Please Help! Need this to pass :/

Answer:

Lateral Area of a Cylinder = 2πrh

=2π x 3 x 6

=36π

Option D

Answer:

[tex]A.\ \tan(x) \to 2.\ \sin(x) \sec(x)[/tex]

[tex]B.\ \cos(x) \to 5. \sec(x) - \sec(x)\sin^2(x)[/tex]

[tex]C.\ \sec(x)csc(x) \to 3. \tan(x) + \cot(x)[/tex]

[tex]D. \frac{1 - (cos(x))^2}{cos(x)} \to 1. \sin(x) \tan(x)[/tex]

[tex]E.\ 2\sec(x) \to\ 4.\ \frac{\cos(x)}{1 - \sin(x)} +\frac{1-\sin(x)}{\cos(x)}[/tex]

Step-by-step explanation:

Given

[tex]A.\ \tan(x)[/tex]

[tex]B.\ \cos(x)[/tex]

[tex]C.\ \sec(x)csc(x)[/tex]

[tex]D.\ \frac{1 - (cos(x))^2}{cos(x)}[/tex]

[tex]E.\ 2\sec(x)[/tex]

Required

Match the above with the appropriate identity from

[tex]1.\ \sin(x) \tan(x)[/tex]

[tex]2.\ \sin(x) \sec(x)[/tex]

[tex]3.\ \tan(x) + \cot(x)[/tex]

[tex]4.\ \frac{cos(x)}{1 - sin(x)} + \frac{1 - \sin(x)}{cos(x)}[/tex]

[tex]5.\ \sec(x) - \sec(x)(\sin(x))^2[/tex]

Solving (A):

[tex]A.\ \tan(x)[/tex]

In trigonometry,

[tex]\frac{sin(x)}{\cos(x)} = \tan(x)[/tex]

So, we have:

[tex]\tan(x) = \frac{\sin(x)}{\cos(x)}[/tex]

Split

[tex]\tan(x) = \sin(x) * \frac{1}{\cos(x)}[/tex]

In trigonometry

[tex]\frac{1}{\cos(x)} =sec(x)[/tex]

So, we have:

[tex]\tan(x) = \sin(x) * \sec(x)[/tex]

[tex]\tan(x) = \sin(x) \sec(x)[/tex] --- proved

Solving (b):

[tex]B.\ \cos(x)[/tex]

Multiply by [tex]\frac{\cos(x)}{\cos(x)}[/tex] --- an equivalent of 1

So, we have:

[tex]\cos(x) = \cos(x) * \frac{\cos(x)}{\cos(x)}[/tex]

[tex]\cos(x) = \frac{\cos^2(x)}{\cos(x)}[/tex]

In trigonometry:

[tex]\cos^2(x) = 1 - \sin^2(x)[/tex]

So, we have:

[tex]\cos(x) = \frac{1 - \sin^2(x)}{\cos(x)}[/tex]

Split

[tex]\cos(x) = \frac{1}{\cos(x)} - \frac{\sin^2(x)}{\cos(x)}[/tex]

Rewrite as:

[tex]\cos(x) = \frac{1}{\cos(x)} - \frac{1}{\cos(x)}*\sin^2(x)[/tex]

Express [tex]\frac{1}{\cos(x)}\ as\ \sec(x)[/tex]

[tex]\cos(x) = \sec(x) - \sec(x) * \sin^2(x)[/tex]

[tex]\cos(x) = \sec(x) - \sec(x)\sin^2(x)[/tex] --- proved

Solving (C):

[tex]C.\ \sec(x)csc(x)[/tex]

In trigonometry

[tex]\sec(x)= \frac{1}{\cos(x)}[/tex]

and

[tex]\csc(x)= \frac{1}{\sin(x)}[/tex]

So, we have:

[tex]\sec(x)csc(x) = \frac{1}{\cos(x)}*\frac{1}{\sin(x)}[/tex]

Multiply by [tex]\frac{\cos(x)}{\cos(x)}[/tex] --- an equivalent of 1

[tex]\sec(x)csc(x) = \frac{1}{\cos(x)}*\frac{1}{\sin(x)} * \frac{\cos(x)}{\cos(x)}[/tex]

[tex]\sec(x)csc(x) = \frac{1}{\cos^2(x)}*\frac{\cos(x)}{\sin(x)}[/tex]

