18 red marbles because add the ratio togather which is 5 and divide 90 by 5=18 for 1
7*5*4 is the volume of the package, =140
140/0.5=280.
In quadrant IV, cosine is positive and sine is negative. This means that
![\cos^2(x)+\sin^2(x)=1 \iff \sin^2(x)=1-\cos^2(x) \implies \sin(x)=-\sqrt{1-\cos^2(x)](https://tex.z-dn.net/?f=%5Ccos%5E2%28x%29%2B%5Csin%5E2%28x%29%3D1%20%5Ciff%20%5Csin%5E2%28x%29%3D1-%5Ccos%5E2%28x%29%20%5Cimplies%20%5Csin%28x%29%3D-%5Csqrt%7B1-%5Ccos%5E2%28x%29)
The cotangent is defined as the ratio between the cosine and sine:
![\cot(x)=\dfrac{\cos(x)}{\sin(x)}=\dfrac{\cos(x)}{-\sqrt{1-\cos^2(x)}}=-\dfrac{2}{7}\iff \dfrac{\cos(x)}{\sqrt{1-\cos^2(x)}}=\dfrac{2}{7}](https://tex.z-dn.net/?f=%5Ccot%28x%29%3D%5Cdfrac%7B%5Ccos%28x%29%7D%7B%5Csin%28x%29%7D%3D%5Cdfrac%7B%5Ccos%28x%29%7D%7B-%5Csqrt%7B1-%5Ccos%5E2%28x%29%7D%7D%3D-%5Cdfrac%7B2%7D%7B7%7D%5Ciff%20%20%5Cdfrac%7B%5Ccos%28x%29%7D%7B%5Csqrt%7B1-%5Ccos%5E2%28x%29%7D%7D%3D%5Cdfrac%7B2%7D%7B7%7D)
So, we have the following equation:
![2\sqrt{1-\cos^2(x)}=7\cos(x)](https://tex.z-dn.net/?f=2%5Csqrt%7B1-%5Ccos%5E2%28x%29%7D%3D7%5Ccos%28x%29)
Squaring both sides yields
![4(1-\cos^2(x))=49\cos^2(x) \iff 4-4\cos^2(x)=49\cos^2(x)\iff 53\cos^2(x)=4](https://tex.z-dn.net/?f=4%281-%5Ccos%5E2%28x%29%29%3D49%5Ccos%5E2%28x%29%20%5Ciff%204-4%5Ccos%5E2%28x%29%3D49%5Ccos%5E2%28x%29%5Ciff%2053%5Ccos%5E2%28x%29%3D4)
The solution to this equation would be
![\cos^2(x)=\dfrac{4}{53}\iff \cos^2(x)=\pm\dfrac{2}{\sqrt{53}}](https://tex.z-dn.net/?f=%5Ccos%5E2%28x%29%3D%5Cdfrac%7B4%7D%7B53%7D%5Ciff%20%5Ccos%5E2%28x%29%3D%5Cpm%5Cdfrac%7B2%7D%7B%5Csqrt%7B53%7D%7D)
But we know that the cosine has to be positive, so we have
![\cos(x)=\dfrac{2}{\sqrt{53}}](https://tex.z-dn.net/?f=%5Ccos%28x%29%3D%5Cdfrac%7B2%7D%7B%5Csqrt%7B53%7D%7D)
And
![\sin(x)=-\sqrt{1-\dfrac{4}{53}}=-\sqrt{\dfrac{49}{53}}=-\dfrac{7}{\sqrt{53}}](https://tex.z-dn.net/?f=%5Csin%28x%29%3D-%5Csqrt%7B1-%5Cdfrac%7B4%7D%7B53%7D%7D%3D-%5Csqrt%7B%5Cdfrac%7B49%7D%7B53%7D%7D%3D-%5Cdfrac%7B7%7D%7B%5Csqrt%7B53%7D%7D)
Finally, the secant is the inverse of the cosine, so it's
![\sec(x)=\dfrac{1}{\cos(x)}=\dfrac{\sqrt{53}}{2}](https://tex.z-dn.net/?f=%5Csec%28x%29%3D%5Cdfrac%7B1%7D%7B%5Ccos%28x%29%7D%3D%5Cdfrac%7B%5Csqrt%7B53%7D%7D%7B2%7D)
The rise in temperature by 11 degrees Fahrenheit can be represented by the temperature change, ΔT = +11 °F. The temperature change is positive because the temperature increased as stated in the question. Moreover, the formula for temperature change is: ΔT = T_final - T_initial. This means that for this case, the final temperature is higher than the initial temperature.
Answer:
8
Step-by-step explanation:
3 times 3 is 9
2 yimes 5 is 10
9 times 2 is 18
18-10 is 8