Does the exponential function, y=(0.15)^x, model exponential growth, or exponential decay?
PLEASE HELP!

It is proved that LHS = RHS

i.e.,  (secθ−cosθ)(cotθ+tanθ) = tanθ secθ

Trigonometry is the branch of mathematics that studies the relationship between angles and the ratio of lengths. The field originated in the Hellenistic world in the 3rd century BC, from the application of geometry to the study of astronomy. The Greeks focused on calculating chords, while Indian mathematicians created the first known tables of values ​​for equational sine ratios, also called trigonometric functions.

According to the Question:

L.H.S = (secθ−cosθ)(cotθ+tanθ)

        = (1/ cosθ −cosθ)( cosθ/sinθ + sinθ/cosθ​ )

        = (1−cos²θ/ cosθ)( cos²θ +sin²θ / sinθcosθ)

since we know that:

sin²θ+cos ²θ = 1

=sin²θ/cosθ(1/sinθ cosθ)

​= sinθ/ cosθcosθ

​= tanθ secθ

= R.H.S

Complete Question:

Prove that:

(secθ−cosθ)(cotθ+tanθ) = tanθsecθ

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Answer:

24

Step-by-step explanation:

To prove that triangles A and B are similar, Hector needs to know that the third pair of corresponding angles in the triangles are congruent, or he needs to know that the corresponding sides of the triangles are proportional.

In triangle similarity, the Angle-Angle (AA) similarity criterion states that if two pairs of corresponding angles in two triangles are congruent, then the triangles are similar. This means that if Hector knows that two angles in triangle A are congruent to two angles in triangle B, he needs to establish that the third pair of corresponding angles are also congruent to prove similarity.

Alternatively, Hector can use the Side-Angle-Side (SAS) similarity criterion. In this case, he needs to know that one pair of corresponding angles is congruent, along with the ratio of the lengths of the sides that include these angles. By establishing that the corresponding sides are proportional, Hector can prove similarity between triangles A and B.

Therefore, to prove that triangles A and B are similar, Hector needs to know either the congruence of the third pair of angles or the proportional relationship between corresponding sides.

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Pretty sure the answer is B The horizontal asymptote y = 10 means that the final concentration will always be greater than 10%.

Step-by-step explanation:

Since the 10 % solution that you're adding to the 30% solution is 10% acid when you add it to the 30 acid percent solution it would never decrease the acidity levels farther than 10 percent no matter how much you put because the solution your adding is at a 10% acidity and the other solution is 30% acidity and has a higher acidity level than the 10% so it could never go lower than the solution you are adding to it.

Really hope I did an okay job at explaining.

Answer:

B on edge

Step-by-step explanation:

Passed the test

Answer:

2/9

Step-by-step explanation:

B

HOPE IT HELPS HAVE A GREAT DAY

Answer:

4/18 = 2/9 = 8/36

Answer:

Communitive property of multiplication :)

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

Hi there!

The straight line on the bottom of the diagram tells us that 20° + (6x-2)° + 90° is equal to 180 degrees:

180 = 90 + 20 + (6x-2)

90 = 20 + (6x-2)

70 = 6x-2

72 = 6x

12 = x

Therefore, x is equal to 12.

I hope this helps!

The comparison of the above products of the given fractions is listed below as follows;

11a.) x<¾ , X<15/7

11b.) x<7, x<6/5

11c.) X<8/9, X<⅕

11d.) x >8/8, X = 7/10

The symbol for greater than = <

The symbol for lesser than = >

The symbol for equal to = (=)

For 11a)

In ¾×15/7

=45/28 = 1.6

Therefore,x<¾ , X<15/7

For 11b.)

7×6/8 = 5.25

Therefore, x<7, x<6/5

For 11c.)

8/9 × ⅕ = 8/45 = 0.17

Therefore, X<8/9, X<⅕

For 11d.)

8/8×7/10 = 0.7

Therefore, x >8/8, X = 7/10

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The proper plot that graphs the given three functions in the same figure is shown below:Given functions are(())=(),(())=12log10(+1)and(ℎ())=1

By using the plot function in MATLAB software, the proper plot that graphs the given three functions in the same figure is shown below:MATLAB Code:clear all; close all; clc; x = -20:0.1:20;

f = x;

g = 12*log10(x+1);

h = 1./x; plot(x,f,'-k','LineWidth',2); hold on; plot(x,g,'-r','

LineWidth',2); plot(x,h,'-b','

LineWidth',2); grid on; xlim([-20,20]); ylim([-50,50]); xlabel('Abscissa (x)'); ylabel('Ordinate (y)'); title('Graphing Functions');

legend('f(x)=x',

'g(x)=12log_{10}(x+1)',

'h(x)=1/x','

Location','northwest');The plot that graphs the given three functions in the same figure is shown below:

Therefore, the proper plot that graphs the given three functions in the same figure is shown above.

