = 0

Also recall that

cos(2x) = 1 - 2 sin²(x)

so the equation is quadratic in sin(x) and can be factorized:

1 - 2 sin²(x) + sin(x) = 0

2 sin²(x) - sin(x) - 1 = 0

(2 sin(x) + 1) (sin(x) - 1) = 0

Solve for x :

2 sin(x) + 1 = 0   or   sin(x) - 1 = 0

sin(x) = -1/2   or   sin(x) = 1

[x = arcsin(-1/2) + 2nπ   or   x = π - arcsin(-1/2) + 2nπ]   or   x = arcsin(1) + 2nπ

(where n is any integer)

x = -π/6 + 2nπ   or   x = -5π/6 + 2nπ   or   x = π/2 + 2nπ

Answer:

2*sqrt(5)

Step-by-step explanation:

By using Pythagoras theorem, we have

4^2+2^2=(the third side)^2

16+4=(the third side)^2

Third side=sqrt(20)=2*sqrt(5)

Answer:

4/5 foot

Step-by-step explanation:

Add the lengths together

1/2 +3/10

Get a common denominator

1/2 *5/5  + 3/10

5/10 + 3/10

8/10

Simplify the fraction by dividing the top and bottom by 2

4/5

[tex]\rm \implies \: Total \: \: length \: \: of \: \: tape \: = \: \frac{1}{2} \: + \: \frac{3}{10} \\ [/tex]

[tex]\bf \large \rightarrow \: \: \frac{5 \: + \: 3}{10} \: = \: \frac{8}{10} \\ [/tex]

Now , simplifying the fraction in simplest form.

[tex]\bf \large \rightarrow \: \: \cancel\frac{8 \: \: ^{4} }{10 \: \: ^{5} } \: = \frac{4}{5} \\ [/tex]

Christian have 4/5 foot of tape have now.

Answer:

98

Step-by-step explanation:

Answer:

y-intercept = -55

x-intercept =25

Step-by-step explanation:

I know how to do this

Answer:

Answer is 3.398

Step-by-step explanation:

Solve by putting into calculator.

Answer:

The answer is "[tex]\bold{6.6 \times 10^{12}\ years}[/tex]"

Step-by-step explanation:

Let the given value is:

[tex]R=\frac{1}{9^{17}}\\\\\to \frac{N_{c_{14}}}{N_{c_{12}}}=\frac{1}{9^{17}}\\\\\to t=\frac{2.303 \times 9^{17}}{5717}=6.6\times 10^{12}\ years[/tex]

Answer:

437.9

Step-by-step explanation:

Volume is pi*r^2*h=pi*(49)*9=437.9

Answer:

47%

Step-by-step explanation:

StartFraction 7 Over 15 EndFraction = 7/15

Equivalent Percentage

7/15 × 100

= 0.4666666666666 × 100

= 46.666666666666%

Approximate to the nearest whole percentage

= 47%

The answer is 47%

Answer:7

Step-by-step explanation:

Answer:

2x-24

I think that you changes the problem...

you went from a derivative to an inverse ???

y = 1/2x + 14

x = 1/2 y + 14

2x = y + 24

y = 2x-24

Step-by-step explanation:

Answer:

[tex]f^{-1}[/tex] (x) = 2x - 28

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = [tex]\frac{1}{2}[/tex] x + 14 ( multiply through by 2 to clear the fraction )

2y = x + 28 ( subtract 28 from both sides )

2y - 28 = x

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x)

[tex]f^{-1}[/tex] (x) = 2x - 28

Given:

Fixed cost = $150

Additional cost = $22.50

To find:

The equation that showing the cost of the gala depends on the number of attendees.

Solution:

Let x be the number of attendees and y be the cost of the gala.

Total cost = Fixed cost +Variable cost

We have,

Fixed cost = $150

Variable cost = Additional cost × Number of attendees

                      = [tex]22.50\times x[/tex]

                      = [tex]22.50x[/tex]

Total cost of gala is:

[tex]y=150+22.50x[/tex]

Therefore, the required equation is [tex]y=150+22.50x[/tex].

Step-by-step explanation:

According to the fundamentals of Mathematics, as well as corresponding mathematical principles, encompassing trigonometry, are acknowledged to provide the intergenerational definitions for subsequent generations.

Thus far, the radius is equated to half the diameter.

hope it helps you...............

Answer:

the answer is (x+1)(x+2)(2x+1)

Answer:

c

Step-by-step explanation:

Profit = 4.5 (240)-1080 = 0

the maximum profit would occur when u sell all 350 tickets,

profit = 4.5(350)-1080 = 495 (not a nor b)

Answer:

The statement that is true is C

Answer:

Jack

Step-by-step explanation:

convert the fractions to decimals to determine the person that painted the larger part of the wall

5/8 = 0.625

7/12 = 0.583

the fraction Jack painted is larger.

Answer:

9/49

Step-by-step explanation:

4 purple beads and 3 green beads= 7 beads

P( green) = green = total = 3/7

Replace the bead

4 purple beads and 3 green beads= 7 beads

P( green) = green = total = 3/7

P( green , replace, green) = 3/7 * 3/7 = 9/49

Answer:

x^ (-19/3)

Step-by-step explanation:

x ^ (-10/3)  ÷ x^3

We know a^b ÷ a^c = a^(b-c)

x ^ (-10/3)  ÷ x^3 = x^(-10/3 - 3) = x^(-10/3 - 9/3) = x^ (-19/3)

Answer:

Last option, y > -3/2x+1

That's the answer you're looking for

Answer:

Step-by-step explanation:

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

Answer:

6 -8n

Step-by-step explanation:

2/3 (9-12n)

Distribute

2/3 *9 - 2/3 *12n

6 -8n

Answer:

pi × 18cm^2

Or approximately,

56.52cm^2 (using 3.14 for pi)

or

56.5487cm^2 (using pi button on calculator)

Step-by-step explanation:

Area of a circle is pi times [radius squared].

All circles are 360°.

Problem can be solved by finding area of whole circle, and then using ratios.

Whole Circle: area = pi × (9cm)^2 = pi × 81cm^2

80° / 360° = Area[shaded] / (pi × 81cm^2)

pi × 18cm^2 = Area[shaded]

((If you read my answer before the edit, I am sorry. I made a calculator error.))

Answer:

Step-by-step explanation:

{7,11,13}

Answer:

a and b) 256

c) 5

d) 400

e) 10

Step-by-step explanation:

160(2) - 16(2)² = 320 - 64 = 256

h(2) = 256

find zeros

0 = -16x²-160x

0 = -16x(x-10)

-16x=0    x = 0

0 = x-10   x = 10

Δx₁,x₂ = 10/2 = 5    max height is at x = 5

find max height using x-value:

-16(5)²+160(5) = -80 + 480 = 400

for e) use second root (x = 10)

Answer:

580

Step-by-step explanation:

Assuming that the answer should be in terms of z scores, we can calculate the z score as

z = (observed value - mean)/(standard deviation)

For the first exam, the observed value is 86, the mean is 71, and the standard deviation is 20. The z score fot that exam is

z = (86-71)/20 = 0.75

Then, for the second exam, Evelyn has to do equivalently well, so the z score must be the same. Therefore, we have

0.75 = (observed score - 550)/40

multiply both sides by 40 to remove a denominator

0.75 * 40 = observed score - 550

add 550 to both sides to isolate the observed score

0.75 * 40 + 550 = observed score = 580

Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

substitute 2.1 for 't' in the given equation

h = 113.391

the center is (-7,5) and the radius is 2