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2 years ago

12

Drag each tile to the table to multiply (6x-y)(2x-y+2)

1 answer:

77julia77 [94]2 years ago

7 0

The other answer is 12x2 – 8xy + 12x + y2 – 2<span>y</span><span />

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Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______

Ludmilka [50]

Answer:

$(a)\ \sec^2(\theta) = 82$

$(b)\ \cot(\theta) = \frac{1}{9}$

$(c)\ \cot(\frac{\pi}{2} - \theta) = 9$

$(d)\ \csc^2(\theta) = \frac{82}{81}$

Step-by-step explanation:

Given

$\tan(\theta) = 9$

Required

Solve (a) to (d)

Using tan formula, we have:

$\tan(\theta) = \frac{Opposite}{Adjacent}$

This gives:

$\frac{Opposite}{Adjacent} = 9$

Rewrite as:

$\frac{Opposite}{Adjacent} = \frac{9}{1}$

Using a unit ratio;

$Opposite = 9; Adjacent = 1$

Using Pythagoras theorem, we have:

$Hypotenuse^2 = Opposite^2 + Adjacent^2$

$Hypotenuse^2 = 9^2 + 1^2$

$Hypotenuse^2 = 81 + 1$

$Hypotenuse^2 = 82$

Take square roots of both sides

$Hypotenuse =\sqrt{82}$

So, we have:

$Opposite = 9; Adjacent = 1$

$Hypotenuse =\sqrt{82}$

Solving (a):

$\sec^2(\theta)$

This is calculated as:

$\sec^2(\theta) = (\sec(\theta))^2$

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

Where:

$\cos(\theta) = \frac{Adjacent}{Hypotenuse}$

$\cos(\theta) = \frac{1}{\sqrt{82}}$

So:

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

$\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2$

$\sec^2(\theta) = (\sqrt{82})^2$

$\sec^2(\theta) = 82$

Solving (b):

$\cot(\theta)$

This is calculated as:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

Where:

$\tan(\theta) = 9$ ---- given

So:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

$\cot(\theta) = \frac{1}{9}$

Solving (c):

$\cot(\frac{\pi}{2} - \theta)$

In trigonometry:

$\cot(\frac{\pi}{2} - \theta) = \tan(\theta)$

Hence:

$\cot(\frac{\pi}{2} - \theta) = 9$

Solving (d):

$\csc^2(\theta)$

This is calculated as:

$\csc^2(\theta) = (\csc(\theta))^2$

$\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2$

Where:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

$\sin(\theta) = \frac{9}{\sqrt{82}}$

So:

$\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2$

$\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2$

$\csc^2(\theta) = \frac{82}{81}$

4 0

2 years ago

Find the equation of a line through B(5,2) which is perpendicular to the line 3x+5=0. Hence find the coordinate of the foot of t

Oduvanchick [21]

Answer:

y=2, the equation of a line which is perpendicular to the line 3x+5=0

A(-5/3,2) the foot of the perpendicular from B to the line

Step-by-step explanation:

d1 : 3x+5=0, so 3x=-5, x=-5/3

y=2, the equation of a line which is perpendicular to the line 3x+5=0

A(-5/3,2) the foot of the perpendicular from B to the line

3 0

2 years ago

[ Cuiu be made.

shutvik [7]

Answer:

24/36 = 12 x 2/12 x 3 = 2/3.

Step-by-step explanation:

4 0

3 years ago

A farm has 75 acres of wheat. The farmer can only harvest 12 acres per day. How many days will all of the fields be harvested?

eduard

7 days because 12 per day 12×6=72 but you need 3 more acres so it would be another day for it to be 7

3 0

3 years ago

You can paint 50 square feet of a surface every 40 minutes. How long does it take you to paint the mural shown below? Explain ho

Ilia_Sergeevich [38]

You need the total of square feet of the mural before you can divide 50 square feet to it and get your answer of how many pints of paint you will need.

For example.

Mural size is 2800 square feet

1 pint per 50 square feet

Work out problem.

2800 square feet ÷ 50 square feet= ?

= 56 pints of paint

7 0

3 years ago

Read 2 more answers