Answer:
approximately ≅ 22minutes that is 3:22:00pm
Step-by-step explanation:
The two boats are at the dock at 3pm and 4pm respectively; let’s write everything in terms of a common start time. Let 3pm be the time t = 0. At time t = 0, the first boat is at the dock and the second boat is at 15 km west of the dock.
At time t, the first boat has moved distance 20t (recall that distance is speed × time), so it is distance 20t from the dock. The second boat has moved distance 15t toward the dock, but it was originally distance 15 away from the dock, so it is now 15 − 15t away from the dock.
At time t, the distance between the two boats is then (by the Pythagorean Theorem)
We want to minimize this quantity.we therefore need to minimize;
To minimize, we note that f
¹
(t) = 1250t − 450, so f
¹(t) = 0 occurs only at the time t =
=
= 0.36. This is the critical number, and since
f ¹¹(t) = 1250 > 0, it is indeed a minimum.
So the boats are closest together at time t = 0.36, which is 0.36 hours (or 21.6 minutes) approximately 22minutes
after 3pm.
that is 3:22:00pm
Diagram attached to the question for interpretation
Answer:
The step 4 and 5 describe the errors Stephen made.
Step-by-step explanation:
Given : Stephen evaluated . His work is shown below.
To find : Which two statements describe the errors Stephen made?
Solution :
Step 1 -
Step 2 -
Step 3 -
Step 4 -
Error is the step as 4 sign is negative.
So correct step is
Step 5 -
Error is the step as there is 4 in place of 3.
So correct step is
The step 4 and 5 describe the errors Stephen made.
Answer:
Reasons:
1. Given
2. Given
3. Definition of bisector
4. Reflexive property
5. SAS Congruence
Step-by-step explanation:
This is quite easy to solve. All that you're expected to do is to complete the reason that justifies each statement given in the two-column proof.
Let's complete the proof as follows:
1. Statement:
1. Reason: Given
We know this statement is true because we are given in the question.
2. Statement: FG bisects <DFE
2. Reason: Given
We also know this because we are told so in the question, as shown in the diagram given.
3. Statement:
3. Reason: Definition of bisector
We know this because an angle bisector divides an angle into two equal halves. Therefore, the definition of bisector justifies why it was stated that
4. Statement:
Reason: Reflexive property.
5. Statement: ∆DFG EFG
5. Reason: SAS Congruence
Two sides (DF and FG) and an included angle (angle 1) of ∆DFG is congruent two corresponding sides (EF and FG) and an included angle (angle 2) of ∆EFG. Therefore, ∆DFG EFG by the Side-Angle-Side (SAS) Congruence Theorem.