A seagull is floating on the surface of the ocean when it takes off and flies upward at a rate of 4 ft per second. After 19 seconds, how far away from the surface of the water will the seagull be?

Use the angle sum identities to expand [tex]\sin(3A)[/tex] and [tex]\cos(3A)[/tex]:

[tex]\sin(3A)=\sin(A+2A)=\sin A\cos(2A)+\cos A\sin(2A)[/tex]

[tex]\cos(3A)=\cos(A+2A)=\cos A\cos(2A)-\sin A\sin(2A)[/tex]

Use the double angle identity to expand [tex]\sin(2A)[/tex]:

[tex]\sin(2A)=2\sin A\cos A[/tex]

So we have

[tex]\sin(3A)=\sin A\cos(2A)+2\cos^2A\sin A[/tex]

[tex]\cos(3A)=\cos A\cos(2A)-2\sin^2A\cos A[/tex]

Then divide the first expression by [tex]\sin A[/tex] and the second by [tex]\cos A[/tex]:

[tex]\dfrac{\sin(3A)}{\sin A}=\cos(2A)+2\cos^2A[/tex]

[tex]\dfrac{\cos(3A)}{\cos A}=\cos(2A)-2\sin^2A[/tex]

Squaring these gives

[tex]\dfrac{\sin^2(3A)}{\sin^2A}=(\cos(2A)+2\cos^2A)^2=\cos^2(2A)+4\cos(2A)\cos^2A+4\cos^4A[/tex]

[tex]\dfrac{\cos^2(3A)}{\cos^2A}=(\cos(2A)-2\sin^2A)^2=\cos^2(2A)-4\cos(2A)\sin^2A+4\sin^4A[/tex]

Subtract the second expression from the first to get the original equation. The [tex]\cos^2(2A)[/tex] terms cancel, leaving us with

[tex]4\cos(2A)\cos^2A+4\cos^4A+4\cos(2A)\sin^2A-4\sin^4A=2[/tex]

Now, notice that

[tex]4\cos(2A)\cos^2A+4\cos(2A)\sin^2A=4\cos(2A)(\cos^2A+\sin^2A)=4\cos(2A)[/tex]

and

[tex]4\cos^4A-4\sin^4A=4(\cos^2A-\sin^2A)(\cos^2A+\sin^2A)=4\cos(2A)[/tex]

because [tex]\cos^2A+\sin^2A=1[/tex] and [tex]\cos^2A-\sin^2A=\cos(2A)[/tex].

So we're left with

[tex]4\cos(2A)+4\cos(2A)=8\cos(2A)=2\implies\boxed{\cos(2A)=\dfrac14}[/tex]

Answer:

Exposure to the UV light is the dependable independent variable.

Step-by-step explanation:

An independent variable does not depend on another variable, but can rather have another variable depending on it. In this case, the chances of getting skin cancer depends on if a person is exposed to a high dose of UV light. The chances of getting skin cancer is the dependent variable, while the exposure to the UV light is the independent dependable variable.

Answer:

Dependable variable

Step-by-step explanation:

Answer for the blank is: 10

The exponents are -2, 3 and 9. Note how the bases are all the same at 4x. When we multiply exponential expressions like this, we add the exponents. So we'll get -2+3+9 = 1+9 = 10 as the final exponent over the base 4x

In short,

[tex](4x)^{-2}*(4x)^3*(4x)^9 =(4x)^{-2+3+9} = (4x)^{10}[/tex]

please help meeee!!!!!! complete the equation below. (4x)^-2(4x)^3(4x)^9 =(4x)=10

Answer:

76 quarters and 83 dimes

Step-by-step explanation:

From the information given, you can write the following equations considering that a quarter represents $0.25 and a dime $0.10:

y=x+7 (1)

0.25x+0.10y=27.30 (2)

x is the number of quarters

y is the number of dimes

Now, you can replace (1) in (2):

0.25x+0.10(x+7)=27.30

0.25x+0.10x+0.7=27.30

0.35x=27.30-0.7

0.35x=26.6

x=26.6/0.35

x=76

Then, you can replace the value of x in (1) to find the value of y:

y=76+7

y=83

According to this, the answer is that there are 76 quarters and 83 dimes in the jar.