Express [tex]\frac{1}{\cos^2(x)}\ as\ \sec^2(x)[/tex] and [tex]\frac{\cos(x)}{\sin(x)}\ as\ \frac{1}{\tan(x)}[/tex]

[tex]\sec(x)csc(x) = \sec^2(x)*\frac{1}{\tan(x)}[/tex]

[tex]\sec(x)csc(x) = \frac{\sec^2(x)}{\tan(x)}[/tex]

In trigonometry:

[tex]tan^2(x) + 1 =\sec^2(x)[/tex]

So, we have:

[tex]\sec(x)csc(x) = \frac{\tan^2(x) + 1}{\tan(x)}[/tex]

Split

[tex]\sec(x)csc(x) = \frac{\tan^2(x)}{\tan(x)} + \frac{1}{\tan(x)}[/tex]

Simplify

[tex]\sec(x)csc(x) = \tan(x) + \cot(x)[/tex]  proved

Solving (D)

[tex]D.\ \frac{1 - (cos(x))^2}{cos(x)}[/tex]

Open bracket

[tex]\frac{1 - (cos(x))^2}{cos(x)} = \frac{1 - cos^2(x)}{cos(x)}[/tex]

[tex]1 - \cos^2(x) = \sin^2(x)[/tex]

So, we have:

[tex]\frac{1 - (cos(x))^2}{cos(x)} = \frac{sin^2(x)}{cos(x)}[/tex]

Split

[tex]\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) * \frac{sin(x)}{cos(x)}[/tex]

[tex]\frac{sin(x)}{\cos(x)} = \tan(x)[/tex]

So, we have:

[tex]\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) * \tan(x)[/tex]

[tex]\frac{1 - (cos(x))^2}{cos(x)} = \sin(x) \tan(x)[/tex] --- proved

Solving (E):

[tex]E.\ 2\sec(x)[/tex]

In trigonometry

[tex]\sec(x)= \frac{1}{\cos(x)}[/tex]

So, we have:

[tex]2\sec(x) = 2 * \frac{1}{\cos(x)}[/tex]

[tex]2\sec(x) = \frac{2}{\cos(x)}[/tex]

Multiply by [tex]\frac{1 - \sin(x)}{1 - \sin(x)}[/tex] --- an equivalent of 1

[tex]2\sec(x) = \frac{2}{\cos(x)} * \frac{1 - \sin(x)}{1 - \sin(x)}[/tex]

[tex]2\sec(x) = \frac{2(1 - \sin(x))}{(1 - \sin(x))\cos(x)}[/tex]

Open bracket

[tex]2\sec(x) = \frac{2 - 2\sin(x)}{(1 - \sin(x))\cos(x)}[/tex]

Express 2 as 1 + 1

[tex]2\sec(x) = \frac{1+1 - 2\sin(x)}{(1 - \sin(x))\cos(x)}[/tex]

Express 1 as [tex]\sin^2(x) + \cos^2(x)[/tex]

[tex]2\sec(x) = \frac{\sin^2(x) + \cos^2(x)+1 - 2\sin(x)}{(1 - \sin(x))\cos(x)}[/tex]

Rewrite as:

[tex]2\sec(x) = \frac{\cos^2(x)+1 - 2\sin(x)+\sin^2(x)}{(1 - \sin(x))\cos(x)}[/tex]

Expand

[tex]2\sec(x) = \frac{\cos^2(x)+1 - \sin(x)- \sin(x)+\sin^2(x)}{(1 - \sin(x))\cos(x)}[/tex]

Factorize

[tex]2\sec(x) = \frac{\cos^2(x)+1(1 - \sin(x))- \sin(x)(1-\sin(x))}{(1 - \sin(x))\cos(x)}[/tex]

Factor out 1 - sin(x)

[tex]2\sec(x) = \frac{\cos^2(x)+(1- \sin(x))(1-\sin(x))}{(1 - \sin(x))\cos(x)}[/tex]

Express as squares

[tex]2\sec(x) = \frac{\cos^2(x)+(1-\sin(x))^2}{(1 - \sin(x))\cos(x)}[/tex]

Split

[tex]2\sec(x) = \frac{\cos^2(x)}{(1 - \sin(x))\cos(x)} +\frac{(1-\sin(x))^2}{(1 - \sin(x))\cos(x)}[/tex]

