PLEASE HELP!!

Prove the trigonometric identity.


tanx+cotxcscxcosx=sec2x


Drag an expression to each box to correctly complete the proof.

Answer:

11 terms.

Step-by-step explanation:

We are given the arithmetic sequence:

17, 13, 9, ...

And we want to find the number of terms required such that the sum is -33.

Recall that the sum of an arithmetic series is given by:

[tex]\displaystyle S = \frac{k}{2}\left( a + x_k\right)[/tex]

Where k is the number of terms, a is the first term, and x_k is the last term.

The desired sum is -33. The first term is 17 as well. Thus:

[tex]\displaystyle (-33) = \frac{k}{2} \left( (17) +x_k\right)[/tex]

Simplify:

[tex]-66 = k(17 + x_k)[/tex]

We can write a direct formula to find the last term x_k. The direct formula of an arithmetic sequence has the form:

[tex]x_ n = a + d(n-1)[/tex]

Where a is the initial term and d is the common difference.

The initial term is 17 and the common difference is -4. Hence:

[tex]\displaystyle x_n = 17 - 4(n-1)[/tex]

Then the last term is given by:

[tex]x_k = 17 - 4(k-1)[/tex]

Substitute:

[tex]\displaystyle -66 = k\left( 17 + \left( 17 - 4(k-1)\right)\right)[/tex]

Solve for k:

[tex]\displaystyle \begin{aligned} -66 &= k(17 + (17 - 4k + 4)) \\ -66 &= k(38 -4k) \\ -66 &= -4k^2 + 38k \\ 4k^2 -38k -66 &= 0 \\ 2k^2 - 19k -33 &= 0 \\ (k-11)(2k+3) &= 0 \\ k-11&= 0 \text{ or } 2k+3 = 0 \\ \\ k &= 11 \text{ or } k = -\frac{3}{2}\end{aligned}[/tex]

Since we cannot have a negative amount of terms, we can ignore the second solution.

Therefore, the given sequence must have 11 terms such that it sums to -33.

Answer:

Here is 2 methods

Step-by-step explanation:

1) we use excel to find n=11 for lasy students

2) mathematical method

[tex]u_1=17\\u_2=13=17+(2-1)*(-4)\\u_3=9=17+(3-1)*(-4)\\\\\\\boxed{u_n=17+(n-1)*(-4)}\\\\\\\displaystyle s_n=\sum_{i=1}^nu_i\\=\sum_{i=1}^n(17+(i-1)*(-4))\\\\\\=(\sum_{i=1}^n 17) + (-4)*\sum_{i=1}^n (i) +4*\sum_{i=1}^n (1)\\\\\\=17*n+4*n-4*\frac{n*(n+1)}{2} \\\\\\=21n-2n^2-2n\\\\\\=-2n^2+19n\\\\=-33\\\\\\\Longrightarrow\ 2n^2-19n-33=0[/tex]

[tex]\Delta=19^2+4*2*33=625=25^2\\\\n=\dfrac{19-25}{4} =-1.5\ (excluded)\ or\ n=\dfrac{19+25}{4}=11\\\\[/tex]

Answer:

-60 and -28

Step-by-step explanation:

-60 + 42= -18

CHECK:

-42-18=-60

-56+-28=-84

CHECK:

-84+28=-56

Hope this helps <3 Need thanks? Comment /hearthelp

Answer:

-60

-28

Step-by-step explanation:

x +42 = -18

Subtract 42 from each side

x+42-42 = -18-42

x = -60

-56 +y = -84

Add 56 to each side

y = -84+56

y = -28

Answer:

7k

Step-by-step explanation:

-k - -(8k): the - sign cancels out the - in 8k so it would only leave -k+8k=7k

Answer:

7k

Step-by-step explanation:

-k - (-8k)

if there is "-" in front on an inner form, change the sign of each quarter to the form.

-k + 8k

Simplify similar tribes with add or subtract.

= 7k

Answer:

c=6.31, a=50.28 degrees, B=75.72 degrees

Step-by-step explanation:

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The remaining parts of the triangle can be found as shown.

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,

[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ B}{\beta} =\dfrac{Sin\ C}{\gamma}[/tex]

where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,

Sin B is the angle and β is the length of the side of the triangle opposite to angle B,

Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.

Given that the length of side a and b is 6 and 7.56, also, the measure of the angle γ is 54°.

