What are the next two terms in the following sequence? 6, 3, 12, 6, 24.....

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( 1 - cos²x ) secx

=> sin²x . secx

Here the rule ( rule 1 ) is the first trigonometric identity [ sin²A + cos²A = 1 ] by simplifying we have , [ 1 - cos²A = sin² ] . So here we substituted 1 - cos²x = sin²x .

=> sin²x [ 1/cosx ]

Here the rule ( rule 2 ) is secx = 1/cosx . So here we substituted secx = 1/cosx .

=> sinx [ sinx/cosx ]

Here the rule ( rule 3 ) is sin²x can be written as sinx . sinx , so we get sinx . sinx [ 1/cosx ] next by simplifying , sinx [ sinx/cosx ].

=> sinx tanx

Here the rule ( rule 4 ) is , in the above we got sinx/cosx and here we know that , sinx/cosx = tanx . So we have tan x .

The proof of the identity that justifies that ( 1 - cos²x ) secx equals sinx(tanx) has been described below with statements and rules.

Statement 1; ( 1 - cos²x ) secx

This is given

Statement 2; sin²x · secx

Rule 1;  From trigonometric identities, we know that;

sin²x + cos²x = 1,

Thus; cos²x = 1 - sin²x

Thus; ( 1 - cos²x ) secx = sin²x · secx

Statement 3; sin²x (1/cosx)

Rule 2;  The rule here according to trigionometric identities is that; secx = 1/cosx. Thus; secx = 1/cosx .

Statement 4; sinx (sinx/cosx )

Rule 3;  The rule here is that sin²x can be expressed as (sinx * sinx)

Thus, we have; sinx . sinx (1/cosx) = sinx (sinx/cosx ).

Statement 5; sinx(tanx)

Rule 4;  The rule here is that; sinx/cosx = tanx.

Thus;  sinx (sinx/cosx ) gives us sinx(tanx)

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Answer:

\(\frac{1}{32} yards^{3}\)

Step-by-step explanation:

\(V=w*h*l\)

↓

\(V= \frac{1}{4} *\frac{1}{4} *\frac{1}{2}\)

=

\(\frac{1}{32} yards^{3}\\\)

Hope this helps!

49 is the smallest possible value of x.

Given: x, y, and z are three perfect square numbers.

What is the least x that can be?

Currently, we have three numbers by the stipulation:

x > y > z > 0

and AP has these figures.

Let's now list every perfect square from 1 to 10 in the following order: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

As a result, we can observe that 25 is equal to the product of 1 plus 49.

The possible outcomes are 1, 25, and 49.

If x = 49 and z = 1, then

x + z / 2 = y

49 + 1 / 2 = y

y = 50 / 2

y = 25

Y is therefore 25 and X is 49.

As a result, 49 is the lowest value of x that can exist.

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When rotated 90 degrees, counterclockwise direction the new coordinates will result in the attached image.

The old coordinate where were rotated are:

A(-5,8)

B (-1, 7)

C(-3, 5)

D(-4, 2)

To rotate a point counterclockwise about the origin, we switch the x and y coordinates and change the sign of the new x  -coordinate.

The new coordinates are after 90 degrees, counterclockwise  are

A' = (-8, -5)

B' = (-7, -1)

C' = (-5, -3)

D' = (-2, -4)

See attached image.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Answer: 290 beans

Step-by-step explanation:

You multiply 145 by 2 since 145 is half of the beans or do 145 divided by 1/2.

145 * 2 = 290.

145/.5 = 290

Hope this helps!!! :)

Answer:

first and third expressions

Step-by-step explanation:

using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{m-n}\)

then

\(\frac{3^{\frac{4}{9} } }{3^{\frac{2}{9} } }\)

= \(3^{\frac{4}{9}-\frac{2}{9} }\) ← first expression

= \(3^{\frac{2}{9} }\) ← third expression

Answer:

221 g

The up pinned pic is of inverse variation typed answer.. If u want word problem type answer here are the steps (EVEN IF THE STEPS ARE DIFFERENT ANSWERS REMAIN SAME)

Step-by-step explanation:

Mass of wire from 22cm = 374g

Mass of wire from 1 cm = 374÷22 = 17g

Mass of wire from 13 cm = 13×17 = 221 g

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

The standard deviation of the random variable X is 2.73861279.

