prove the identity
sin2theta = 2 tan theta over 1 + tan squared theta

help!

Answer:

option b is the answer of the above

Answer:

Step-by-step explanation:

1. The function f(t) represents the concentration of medication in the bloodstream over time. The function has a parabolic shape, with the maximum value at t = 8 hours.

To find the maximum concentration of the medication, we can set the derivative of the function equal to 0 and solve for t. The derivative of f(t) is:

f'(t) = -30t + 120

Setting this equal to 0 and solving for t, we get:

-30t + 120 = 0

-30t = -120

t = 4

Therefore, the maximum concentration of the medication occurs at t = 4 hours. At this time, the concentration of the medication is:

f(4) = -15(4)^2 + 120(4) = 120 mg

It's important to note that this function represents the concentration of the medication in the bloodstream, not the total amount of medication that has been taken. The total amount of medication taken over a given time period can be found by integrating the function over that time period.

2. To determine the maximum amount of medication in the bloodstream, we need to find the maximum concentration of the medication and then multiply that concentration by the volume of the bloodstream.

We have already determined that the maximum concentration of the medication is 120 mg/L. The volume of the bloodstream in an adult is approximately 5 liters. Therefore, the maximum amount of medication in the bloodstream is:

120 mg/L * 5 L = 600 mg

This is the maximum amount of medication that can be present in the bloodstream at any given time. It's important to note that this amount may be affected by various factors, including the rate at which the medication is metabolized and eliminated from the body.

3. To determine the concentration of medication in the bloodstream after 2 hours, we can substitute 2 for t in the function f(t) and solve for the concentration. The function for the concentration of medication in the bloodstream is:

f(t) = -15t^2 + 120t

Substituting 2 for t, we get:

f(2) = -15(2)^2 + 120(2) = 60 mg/L

Therefore, the concentration of the medication in the bloodstream after 2 hours is 60 mg/L. It's important to note that this represents the concentration of the medication at a specific point in time, not the total amount of medication that has been taken. The total amount of medication taken over a given time period can be found by integrating the function over that time period.

Answer:

A.1

Step-by-step explanation:

The line crosses when Y is one and X is 0 thus creating an intercept on the y line

The examples of SAS congruence postulates are

The SAS is stands for Side-Angle-Side congruence postulate which states that triangles are congruent if two sides and an included angle of a triangle are congruent with two sides and an included angle of a second triangle. Note that we need to include the angle between the two sides.

Example 1 : Let's say you have one triangle, ∆ABC with side lengths 5 and 10 and the angle included between those two sides is 30 degrees. If you have a second triangle, ∆DEF that also has side lengths 5 and 10 with a 30 degree angle in between, then by the SAS Postulate ∆ABC is similar to ∆DEF.

Example 2 : Point C is the midpoint of BF

so, AC = CE

Statement Reason

AC = CE C is mid point so, it

divides equal parts .

BC = CF C is mid-point

∠ACB =∠ECF Opposite angles

Thus, by the Side Angle Side postulate, the triangles are congruent i.e,∆ABC ≅ ∆CEF

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The graph of the function y tan 3 4x has a vertical asymptote at x = π/12, which means that as x approaches π/12 from either side, the output of the function increases without bound.

The graph of the function y tan 3 4x has a vertical asymptote at x = π/12, which means that as x approaches π/12 from either side, the output of the function increases without bound. This is because when x = π/12, the denominator of the tangent function (3/4x) is 0, which creates an undefined value. As a result, the output of the function increases without bound as x approaches π/12. This is why x = π/12 is an asymptote of the graph. Asymptotes can be thought of as boundary lines, beyond which the graph of the function cannot cross. In this case, the graph of y tan 3 4x will approach the vertical asymptote of x = π/12, but will never cross it.

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Thousands, hundreds and tens are three types of values and there are many more.

Value in mathematics is a number that represents the outcome of a computation or function. In the aforementioned example, you may inform your teacher that 5 + 6 Equals 30 or that x + y = 9 if x = 6 and y = 3. A variable or constant can also be referred to as a value.

The number 4 is in this case in the tens column. As a result, the place value of the number four is tens or tens.

Thousands, hundreds and tens are three types of values and there are many more like ones etc. Moreover after solving any problem for unknown variable the resulting numerical solution can also be termed as value.

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a) The area of the window seat when x=3 is 8 ft².

b) Polynomial that represent area of the window is  x² - 1

What is trapezium?