Cancel out like factors

[tex]2\sec(x) = \frac{\cos(x)}{1 - \sin(x)} +\frac{1-\sin(x)}{\cos(x)}[/tex] --- proved

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- \cfrac{3}{4}}(x-\stackrel{x_1}{(-4)}) \implies y +4= -\cfrac{3}{4} (x +4) \\\\\\ y+4=-\cfrac{3}{4}x-3\implies {\Large \begin{array}{llll} y=-\cfrac{3}{4}x-7 \end{array}}[/tex]

Answer:

y = -3/4x - 7

Step-by-step explanation:

Given: slope = m = -3/4

Plug this value into the standard slope-intercept equation of y = mx + b.

y = -3/4x + b

To find b, we want to plug in a value that we know is on this line: in this case, point (-4, -4). Plug in the x and y values into the x and y of the standard equation.

-4 = -3/4(-4) + b

To find b, multiply the slope and the input of x(-4)

-4 = 3 + b

Now, subtract 3 from both sides to isolate b.

-7 = b

Plug this into your standard equation.

y = -3/4x - 7

This is your equation.

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Answer:

8 = x²

Step-by-step explanation:

Logarithmic form: logₓ(8) = 2

Exponential form: 8 = x²

The graph also shows two other local maxima, at x=0.5 and x=1.5.

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Answer:

the answer is

B. 145° 12' 0"

Answer:

[tex]speed = \frac{distance}{time} \\ = \frac{3}{( \frac{30}{60} )} \\ = 3 \times 2 \\ = 6 \: miles \: per \: hour[/tex]

Answer: A. Quadrilateral

Step-by-step explanation:

The name for a polygon with 4 sides is a quadrilateral. Quadrilateral is a two-dimensional shape with four straight sides and four angles. The most common type of quadrilateral is the rectangle, which has four right angles. Other types of quadrilaterals include squares, parallelograms, trapezoids, and rhombuses.

Answer:

quadrilateral!!

Step-by-step explanation:

look at the beginning of the word, quad. Quad means 4 and is referring to a 4 sided figure.

Answer:

1/8 pound per person

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

49-31+12= 30

___________

Answer:

To solve this problem, we can set up the following equation:

Huilan's age + Thomas's age = 79

Let H be Huilan's age and T be Thomas's age. We can then rewrite the equation as:

H + T = 79

We are told that Huilan is 7 years older than Thomas, so we can write the following equation:

H = T + 7

Substituting the second equation into the first equation, we get:

(T + 7) + T = 79

Combining like terms, we get:

2T + 7 = 79

Subtracting 7 from both sides, we get:

2T = 72

Dividing both sides by 2, we get:

T = 36

Therefore, Thomas's age is 36 years.

Step-by-step explanation:

Answer:

let Thomas age be a

there fore, hullans age is a+7

(a+7)+a=79

2a=79-7

2a=72

a=36

Answer:

1st question :55%

2nd ":122.22%

3rd ":81.82%

Answer:

The shopper can but 12 jackets.

Step-by-step explanation:

80*.6 (100% - 40% = paying 60% or .6) = 48

576 / 48 = 12

Here we have a problem of percentage discounts, such that we need to find how much a given price decreases, and how many jackets we can buy considering the decreased price.

We will find that the number is 12.

Now let's see how we can get that result:

If something has an original price P, and we discount an x% of that price, the new price will be:

[tex]np = P\cdot(1 - x\%/100\%)[/tex]

Here we know that the regular price of a jacket is $80

And we have a discount of 40%

This means that the new price of these jackets will be:

[tex]np = \$80\cdot (1 - 40\%/100\%) = \$80\cdot (1 - 0.4) = \$80\cdot 0.6 = \$48[/tex]

Now we want to know how many of these jackets we can buy with $576

This will be equal to the quotient between the money we have and the new price of each jacket:

[tex]N = \$576/\$48 = 12[/tex]

This means that we can buy exactly 12 jackets at the sale.

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Answer:

B. 0.20 per century

Step-by-step explanation:

I calculated it logically

Answer:

(1/6) of the students did not pass.

