Find the volume of this cone.Use 3 for TT.14 ft14 ftV = Tr?h=3V ~ [?]ft

The expression sin²x/(1+cosx) can be simplified to 1-cosθ

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Recall that sin²x = 1 - cos²x. Thus, we have:

sin²x/(1+cosx) = (1-cos²x) / (1+cosx)

                      = (1²-cos²x) / (1+cosx)

                      = (1+cosx)(1-cosx) / (1+cosx)

                      = 1-cosx

                      = 1-cosθ        (If x = θ)

Note: Using difference of two squares, 1²-cos²x = (1+cosx)(1-cosx)

Therefore, the expression sin²x/(1+cosx) can be simplified to 1-cosθ

Learn more about Trigonometry on:

brainly.com/question/11967894

#SPJ1

Answer:

Step-by-step explanation:

To answer this, divide 67 by 2, writing the answer as a mixed number:

67

---- = 33 1/2

 2

thus, 2 can go into 67 33 times, keeping in mind that there's a remainder (1/2).

The solution to the equation 1/2 - x + 3/2 = x - 4 is x = 3.

We have Equation 1/2 - x + 3/2 = x - 4

Now, solving the equation for x we get

/2 - x + 3/2 = x - 4

First, let's combine the like terms on both sides of the equation:

(1/2 + 3/2) - x = x - 4

4/2 - x = x - 4

2 - x = x - 4

Next, let's move the term with x to the left side by adding x to both sides:

2 - x + x = x - 4 + x

2 = 2x - 4

Then, let's move the constant term -4 to the right side by adding 4 to both sides:

2 + 4 = 2x - 4 + 4

6 = 2x

6/2 = 2x/2

3 = x

Therefore, the solution to the equation is x = 3.

Learn more about Equation here:

https://brainly.com/question/29657983

#SPJ6

Skipper's finance charge at the end of the billing period is given as follows:

$14.77.

The finance charge is obtained using simple interest, as there is a simple compounding per year for the debt, and the charge is the amount of interest accrued during the period of one month.

The amount of interest accrued after t years, using simple interest, is given as follows:

I(t) = Prt.

The parameters for the equation are given as follows:

Considering a period of one month = 1/12 of an year, the values of these parameters for this problem are given as follows:

P = 933, r = 0.19, t = 1/12.

Hence the finance charge for Skipper's purchase is calculated as follows:

I = 933 x 0.19 x 1/12 = $14.77.

(rounding to the nearest penny = nearest cent).

More can be learned about simple interest at https://brainly.com/question/20690803

#SPJ1

Answer:

Step-by-step explanation:480 x o.75=360

and now you add this amount on payed

360 + 480=840 was original price

The length of CD is approximately 27.931 meters.

To find the length of CD, we can use the concept of similar triangles and trigonometric ratios.

Let's start by drawing a diagram to visualize the situation:

      A----------B

     /           /

    /           /

   /           /

  D----------C

  |

  |

  |

  F

We are given that road AB slopes at 10.2 degrees to the horizon and road BC slopes at 6.3 degrees to the horizon. From the diagram, we can see that angle DAF is the same as the slope angle of road AB (10.2 degrees), and angle DCF is the same as the slope angle of road BC (6.3 degrees).

Now, we can set up the following trigonometric equations using the given information:

tan(10.2 degrees) = CD / AD (equation 1)

tan(6.3 degrees) = CD / BF (equation 2)

Since AD and BF are perpendicular, we can consider them as vertical heights. Let's calculate the lengths of AD and BF.

For road AB, we can use the definition of tangent:

tan(10.2 degrees) = height AB / length AB

Solving for the height AB, we have:

height AB = tan(10.2 degrees) * length AB

height AB = tan(10.2 degrees) * 800m

height AB ≈ 147.294m

Similarly, for road BC:

height BC = tan(6.3 degrees) * length BC

height BC = tan(6.3 degrees) * 300m

height BC ≈ 33.706m

Now, we can substitute these values into equations 1 and 2:

tan(10.2 degrees) = CD / 147.294m (equation 1)

tan(6.3 degrees) = CD / 33.706m (equation 2)

Solving equation 1 for CD:

CD = tan(10.2 degrees) * 147.294m

CD ≈ 27.931m

Therefore, the length of CD is approximately 27.931 meters.

for such more question on length

https://brainly.com/question/20339811

#SPJ8

The total amounts of money which Mrs. Reynolds now has according to the descriptions in the task content is; $68.