Area of trapezium = 1/2 (a+b)*h

a= x ft

b = x+2 ft

c = x-1 ft

a ) When x=3;

a = 3 ft

b = 3 + 2 = 5 ft

c = 3-1 = 2 ft

Now, Area of window seat = 1/2 (3+5) 2

= 1/2 * 8 * 2

= 8 ft²

Hence, area of window seat is 8 ft².

b) Polynomial that helps represent the area of window seats

= 1/2(a+b)*h

= 1/2(x + x +2) * (x-1)

= 1/2 (2x+2)*(x-1)

= 1/2 * 2(x+1)* (x-1)

= (x+1) * (x-1)

= x² - 1

Hence, the Polynomial that represent area of the window is  x² - 1.

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Answer:

Gordon types 280 words per minute

Step-by-step explanation:

2240word/8min

280/min is the same as 4.6/second (280/60)

The conditions for a binomial setting have been met for this scenario are;

The conditions for a binomial experiment to be true are;

Now, in this case we keep shuffling the standard deck of 52 playing cards and picking the first in each case and replacing until we get a queen. This means that each trial is independent and does not depend on the success or failure of another event.

Secondly, the probability of success remains the same in each trial because we can't predict when we will get a queen.

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A vector that points in the same direction as the vector (i^+j^) and whose magnitude is 9 is (9i^/ √2 + 9j^/ √2).

Therefore the answer is 9i^/ √2 + 9j^/ √2.

The vector direction is same as i^ + j^. We can obtain a unit vector in that direction by dividing the vector with magnitude of i^ + j^, which is √(1² + 1²) = √2.

Unit vector is (i^ + j^)/ √2.

Given that the required vector is of magnitude 9. We can determine the required vector thus by multiplying the magnitude with the unit vector in the direction, that is

9×(i^ + j^)/ √2

= 9i^/ √2 + 9j^/ √2

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Answer:

Speed and Time are two examples of inverse proportion

Answer:

AC is longest

BC is middle

AB is shortest

Answer:

y = 1/4x + 4

Step-by-step explanation:

Knowledge Needed

Slope: The amount the y-value changes on a constant line when the x-value increases by 1.

Slope Formula:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

y-intercept: When the line has a x-value of , or when it intersects the y-axis.

Slope-Intercept Form: y = mx+b

m is slope, b is y-intercept.

Leave y and x as variables so you can graph it.

Question

First, plug the points into the slope formula.

[tex]\frac{3-5}{-4-4}[/tex]

[tex]\frac{-2}{-8}[/tex]

1/4

y = 1/4x + b

Solve for b:

Use any of the 2 points to plug back in. I'll use (4,5).

We have: y = 1/4x + b

(5) = 1/4(4) + b

5 = 1 + b

5 - 1= 1 - 1 + b

b = 4

y = 1/4x + 4

The answer is the square of the orbital period, t, of a planet is equal to the cube of the average distance, a, of the planet from the sun.

Translated into words, the equation t2 = a3 can be written as:

"The square of the orbital period, t, of a planet is equal to the cube of the average distance, a, of the planet from the sun."

The length of time it takes an astronomical object to complete one orbit around another object is known as the orbital period (also known as the revolution period). In astronomy, it often refers to bodies like planets or asteroids revolving about the Sun, as well as moons circling other stars, exoplanets, and double stars.

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Translated into words, the equation t2 = a3 can be written as:

"The square of the orbital period, t, of a planet is equal to the cube of the average distance, a, of the planet from the sun."

The orbital period is the amount of time it takes an astronomical object to complete an orbit around another one (also known as the revolution period). In astronomy, it frequently refers to objects revolving about the Sun, such as planets or asteroids, as well as moons orbiting around other stars, exoplanets, and double stars.

Steps to graph-solve a problem:

Generally, Identify the problem you are trying to solve and determine if a graph is an appropriate tool to help you solve it. Graphs are often used to represent relationships between different data points or to show changes in data over time.

Collect the data that you will need to create the graph. This may involve conducting research, conducting experiments, or gathering information from other sources.

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The complete Question was not found

We can solve using a graph by looking up the points on the graph.

We know that a graph can be regarded as a representation of facts and the graph is plotted in two axes. There is the vertical axis of the graph and there is the horizontal axis of the graph.

The vertical axis of the graph is called the y axis while the horizontal axis of the graph is called the x axis. The independent variable goes to the x axis while the dependent variable goes to the y axis.

