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labwork [276]
3 years ago
7

Find the value of tan theta if sin theta = 12/13 and theta is in quadrant 2

Mathematics
1 answer:
ivanzaharov [21]3 years ago
3 0

Answer:

اhello : tan θ = - 12/5

Step-by-step explanation:

tan θ = sin θ / cos θ .... (*)

(cosθ)² + (sinθ)² = 1   ... (**)

theta is in quadrant 2 : cosθ ≤ 0

Substitute sinθ = 12/13  into (**) and solve for cosθ :

(cosθ)² + (12/13)² = 1  

(cosθ)²  = 1   - 144/169

(cosθ)²  = 25/169

cosθ = - 5 /13  because  cosθ ≤ 0

by (*) : tan θ = (12/13)/ (-5/13) = (12/13) ×(-13/5)

tan θ = - 12/5

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Elimination method: ax+by=r, -bx+cy=s
Alex17521 [72]
\left[\begin{array}{ccc}ax+by=r\\\\-bx+cy=s\end{array}\right]

Isolate x for ax+by=r

x= \frac{r-by}{a} ; a \neq 0

Subsititute x= \frac{r-by}{a}

-b \frac{r-by}{a} +cy=s

Isolate r for : -b \frac{r-by}{a}+cy=s

r=- \frac{as-acy-b^2y}{b} ; a \neq 0;b \neq 0

For x : \frac{r-by}{a}

Subsititute r = - \frac{as-acy-b^2y}{b}

x= -\frac{as-acy-b^2y}{b}/a

x =  \frac{cy-s}{b}

The solutions to the system of equations are:

r= -\frac{as-acy-b^2y}{b} and <span> x = \frac{cy-s}{b}
</span>
hope this helps!


3 0
2 years ago
What is the solution to this equation?
sattari [20]

Answer:

Step-by-step explanation:

x -  9 = 17

x = 26

the answer is D

4 0
3 years ago
find the volume of a cylinder with a diameter of 10 inches and a height that is 3 times the radius. Use the 3.14 for pie and rou
Paul [167]

Answer:

1177.5 inches

Step-by-step explanation:

Volume of a cylinder = \pi r^{2} *h, where h is the height

Radius = 10/2 = 5                    radius is half the diameter

Height = 3*5 = 15                     height is 3 times the radius

V = 3.14 * (5^2) * (15)

= 3.14 *25 * 15

= 1177.5

6 0
3 years ago
Consider the function f(x) = 2^x
Sonja [21]

Answer:

The graph of function g is the graph of function f shifted 6 units up

Step-by-step explanation:

If you plug in the values, g(x) = 2^{x} + 6. If the 6 was added or subtracted from the x in the exponent, it would shift horizontally (left and right), but adding 6 to f(x) separately moves the graph vertically (up and down). Hope this helps.

4 0
3 years ago
Given the vectors A⃗ and B⃗ shown in the figure ((Figure 1) ), determine the magnitude of B⃗ −A⃗. A is 28 degrees above the posi
Vlad [161]

This problem is represented in the Figure below. So, we can find the components of each vector as follows:


\bullet \ cos(28^{\circ})=\frac{Adjacent}{Hypotenuse}=\frac{A_{x}}{44} \\ \\ \therefore A_{x}=44cos(28^{\circ})=38.85m \\ \\ \\ \bullet \ sin(28^{\circ})=\frac{Opposite}{Hypotenuse}=\frac{A_{y}}{44} \\ \\ \therefore A_{y}=44sin(28^{\circ})=20.65m


\bullet \ cos(56^{\circ})=\frac{Adjacent}{Hypotenuse}=\frac{-B_{x}}{26.5} \\ \\ \therefore B_{x}=-26.5cos(56^{\circ})=-14.81m \\ \\ \\ \bullet \ sin(56^{\circ})=\frac{Opposite}{Hypotenuse}=\frac{B_{y}}{26.5} \\ \\ \therefore B_{y}=26.5sin(56^{\circ})=21.97m


Therefore:

\vec{A}=(38.85, 20.65)m \\ \\ \vec{B}=(-14.81, 21.97)m


So:

\vec{B}-\vec{A}=(-14.81, 21.97)-(38.85, 20.65)=(-53.66,1.32)


Finally, the magnitude is:


\boxed{\left| \vec{B}-\vec{A}\right|=\sqrt{(-53.66)^2+(1.32)^2}=53.67m}

7 0
3 years ago
Read 2 more answers
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