Now, Using the law of cosine, we can write,

[tex]c =\sqrt{a^2 + b^2 -2ab\cdot \cos\gamma}[/tex]

[tex]c =\sqrt{(6)^2 + (7.56)^2 -2(6)(7.56)\cdot \cos(54^o)}[/tex]

c = √39.8297

c = 6.311

Now, using the sine law the ratio of the sides and angles can be written as,

[tex]\dfrac{\sin\alpha}{a} =\dfrac{\sin\beta}{b} =\dfrac{\sin\gamma}{c}[/tex]

[tex]\dfrac{\sin\alpha}{6} =\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}[/tex]

[tex]\dfrac{\sin\alpha}{6}=\dfrac{\sin (54^o)}{6.311}[/tex]

α = 50.2775°

[tex]\dfrac{\sin\beta}{7.56} =\dfrac{\sin (54^o)}{6.311}[/tex]

β = 75.726°

Hence, the remaining parts of the triangle can be found as shown.

Learn more about Sine Rule here:

https://brainly.com/question/17289163

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[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{There is approximately 5 branches of chemistry.}\\\\\large\textsf{The branches are...}}\\\\\bullet\large\text{Analytical chemistry}\\\bullet\large\text{Biochemistry}\\\bullet\large\text{Inorganic chemistry}\\\bullet\large\text{Physical chemistry}\\\bullet\large\text{Organic chemistry}[/tex]

[tex]\star\large\textsf{\ \underline{\underline{Analytical chemistry}} is the science that prevails, communicates, and}\\\large\textsf{process the information about its arrangement of the matter.}\\\\\star\large\textsf{\ \underline{\underline{Biochemistry}} is the study of the process in the cellular \& molecular}\\\large\textsf{level}[/tex]

[tex]\star\large\textsf{\ \underline{\underline{Inorganic chemistry}} is the behavioral mood of the inorganic and the} \\\large\textsf{organometallic compounds. It is distributed with the synthesis.}\\\\\star\large\textsf{\ \underline{\underline{Physical chemistry}} is the changing and exchange of the materials.}[/tex]

[tex]\star\large\textsf{\ \underline{\underline{Organic chemistry}} is the study of the structure, property,}\\\large\textsf{(or properties) \& reactions of the organic compounds}[/tex]

[tex]\large\boxed{\frak{Good \ luck \ on \ your \ assignment \ \& \ enjoy\ your\ day!}}[/tex]

~[tex]\rm{Amphitrite1040:)}[/tex]

Step-by-step explanation:

this is confusing.

first the description says "the internal dimensions".

and then it tells us the thickness of the tank walls (1cm).

so, I am not sure what the given numbers describe.

in any case, the volume is length × width × height.

so, either

48×38×32

or

46×36×31 (as for length and width we need to consider 2 walls, one on each end, for the height only one wall, as the tank is open and lidless.

whatever you choose, make sure to mark the result as cm³.

Answer:

Hello

y=(x+1)/12 +1

Step-by-step explanation:

[tex]\text{As the directrice is horizontal:}\\\\\\y=-2 ==> k=-2\\\\Focus=(a,b)=(-1,4)\\\\\boxed{y=\dfrac{x-a}{2(b-k)} +\dfrac{b+k}{2} }\\\\\\y=\dfrac{x+1}{2(4+2)} +\dfrac{4-2}{2} }\\\\\boxed{y=\dfrac{x+1}{12} +1}\\[/tex]

Answer:

A. A, B, C, D

Step-by-step explanation:

A. 4.99 ÷ 2.25 = 2.1777...

B. 5.50 ÷ 1.75 = 3.142857143

C. 10.99 ÷ 4.50 = 2.44222...

D. 2.99/0.5 = 5.98/1

Answer:

a. A, C, B, D

Step-by-step explanation:

A. 9/4 = 2.25

2.25/4.99 = 1/x

2.25x ÷ 2.25 = x

4.99 ÷ 2.25 = 2.22

$2.22 per pound

B. 7/4 = 1.75

1.75/5.50 = 1/x

1.75x ÷ 1.75 = x

5.50 ÷ 1.75 = 3.14

$3.14 per pound

C. 9/2 = 4.5

4.5/10.99 = 1/x

4.5x ÷ 4.5 = x

10.99 ÷ 4.5 = 2.44

$2.44 per pound

D. 1/2 = 0.5

0.5/2.99 = 1/x

0.5x ÷ 0.5 = x

2.99 ÷ 0.5 = 5.98

$5.98 per pound

Answer:

f(x) = 4(x+3)(x-2)

