Use basic trigonometric identities to simplify the expression: tan^3(x) + tan (x)=?

y represents a function of exponential decay with 45%.

What is exponential decay?

Consider the function:

y= a(1 ± r)ˣ

where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is plus sign, then there is exponential growth happening by r fraction or 100r %.

If there is a negative sign, then there is exponential decay happening by r fraction or 100r %.

Here, we have

If we compare the given function with the exponential function, then it can be observed that the value of (1±r) is less than 1, therefore, the function will be of exponential decay.

Now, if the (1-r) is compared with 0.55 given in the function then the value of r will be,

1 - r = 0.55

-r = 0.55 - 1

-r = -0.45

r = 0.45

r = 45%

Hence,  y represents a function of exponential decay with 45%.

To learn more about the exponential decay from the given link

https://brainly.com/question/30155560

#SPJ1

Answer:

26

Step-by-step explanation:

w = 5 so 7w is 7 x 5 = 35 and x = 9 so it’s 35 - 9 which is 26

Answer: 18

Step-by-step Explanation:

Subtract: 5 from 41 | 41-5= 36

Divide: by 2 | 36/2= 18

Answer:18

Step-by-step explanation:

SUBTRACT41 FROM 5

THAT GIVES YOU 38

THEN DIVIDE 38/2 AND IT WILL GIVES 18

In the given study comparing the effects of regular-fat cheese to reduced-fat cheese on LDL cholesterol levels, the dependent variable(s) refers to the outcome(s) that are being measured or observed. In this case, the dependent variable in this study is: b. LDL levels

The dependent variable is the variable that is measured or observed to assess the effect of the independent variable(s). In this case, the study is comparing the effects of regular-fat cheese and reduced-fat cheese on LDL cholesterol levels.

LDL cholesterol levels are the outcome being measured to determine the impact of the different types of cheese on cholesterol. Therefore, option b, LDL levels, is the dependent variable in this study. Options a (regular fat cheese) and c (reduced fat cheese) are not the dependent variables but rather the independent variables, as they are the different conditions being compared to assess their effect on LDL levels.

Option d (both a and b) and option e (both b and c) are incorrect because regular-fat cheese (option a) is an independent variable, not a dependent variable.

To know more about dependent variable refer here:

https://brainly.com/question/1479694?#

#SPJ11

option C again correct if I'm wrong

An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b. A geometric sequence has a constant ratio between each pair of consecutive terms. This would create the effect of a constant multiplier.

The table shows the estimated digit and significant figures of each measurement and their representation with x.

Number of Measurement Estimated Digit Significant Figures

14.8 m 3 ✓

$10.25 - ✓

0.05 L - ✓

1.000 g/mL - ✓

1.200 - ✓

6200 cm - ✓

403 kg - ✓

For each measurement, the estimated digit is replaced with an x to represent the number with the correct number of significant figures. The correct representations for each measurement are:

Note that in some cases, the representation requires adding zeros to the right of the decimal point to indicate the number of significant figures. In other cases, the representation requires rounding up or down to the correct number of significant figures.

Learn more about decimal :

https://brainly.com/question/29765582

#SPJ4

Answer: i think C sorry if i get it wrong :)

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

Answer:

Rent in 10th year = $5345.90

Step-by-step explanation:

Rent of apartment during first year = $1800 per month

But growth in rent with 11.5% per year will be represented by the exponential function,

Rent in 't'th year = \(\text{Initial rent}(1+\frac{\text{Growth rate}}{100})^{\text{time}}\)

                          = \(1800(1+\frac{11.5}{100})^t\)

                          = \(1800(1.115)^t\)

Therefore, rent during 10th year will be,

Rent in 10th year = \(1800(1.115)^{10}\)

                            = $5345.90

Answer:

4794

Step-by-step explanation:

Answer:

x- 7.50 i think i hope i helped

Step-by-step explanation: there no explanation

The slope of the line passing through the points (-2, 6) and (5, -3) will be [m] = - 9/7.

The slope intercept of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept.

Given is a straight line passing through the points (-2, 6) and (5, -3).

