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Katen [24]
3 years ago
14

Solve the above attached questionThanks​

Mathematics
1 answer:
seropon [69]3 years ago
4 0

Answer:

23

Step-by-step explanation:

Given,

tan²A - 5tanA + 1 = 0

tan²A - 5tanA = -1

tanA(tanA - 5) = -1

tanA - 5 = -1/tanA

We know that 1/tanA= cotA

So,

tanA - 5 = -cotA

tanA + cotA= 5

Now, Making square of both sides,

(tanA +cotA)² = 5²

Expanding RHS by (a + b)² = a² + b² +2ab tan²A + cot²A + 2tanA.cotA= 25

tan²A + cot²A + 2tanA ×(1/tanA) = 25

tan²A + cot²A + 2 = 25

tan²A + cot²A = 25-2

tan²A + cot²A = 23

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Help please I have no clue how to do this please show work thanks
bazaltina [42]

Terms that have the same variable part are called like terms. Like terms can be added or subtracted to form a single term.

1.

16x - 4x = -48

First, combine the like terms 16x and -4x.

12x = -48

Now divide both sides by 12.

x = -4

2.

7m - 5 - 13m = 25

First, combine the like terms 7m and -13m.

-6m - 5 = 25

Now add 5 to both sides.

-6m = 30

Divide both sides by -6.

m = -5

3.

12.25 = 0.5q + 3.75

Subtract 3.75 from both sides.

8.5 = 0.5q

Multiply both sides by 2.

17 = q

q = 17

4.

2(2x - 4) + x = 7

Distribute the 2.

4x - 8 + x = 7

Combine 4x and x.

5x - 8 = 7

Add 8 to both sides.

5x = 15

Divide both sides by 5.

x = 3

5.

8 = 3(3x + 8) - x

Distribute the 3.

8 = 9x + 24 - x

Combine 9x and -x.

8 = 8x + 24

Subtract 24 from both sides.

-16 = 8x

Divide both sides by 8.

-2 = x

x = -2

6 0
3 years ago
Convert from rectangular to polar coordinates:Note: Choose r and θ such that r is non-negative and 0 ≤ θ < 2πa. (6,0)b. (9,9/
Anuta_ua [19.1K]

Answer:

The polar coordinates are as follow:

a. (6,2π)

b. (18, π/3)

c. (2√2 , 3π/4)

d. (2, 5π /6)

Step-by-step explanation:

To convert the rectangular coordinates into polar coordinates, we need to calculate r, θ .

To calculate r, we use Pythagorean theorem:

r = \sqrt{ x^{2} +y^{2} } ---- (1)

To calculate the θ, first we will find out the θ '  using the inverse of cosine as it is easy to calculate.

So,    θ '  = cos ⁻¹  (x/r)

If  y  ≥  0  then  θ  =  ∅

If  y  <  0  then  θ  =  2 π  −  ∅

For a. (6,0)

Sol:

Using the formula in equation (1). we get the value of r as:

r = \sqrt{6^{2} + 0^{2}  }

r = 6

And ∅  = cos ⁻¹  (x/r)

∅ = cos ⁻¹  (6/6)

∅  =cos ⁻¹   (1) = 2π

As If  y  ≥  0  then  θ  =  ∅

So ∅ = 2π

The polar coordinates are (6,2π)

For a. (9,9/\sqrt{3})

Sol:

r = 9 + 3(3) = 18

and ∅  = cos ⁻¹  (x/r)

∅ = cos ⁻¹  (9/18)

∅ = cos ⁻¹   (1/2) = π/3

As  If  y  ≥  0  then  θ  =  ∅

then θ  = π/3

The polar coordinates are (18, π/3)

For (-2,2)

Sol:

r =√( (-2)²+(2)² )

r = 2 √2

and ∅  = cos ⁻¹  (x/r)

∅ = cos ⁻¹  (-2/ 2 √2)

∅ = 3π/4

As  If  y  ≥  0  then  θ  =  ∅

then   θ  = 3π/4

The polar coordinates are (2√2 , 3π/4)

For (-√3, 1)

Sol:

r = √ ((-√3)² + 1²)

r = 2

and ∅  = cos ⁻¹  (x/r)

∅  = cos ⁻¹ ( -√3/2)

∅  = 5π /6

As  If  y  ≥  0  then  θ  =  ∅

So  θ  = 5π /6

The polar coordinates are (2, 5π /6)

6 0
3 years ago
Enter the range of values for x using the picture shown
yarga [219]

We are asked to find a range for x. Let's start by finding the maximum value. We know, by definition, that a side opposite a larger angle has a longer length. For example, if you think about a right triangle, the hypotenuse (the longest side) is always opposite of the right angle (the largest angle). We are given two side lengths: 23 is opposite of 42 degrees, and 21 is opposite of 3x + 15. Because 42 is opposite the longer side, 42 degrees is a larger angle than 3x + 15. We can set up the inequality and solve for x:

\begin{gathered} 3x+15

Now, let's look at the minimum value. We know that the angle definitely has to be larger than 0. So, we can set up that inequality and solve for x:

\begin{gathered} 3x+15>0 \\ 3x>-15 \\ x>-5 \end{gathered}

Now, we have our final range: -5 < x < 9

8 0
1 year ago
A cone has a radius of 5.1 inches and a height of 5 inches.
Luda [366]
Where’s the cone? Is there a picture of a cone? I can’t really solve this, I’m sorry if I bother you
8 0
3 years ago
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Naya [18.7K]

Answer:

D. reflection across a vertical line

Step-by-step explanation:

Reflection is basically a mirror image. Since you can see that the first triangle is flipped over to get the second one, this is a reflection.

It is not a vertical translation; this means that the triangle shifted up or down.

It is not a horizontal translation, this means that the triangle shifted left or right.

It is not a rotation about point A either, this would have meant that the triangle spun around.

3 0
3 years ago
Read 2 more answers
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