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Given function in the question is,

\(f(x)=2-5x-x^2\)

To find the difference coefficient for the given function, we use the expression as \(\frac{f(3+h)-f(3)}{h}\).

\(f(3+h)=2-5(3+h)-(3+h)^2\)

             \(=2-15-5h-(9+h^2+6h)\)

             \(=(2-15-9)-(5h+6h)-h^2\)

             \(=-22-11h-h^2\)

             \(=-(22+11h+h^2)\)

\(f(3)=2-5(3)-(3^2)\)

       \(=2-15-9\)

       \(=-22\)

Now substitute these values in the expression for the difference coefficient,

\(\frac{f(3+h)-f(3)}{h}=\frac{-(22+11h+h^2)-(-22)}{h}\)

                 \(=\frac{-22-11h-h^2+22}{h}\)

                 \(=\frac{-11h-h^2}{h}\)  

                 \(=-(11+h)\)

     Therefore, Value of the difference quotient for the given function is\(-(11+h)\).

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Answer:

13 dollars

and slope is 3

Step-by-step explanation:

To calculate the interest earned over a period of time, we can use the formula for compound interest. In this case, Natalie Engineering invested $95,000 at an interest rate of 6.5 percent, compounded annually for 5 years. The company earned $30,875.00 in interest over this period.

The formula for compound interest is given by:

\(A = P(1 + r/n)^(nt) - P\)

Where:

A is the final amount (including both the principal and the interest),

P is the principal amount (initial investment),

r is the interest rate (as a decimal),

n is the number of times interest is compounded per year, and

t is the number of years.

In this case, the principal amount (P) is $95,000, the interest rate (r) is 6.5% (or 0.065), the number of times interest is compounded per year (n) is 1 (since it is compounded annually), and the number of years (t) is 5.

Substituting these values into the formula, we have

\(A = 95,000(1 + 0.065/1)^(1*5) - 95,000\)

Simplifying the expression:

A = 95,000(1.065)^5 - 95,000

Using a calculator, we find that A ≈ 125,875.00.

To calculate the interest earned, we subtract the principal amount from the final amount:

Interest = A - P = 125,875.00 - 95,000 = 30,875.00

Therefore, Natalie Engineering earned $30,875.00 in interest over the 5-year period.

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The function f(x)=-2(x+2)(x+6) already has an inverse that is a function, and there is no need to restrict the domain.

To restrict the domain of the function f(x)=-2(x+2)(x+6) so that the inverse is a function, we need to consider the concept of a one-to-one function.

A one-to-one function is a function in which each input value (x) corresponds to exactly one output value (f(x)), and vice versa. In other words, there are no repeated output values for different input values.

To ensure that the inverse of f(x) is a function, we need to restrict the domain in a way that eliminates any potential for repeated output values. In this case, we have a quadratic function, and to restrict the domain, we need to identify the values of x that result in repeated output values.

To do this, we can analyze the factors of the quadratic function. The factors of f(x)=-2(x+2)(x+6) are (x+2) and (x+6). Since these factors are linear and distinct, we can conclude that there are no repeated output values.

Therefore, the function f(x)=-2(x+2)(x+6) already has an inverse that is a function, and there is no need to restrict the domain.

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Jem dug 5.7 meters for the well, including an extra 1.2 meters until water flowed. The water depth is 2.3 meters, leaving the same 5.7 meters unfilled.



Jem initially dug 4.5 meters deep into the soil for the well. Then, he dug an additional 120 cm (or 1.2 meters) deeper until water started flowing. Therefore, the total depth that Jem dug initially was 4.5 meters + 1.2 meters = 5.7 meters.

After 2 days, the water in the well was 230 cm (or 2.3 meters) deep. To determine the part of the well that was not filled with water, we subtract the water depth from the total depth of the well.

Total depth of the well = Depth dug + Water depth

Total depth of the well = 5.7 meters + 2.3 meters

Total depth of the well = 8 meters

Part of the well not filled with water = Total depth of the well - Water depth

Part of the well not filled with water = 8 meters - 2.3 meters

Part of the well not filled with water = 5.7 meters

Therefore, Jem dug a total depth of 5.7 meters and there is 5.7 meters of the well that is not filled with water.

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Answer:

I think the answer you're looking for is 86400

Step-by-step explanation:

If the area of the rectangle is 15, the dimensions of the rectangle are l = √(15) and w = √(15).

The question is referring to a rectangle, we can use the formula for the area of a rectangle, which is A = lw, where A is the area, l is the length, and w is the width.

We are given that the area of the rectangle is 15, so we can set up an equation:

l * w = 15

We are not given any information about the length, so we cannot solve for l and w separately. However, if we assume that the rectangle is a square (i.e., l = w), then we can solve for the dimensions:

l * l = 15

l² = 15

l = √(15)

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The number of rectangular table is equal to 5 rectangular tables.