We have a straight line that passes through the coordinates as follows -

(-2, 6)

(5, -3)    

The slope of the line can be calculated using the formula -

m = (y₂ - y₁)/(x₂ - x₁)

m = (- 3 - 6)/(5 + 2)

m = - 9/7

m = - 9/7

Therefore, the slope of the line passing through the points (-2, 6) and (5, -3) will be [m] = - 9/7.

To solve more questions on straight lines, visit the link below-

https://brainly.com/question/27730503

#SPJ1

Answer:

80 degrees

Step-by-step explanation:

Answer:

A)  10.8

Step-by-step explanation:

Answer:

I think point b but egh

Step-by-step explanation:

im not really for sure...

Answer:

22.3 x 1.8 = 40.14

Step-by-step explanation:

22.3

x  1.8  

________

1784

2230

________

40.14

Answer:

40.14

Step-by-step explanation:

22.3

× 1.8  ← Forget about the decimal places and multiply by the one's place.

1 7 8 4

2 2 3 0 ← Put a 0 to hold the one's place and multiply 223 by ten's place.

4 0 . 1 4 ← Add those 2 numbers and keep 2 decimal places.

Answer:

0.75

Step-by-step explanation:

V=whl=0.5·3·0.5=0.75

Divide 1 by 2 and you get 0.5

Answer:

about 64.29%

Step-by-step explanation:

900/1400= 0.64285...

=about 64.29%

According to the graph of the function, it is found that:

a) h(2) = 1.

b) h(x) = -3 when x = -4.

Looking at the graph, h(2) is given by the value of y when x = 2, that is, the value of the vertical axis when the horizontal axis is of 2. Hence, h(2) = 1.

Looking at the graph, it is given by x when y = -3, that is, the value of the horizontal axis when the vertical axis is of -3, hence, h(x) = -3 when x = -4.

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

The five-number summary and the interquartile range for the data set are given as follows:

In this problem, we have that:

More can be learned about five number summaries at https://brainly.com/question/17110151

#SPJ1

The solution of the differential equation y'' + 6y' - 7y = 60e^3t with initial conditions y(0) = 3 and y'(0) = 4 is \(y = (2/7)e^(-7t) + (17/7)e^t + 4e^3t.\)

To find a particular solution to the differential equation y'' - 8y' + 16y = 256t^3, we can use the method of undetermined coefficients. Since 256t^3 is a polynomial of degree 3, we assume a particular solution of the form yp = At^3 + Bt^2 + Ct + D, where A, B, C, and D are constants.

Differentiating yp with respect to t gives yp' = 3At^2 + 2Bt + C, and differentiating again gives yp'' = 6At + 2B.

Substituting these into the differential equation, we have:

6At + 2B - 8(3At^2 + 2Bt + C) + 16(At^3 + Bt^2 + Ct + D) = 256t^3

Simplifying this equation, we get:

16At^3 + (16B - 48A)t^2 + (6A - 16C + 32B)t + (2B - 8C + 16D) = 256t^3

To match the coefficients on both sides, we equate the corresponding terms:

16A = 256, 16B - 48A = 0, 6A - 16C + 32B = 0, 2B - 8C + 16D = 0

Solving these equations, we find A = 16, B = 12, C = 8, and D = -4.

Therefore, a particular solution to the differential equation is yp = 16t^3 + 12t^2 + 8t - 4.

For the differential equation y'' + 4y' + 3y = 12te^4t, we follow the same method. Since 12te^4t is a product of a polynomial and an exponential function, we assume a particular solution of the form yp = (At + B)e^4t.

Differentiating yp with respect to t gives yp' = A(e^4t + 4te^4t) + Be^4t, and differentiating again gives yp'' = A(8te^4t + 8e^4t) + B(e^4t).

Substituting these into the differential equation, we have:

A(8te^4t + 8e^4t) + B(e^4t) + 4(A(e^4t + 4te^4t) + Be^4t) + 3((At + B)e^4t) = 12te^4t

Simplifying this equation, we get:

(8A + 4B)t + (8A + B) + (4A + 3B)e^4t = 12te^4t

To match the coefficients on both sides, we equate the corresponding terms:

8A + 4B = 12, 8A + B = 0, 4A + 3B = 0

Solving these equations, we find A = 3/7 and B = -8/7.