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Answer:

f(f(3))=101

Step-by-step explanation:

To solve this problem, first solve for f(3):

[tex]f(3)=(3)^2+1\\f(3)=9+1\\f(3)=10[/tex]

Then, insert f(3) into f(2) by substituting f(3) in place of x:

[tex]f(f(3))=f(10)\\f(10)=(10)^2+1\\f(10)=101[/tex]

We are aware that to reverse a number, the TENS and ONE's positions must be reversed. As a result, its reverse "ba" usually takes the form (10 times "b" multiplied by "a")

When a number has two digits, it is called a 2-digit number.

2-digit numbers have two digits and range from 10 to 99.

They are unable, to begin with, zero since it will then be regarded as a single-digit number.

Any number between 1 and 9 can be used as the digit in the tens place.

For instance, the numbers 45, 78, and 12 have two digits.

When it comes to two-digit numbers and their reversal, there are two common logics.

The two-digit number "ab" has the generic form (10 times a) Plus b.

We are aware that the TENS and ONE's positions should be switched in order to reverse a number.

As a result, the typical form of its reverse "ba" is (10 times "b" multiplied by "a")

Therefore, we are aware that to reverse a number, the TENS and ONE's positions must be reversed. As a result, its reverse "ba" usually takes the form (10 times "b" multiplied by "a")

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Answer:

4i

Step-by-step explanation:

Any negative numbers do not have any real square roots, only imaginary ones.

[tex]\sqrt{-16} = i\sqrt{16} = 4i[/tex]

hope this helps :)

The mode of the given data set is 11.

A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.

In statistics, the value that consistently appears in a particular collection is referred to as the mode. The mode or modal value in a data collection is sometimes referred to as the value or number that occurs most frequently in the data set. In addition, to mean and median, it is one of the three measures of central tendency.

The mode is the value that occurs the most often in a given set of data.

In the data set provided here, the mode is 11, hence 11 should occur the most number of times.

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According to question,

We know that,

To determine the percentage,

we have to divide the value by the total value and then multiply the resultant by 100,

Percentage formula

Is /of=%?100

Or

Part/whole=%/100

With the help of question,

Given data,

Put the value of percentage formula,

98.25/100×10

=9.825

98.25%×10 is the same outcome of 9.825.

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9 ones, 9 tens  99.77 is equal to 7 tenths 7 hundredths.

The place value of the digits that come after a decimal point is defined in mathematics as tenths and hundredths. When we count from right to left, the place values of the digits in a number are ones, tens, hundreds, and thousands.

The columns are labelled tenths, hundredths, thousandths, and so forth from left to right following the decimal point. The tenths column is the first digit following the decimal point. The column for hundredths is the second digit following the decimal point. The column for thousandths is the third digit following the decimal point.

The digit after the decimal point, or in the tens place, is known as the divisor. The first digit to the right of the decimal place is the tenths place digit.

9 tens = 9 x 10 = 90

9 ones =9 x 1 = 9

7 tenths = 7x 1/10 =0.7

7 hundredths = 7 x 1/100 = 0.07

= 90 + 9 +0.7 +0.07

= 99.77

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The equation in point slope form is y - 21 = 7(x - 3).

What is point - slope form of the line?

A line's equation in point slope form is y - y1 = m. (x – x1). As a result,

y = mx and y - 0 = m(x - 0) are the equations for a line passing through the origin with a slope of m.

To find the equation in point slope form for the given table of height of a plant first we have to find the slope.

Here

Slope = change in height / Change in time

From given table,

Change in height = 14 and Change in time = 2

⇒ Slope = 14 / 2 = 7

Now to find the point slope form.

We know that the equation in point slope form for point [tex](x_1, y_1)[/tex] and slope m is written as,

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex](x_1, y_1) = (3, 21), m = 7[/tex]

So, the equation becomes

[tex]y-21 = 7(x-3)[/tex]

Hence, the equation in point slope form is y - 21 = 7(x - 3).

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Answer:

a=7 b=2 c=0.2 d=9 e=0.064 f=8 g=16 h=0.03 i=0.714

Step-by-step explanation:

Step-by-step explanation:

So this below is a solution I devised myself when I was around 11 yrs old doing math competitions with my friend so… (I don’t have a name for this solution, and can’t give any reference material)

alright so notice that when you subtract the remainder from the divisor in this question, all of their the values equate to 4:

6–2 = 4

9–5 = 4

11–7 = 4

I am going to use this property to devise a method from the problem.