Ans: (1/6)30 = 5 of the students did not pass

To solve this question, we need to first figure out, in fractional form, the number of students who did not pass. The problem tells us that 5/6 of the students passed. Therefore, we know that 1/6 of the students did not pass, because 5/6 + 1/6 = 1. So, all we need to do is multiply 1/6 by the total number of students:

1/6 * 36 = 6

So, 6 students did not pass.

Answer:

10 females, 15 males

Step-by-step explanation:

Let the number of females in the class be x. As the number of males is 5 more than the number of females, which is x, the number of males would be shown as x+5.

The number of females plus the number of males equal 25, so we get this equation:

x + (x+5) = 25

x + x + 5 = 25

2x + 5 = 25

2x = 20

x = 10.

So, there are 10 females, and since there are 5 more males than females, there are 10 + 5 = 15 males.

The total amount of interest you will have to pay is $21,849.92. As a result, choice A is accurate.

Compound monthly is the term used to describe a loan's interest rate, which is added to the principle each month and charged in installments. For instance, a $1,000 loan with a 12% annual interest rate compounded monthly would become $1,010 after the first month if the interest rate was 1%.

Monthly compounding is calculated by multiplying the principal amount by one plus the interest rate by the number of periods, raised to the power of the number of periods. This quantity is subtracted from the principal amount to determine the interest amount.

Thus;

[tex]Interest = 44,500(1 + 0.1311/100)^{6.5} \\= $21,849.92[/tex]

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Answer:

-134/4

Step-by-step explanation:

It equals -33.75.

Answer:

Explanation:

90 × (-3/4) = -135/2

-135/2 × (-3/4) = 405/8

405/8 × (-3/4) = -1215/32

Answer:

research it many my answer will be wrong

3

Step-by-step explanation:

-3 square is 9, adding 3 you will have 12. 10-6 is 4. so dividing 12 by 4 would give you 3.

Step-by-step explanation:

as the description says, the higher the ratio the better.

9/10 = 0.9

12/15 = 4/5 = 0.8

so, Tasha has the better batting average, as she has the higher ratio.

9/10 = 27/30

12/15 = 24/30

27/30 is higher than 24/30.

Answer:

45 degree , bc the ends are all 90 degree so divide 90 by two since the line crosses right in between

Answer:

45°

That looks like an Isosceles triangle so two sides are equal

The angle near O would be 90° cause that looks like an right angle

180-90=90

To find each angle divide by 2

90÷2=45

The sample space when choosing one marble will be B s=(purple, pink, red, blue, green, orange, yellow}

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample space may contain a variety of outcomes.

A paper bag has seven colored marbles. The marbles are pink, red, green, blue, purple, yellow, and orange. The sample space when choosing one marble will be all the colors. The correct option is B.

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The given polynomial is a factor of P(x) because P(-5)=0.

The Remainder Theorem states that if a synthetic division of a polynomial by x = a results in a zero remainder, then x = an is a zero of the polynomial (thanks to the Remainder Theorem), and x an is also a factor of the polynomial (courtesy of the Factor Theorem).

The Factor Theorem states that x - c is only a factor of P(x) when P(c) = 0.

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Answer:

[tex]y = 0.75x - 6[/tex]

Step-by-step explanation:

Given

Parallel to:

[tex]y = 0.75x[/tex]

Passes through

[tex](8,0)[/tex]

Required

The equation

The slope intercept form of an equation is:

[tex]y = mx + b[/tex]

Where:

[tex]m \to[/tex] slope

So, by comparison:

[tex]m = 0.75[/tex]

For a line parallel to [tex]y = 0.75x[/tex], it means they have the same slope of:

[tex]m = 0.75[/tex]

The equation of the line is then calculated using:

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

Where:

[tex]m = 0.75[/tex]

[tex](x_1,y_1) = (8,0)[/tex]

So, we have:

[tex]y = 0.75(x - 8) + 0[/tex]

Open bracket

[tex]y = 0.75x - 6 + 0[/tex]

[tex]y = 0.75x - 6[/tex]

Answer:

-132

Step-by-step explanation:

Split the summation to make the starting value of  

k equal to 1.

Answer:S6 = - 132

Step-by-step explanation:

Answer:

b is a polynomial

Step-by-step explanation:

[tex]f(x) = {x}^{3} - 11 {x}^{2} + {3}^{x} [/tex]