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Sloan [31]
3 years ago
10

Please help me with these rotation problem.​

Mathematics
1 answer:
FrozenT [24]3 years ago
3 0

Answer:

  see below

Step-by-step explanation:

In the attachment, the points are listed in the order given in the problem statement. (They are listed to the right of the "rotation matrix", with x-coordinates above y-coordinates.)

__

I really don't like to do repetitive calculations, so I try to use a graphing calculator or spreadsheet whenever possible. Angles are measured CCW.

As always, the rotation transformations are ...

  180° — (x, y) ⇒ (-x, -y)

  270° — (x, y) ⇒ (y, -x)

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Tutorial Exercise A boat leaves a dock at 2:00 PM and travels due south at a speed of 20 km/h. Another boat has been heading due
ANTONII [103]

Answer:

Both the boats will closet together at 2:21:36 pm.

Step-by-step explanation:

Given that - At 2 pm boat 1 leaves dock and heads south and boat 2 heads east towards the dock. Assume the dock is at origin (0,0).

Speed of boat 1 is 20 km/h so the position of boat 1 at any time (0,-20t),

        Formula :   d=v*t

at 2 pm boat 2 was 15 km due west of the dock because it took the boat 1 hour to reach there at 15 km/h, so the position of boat 2 at that time was (-15,0)

the position of boat 2 is changing towards east, so the position of boat 2 at any time (-15+15t,0)

      Formula : D=\sqrt{(x2-x1)^2+(y2-y1)^2}

⇒                     D = \sqrt{20^2t^2+15(t-1)^2}

Now let           F(t) = D^2(t)

                ∵    F'(t) = 800t + 450(t-1) =  1250t -450\\F'(t) =0

⇒                     t= 450/1250

⇒                     t= .36 hours

⇒                       = 21 min 36 sec

Since F"(t)=0,

∴ This time gives us a minimum.

Thus, The two boats will closet together at 2:21:36 pm.

3 0
3 years ago
If you have 5 blue marbles, 8 yellow marbles, and 2 green marbles. What is the probability of pulling a yellow marble?
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Add all them up. 5+8+2 = 15

How many yellows? 8/15 = 0.533 ~~ 53%
3 0
2 years ago
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Find the slope of the line (18,0)(10,-5)
Leya [2.2K]

Answer:

m=\frac{5}{8}

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>Algebra I</u>

  • Slope Formula: m=\frac{y_2-y_1}{x_2-x_1}

Step-by-step explanation:

<u>Step 1: Define</u>

Point (18, 0)

Point (10, -5)

<u>Step 2: Find slope </u><em><u>m</u></em>

Simply plug in the 2 coordinates into the slope formula to find slope <em>m</em>

  1. Substitute [SF]:                    m=\frac{-5-0}{10-18}
  2. Subtract:                              m=\frac{-5}{-8}
  3. Simplify:                               m=\frac{5}{8}
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2 years ago
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Marysya12 [62]

Answer:

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Step-by-step explanation:

you divide 60 min by 15 to get 4 then u multiply 12 × 4 =48 then multiply 48 × 2=96

8 0
3 years ago
How are percent transmittance and absorbance related algebraically?
statuscvo [17]

Answer:

So, if all the light passes through a solution without any absorption, then absorbance is zero, and percent transmittance is 100%. If all the light is absorbed, then percent transmittance is zero, and absorption is infinite.

Absorbance is the inverse of transmittance so,

A = 1/T

Beer's law (sometimes called the Beer-Lambert law) states that the absorbance is proportional to the path length, b, through the sample and the concentration of the absorbing species, c:  


A ∝ b · c

As Transmittance, T =\dfrac{P}{P_0}

% Transmittance, \%T=100\times T

Absorbance,

A=\log_{10} \dfrac{P_0}{P}\\\\A =\log_{10}\times \dfrac{1}{T}\\\\A=\dfrac{\log_{10} 100}{\%T}\\\\A=(2 - log_{10})\times \%T

Hence, A=\log_{10}\times \dfrac{1}{T} is the algebraic relation between absorbance and transmittance.


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