There are 76 quarters and 83 dimes in the jar.

Thomas collects dimes and quarters in his change jar.

If he has 7 more dimes than quarters, and the total amount of money in the jar is $27.30.

Let, x be the number of the dimes.

And y be the number of quarters.

If he has 7 more dimes than quarters,

[tex]\rm y=x+7[/tex]

The total amount of money in the jar is $27.30.

[tex]\rm 0.25x+0.10y=27.30[/tex]

Substitute the value of y in equation 2

[tex]\rm 0.25x+0.10y=27.30\\\\ \rm 0.25x+0.10(x+7) =27.30\\\\ 0.25x + 0.10x + 0.7= 27.30\\\\0.35x=27.30-0.7\\\\0.35x=26.6\\\\x = \dfrac{26.6}{0.35}\\\\\rm x =76[/tex]

Substitute the value of x in equation 1

[tex]\rm y = x+7\\\\y =76+7\\\\y=83[/tex]

Hence, there are 76 quarters and 83 dimes in the jar.

To know more about Equation click the link given below.

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Answer:

7/4=5/3 is the answer

Answer:

Step-by-step explanation:

Terms           Coefficient

7p                    7

-6z                    -6

-80                  constant term

Answer:

$60

Step-by-step explanation:

10x6=60. 6+6+6+6+6+6+6+6+6+6= 60

Answer:

9+11x

Step-by-step explanation:

Answer:

12/25

Step-by-step explanation:

Find the common factor that multiplies to 24 and 25. Then divided, and keep going until you CANNOT find one.

Answer:

[tex]\frac{12}{25} \\[/tex]

Step-by-step explanation:

[tex]\frac{24}{50} \\\\\mathrm{Factor\:the\:number:\:}\:24=2\times\:12\\\\=\frac{2\times\:12}{50}\\\\\mathrm{Factor\:the\:number:\:}\:50=2\times\:25\\\\=\frac{2\times\:12}{2\times\:25}\\\\\mathrm{Cancel\:the\:common\:factor:}\:2\\\\=\frac{12}{25}[/tex]

Answer:

-5

Step-by-step explanation:

3x + 6 = -9

3x = -15

x = -5

Answer:

[tex] \boxed{ \bold { \huge{ \boxed{ \sf{x = - 5}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ - 9 = 3x + 6}[/tex]

Swap the sides of the equation

[tex] \longrightarrow{ \sf{3x + 6 = - 9}}[/tex]

Move 6 to right hand side and change its sign

[tex] \longrightarrow{ \sf{3x = - 9 - 6}}[/tex]

The negative integers are always added but possess the negative ( - ) sign

[tex] \longrightarrow{ \sf{3x = - 15}}[/tex]

Divide both sides by 3

[tex] \longrightarrow{ \sf{ \frac{3x}{3} = \frac{ - 15}{3} }}[/tex]

Calculate

[tex] \longrightarrow{ \sf{x = - 5}}[/tex]

Hope I helped!

Best regards! :D

A.) [tex]\frac{24\pi }{5} < \frac{63}{4} < 15.758 < 956\sqrt{e}[/tex] is the set of numbers correctly ordered from least to greatest (ascending order).

Ascending order is a method of arranging numbers from smallest value to largest value. The order goes from left to right. Ascending order is also sometimes named as increasing order.

[tex]\frac{24\pi }{5} = 15.0796\\\\\frac{63}{4} = 15.75\\\\956\sqrt{e} = 1576.177[/tex]

15.079 < 15.75 < 15.758 < 1576.177

[tex]\frac{24\pi }{5} < \frac{63}{4} < 15.758 < 956\sqrt{e}[/tex]

Learn more about ascending order here

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Answer:

A=30cm, B=39cm

Step-by-step explanation:

They are an enlargement. Therefore, the sides are larger by the same proportion, otherwise, it wouldn't be an enlargement. Therefore, the bottom side of the big one is 3 times that of the small one. Therefore, the other sides are also 3 times, making A = 30cm and B = 39cm.

Answer:

A

12cm to 36cm is mulitiply by 3, so that means that you mutiply each of the other sides by 3 to get your answer

Answer:

G.

