two poles 8m and 13m high
are placed opposite to each other across a 12
metre long road find the distance
between their tops

Answer:

The equation of the tangent line

[tex]y - \frac{\pi }{4} = (\frac{-\pi }{2} +1)( x - \frac{\pi }{4} )[/tex]

Step-by-step explanation:

Step(i):-

Given function y = x cot (x) ....(i)

Differentiating equation (i) with respective to 'x' , we get

[tex]\frac{dy}{dx} = x (-Co sec^{2} (x)) +cot(x) (1)[/tex]

Step(ii):-

The slope of the tangent line

[tex]\frac{d y}{d x} = -x Co-sec^{2} (x) +cot x[/tex]

[tex](\frac{d y}{d x} )x_{=\frac{\pi }{4} } = -\frac{\pi }{4} Co-sec^{2} (\frac{\pi }{4} ) +cot \frac{\pi }{4}[/tex]

We will use trigonometry formulas

[tex]Cosec(\frac{\pi }{4} ) = \sqrt{2}[/tex]

[tex]sec(\frac{\pi }{4} ) = \sqrt{2}[/tex]

[tex]Cot(\frac{\pi }{4} ) = 1[/tex]

Now the slope of the tangent

[tex]\frac{dy}{dx} =-\frac{\pi }{4} (\sqrt{2})^{2} )+1[/tex]

[tex]\frac{dy}{dx} =-\frac{\pi }{2} +1[/tex]

Step(iii):-

Given

Substitute [tex]x=\frac{\pi }{4}[/tex] in y = x cot (x)

               [tex]y = \frac{\pi }{4} cot (\frac{\pi }{4} )[/tex]

              [tex]y = \frac{\pi }{4}[/tex]

The point of the tangent line  [tex](x ,y ) = (\frac{\pi }{4} , \frac{\pi }{4} )[/tex]

The equation of the tangent line

[tex]y - y_{1} = m ( x - x_{1} )[/tex]

[tex]y - \frac{\pi }{4} = (\frac{-\pi }{2} +1)( x - \frac{\pi }{4} )[/tex]

I will assume you want it in the form of y>mx+b

0.5x-2y>3

0.5x-3>2y

0.25x-1.5>y

Answer:

[tex]x>4y+6[/tex]

Step-by-step explanation:

[tex]0.5x-2y>3[/tex]

First, we will have to add 2 to both sides.

[tex]0.5x-2y+2y>3+2y[/tex]

This equals to

[tex]0.5x>2y+3[/tex]

Now, we will make this into a fraction and divide. We will divide by 0.5.

[tex]\frac{0.5x}{0.5} >\frac{2y+3}{0.5}[/tex]

Now that we divided, we got our answer!

[tex]x>4y+6[/tex]

Hope this helps!

Answer:

5x + 1 = 4x

You can really put any letter for "a number":

5n + 1 = 4n

Answer:

C.0.1

Step-by-step explanation:

Because this is 10% confidence confirmed

Answer: 991

square root of 982081 hope this helps

Answer:

158

Step-by-step explanation:

2(x square + y square)

2 (X+y) square -2 xy

2(10) square -2(21)

2×100-42

200-42

=158

let the nisha be x and nishan be y

Step-by-step explanation:

ATQ

your statement is x=2y

Answer: He spends 1.5 hours on the first part of trip and 3 hours on the second part of trip

Step-by-step explanation:

Let x = the number of hours for first part

Let y = the number of hours for second part

Concept: speed × time = distance

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

x+y=4.5

59x+57y=259.5

-----

y=4.5-x

59x+57y=259.5

-----

59x+57(4.5-x)=259.5

59x+256.5-57x=259.5

2x+256.5=259.5

2x=3

x=1.5

4.5-1.5=3 hrs

Given :

A line 2x + 1 =0 .

To Find :

The slope of the given line .

Solution :

We know , slope of line is given by the tangent of the angle between the x-axis and the line .

Now, for line 2x + 1 =0 i.e [tex]x=\dfrac{-1}{2}[/tex] .

The line is perpendicular to x-axis and cuts the x-axis at [tex]\dfrac{-1}{2}[/tex] .

Therefore , the angle between the line and x-axis is [tex]90^o[/tex] .

So , slope [tex]m=\tan\ 90^o[/tex] i.e undefined .

Therefore , the slope of given line is not defined .

Hence , this is the required solution .

Answer:

5 + y - 2 - 6 y + y; 8 y + 3

Step-by-step explanation:

this is the answer

Step-by-step explanation:

2x+3

Answer:

2x+3x

Step-by-step explanation:

Answer:

it would cost them $100

Answer:

it would cost them $100

Step-by-step explanation:

Answer : The equation for 'h' is [tex]h=\frac{2A}{b}[/tex]

Step-by-step explanation :

The given equation is:

[tex]A=\frac{1}{2}bh[/tex]

Now we have to determine the equation for 'h'.

[tex]A=\frac{1}{2}bh[/tex]

Multiplying the equation by 2.

[tex]2\times A=2\times \frac{1}{2}\times bh[/tex]

on simplifying, we get:

[tex]2\times A=bh[/tex]

Dividing the equation by 'b'.

