Question

A polynomial, h(t) = 2t - at + bt + 4 represents Mr. Bill's height in metres at 't seconds. "-Mr." Bill is rapidly approaching a tall brick wall which is 100 metres high and will reach the wall in 3 seconds. "-You" need to find out if Mr. Bill will clear the wall (pass over it) or slam into it! Oh, → h(t) = 2t at + bt+4 has a remainder of 9 when divided by (t-1) and a remainder of "-36" when divided by (t+2).
a) What Theorem do you have to use to answer this question? Explain why.
b) b) Now, find the values of 'a' and 'b'. Make sure that you show ALL of your work. Include a BRIEF explanation of each step.
c) Now, will Mr. Bill make it over the wall or is he plasticine chunky salsa?

Answer 1

The value of a and b in terms of equation are; a = 3 + b and b = a + 18.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given polynomial, h(t) = 2t - at + bt + 4 represents Mr. Bill's height in metres at 't seconds. "-Mr." Bill is rapidly approaching a tall brick wall which is 100 metres high and will reach the wall in 3 seconds.

h = 100 metres

t = 3 seconds

Now substitute the values;

h(t) = 2t - at + bt + 4

100 = 2(3) - a(3) + b(3) + 4

100 = 6 - 3a + 3b + 4

3a + 90 = 3b

We need to find out if Mr. Bill will clear the wall or slam into it!

h(t) = 2t - at + bt+4 has a remainder of 9 when divided by (t-1) and a remainder of "-36" when divided by (t+2).

When t = 1

Then;

h(t) = 2t - at + bt + 4

9 = 2(1) - a(1) + b(1) + 4

9 = 6 - a + b

a = 3 + b

When time t = -2

Then; h(t) = 2t - at + bt + 4

-36= 2(-2) - a(-2) + b(-2) + 4

-36 = -4 + 2a - 2b + 4

-18 = a - b

b = a + 18

Learn more about equations here;

brainly.com/question/25180086

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