The number of circular table is equal to 5 circular tables.

In order to write a linear system of equations to describe this situation, we would a assign variable to the number of circular table and the number of rectangular table respectively, and then translate the word problem into a linear equation as follows:

Since there are 9 tables and 80 chairs set up with 8 chairs each for the circular table and 10 chairs each for the rectangular table, a linear equation to model this situation is given by:

8x + 10y = 80    .......equation 1.

x + y = 9            .......equation 2.

In this scenario, we would use an online graphing calculator to plot the linear system of equations in order to determine the solution (point of intersection) as shown in the image attached below, which is at the ordered pair (5, 4).

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Answer:

you know i think it is 9 10/9 as a mixed number sooo i hope this help

Answer:

1 1/9

Step-by-step explanation:

I don't have an explanation, you're just gonna have trust me on this one

For ∫(4+x^2)^(3/2) dx, let x = 2√(tanθ) or x^2 = 4tan^2θ. After substituting, the integral becomes ∫8tan^2θ(sec^2θ) dθ.

Simplifying further, we get 8∫tan^2θsec^2θ dθ.

For ∫(9-x^2)/(x^2) dx, let x = 3sinθ or x^2 = 9sin^2θ. After substituting, the integral becomes ∫(9-9sin^2θ)/(9sin^2θ) dθ.  Simplifying further, we get ∫(1-sin^2θ)/sin^2θ dθ.

For ∫(3-2x-x^2)/x dx, let x = -tanθ or dx = -sec^2θ dθ. After substituting, the integral becomes ∫(3+2tanθ+tan^2θ)/(-tanθ) dθ.

Simplifying further, we get -∫(tan^2θ+2tanθ+3)/tanθ dθ.

4. For ∫13/(1+x^2)^(3/2) dx, let x = tanθ or dx = sec^2θ dθ.

After substituting, the integral becomes ∫13/(sec^2θ)^(3/2) sec^2θ dθ. Simplifying further, we get 13∫secθ dθ.

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The correct answer is E) None of these. The expression "-3 + 4 6/5" involves both addition and multiplication operations.

According to the order of operations (PEMDAS/BODMAS), multiplication should be performed before addition.

First, let's evaluate 4 * 6/5=

4 * 6/5 = 24/5 = 4.8

Now, we can substitute this value back into the expression:

-3 + 4.8 = 1.8

Therefore, the value assigned to x after the assignment statement is executed is 1.8, which is not an integer. Since x is declared as an int variable, it cannot hold a decimal value, so the correct answer is E) None of these.

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Given:

The function is \(y=x(x+2)^2\).

To find:

The zeros and their multiplicity.

Solution:

A polynomial is defined as

\(y=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}\)       ...(i)

where, a is a constant, \(c_1,c_2,...,c_n\) are zeros with multiplicity \(m_1,m_2,...,m_n\) respectively.

We have,

\(y=x(x+2)^2\)

It can be written as

\(y=(x-0)^1(x-(-2))^2\)          ...(ii)

On comparing (i) and (ii), we get

\(c_1=0,m_1=1\)

\(c_2=-2,m_2=2\)

Therefore, the zeros of the given function are 0 and -2 with multiplicity 1 and 2 respectively.

Answer:

Area - l*w

area is 4500 cm 2

perimeter - l + w * 2

perimeter is 280 cm

Answer:

6,832 pounds of food

Step-by-step explanation:

If we chose different intervals for binning data in a frequency table can affect the level of detail, the frequency of values, and the distribution of values in each bin. It's important to choose an interval size that is appropriate for the dataset and provides meaningful insights into the data.  Here are some ways in which the frequency table could be affected.

Choosing different intervals will result in a different number of bins, which affect the detail. For example, a smaller interval size will result in more bins, which may give a more detailed view of the data.

The frequency of values in each bin will change depending on the interval size. For example, if we have a dataset with values from 0 to 100, and we choose an interval size of 10, we will have 10 bins, each with a frequency count of values falling into that range.

The distribution of values in each bin may vary depending on the interval size. For example, if we have a dataset with values ranging from 0 to 100 and we choose an interval size of 5, we may get a more detailed view of the distribution of values.

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Answer:

36 i think

Step-by-step explanation:

16 divided by 4 is 4

36 divided by 4 is 9

4*9=36

Answer:

324 square inches

Step-by-step explanation:

1/4 of 16 = 4

16-4 = 12

1/4 of 36 = 9

36-9 = 27

A= l*w

A= 27 x 12

A= 324 square inches

Answer:

i think it is A because i got 40.0 degrees

Step-by-step explanation:

example i made this to show how how i use questions like this, But i may or may not be wrong if so go back through the lesson or use a tutor for school have a great day:)