Answer:
6/35 miles per hour
Step-by-step explanation:
To find the unit rate, put distance over time
distance = 1/7 miles
time = 5/6 of an hour
miles/hours
(1/7)/(5/6)
(1/7)*(6/5)
6/35 miles per hour
Answer:
640 ft^3
Step-by-step explanation:
In this case we must divide the area into two parts, in the prism and in the pyramid, the sum of the volume of these parts would be the total volume
However
for the volume of the prism it would be the multiplication of the three sides, that is:
8 * 8 * 9 = 576
i.e. 576 ft ^ 3
For the pyramid, the formula is the multiplication of the area of the base by the height divided by 3, we know that the area of the base is 8 * 8 and that the height is 3, therefore:
8 * 8 * 3/3 = 64
64 ft ^ 3 is the volume of the pyramid
The total would be:
576 + 64 = 640
Total volume would be 640 ft ^ 3
If one adult ticket costs
, then three adult tickets cost ![3c](https://tex.z-dn.net/?f=%203c%20)
Similarly, if one child ticket costs
, then nine child tickets cost ![9k](https://tex.z-dn.net/?f=%209k%20)
So, in total, the price will be
![3c+9k](https://tex.z-dn.net/?f=%203c%2B9k%20)
Answer:
26, 30
Step-by-step explanation:
If you subtract from the sum the excess of the second over the first, you have a sum that is twice the first.
first number = (56 -4)/2 = 26
The second number is 4 more, so is ...
second number = 26 +4 = 30
_____
Check
Their total is 26 +30 = 56, as required.
Answer:
![\cos 2 \theta = \dfrac{119}{169}\\\\\sin2 \theta = \dfrac{120}{169}\\\\\tan 2\theta = \dfrac{120}{119}](https://tex.z-dn.net/?f=%5Ccos%202%20%5Ctheta%20%3D%20%5Cdfrac%7B119%7D%7B169%7D%5C%5C%5C%5C%5Csin2%20%5Ctheta%20%20%3D%20%5Cdfrac%7B120%7D%7B169%7D%5C%5C%5C%5C%5Ctan%202%5Ctheta%20%3D%20%5Cdfrac%7B120%7D%7B119%7D)
Step-by-step explanation:
![\text{Given that,} \cos \theta = \dfrac{12}{13}\\ \\\text{Now,}\\\\\cos 2 \theta = 2 \cos^2 \theta - 1\\\\\\~~~~~~~~~=2 \left( \dfrac{12}{13} \right)^2 - 1\\\\\\~~~~~~~~~=2 \left( \dfrac{144}{169} \right) - 1\\\\\\~~~~~~~~~=\dfrac{288}{169}-1\\\\\\~~~~~~~~~=\dfrac{119}{169}](https://tex.z-dn.net/?f=%5Ctext%7BGiven%20that%2C%7D%20%5Ccos%20%5Ctheta%20%3D%20%5Cdfrac%7B12%7D%7B13%7D%5C%5C%20%5C%5C%5Ctext%7BNow%2C%7D%5C%5C%5C%5C%5Ccos%202%20%5Ctheta%20%3D%202%20%5Ccos%5E2%20%5Ctheta%20-%201%5C%5C%5C%5C%5C%5C~~~~~~~~~%3D2%20%5Cleft%28%20%5Cdfrac%7B12%7D%7B13%7D%20%5Cright%29%5E2%20-%201%5C%5C%5C%5C%5C%5C~~~~~~~~~%3D2%20%5Cleft%28%20%5Cdfrac%7B144%7D%7B169%7D%20%5Cright%29%20-%201%5C%5C%5C%5C%5C%5C~~~~~~~~~%3D%5Cdfrac%7B288%7D%7B169%7D-1%5C%5C%5C%5C%5C%5C~~~~~~~~~%3D%5Cdfrac%7B119%7D%7B169%7D)
![\sin 2\theta = 2 \sin \theta \cos \theta\\\\\\~~~~~~~~=2\sqrt{1 -\cos^2 \theta} \cdot \cos \theta~~~~~~~~~~~;[\text{In quadrant I, all ratios are positive.}]\\\\\\~~~~~~~~=2 \sqrt{1- \left( \dfrac{12}{13} \right)^2} \cdot \left(\dfrac{12}{13} \right)\\\\\\~~~~~~~~=\left( \dfrac{24}{13} \right) \sqrt{1- \dfrac{144}{169}}\\\\\\~~~~~~~~=\dfrac{24}{13}\sqrt{\dfrac{25}{169}}\\\\\\~~~~~~~=\dfrac{24}{13} \times \dfrac{5}{13}\\\\\\~~~~~~=\dfrac{120}{169}](https://tex.z-dn.net/?f=%5Csin%202%5Ctheta%20%3D%202%20%5Csin%20%5Ctheta%20%5Ccos%20%5Ctheta%5C%5C%5C%5C%5C%5C~~~~~~~~%3D2%5Csqrt%7B1%20-%5Ccos%5E2%20%5Ctheta%7D%20%5Ccdot%20%5Ccos%20%5Ctheta~~~~~~~~~~~%3B%5B%5Ctext%7BIn%20quadrant%20I%2C%20all%20ratios%20are%20positive.%7D%5D%5C%5C%5C%5C%5C%5C~~~~~~~~%3D2%20%5Csqrt%7B1-%20%5Cleft%28%20%5Cdfrac%7B12%7D%7B13%7D%20%5Cright%29%5E2%7D%20%5Ccdot%20%5Cleft%28%5Cdfrac%7B12%7D%7B13%7D%20%5Cright%29%5C%5C%5C%5C%5C%5C~~~~~~~~%3D%5Cleft%28%20%5Cdfrac%7B24%7D%7B13%7D%20%5Cright%29%20%5Csqrt%7B1-%20%5Cdfrac%7B144%7D%7B169%7D%7D%5C%5C%5C%5C%5C%5C~~~~~~~~%3D%5Cdfrac%7B24%7D%7B13%7D%5Csqrt%7B%5Cdfrac%7B25%7D%7B169%7D%7D%5C%5C%5C%5C%5C%5C~~~~~~~%3D%5Cdfrac%7B24%7D%7B13%7D%20%5Ctimes%20%5Cdfrac%7B5%7D%7B13%7D%5C%5C%5C%5C%5C%5C~~~~~~%3D%5Cdfrac%7B120%7D%7B169%7D)
![\tan 2 \theta = \dfrac{\sin 2\theta}{\cos 2\theta}\\\\\\~~~~~~~~~=\dfrac{\tfrac{120}{169}}{ \tfrac{119}{169}}\\\\\\~~~~~~~~~=\dfrac{120}{169} \times \dfrac{169}{119}\\\\\\~~~~~~~~~=\dfrac{120}{119}](https://tex.z-dn.net/?f=%5Ctan%202%20%5Ctheta%20%3D%20%5Cdfrac%7B%5Csin%202%5Ctheta%7D%7B%5Ccos%202%5Ctheta%7D%5C%5C%5C%5C%5C%5C~~~~~~~~~%3D%5Cdfrac%7B%5Ctfrac%7B120%7D%7B169%7D%7D%7B%20%5Ctfrac%7B119%7D%7B169%7D%7D%5C%5C%5C%5C%5C%5C~~~~~~~~~%3D%5Cdfrac%7B120%7D%7B169%7D%20%5Ctimes%20%5Cdfrac%7B169%7D%7B119%7D%5C%5C%5C%5C%5C%5C~~~~~~~~~%3D%5Cdfrac%7B120%7D%7B119%7D)