Step-by-step explanation:

Length = Square root of Square area

= √8 (-√8 is rejected as length is positive)

We know that √4 < √8 < √9 because 4 < 8 < 9.

=> 2 < √8 < 3.

The only answer that is in this range is G.

Answer:

x=7

Step-by-step explanation:

As seen from the higher two numbers, there is a distinct ratio between the shorter side and the longer side. To find the ratio we simply get the given two without the x and we get 8:12 which simplifies to 2:3 or 1: 1.5

This means in order to find 3x-6, we need to multiply 10 by 1.5 which means:

3x-6=15

3x=21

x=7

Hope this helped!

Answer:

60

Step-by-step explanation:

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

Explanation:

Angle PQT = 35 degrees is given. This inscribed angle subtends or cuts off minor arc PT. This is the shortest distance along the circle from P to T. Any other inscribed angle that cuts off this same arc will also be the same measure. Note how angle PRT is such an inscribed angle, so,

angle PRT = 35 degrees

which we'll use later.

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

Focus on triangle ROS. Interior angle O is 180-82 = 98 degrees due to it being supplementary to the 82 degree angle shown.

Triangle ROS is isosceles with OR = OS being the two equal radii. The opposite base angles R and S are congruent angles. Call them x for now

(angle O) + (angle R) + (angle S) = 180

98+x+x = 180

2x+98 = 180

2x = 180-98

2x = 82

x = 82/2

x = 41

For triangle ROS, interior angle R is 41 degrees. Put another way,

angle ORS = 41 degrees

we'll use it below along with angle PRT

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

angle PRS = (angle PRT) + (angle ORS)

angle PRS = (35) + (41)

angle PRS = 76 degrees

Answer:

3.6/5, 4. 9, 5. 11/2

Step-by-step explanation:

3. 2/5/6

= 2× 6/5

= 12/5

4. 7/9/7

= 7× 7/9

= 9

5. 8/11/4

= 8×4/11

= 11/2

hope you understand this answer

sorry if the answer is wrong

Answer:

y = 4x + 8

Step-by-step explanation:

Slope-intercept form:

m = 4

x-intercept = -2, it means x = -2, y = 0

Using this point we get the value of b

The form now is:

X= -5

-13.5 ÷ 2.7= -5

-5=x

Answer:

x=5

Step-by-step explanation:

Answer: x = -2

Step-by-step explanation:

3x+5 -13x =25     combine like terms on the left side

-10x + 5 = 25        Subtract 5 from both sides

        -5      -5

-10x = 20     Divide both sides -10

x = -2

Answer:

[tex]x = -2[/tex]

Step-by-step explanation:

If we have the equation [tex]3x+5-13x=25[/tex], we can isolate x on one side and find it's value.

Let's combine like terms.

[tex]-10x + 5 = 25[/tex]

Subtract 5 from both sides:

[tex]-10x + 5 - 5 = 25 - 5\\\\-10x = 20[/tex]

Divide both sides by -10:

[tex]-10x\div-10 = 20\div-10\\\\x = -2[/tex]

So [tex]x = -2[/tex].

Hope this helped!

Answer:

8x + 1 + 6x + 5 = 90

14x +  6 = 90

14x = 84

x = 6

<DCB is 6x+5

6(6) + 5

36 + 5

41

Answer:

∠ DBC = 41°

Step-by-step explanation:

∠ DBC + ∠ DBA = 90° , substitute values

6x + 5 + 8x + 1 = 90, that is

14x + 6 = 90 ( subtract 6 from both sides )

14x = 84 ( divide both sides by 14 )

x = 6

Thus

∠ DBC = 6x + 5 = 6(6) + 5 = 36 + 5 = 41°

Answer:

-2.5(z+2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

66 mile per hour .

Answer:

Step-by-step explanation:

To find the value of x when y = 24, we must first find the relationship between them

where k is the constant of proportionality

when

x = 16

y = 2

Substitute the values into the above formula and solve for k

That's

Cross multiply we have the answer as

k = 8

So the formula for the variation is

Now when y = 24

We have

Square both sides

We have the final answer as

Hope this helps you