Step-by-step explanation:

The quadratic function is

f(x) = a(x-b1)(x-b2)  where a is a coefficient and b1 and b2 are the zeros

f(x) = a(x- -3)(x-2)

f(x) = a(x+3)(x-2)

The leading coefficient is a and we know a =4

f(x) = 4(x+3)(x-2)

Answer:

-1/5

Step-by-step explanation:

We know that a^b * a^c = a^(b+c)

(−5)^5(−5)^−6

(-5) ^(5+-6)

(-5)^-1

We know that a^-b = 1/a^b

1/(-5)^1

1/-5

-1/5

Answer:

f(x) + g(x) is 2(2x² - 4x - 3)

Step-by-step explanation:

[tex]f(x) + g(x) = (x)(2x + 5) + ( {2x}^{2} - 13x + 6) \\ = (2 {x}^{2} + 5x) + (2 {x}^{2} - 13x + 6) \\ = 4 {x}^{2} - 8x - 6 \\ = 2(2 {x}^{2} - 4x - 3)[/tex]

Answer:

6.32

Step-by-step explanation:

6.32 is also the same as 6.320,

so rounding it to two decimal points is 6.32

Answer:

3

Step-by-step explanation:

18,049 / 14 = 1289 and 3/14

So the remainder = 3

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

3

Step-by-step explanation:

Quotient = 18049/14=1289

Using Formula,

Dividend = (Divisor x Quotient) + Remainder

Remainder = Dividend-(Divisor x Quotient)

Remainder = 18049-(14x1289)=3

Answer:

5/2

Step-by-step explanation:

tan&= 2/5(p/b)

here,

p=2,b=5

cot&=b/p

=5/2

Answer:

16 units

Step-by-step explanation:

period = length of an interval that contains exactly one copy of the repeating pattern, so from one peak to another peak.

in this graph its the peaks are 1 and 17, hence the period is 16

Answer:

1

Step-by-step explanation:

√(4-3²+(3-3)²

√1¹+0

√1

1

Answer:

Step-by-step explanation:

Since x- coordinates are same, the distance is the difference of the y-coordinates:

Answer:

√122

Step-by-step explanation:

To find the distance/length between two points

Use this formula: [tex]\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

[tex]\sqrt{(1 - 2)^2 + (3 + 8)^2}[/tex]

[tex]\sqrt{(-1)^2 + (11)^2}[/tex]

[tex]\sqrt{1 + 121}[/tex]

[tex]\sqrt{122}[/tex]

Answer:

π is equal to 3.14

A=πr^2 is the equation to get the area of a circle where r is the radius.

Answer:

π=A/12r2

Step-by-step explanation:

A=12πr2

divide both sides by 12r2

A/12r2=12r2/12r2

π=A/12r2

Answer:

7 pots of coffee (If you want to be precise its 6 2/3)

Step-by-step explanation:

So basically you need 10 cups of coffe in fifteen minutes, so 60/15=4 then time 10. so 40 is how much coffee you need in a hour, but we are solving the pot so 40/6= 6 2/3. but it says how many pots so we round it up so its 7. (Unless you wanna be precise)

Answer:

The green box would be [tex]\frac{1}{8}[/tex].

Step-by-step explanation:

[tex]\frac{1}{2^{3}} = \frac{1}{8}[/tex]

Answer:

Step-by-step explanation:

R.A. = 50(1 - .5)^3

your question askes for the decay factor "green box"

that number is 1/2 (.5)

Answer: x = 17/3 or 5 2/3

Step-by-step explanation:

Let the number be x

ATQ

6(x -4) = 10

6x-24 = 10

6x = 10+24

6x = 34

x = 34/6

x = 17/3

please click thanks and mark brainliest if you like :)

The number is 17/3 if the six times the difference of a number and 4 is no more than 10 the answer is 17/3.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The question is incomplete.

The complete question is:

Six times the difference between a number and 4 is no more than 10. Find the number.

It is given that:

Let x be the number:

From the statement: "six times the difference of a number and 4 is no more than 10"

We can frame a linear equation in one variable:

6(x -4) = 10

Using distributive property:

6x -24 = 10

6x = 34

x = 34/6

x = 17/3

Thus, the number is 17/3 if the six times the difference of a number and 4 is no more than 10 the answer is 17/3.