It follows from the task content that;

On this note;

Hence, it follows that the amount of money, s she has now is;

Read more on addition and subtraction;

https://brainly.com/question/25421984

We have the following equation:

by moving -3y to the left hand side, we have

which is in the form

By comparing both equations, we can see that a=-1, b=3 and c=-3. By substituting these values in the quadratic formula, we get

which gives

which leads to

but

Therefore, the solutions are:

Let total number of units = x

As per the given data, 60% units constitutes 66 offices.

Hence,

Solving further for x we have,

Thus, there are total number of 110 offices in a building.

Answer:

C

Step-by-step explanation:

Answer:

7/10 or 0.7

Step-by-step explanation:

first bag = 3/15

second bag 5/10

make them alike

first bag 3/30

second bag 15/30

add

18/30

simplify = 7/10

Answer:

1.05

Step-by-step explanation:

We start of with 100 * (1.7)^t

So the change in 100 is (1.7)^t(years). Well, that is in years, we need months. There are 12 months in a year, this is good to remember for several reasons ;). Since they ask for "Every month, the number of exercises increases by a factor of:", we must plug in 1/12 as t.

We can rewrite this as:

100 * (1.7)^1/12

Just plug the (1.7)^1/12 into a calculator, which is a cool device that can do boring math for you, and you should get 1.045... blah blah blah(a bunch of other useless numbers).

So now we have:

100*1.045

Well, the problem said "Round your answer to two decimal places."

So we need to round the 1.045.

5 is right in the middle, but if you know rounding, your probably know that the 5 goes up. So yay, your 1.045 is now 1.05.

So in the end, we get:

1.05

Ti⊂k∫∈s ω∅∅p :)

The number of exercises increases by a factor of approximately 14.17 each month.

To determine the monthly rate of change in the number of exercises, we need to find the factor by which the number of exercises increases each month.

The given function, Eyear(t) = 100 × \((1.7)^t\), represents the total number of exercises after t years. To convert this to a monthly rate, we need to divide the yearly rate by 12 (since there are 12 months in a year).

So, the monthly rate of change in the number of exercises is:

E_month(t) = Eyear(t)/12

Substituting the given function, we have:

Emonth(t) = 100 × \((1.7)^t\)/12

To find the factor by which the number of exercises increases each month, we can compare the value of E_month(t) at t = 1 to the value at t = 0:

E_month(1) = 100 × \((1.7)^t\)/12 = (100 × 1.7)/12 = 14.17

Therefore, the number of exercises increases by a factor of approximately 14.17 each month.

Learn more about exponential functions click;

https://brainly.com/question/29287497

#SPJ2

Answer:

28

Step-by-step explanation:

14x2=28

Therefore x=28

Answer:

a) {3,5}{3,10}{5,10}

b) \(P(A)=\frac{1}{3}\)

c) \(P(B)=\frac{2}{3}\)

d) \(P(C)=\frac{1}{3}\)

e) \(P(A and C)=0\)

f) \(P(A or B)=1\)

g) \(P(B and C)=\frac{1}{3}\)

h) \(P(A or C)=\frac{2}{3}\)

i) \(P(C given B)=\frac{1}{2}\)

j) \(P(C given A)=0\)

k) \(P(not B)=\frac{1}{3}\)

l) \(P(not C)=\frac{2}{3}\)

Yes, events A and B are mutually exclusive. Because the results can either be even or odd, not both. No, events B and C are not mutually exclusive because the result can be both, odd and prime.

