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denis-greek [22]
2 years ago
9

Find the exact value of tan A in simplest radical form.

Mathematics
1 answer:
spin [16.1K]2 years ago
6 0

Answer:

tan(A) = \frac{2\sqrt{15}}{11}

Step-by-step explanation:

Given:

Right ∆ABC

AB = 61

BC = 60

AC = 11

Required:

Value of tan A in radical form

SOLUTION:

tan(A) = \frac{opposite}{adjacent}

Opposite = 60

Adjacent = 11

tan(A) = \frac{60}{11}

tan(A) = \frac{\sqrt{4*15}}{11}

tan(A) = \frac{2\sqrt{15}}{11}

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If tan theta = 12/5 and cos theta < 0, what is sin theta ?
Talja [164]
1 + tan ² Ф=sec²Ф
1+(12/5)²=sec²Ф
169/25=sec² Ф
sec Ф=⁺₋√(169/25)=⁺₋13/5

sec Ф=1/cos Ф ⇒cosФ=1/sec Ф
 cos Ф>0   ⇔  sec Ф>0  ⇔  sec Ф=+ 13/5

cos Ф=1/secФ
cos Ф=1 / 13/5=5/13

we can calculate the sin Ф, with this method.
sin²Ф + cos²Ф=1  ⇒ sin Ф=⁺₋√(1-cos² Ф)
sin Ф=⁺₋√[1-(5/13)²]=⁺₋12/13
like cos Ф>0 and tan Ф>0   ⇒ sin Ф>0 ⇒sin Ф=12/13

answer: d.12/13

other method
tan Ф=sin Ф / cos Ф
12/5=sin Ф / 5/13
sin Ф=(12/5)*(5/13)=12/13

answer: d.12/13

8 0
3 years ago
What is x divided by 2?
Aleonysh [2.5K]
X/2 is the same thing as 1/2x
7 0
3 years ago
As a salesperson for an electronic parts distributor, you are given two options for your salary structure. The first option has
kumpel [21]

Answer:

The amount of sale is approximately 5714.

Step-by-step explanation:

Let x be the sales made that will result to the same salary and let y be the same weekly salary.

We can represent both salaries as follows:

300 + 0.04x = y

100 + 0.075x = y

Subtracting the second equation from the first, we have:

200 – 0.035x = 0

0.035x= 200

x = 200/0.035

x ≈ 5714.

Therefore, the amount of sale is approximately 5714.

3 0
3 years ago
Factor the expression 2x4y – 18x2y3 completely.
Annette [7]

Answer:

B. 2x2y(x – 3y)(x + 3y)

Step-by-step explanation:

2 {x}^{4} y - 18 {x}^{2}  {y}^{3}  \\  = 2 {x}^{2} y( {x}^{2}  - 9 {y}^{2} ) \\  = 2 {x}^{2} y \{ {x}^{2}  -  {(3y)}^{2} \} \\  \purple {\boxed{ \bold{ = 2 {x}^{2}  y(x - 3y)(x + 3y)}}}

5 0
3 years ago
Read 2 more answers
A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by V = x2h
creativ13 [48]

It is given in the question that

A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by

V = x^2h cm^3

And the edge length of the base is 12 cm, the edge length of the base is decreasing at a rate of 2 cm/min, the height of the box is 6 cm, and the height is increasing at a rate of 1 cm/min.

Here we differentiate V with respect to t, and we use product rule, that is

V = 2xh(dx/dt)+ x^2(dh/dt)

Substituting the given values , we will get

[tex]dV/dt = 2(12)(6)(-2)+ 12^2(1)[/tex]

dV/dt = -288+144 = -144cm^3/min

So at that moment, the volume is decreasing at the rate of

144 cm^3/min

4 0
3 years ago
Read 2 more answers
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