Standard deviations is a measure of the spread of a data set around the mean. It is calculated by taking the square root of the variance of the data set and is used to measure the variability of a data set from the mean. Standard deviations are used to measure the probability of a certain outcome occurring and can be used to compare different data sets to see how much variability there is in the data.

Standard deviation is a measure of dispersion of data points around the mean of the data set. It is a measure of the variability of the data set. It is calculated by taking the square root of the variance of the data set.

Variance is the average of the squared differences of each data point from the mean. It is calculated by taking the sum of the squares of the differences of each data point from the mean and dividing by the number of data points minus one.

In this case, the mean of the data set is 3, because the probabilities of -2 and 5 are equal.

The variance of the data set is calculated as follows:

Variance = (0.3*(3-(-2))2 + 0.2*(3-3)2 + 0.5*(3-5)2) / (3-1)

Variance = (0.3*25 + 0 + 0.5*4) / 2

Variance = 7.5

The standard deviation of the data set is calculated by taking the square root of the variance, which is equal to 2.73861279.

Therefore, the standard deviation of the random variable X is 2.73861279.

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Answer:

I'd say 2

Step-by-step explanation:

Answer:

i hope this helpes

Step-by-step explanation:

a) A group of 16 pays $40 + ($2 x (16 - 10)) = $40 + $6 = $46.

b) The cost function can be represented as C(x) = 40 + 2(x - 10) for x > 10 and C(x) = 40 for x <= 10, where x is the number of people in the group and C(x) is the cost for the group.

c) The domain of the cost function is all non-negative real numbers less than or equal to 50 (0 <= x <= 50), since the maximum group size is 50. The range of the cost function is all non-negative real numbers greater than or equal to 40 (C(x) >= 40), since the minimum charge for a group is $40.

Answer:

a) $52

b) C(x) = 40 + 2x, if x > 10 and x ≤ 50

C(x) = 40, if x ≤ 10

c) Domain = {x ≥ 1 and x ≤ 50}

Range = { from 40 to 140}

If \($&f(x)=\frac{19}{x^{2}} \\\) then the inverse function exists  \($&f^{-1}(x)=\sqrt{\frac{19}{x}}\).

An inverse function in mathematics exists function which "reverses" the another function.

Let f(x) = y, then the inverse function, \($x=f^{-1}(y)$\)

\($&f(x)=\frac{19}{x^{2}} \\\)

\($&y=\frac{19}{x^{2}} \\\)

\($&x^{2}=\frac{19}{y} \\\)

simplifying the equation, we get

\($&x=\sqrt{\frac{19}{y}} \\\)

\($&x^{-1}=f^{-1}(y)=\sqrt{\frac{19}{y}} \\\)

\($&f^{-1}(y)=\sqrt{\frac{19}{y}},\)  then \($&f^{-1}(x)=\sqrt{\frac{19}{x}}\).

If \($&f(x)=\frac{19}{x^{2}} \\\) then the inverse function exists  \($&f^{-1}(x)=\sqrt{\frac{19}{x}}\).

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9514 1404 393

Answer:

  15

Step-by-step explanation:

When the smaller number is a divisor of the larger one, it is their highest common factor.

  HCF(15, 45) = 15

Answer:

The probability is \(P( X > 12.10 ) =0.0004\)

Step-by-step explanation:

From the question we are told that  

    The mean is  \(\mu = 11.95 \ ounce\)

     The  standard deviation is  \(\sigma = 0.045 \ ounce\)

 Generally the  probability that a bottle has more than 12.10 ounces poured into it, causing it to overflow is mathematically represented as

      \(P( X > 12.10 ) = P( \frac{X - \mu }{\sigma } > \frac{ 12.10 - 11.95}{0.045} )\)

\(\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )\)

     \(P( X > 12.10 ) = P( Z > 3.33 )\)

From the z table  the area under the normal curve to the right corresponding to  3.33   is

     \(P( Z > 3.33 ) = 0.0004\)

=>  \(P( X > 12.10 ) =0.0004\)

The hospital can get 4.15 milligrams from these three companies.

A linear equation is one in which the highest power of any variable is not more than 1. A linear equation in 2 variables can be solved by substitution method, if we have two simultaneous equations.

