Refer to the image below
if you want to understand how to identify opposite or adjacent sides; notice that if you look directly at the angle, you will see the side opposite to it, while the adjacent side is the one that touches the angle.
The year 1915 marks a population of 15,689. In 1940, it increased to 39,381. The required time to reach this figure is t = 137.9 years. Step-by-step explanation: To answer, we apply an exponential growth formula: A = P (1 + r) t, where P is the original number of individuals, r is the growth rate in decimal, and t is the time in years. Plugging in provided values: A = 6,250 (1 + 0.0375)^t. For the year 1915, as 1915-1890 translates to 25 years: A = 6,250 (1.0375)^25 yields 15,689. For 1940, as 1940-1890 indicates 50 years passed: A = 6,250 (1.0375)^50 results in 39,381. To find when the population hits 1,000,000, substitute A=1,000,000 and solve for t. This leads to 1,000,000/6,250 = (1.0375)^t implying log(160) = t * log(1.0375) results in t being approximately 137.9 years.
A vertical throw refers to an instance where an object is tossed straight up with an initial speed, v_o, and is allowed to ascend and eventually fall back to the starting altitude due to gravitational forces acting on it without any friction involved. To find the time at which it reaches a height of 120 feet, we must use the projectile equation which models its height in relation to time. The equation is rearranged as necessary to form a second-degree equation, resolving the variable t to determine at which times the height equals 120 ft.
The diagram is not available, so I included a supplementary figure.
Response:
The segments ST and UT are equal in length.
Detailed explanation:
As seen in the additional figure
∵ ST and UT act as tangents to circle K at points S and U respectively
∵ SK and UK are the radii of circle K
- A tangent is perpendicular to the radius at the point where it touches the circle.
Thus, ST ⊥ KS at point S
Thus, m∠KST = 90°
Thus, UT ⊥ KU at point U
Thus, m∠KUT = 90°
Therefore, m∠KST = m∠KUT
In triangles KST and KUT
∵ KS = KU because they are both radii
∵ m∠KST = m∠KUT confirms the equality
∵ KT is common to both triangles
- Therefore, the triangles are congruent according to the HL criterion
∴ Δ KST ≅ KUT as per the HL criterion
- Thus, from the congruency result
∴ ST = UT
The segments ST and UT are equal in length.