Step-by-step explanation:

a)

In order to solve part a of the problem, we need to find the possible outcomes, in this case, the possible outcomes are:

{3,5}{3,10} and {5,10}

We could think of the oppsite order, for example {5,3}{10,3}{10,5} but these are basically the same as the previous outcomes, so we will just take three outcomes in our sample space. We can think of it as drawing the two chips at the same time.

b)

Now the probability of the sum of the chips to be even. There is only one outcome where the sum of the chips is even, {3,5} since 3+5=8 the other outcomes will give us an odd number, so:

\(P=\frac{#desired}{#possible}\)

\(P(A)=\frac{1}{3}\)

c) For the probability of the sum of the chips to be odd, there are two outcomes where the sum of the chips is odd, {3,10} since 3+10=13 and {5,10} since 5+10=15 the other outcomes will give us an even number, so:

\(P(B)=\frac{2}{3}\)

d) The probability of the sum of the chips is prime. There is only one outcome where the sum of the chips is prime, {3,10} since 3+10=13 the other outcomes will give us non prime results, so:

\(P(C)=\frac{1}{3}\)

e) The probability of the sum of the chips to be even and prime. There are no results where we can get an even and prime number, since the only even and prime number there is is number 2 and no outcome will give us that number, so:

P(A and C)=0

f) The probability of the sum of the chips is even or odd. We can either get even or odd results, so no matter what outcome we get, we will get an odd or even result so:

\(P(A or B)=1\)

g) The probability of the sum of the chips is odd and prime. There is only one outcome where the sum of the chips is odd and prime, {3,10} since 3+10=13 the other outcomes will give us non prime results, so:

\(P(B and C)=\frac{1}{3}\)

h) The probability of the sum of the chips is even or prime. There are two outcomes where the sum of the chips is even or prime, {3,10} since 3+10=13 and {3,5} since 3+5=8 so:

\(P(A or C)=\frac{2}{3}\)

i) The probability of the sum of the chips is prime given that the sum of the chips is odd. There are two possible results where the sum of the chips is odd {3,10} and {5,10} and only one of those results is even, {3,10}, so

\(P(C given B)=\frac{1}{2}\)

j) The probability of the sum of the chips is prime given that the sum of the chips is even. There is only one possible even result: {3,5} but that result isn't prime, so

\(P(C given A)=0\)

k) The probability of the sum of the chips is not odd. There is only one outcome where the sum of the chips is not odd (even), {3,5} so:

\(P(not B)=\frac{1}{3}\)

l) The probability of the sum of the chips is not prime. There are two outcomes where the sum of the chips is not prime, {3,5} and {5,10} so:

\(P(not C)=\frac{2}{3}\)

Are events A and B mutually exclusive?

Yes, events A and B are mutually exclusive.

Why or why not?

Because the results can either be even or odd, not both.

Are events B and C mutually exclusive?

No, events B and C are not mutually exclusive.

Why or Why not?

Because the result can be both, odd and prime.

Answer:

  \(1-\dfrac{2}{3}\sqrt{3}\)

Step-by-step explanation:

Maybe you want to simplify ...

  \((1-\sqrt{3})\dfrac{1}{3+\sqrt{3}}\)

Multiply numerator and denominator by the 'conjugate' of the denominator:

  \((1-\sqrt{3})\dfrac{1}{3+\sqrt{3}}\cdot\dfrac{3-\sqrt{3}}{3-\sqrt{3}}=\dfrac{(1-\sqrt{3})(3-\sqrt{3})}{9-3}=\dfrac{3-4\sqrt{3}+3}{6}\\\\\boxed{1-\dfrac{2}{3}\sqrt{3}}\)

Answer:

4,8 is the answer

hope it helped

can you make me brianliest

Answer:

Step-by-step explanation:

A.-5+(n-1)*2 and n belong to 1 to ponitive infinity

\( \huge \pink{ \underbrace { \overbrace { \ SAS}}}\)

Answer:

$30.00

Step-by-step explanation:

The original price of the sweater is $75.00.  The new sale price is the original price of  100% less  60% of the original price.  That means the sales price is 40% of the original price.

You can do this 2 ways:

1.  $75 x 60% or .60 = $45

  $75-45 = $30

or

2.  $75 x 40% or .40 = $30

Answer:

3 whole but 3.4 as a decimal

Step-by-step explanation:

Answer:

y-7=-2/1 (x-1)

Step-by-step explanation:

Hope this helps!

The parabοla is degenerate and it can be said that it is just a pοint.