Therefore, a particular solution to the differential equation is yp = (3/7t - 8/7)e^4t.

For the differential equation y'' + 6y' - 7y = 60e^3t with initial conditions y(0) = 3 and y'(0) = 4, we can use the method of undetermined coefficients.

We assume a particular solution of the form yp = Ae^3t, where A is a constant.

Differentiating yp with respect to t gives yp' = 3Ae^3t, and differentiating again gives yp'' = 9Ae^3t.

Substituting these into the differential equation, we have:

\(9Ae^3t + 6(3Ae^3t) - 7(Ae^3t) = 60e^3t\)
Simplifying this equation, we get:

15Ae^3t = 60e^3t

To match the coefficients on both sides, we equate A = 4.

Therefore, a particular solution to the differential equation is yp = 4e^3t.

To find the general solution, we add the particular solution to the homogeneous solution (which satisfies the equation without the forcing term). The homogeneous solution can be found by assuming a solution of the form y = e^rt and substituting it into the characteristic equation r^2 + 6r - 7 = 0. Solving this equation, we find r = -7 or r = 1.

Therefore, the general solution to the differential equation is y = c1e^(-7t) + c2e^t + 4e^3t, where c1 and c2 are constants.

Using the initial conditions y(0) = 3 and y'(0) = 4, we can substitute these values into the general solution and solve for the constants.

Plugging in t = 0, we have 3 = c1 + c2 + 4.

Plugging in t = 0, we have 4 = -7c1 + c2 + 12.

Solving these equations, we find c1 = 2/7 and c2 = 17/7.

Therefore, the solution of the differential equation y'' + 6y' - 7y = 60e^3t with initial conditions y(0) = 3 and y'(0) = 4 is y =\((2/7)e^(-7t) + (17/7)e^t + 4e^3t.\)

Learn more about differential equation  from the given link

https://brainly.com/question/1164377

#SPJ11

Answer:

10

Step-by-step explanation:

First add: (All the classes)

24+26+28= 78 students

Then divide: (Total students by students per teacher)

78/6= 13

Then subtract: (Adult needed minus teachers)

13- 3=10

Hope this helps! :)

Answer:

200

Step-by-step explanation:

103+94

=100+100

=200

Answer:

197 the nearest ten is 200

Step-by-step explanation:

he need to put the nearest ten

The experiment type of research study is being used.

What is an experiment ?

A method used in a controlled environment to find an unknown effect or law, test or establish a hypothesis, or provide an example of an established law

In the scenario described, individuals are chosen at random to participate in a new intervention, which appears to be an example of an experiment.

As opposed to option A, where the participants are being observed in their natural context, this is not a naturalistic observation example.

The lack of a relationship means that it is neither a correlation research, as in option C, nor a survey, as in option D.

Option B is the appropriate response, thus.

So, the experiment  type of research study is being used.

To know more about experiment from the link given below.

https://brainly.com/question/26117248

#SPJ4

From the graph, we can observe that the function has a maximum of 1 at x = 1

The maximum value of a function is the place where a function reaches its highest point

Consider the graph below, the region where the graph is increasing and decreasing is shown below:

Using interval notation, the intervals are:

Answer Summa

Answer:

Step-by-step explanation:

when it says a sequence is arithmetic, it means that is has a common difference and come in the form a+(n-1)d, where a is the first term of the sequence, n is the number of terms and d is the common difference (the difference between each term.

example: 6, 3, 0, -3, -6

the common difference is 3, therefore its form is 6+(n-1)(-3) = 9-3n

if u wanted to find the 7th term in the sequence (\(a_7\)), you'd put 7 in place of n in the equation.

geometric sequences have common ratios and come in the form ar^n-1

where a is the first term, r is the common ratio (basically the common difference but in the form of a fraction) and n is the number of terms.

Answer:

C Subtraction property of equality

Step-by-step explanation:

You are subtracting 21 from both sides in step 3

Answer:

I would guess C

Step-by-step explanation:

I hope I'm correct, good luck.