Driving along, terry notices that the last four digits on his car's odometer are palindromic. a mile later, the last five digits are palindromic. after driving another mile, the middle four digits are palindromic. one more mile, and all six are palindromic. what was the odometer reading when terry first looked at it? form a linear system of equations that expresses the requirements of this puzzle.

Answers

Answer 1

Answer: Designate the initial digits, left to right, as {a, b, c, d, d, c}.

After adding one mile, the digits are {a, b, c, d, c, b}, so the relevant equation is
10c +b = 10d +c +1

After adding another mile, the digits are {a, b, c, c, b, e}, so the relevant equation is
100c +10b +e = 100d +10c +b +1

After another mile, the digits are {a, b, c, c, b, a}, so the relevant equation is
a = e +1

In summary, we have 3 equations in 5 unknowns.
b + 9c -10d = 1
9b +90c -100d +e = 1
a - e = 1
along with the constraints {a, b, c, d, e} ∈ {0, ..., 9}

_____
These have the solution {a, b, c, d, e} = {1, 9, 8, 8, 0}, so the odometer readings were
198888
198889
198890
198891

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[10 points] Let v1, v2 and v3 be three linearly independent vectors in R 3 . (a) Find the rank of the matrix A = (v1 − v2) (v2 − v3) (v3 − v1) . (b) Find the rank of the matrix B = (v1 + v2) (v2 + v3) (v3 + v1) .

Answers

Answer:

The solution and complete explanation for the above question and mentioned conditions is given below in the attached document.I hope my explanation will help you in understanding this particular question.

Step-by-step explanation:

Please help! (95 points)

Answers

Answer:

303.61

Step-by-step explanation:

if you need explantion tell me and i will edit my answer

Answer:

24.4M

Step-by-step explanation:

Susan reads a book at a rate of 1 page every 3 minutes. If her reading rate remains the same, which method could be used to determine the number of minutes for her to read 18 page? *

Answers

Answer:

54 minutes

Step-by-step explanation:

Hope I helped!

I can almost guarantee this answer is correct.

Have a nice day!

Answer:

54 minutes

Step-by-step explanation:

Every 3 minutes she reads 1

18x3=54

Hope it helps

which of the following statistic measures the most frequently occuring value in a set of data A.) range B.) mean C.) mode D.) median

Answers

Answer:

This is mode defined

Step-by-step explanation:

Organisms A and B start out with the same population size. Organism A's population doubles every day. After 5 days, the population stops growing and a virus cuts it in half every day for 3 days. Organism B's population grows at the same rate but is not infected with the virus. After 8 days, how much larger is organism B's population than organism A's population? Answer the questions to find out. The expression showing organism A's decrease in population over the next 3 days is ( 1 2 ) ( 2 1 ) 3 . This can be written as (2–1)3. Write (2–1)3 with the same base but one exponent.

Answers

Answer:

The number of times organism B's population is larger than organism A's population after 8 days is 32 times

Step-by-step explanation:

The population of organism A doubles every day, geometrically as follows

a, a·r, a·r²

Where;

r = 2

The population after 5 days, is therefore;

Pₐ₅ = = 32·a

The virus cuts the population in half for three days as follows;

The first of ta·2⁵ he three days = 32/2 = 16·a

The second of the three days = 16/2 = 8·a

After the third day, Pₐ = 8/2 = 8·a

The population growth of organism B is the same as the initial growth of organism A, therefore, the population, P₈ of organism B after 8 days is given as follows;

P₈ = a·2⁸ = 256·a

Therefore, the number of times organism B's population is larger than organism A's population after 8 days is P₈/Pₐ = 256·a/8·a = 32 times

Which gives, the number of times organism B's population is larger than organism A's population after 8 days is 32 times.

Final answer:

Organism A's population at the end of 5 days is 2^5. After 5 days, a virus cuts it in half for 3 days. Organism B's population at the end of 8 days is 2^8. To find the difference, subtract organism A's population from organism B's population.

Explanation:

Organism A's population doubles every day for 5 days, so the population at the end of 5 days is 25. After 5 days, a virus cuts the population in half for 3 days, so we need to find (25) * (2-1)3. Using the rule of exponents, we can rewrite this expression as (25+(-1*3)), which simplifies to 2-4.

Organism B's population grows at the same rate but is not infected with the virus. After 8 days, the population is 28.

To find out how much larger organism B's population is than organism A's population, we need to subtract the population of organism A from organism B. So, 28 - 2-4 is the answer.

Learn more about Population growth and virus impact here:

brainly.com/question/32372080

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Find mA. 110°
B. 70°
C. 250°
D. 55°

Answers

Answer:

A:100°

Step-by-step explanation:

BECAUSE IS THE SAME

it’s A 110

Same side interior angles are equal

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Materials: Tall clear drinking glass or vase At least four of the following liquids: Fresh water Salt water Vegetable oil Rubbing alcohol Dish soap Honey Corn syrup Milk Maple syrup At least three different small items of your choice, such as: Ping pong ball Small screw, bolt, or nut Popcorn kernel Peanut Blueberry Grape Cherry tomato Instructions: Select four liquids and predict how you think they compare in density by ranking them from most dense to least dense in the data table below. Measure out ¼ cup volume of each liquid, and pour them one at a time into the clear glass or vase. Record your observations in the lab worksheet. Gently add the first small item to the liquids, and record your observation of where it settles. Repeat with the other small items. Clean up all lab materials (the liquids can be poured down the sink), and complete the lab worksheet. Data Table: Prediction: Rank the four liquids from lowest density (top) to highest density (bottom) Observation: Rank how the four liquids really compare, from lowest density (top) to highest density (bottom) Observations: What objects did you place in the liquid, and where did each settle? Object Layer where it settled Observations and Conclusions: Define density, and describe how this activity helps you compare the density of four different liquids without making mass measurements. How did the observations compare to your predictions? Did any of the results surprise you? How would the density of water change if you measured out ½ cup instead of ¼ cup? Explain your answer in complete sentences.

PLEASE HELP I WILL BRAINLIST PLEASE