[tex]\frac{2\times A}{b}=\frac{bh}{b}[/tex]

[tex]\frac{2\times A}{b}=h[/tex]

or,

[tex]h=\frac{2A}{b}[/tex]

Therefore, the equation for 'h' is [tex]h=\frac{2A}{b}[/tex]

Answer: B

Step-by-step explanation:

Answer:

log7(x-2)

Step-by-step explanation:

Use of property: log(ab) = log(a) + log(b)

Answer:

Let x be the amount Nick's little sister is given.

x = 10 - 4

Answer:

Step-by-step explanation:

y - 7 = -3(x - 2)

y - 7 = -3x + 6

y = -3x + 13

Answer:

36 and 49

Step-by-step explanation:

6x6 and 7x7

Answer:

X= 12 or 18 (see below)

Step-by-step explanation:

This could be read two different ways.

0=2/3x-12

12=2/3x

12÷2/3=x

12*3/2=x

18=x

—-OR—-

0=2/3(x-12)

0=2/3x-8

8=2/3x

8÷2/3=x

8*3/2=x

12=x

Plug in the value to solve the expression.

[tex](-7)^2+4(-7)-2[/tex]

[tex]49-28-2[/tex]

[tex]19[/tex]

Hope this helps.

頑張って!

Hey there!

a^2 + 4a - 2

= -7^2 + 4(-7) - 2

= -49 - 28 - 2

= -77 - 2

= -79

Therefore, your answer is: -79

Therefore, your answer is: -79

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

6.79

Step-by-step explanation:

6.79 x 10 = 67.9

The unknown number z would be 6.79

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

WE have been given that 67.9 is ten times as much as unknown number;

Let the unknown number be z;

Z x 10 = 67.9

Now divide by 10 on both sides, we get;

Z = 67.9/10

Z = 6.79

Therefore,

6.79 x 10 = 67.9

Hence, the unknown number z would be 6.79

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Answer:

The restaurant is not at half way

Step-by-step explanation:

Given

[tex]Total\ Distance = 72[/tex]

[tex]Diego = 16x - 3[/tex]

[tex]Anya = 5x + 2[/tex]

Required

Accept or reject Diego's claim

To do that, we need to determine the value of x by:

Diego + Anya =Total Distance

Substitute values for each parameter

[tex]16x - 3 + 5x + 2 = 72[/tex]

Collect Like Terms

[tex]16x + 5x = 72 + 3 - 2[/tex]

[tex]21x = 73[/tex]

Divide both sides by 21

[tex]x = \frac{73}{21}[/tex]

Substitute the value of x in Diego and Anya's distance

[tex]Diego = 16x - 3[/tex]

[tex]Diego = 16 * \frac{73}{21} - 3[/tex]

[tex]Diego = \frac{1168}{21} - 3[/tex]

[tex]Diego = \frac{1168 - 63}{21}[/tex]

[tex]Diego = \frac{1105}{21}[/tex]

[tex]Diego = 52\frac{13}{21}[/tex]

[tex]Anya = 5x + 2[/tex]

[tex]Anya = 5 * \frac{73}{21} + 2[/tex]

[tex]Anya = \frac{365}{21} + 2[/tex]

[tex]Anya = \frac{365 + 42}{21}[/tex]

[tex]Anya = \frac{407}{21}[/tex]

[tex]Anya = 19\frac{8}{21}[/tex]

Since, both distances are not equal,

Then Diego's claim is false and incorrect

Answer:

You would have to break the polynomial down into smaller binomials or monomials. Take x^2-6x-9 for instance. It would break down into (x+3)(x-3) through the a^2+2ab+b^2 formula. After that set the two nomials equal to zero and solve for x. After that, you would plug back in x to see whatever x works. You may more than two nomials after breaking it apart so keep that in mind.

The expression equivalent to 6x + 18 is 3(2x + 6) thus option (B) is correct.

An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that are all constrained and create an equation.

Expression is very useful to determine the end or root value of constraint.

As per the given,

6x + 18

Take 3 as common,

3(2x + 6)

Hence "The expression equivalent to 6x + 18 is 3(2x + 6)".

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Answer:

The weight is 4 pounds :D

Step-by-step explanation:

Answer:

299

Step-by-step explanation:

Answer:

Lydia must sell 552 burritos

Step-by-step explanation:

3(2x+4),  2(3x+6) and 6(x + 2) are the expressions are equivalent to 6X +12

An expression is combination of variables, numbers and operators.

The given expression is 6X +12

We have to find the equivalent expressions of 6x+12

Let us take 6 as a common factor we get

6(x+2)

so 6(x+2)  is equivalent expression of 6X +12

Now let us take 3 as common factor

3(2x+4)

so 3(2x+4)  is equivalent expression of 6X +12

Now let us take 2 as common factor

2(3x+6)

so 2(3x+6)  is equivalent expression of 6X +12

Hence,  3(2x+4),  2(3x+6) and 6(x + 2) are the expressions are equivalent to 6X +12

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Answer:

$56.82

Step-by-step explanation:

The sum of all the stuff she bought is 10+20+23, so 53.

Now you need to find the tax, so you multiply 53 x 7.2%, and to change a % to a number you move the decimal place two to the left, so you get .072

$53 x .072 = $3.816 sales tax

$53 for the stuff plus $3.816 tax = $56.816

and since money is only two decimal places and the 6 is higher than 5, you have to round up to the nearest penny, so $56.82!

Answer:

56.81$ she paid

Step-by-step explanation:

Answer:

9.25

Step-by-step explanation:

M₄ means the area using 4 rectangles with heights equal to the function evaluated at the midpoints.

The width of each rectangle is (4−0)/4 = 1.

The area of each rectangle is:

M₁ = (1) (1.12) = 1.12

M₂ = (1) (1.80) = 1.80

M₃ = (1) (2.69) = 2.69

M₄ = (1) (3.64) = 3.64

The total area is therefore:

M = 1.12 + 1.80 + 2.69 + 3.64

M = 9.25