what is the simple formula corresponding to the explicit formula if the first term of the sequence is -10 and the difference bet
ween terms in the sequence is 5?
1 answer:
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Answer:
x = 2√2
y = 2√6
Step-by-step explanation:
Consider the ratio of the two legs of the two smaller interior right triangles. (refer to attached diagrams for the triangles - I have outlined one in blue and the other in red)
These will be equal since the triangles are similar
shorter leg : longer leg
(blue triangle = red triangle)
⇒ x : 4 = 2 : x
⇒ x/4 = 2/x
⇒ x² = 8
⇒ x = √8
⇒ x = 2√2
Now we have x, we have the two legs of the right triangle with hypotenuse labelled y.
Using Pythagoras' Theorem a² + b² = c² (where a and b are the legs and c is the hypotenuse)
⇒ 4² + (2√2)² = y²
⇒ y² = 24
⇒ y = √24
⇒ y = 2√6
<u>Correct </u><u>Inputs </u><u>:-</u>
In ΔABC right angled at A, D and E are points on BC, C such that BD = CD and AD ⊥ BC
Let us know about definition of altitude first. The altitude of a triangle is the perpendicular line segment drawn from the vertex to the opposite side of the triangle.
Median is the line segment from a vertex to the midpoint of the opposite side.
<u>Let us Check all options one by one </u>
- CD is line segment which starts from vertex C but don't falls on opposite side AB thus it is not an altitude.❌
- BA is line segment which starts from vertex B and falls perpendicularly on opposite sides AC and is thus an altitude.✔️
- AD is line segment which starts from vertex A and falls perpendicularly on opposite side BC and is thus an altitude.✔️
- AE is a line segment which starts from vertex A but doesn't falls perpendicularly on opposite side BC and is thus not an altitude.❌
- AD falls on BC with D as mid point because BD = CD and is thus a median. ✔️