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Morgarella [4.7K]
3 years ago
10

Consider the given vector equation. r(t) = 2eti + 3e−tj (a) find r'(t). r'(t) = <2et,−3e−t> (b) sketch the plane curve tog

ether with the position vector r(t) and the tangent vector r'(t) for the given value of t = 0.

Mathematics
1 answer:
Fofino [41]3 years ago
6 0
(a) Differentiate each of the components to get r'(t). The rule is
.. d/dt (a*e^(bt)) = a*b*e^(bt)
The answer you have shown is the correct one.

(b) See the figure. The red curve is the position r(t) for 0 ≤ t ≤ 2. The dashed orange line is the tangent line, whose equation is
.. L(t) = r(0) +r'(0)*t = (2 +2t)i +(3 -3t)j

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Solve the triangle given two angles and one side.
Rasek [7]

Answer:

a = 102.05

b = 393.76

B = 93°

Step-by-step explanation:

The law of sines tells you ...

a/sin(A) = b/sin(B) = c/sin(C)

Since the sum of angles in a triangle is 180°, angle B must be ...

B = 180° -72° -15° = 93°

and the unknown sides must be ...

a = c/sin(C)·sin(A) = 375·sin(15°)/sin(72°) ≈ 102.05192

B = 93°

b = 375·sin(93°)/sin(72°) ≈ 393.75796

_____

The rounding requirement got cut out of your picture, so we can't help you with that.

3 0
3 years ago
Grace folded clothes for 25mins then she worked on a puzzle for 45mins she started folding clothes at 8:20am what time did she f
Wittaler [7]

Answer:

9:30am

Step-by-step explanation:

Given data

Start time= 8:20am

Folding time= 25min

Time spent on Puzzle= 45min

Total time = 25+45= 70min= 1:10 min

Therefore the time she finishes is

8:20+ 1:10= 9:30 am

Hence she finished by 9:30am

5 0
3 years ago
Find x in this 45°-45°-90° triangle.<br><br> x=
Blababa [14]

Answer:

24

Step-by-step explanation:

This is the same question as before just flipped around

6 0
3 years ago
Please show work and help!!
grandymaker [24]
A.25
Work:
-5x-5=25
Hope his helps.
4 0
3 years ago
Read 2 more answers
If a person invests $100 at 4% annual interest, find the approximate value of
tekilochka [14]

Answer:

$140

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Algebra I</u>

Simple Interest Rate Formula: \displaystyle A = P(1 + rt)

  • <em>P</em> is principle amount
  • <em>r</em> is rate
  • <em>t</em> is time

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify variables</em>

<em>P</em> = 100

<em>r</em> = 4% = 0.04

<em>t</em> = 10

<u>Step 2: Find Interest</u>

  1. Substitute in variables [Simple Interest Rate Formula]:                                 A = 100(1 + 0.04 · 10)
  2. (Parenthesis) Multiply:                                                                                      A = 100(1 + 0.4)
  3. (Parenthesis) Add:                                                                                            A = 100(1.4)
  4. Multiply:                                                                                                             A = 140
5 0
3 years ago
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