Trigonometric Identities.
To solve this problem, we need to keep in mind the following:
* The tangent function is negative in the quadrant II
* The cosine (and therefore the secant) function is negative in the quadrant II
* The tangent and the secant of any angle are related by the equation:
![\sec ^2\theta=\tan ^2\theta+1](https://tex.z-dn.net/?f=%5Csec%20%5E2%5Ctheta%3D%5Ctan%20%5E2%5Ctheta%2B1)
We are given:
![\text{tan}\theta=-\frac{\sqrt[]{14}}{4}](https://tex.z-dn.net/?f=%5Ctext%7Btan%7D%5Ctheta%3D-%5Cfrac%7B%5Csqrt%5B%5D%7B14%7D%7D%7B4%7D)
And θ lies in the quadrant Ii.
Substituting in the identity:
![\begin{gathered} \sec ^2\theta=(-\frac{\sqrt[]{14}}{4})^2+1 \\ \text{Operating:} \\ \sec ^2\theta=\frac{14}{16}+1 \\ \sec ^2\theta=\frac{14+16}{16} \\ \sec ^2\theta=\frac{30}{16} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Csec%20%5E2%5Ctheta%3D%28-%5Cfrac%7B%5Csqrt%5B%5D%7B14%7D%7D%7B4%7D%29%5E2%2B1%20%5C%5C%20%5Ctext%7BOperating%3A%7D%20%5C%5C%20%5Csec%20%5E2%5Ctheta%3D%5Cfrac%7B14%7D%7B16%7D%2B1%20%5C%5C%20%5Csec%20%5E2%5Ctheta%3D%5Cfrac%7B14%2B16%7D%7B16%7D%20%5C%5C%20%5Csec%20%5E2%5Ctheta%3D%5Cfrac%7B30%7D%7B16%7D%20%5Cend%7Bgathered%7D)
Taking the square root and writing the negative sign for the secant:
Answer:
Step-by-step explanation:
50%
Answer:
(x-7) (x-2)
Step-by-step explanation:
(x-2) × (x-7)
=x^2-9x+14
I think you mean x2 is x square.(x^2)
Answer:
i776
f55
Step-by-step explanation:
Answer:
![V=5\sqrt{3}\ m^3](https://tex.z-dn.net/?f=V%3D5%5Csqrt%7B3%7D%5C%20m%5E3)
Step-by-step explanation:
we know that
The volume of a trough is equal to
![V=BL](https://tex.z-dn.net/?f=V%3DBL)
where
B is the area of equilateral triangle
L is the length of a trough
step 1
Find the area of equilateral triangle B
The area of a equilateral triangle applying the law of sines is equal to
![B=\frac{1}{2} b^{2} sin(60\°)](https://tex.z-dn.net/?f=B%3D%5Cfrac%7B1%7D%7B2%7D%20b%5E%7B2%7D%20sin%2860%5C%C2%B0%29)
where
![b=2\ m](https://tex.z-dn.net/?f=b%3D2%5C%20m)
![sin(60\°)=\frac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=sin%2860%5C%C2%B0%29%3D%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)
substitute
![B=\frac{1}{2}(2)^{2} (\frac{\sqrt{3}}{2})](https://tex.z-dn.net/?f=B%3D%5Cfrac%7B1%7D%7B2%7D%282%29%5E%7B2%7D%20%28%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%29)
![B=\sqrt{3}\ m^{2}](https://tex.z-dn.net/?f=B%3D%5Csqrt%7B3%7D%5C%20m%5E%7B2%7D)
step 2
Find the volume of a trough
![V=BL](https://tex.z-dn.net/?f=V%3DBL)
we have
![B=\sqrt{3}\ m^{2}](https://tex.z-dn.net/?f=B%3D%5Csqrt%7B3%7D%5C%20m%5E%7B2%7D)
![L=5\ m](https://tex.z-dn.net/?f=L%3D5%5C%20m)
substitute
![V=(\sqrt{3})(5)](https://tex.z-dn.net/?f=V%3D%28%5Csqrt%7B3%7D%29%285%29)
![V=5\sqrt{3}\ m^3](https://tex.z-dn.net/?f=V%3D5%5Csqrt%7B3%7D%5C%20m%5E3)