The property above means

(n+ 4) % 6 = 0

(n+ 4) % 9 = 0

(n+ 4) % 11 = 0

where n is the dividend

notice that for n to be in accordance with the restriction of the question, n+4 must be a multiple of 6, 9 and 11 simultaneously (common multiple)

Since the question asks for the number of “n”s that are three-digit positives…

100 <= n <= 999 (which means)

104<= n+4 <= 1003

ok, so now we have to find the common multiples of 6,9,11 within the range 104~ 1003

the least common multiple of 6,9,11 is 198.

the smallest multiple of 198 that is larger than or equal to 104 is 198, which is 1*198… the largest multiple of 198 smaller than 1003 is 990, which is 5*198

so that means we have all the way from the first multiple of 198 to the fifth multiple of 198, inclusive, which is (5–1) + 1 = 5

and there we have it!!!

the answer is 5

P.S. we could also just count the multiples, but the (5–1)+1 is there because it may not always be countable, and the +1 is there to account for the first number that was subtracted

Answer:

He pays:

$368.94

Step-by-step explanation:

20 miles ⇒ 1 gallon

2365 miles ⇒ A gallons

A = 2365 miles * 1 gallon / 20 miles

A = 118,25 gallons

Then:

$3.12 ⇒ 1 gallon

$B ⇒ 118.25 gallons

B = 118.25 gallons * $3.12 / 1 gallon

B = $368,94

In Angle abc and angle pqr ab:pq=4:5 and a(angle pqr)=125cm² then the measure of angle ABC is 100 cm².

Generally, To find the measure of angle ABC in the triangle ABC, we can use the fact that the ratios of the measures of the angles in a triangle sum to 180 degrees.

We are given that the ratio of the measures of angles ABC to PQR is 4:5. This means that if we let x represent the measure of angle ABC, then the measure of angle PQR is 5x/4.

The measure of angle PQR is also given to be 125 cm². We can use this to set up the equation:

5x/4 = 125

Solving for x, we find that the measure of angle ABC is:

x = 100

Therefore, the measure of angle ABC is 100 cm².

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The number of roots of the given equation x³ -3x² + 4 = 0 is equal to 3 which are -1, 2, 2.

As given in the question,

Given equation is written as:

x³ -3x² + 4 = 0

Number of roots of the given equation are as follow ;

Let f(x) = x³ -3x² + 4

For x = 1

f(1) = 1³ - 3(1)² + 4

    = 2 ≠ 0

x = 1 is not the roots.

Now, x = -1 ,

f(-1) = (-1)³ - 3(-1)² + 4

      = -1 -3 + 4

      = 0

x = -1 is the roots of the given equation x³ -3x² + 4 = 0

x³ -3x² + 4 = 0

⇒x³ + x² -4x² -4x + 4x + 4 =0

⇒x² ( x + 1) - 4x( x + 1) + 4(x+1) =0

⇒(x+1) ( x² -4x +4 ) = 0

⇒(x+1)( x - 2 )² = 0

⇒ x = -1, 2, 2

Therefore, the number of roots of the given equation x³ -3x² + 4 = 0 are 3 and given by x = -1 , 2, 2.

The above question is incomplete , the complete question is :

How many roots does the equation x³ -3x² + 4 = 0 have ?

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The quadratic equation whose roots are 2√3 and 2-√3 can be written in the form ax² + bx + c = 0.

To solve this equation, we can use the formula x = (-b  ±  √(b²-4ac))/2a.

Substituting the values of 2√3 and 2-√3 for x, we get:

2√3 = (-b + √(b²-4ac))/2a

2-√3 = (-b - √(b²-4ac))/2a

Subtracting the two equations, we get:

0 = √(b²-4ac)

Taking the square of both sides, we get:

b² - 4ac = 0

Rearranging the equation, we get:

ax² + bx + c = 0, where

a = 1

b = 0

c = -4ac

Therefore, the quadratic equation whose roots are 2√3 and 2-√3

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Horizontal asymptotes are found by looking at the degree of the numerator and denominator of a function. Vertical asymptotes are found by solving for all x-values where the denominator equals 0.

Horizontal asymptotes are horizontal lines that a graph of a function approaches as it goes towards positive or negative infinity. To find them, look at the degree of the numerator and denominator of a function. If the degree of the numerator is less than the degree of the denominator, the graph will approach the x-axis asymptote. If the degree of the numerator is equal to the degree of the denominator, the graph will approach the y-axis asymptote. Vertical asymptotes are vertical lines that a graph of a function approaches as it goes towards positive or negative infinity. To find them, solve for all x-values where the denominator equals 0. This will give you the x-values of the vertical asymptotes.

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