Answer:
20909.09 grams
Step-by-step explanation:
= 230 grams / 11 grams × 1000 grams = 20.90909... × 1000 = 20909.09 grams
Answer:
475 mph
Step-by-step explanation:
Distance = rate × time
time = distance / rate
If x is the speed of the plane in still air:
2100 / (x + 25) = 1890 / (x − 25)
Cross multiply:
2100 (x − 25) = 1890 (x + 25)
Distribute and solve:
2100x − 52500 = 1890x + 47250
210x = 99750
x = 475
325 meters if using full height of 324 meters for tower
277 meters if using observation platform height of 276 meters.
When the depression is 37 degrees, you can create a right triangle with the angles 90, 37, and 53 degrees. The distance from a point directly underneath the observer will be:
h/tan(37)
where
h = height of the observer.
And when the depression is 72 degrees, the distance will be:
h/tan(72)
So the distance between the two points will be the absolute value of:
h/tan(72) - h/tan(37)
=(tan(37)h)/tan(37)tan(72) - tan(72)h/(tan(37)tan(72))
=(tan(37)h - tan(72)h) /(tan(37)tan(72))
=h(0.75355405 - 3.077683537)/(0.75355405 * 3.077683537)
=h(0.75355405 - 3.077683537)/(0.75355405 * 3.077683537)
=h(-2.324129487/2.319200894)
=h*-1.002125125
And since we're looking for absolute value
=h*1.002125125
As for the value of "h" to use, that's unspecified in the problem. If you take h
to be the height of the Eiffel Tower, then it's 324 meters. If you take h to be
the highest observation platform on the Eiffel Tower, then it's 276 meters. In
any case, simply multiply h by the value calculated above:
=h*1.002125125
=324*1.002125125
= 324.6885406 m
=h*1.002125125
=276*1.002125125
=276.5865346
A scaled copy with the scale factor being 3/4 it would be smaller because it’s less than one so whenever there is a fraction that’s less than one then the shape would be smaller aswell
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
• 1 + cot² x = csc²x and csc x = 
• sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Consider the left side
sin²Θ( 1 + cot²Θ )
= sin²Θ × csc²Θ
= sin²Θ × 1 / sin²Θ = 1 = right side ⇔ verified
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Consider the left side
cos²Θ - sin²Θ
= cos²Θ - (1 - cos²Θ)
= cos²Θ - 1 + cos²Θ
= 2cos²Θ - 1 = right side ⇒ verified