Here, we know that

Company A's supply of medicine = 1.7 mg

also, company A's supply = 2( B's supply - C's supply)

⇒ 1.7 = 2( B - C)

⇒ 1.7 = 2B - 2C .... (1)

Moreover, we are given that

A's supply = C's supply + 0.9

⇒ 1.7 = C + 0.9

⇒ 1.7 - 0.9 = C

⇒ 0.8 = C

Now, substituting the value of C in (1), we get,

1.7 = 2B - 2(0.8)

1.7 = 2B - 1.6

1.7 + 1.6 = 2B

⇒ B = 3.3/2

B = 1.65

Thus, the total supply from all three companies is (1.7 + 1.65 + 0.8) = 4.15 mg

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The top angle is right (90 degrees, kinda looks like a bent elbow).

The 2nd is acute (smaller than 90, kind of 'cute' bc it's small).

The 3rd is obtuse (greater than 90, I have nothing corny to say, sorry).

4th is acute.

5th is straight because it's a straight line.

6th is also obtuse.

Have a good day :)

The probability Julian chooses a blue hat is 1/3.

Probability refers to the branch of math which deals with finding out the likelihood of the occurrence of an event.

Total hat is:

= 25+20+40+30+25+1

= 150.

There are a total of 150 hats to choose from.

The number of blue hats to choose from is:

= 40 + 10

= 50.

The probability that Julian chooses a blue hat is:

= 50/150

= 1/3

= 0.33 or 33.33%.

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Answer:

It's 16, i did the unit test already.

Step-by-step explanation:

Answer:

(D)

Step-by-step explanation:

Given that Kendra is making a large salad for a party. She buys lettuce for $2.25 per pound and tomatoes for $2.65 per pound. She spends at least $8.

x represent the number of pounds of lettuce that Kendra buys and y represent the number of pounds of tomatoes that Kendra buys.

We are to select the inequality that represents the situation.

We have

total amount of money that Kendra spends on lettuce is given by

and the total amount of money that she spends on tomatoes is

Therefore, the inequality can be written as

Thus, option (D) is CORRECT.

Answer:

(2, -1)

Step-by-step explanation:

First off, we need to find the coordinates of D. We do this by applying the partitioning formula. It is (m/m+n)(x2-x1) +x1 for x and (m/m+n)(y2-y1)+y1 for y. The value of m is 5 and n is 3. You would need to input the valuables in. This will create (5/8)(10-2)+2 for x and (5/8)(2-(-6))-6 for y. In the end, we will have 7 for x and  -1 for y. To find c we just need to find what coordinates follow the x axis and for what y. We see that C follows the x coordinates of point A and y coordinates follow point D.

Answer:

513.45

Step-by-step explanation:

use intelligence

Answer:

3

Step-by-step explanation:

An equilateral triangle means all sides have the same length and there are 3 sides to a triangle. Therefore, the answer is 3.

"The correct answer is option A." The missing coordinates of point Q are (a, c/2).We are given the coordinates of points P and N as (0, c) and (2a, 0), respectively. We are also given that point Q lies on the same line as points P, Q, and N. We need to find the missing coordinates of point Q.

Since point Q lies on the same line as P, Q, and N, its x-coordinate must be halfway between the x-coordinates of points P and N. That is, the x-coordinate of Q is:

x-coordinate of Q = (x-coordinate of P + x-coordinate of N) / 2

x-coordinate of Q = (0 + 2a) / 2 = a

So, we know that the x-coordinate of point Q is a.

To find the y-coordinate of point Q, we can use the fact that point Q lies on the same line as point P, which has coordinates (0, c). The equation of the line passing through P and N is:

y - c = (0 - c) / (2a - 0) * (x - 0)

Simplifying this equation gives:

y - c = -c/2a * xy = -c/2a * x + c

Substituting x = a in this equation gives:

y = -c/2a * a + cy = -c/2 + cy = c/2

So, we know that the y-coordinate of point Q is c/2.

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The length of the fence must be 618cm

The volume that it can hold is 1,909,620 cm³

First, the fence is just equal to the circumference of the cylinder, remember that the circumfernce of a circle of diameter D is:

C = П*D

Here we use П = 3, then:

C = П*206cm

C = 3*206cm = 618cm

Now the volume, for a cylinder of diameter D and height H, the volume is:

V = П*(D/2)²*H

Replacing the values that we know we will get:

V = 3*(206cm/2)²*60cm = 1,909,620 cm³

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Answer:

Step-by-step explanation:

pix

Answer:

30

Step-by-step explanation:

150/5 = 30

30+30+30+30+30 = 150

Answer:

15033

Step-by-step explanation:

14,406 -(-627)