Learn more about the linear equation here:

brainly.com/question/11897796

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Answer:

180

Step-by-step explanation:

[tex]\frac{6}{2} x^{2} | \frac{8}{2}[/tex]

192-12=180

Answer:

C

A

Step-by-step explanation:

adjacent means neighboring, right next to it. that would be 1 and 4.

supplementary means being a complementary, an additional angle, so that in sum both angles together have 180 degrees. and that is only 1.

so, C is the answer.

angle 7 = 115 degrees.

so, angle 8 is supplementary to angle 7.

they are being mirrored on the other side of the line.

so, angle 6 = angle 7, and angle 5 = angle 8.

and the same quadruple of angles have to appear, where the crossing line crosses another, parallel line. they have to be the same angles there again.

so, angle 3 = angle 7, angle 4 = angle 8, angle 1 = angle 5, angle 2 = angle 6.

and because angle 6 is also = angle 7, we have angle 2 = angle 7 = 115 degrees.

Answer:

C and A

Step-by-step explanation:

∠ 5 and ∠ 1 are adjacent ( next to each other) on the same line

The angles on a straight line sum to 180° ( supplementary )

Then ∠ 1 is adjacent and supplementary to ∠ 5 → C

----------------------------------------------------------------------------

∠ 2 and ∠ 7 are alternate exterior angles and are congruent , then

∠ 2 = ∠ 7 = 115° → A

Answer:

answer B:

[tex]x= \dfrac{\pi}{2}\ or\ \dfrac{\pi}{6}\ or\ x=\dfrac{5\pi}{6}[/tex]

Step-by-step explanation:

[tex]2cos^2 x + 3sin x=3\\\\\Longrightarrow\ 2*(1-sin^2 x)+3sin x -3=0\\\\\Longrightarrow\ 2-2sin^2 x+3 sin x -3=0\\\\\Longrightarrow\ -2sin^2 x+3 sin x -1=0\\\\\Longrightarrow\ 2sin^2 x-3 sin x +1=0\\\\\Delta=3^2-4*2*1=1\\\\sin\ x=\dfrac{3-1}{4} \ or\ sin\ x=\dfrac{3+1}{4}\\\\sin\ x=\dfrac{1}{2} \ or\ sin\ x=1\\\\\Longrightarrow\ x= \dfrac{\pi}{6}\ or\ x= \dfrac{5\pi}{6}\ or\ x=\dfrac{\pi}{2} \\[/tex]

Answer:

24

Step-by-step explanation:

trudt

Answer:

30.7

Step-by-step explanation:

Assuming the angled are degrees and not radian.

side BC= (11÷sin67)•sin28= 5.6

angle ABC= 180-67-28=85°

A= 11•5.6•sin85÷2≈30.68

Answer:

30$

Step-by-step explanation:

12/400=0.03$ cost per g

1 kg = 1000 g

price per kg = 0.03*1000=30$

Answer:

Step-by-step explanation:

Length 1 = 8x^2 - 5x - 2

Length 2 = 7x - x^2 + 3

Part A

Length of the two sides = 8x^2 - 5x - 2 + 7x - x^2 + 3

Length of the two sides = 8x^2 - x^2 - 5x + 7x - 2 + 3

Length of the two sides = 7x^2 + 3x + 1

Part B

The perimeter is 4x^3 - 3x^x + 2x - 6

The Third side must be Perimeter - the sum of the two sides.

The third side must be 4x^3 - 3x^x + 2x - 6 - 7x^2 - 3x - 1

The third side = 4x^3 - 4x^x -7x^2  - x - 7

Part C

The problem is now does this show closure. I would say it does not.  I don't think 4x^x is in the quadratic family. Let's take a simpler example of closure.

Suppose we say 4 + 5 = 9 and we say further that we are working with all the integers. 9 is an integer and so are 4 and 5.  So the integers are closed by addition.

4 - 5 = - 1  The answer (-1) is still an integer, so the example still shows closure.

But the question has things in it that show closure only if the set of numbers is the real numbers and even then I'm not certain. We have to ask what x^x is.

Answer:

22+c=54

Step-by-step explanation:

22 + his age =54

Answer:

8

Step-by-step explanation:

3(y - 1) + 2x²

Let x =2 and y =1

3(1-1)+2 (2)^2

3(0) +2(4)

0+8