Answer:
(0, 33) : Yes
(4.8, 30.5) : Yes
Step-by-step explanation:
height of at least 24 ft : y >= 24
horizontal distance of no more than 10 ft. : 0 <= x <= 10
The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft.:
y >= 3x and y <= 33
So Constraints:
24 <= y <= 33
y >= 3x
0 <= x <= 10
Now check to see if those coordinate points meet all the constraints
(0, 33) : Yes
(4.8, 30.5) : Yes
(9, 26) : No (because 26 is less than (3 * 9) = 27)
(4, 36)
: No (because 36 > 33, must be 24 <= y <= 33)
(2, 22): No (because 22 <24, must be 24 <= y <= 33)
Answer: 693 years
Step-by-step explanation:
Expression for rate law for first order kinetics is given by:

k = rate constant
t = time taken for decomposition = 1
= Initial amount of the reactant
= amount of the reactant left =



for half life : 

Putting in the values , we get


Thus half life of this isotope, to the nearest year is 693.
Answer:
m∠ABC = 119° and DC = 105 feet
Step-by-step explanation:
For better understanding of the solution see the attached figure of the trapezium ABCD :
m∠BCD = 61°
By using the property, Sum of interior opposite angles in a trapezium is supplementary ⇒ m∠BCD + m∠ABC = 180°
⇒ m∠ABC = 180° - 61°
⇒ m∠ABC = 119°
Now, to find length of DC,
Draw a perpendicular BE on CD ⇒ CD = DE + EC
AB = DE
⇒ DE = 80 feet
In ΔBEC, By using Pythagoras theorem
EC² = BC² - BE²
⇒ EC² = 65² - 60²
⇒ EC = 25 feet
Hence, DC = 80 + 25
= 105 feet
The answer should be "filtration" because distillation is for liquids. Filtration filters out the unwanted products.