A parabοla is a curve whοse equatiοn places a pοint οn it at a same distance frοm bοth a fixed pοint and a fixed line. The parabοla's fixed pοint is referred tο as the fοcus, and its fixed line is referred tο as the directrix.

The fixed pοint dοes nοt lie οn the fixed line, which is anοther crucial factοr tο remember. A parabοla is a lοcus οf any pοint that is equally distant frοm bοth the fοcus and directrix οf twο supplied pοints. The pοint where a parabοla makes its sharpest turn is knοwn as the vertex.

If a parabοlic functiοn has the shape οf a "," it has a maximum value; οtherwise, it has a minimum value.

If the fοcus οf a parabοla is given by (a,b) and the directrix is a hοrizοntal line given by y=c, then the equatiοn οf the parabοla is

\((y-b)^2=4a(x-a)-(b-c)^2.\)

In this case, the fοcus is (-8,8) and the directrix is x=-6, which is a vertical line.

Therefοre, the axis οf the parabοla is hοrizοntal, and the vertex is halfway between the fοcus and the directrix, which is (-1,8).

We can use the fοrmula abοve tο find the value οf a:

\((y-8)^2 = 4a(x+8)\)

Setting y=8 and x=-1 (the cοοrdinates οf the vertex),

we get:0 = 4a(-7)a=0

This means that the parabοla is actually a vertical line passing thrοugh the vertex (-1,8), with nο x-term.

Therefοre, the parabοla is degenerate and it can be said that it is just a pοint.

Learn more about parabola, by the following link.

brainly.com/question/1214333

#SPJ1

To describe the center of the data, we can use either the mean or the median.

To describe the variation of the data, we can use either the range or the interquartile range (IQR).

Looking at the dot plot, it seems that the data is somewhat skewed to the right, with a few high-priced outliers. In this case, the median and the IQR may be more appropriate measures of the center and variation, respectively, as they are less sensitive to outliers.

To find the median and IQR:

Arrange the data in order from smallest to largest.

Find the median, which is the middle value. If there are an even number of values, take the average of the two middle values.

Find the first quartile, which is the median of the lower half of the data.

Find the third quartile, which is the median of the upper half of the data.

Calculate the IQR as the difference between the third quartile and the first quartile.

Here are the steps applied to the dot plot:

We can see that the smallest value is about 20 and the largest value is about 120, giving a range of 100 dollars.

The median is approximately 60 dollars, as it is the middle value between the 11th and 12th data points when the data is arranged in order.

The first quartile is approximately 40 dollars, as it isthe median of the lower half of the data points, which are found below the median.

The third quartile is approximately 80 dollars, as it is the median of the upper half of the data points, which are found above the median.

The IQR can be calculated as the difference between the third quartile and the first quartile, which is approximately 40 dollars.

Therefore, the most appropriate measures to describe the center and the variation for this data set are the median and the interquartile range (IQR), respectively. The median is approximately 60 dollars, and the IQR is approximately 40 dollars.

Answer:

which one substitution or elimination

Step-by-step explanation:

Substitution: (-1,-3 )

Elimination: (-1,-3)

i hope this helps you :)

Please mark me brainlest

Answer:

1- 27

2- 36

3- -200

this is the answer

4.2 x 10^8 is  2*10^6  times the value of 2.1 x 10^2 when division is performed.

The concept that will be used to solve the question is division operation.

We were given 4.2 x 10^8 which is greater than  2.1 x 10^2

The operation can be expressed as :

4.2 x 10^8 =( n *2.1 x 10^2)

where n = the number of times that 4.2 x 10^8  is greater than 2.1 x 10^2

Then make n the subject of the formular which is

n = 4.2 x 10^8/2.1 x 10^2

n = 2*10^6

Therefore, the values of 4.2 x 10^8 is greater than 2.1 x 10^2 in 2*10^6 times.

Read more about division at:

brainly.com/question/11421834

#SPJ1

Answer:

\(x=15\)

Explanation:

Solving the inequality for x would give you \(x>9\), therefore, \(x=15\) would be the only option. While you might think \(x=9\) should also be a solution, it would only be one if \(x\geq 9\).

Hope this helps! :)