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vladimir1956 [14]
3 years ago
14

Please help it would be much appreciated!

Mathematics
1 answer:
sergiy2304 [10]3 years ago
8 0

Answer:

Part a) Option d

Part b) Option a

Step-by-step explanation:

Part a

if we look at the options given and the data available

Option a) x^4+9

Putting x= 2 we get (2^4) + 9 =25

Putting x= 3 we get (3^4) + 9 =90 but f(x) =125 so not correct option

Option b) (4^x)+9

Putting x= 2 we get (4^2) + 9 =25

Putting x= 3 we get (4^3) + 9 =73 but f(x) =125 so not correct option

Option c) x^5

Putting x= 2 we get (2^5)  =32 but f(x) =25 so not correct option

Option d) 5^x

Putting x= 2 we get (5^2)  =25

Putting x= 3 we get (5^3)  =125

Putting x= 4 we get (5^4)  =625

So Option d is correct.

Part (b)

3(2)^3x

can be solved as:

=3(2^3)^x

=3(8)^x

So, correct option is a

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At heart we're being asked for a line through two points,


(40^\circ \textrm{ C}, 355 \textrm { m/s}) \quad \textrm{and} \quad (49^\circ \textrm{ C}, 360 \textrm { m/s})


In general the line through (a,b) and (c,d) is


(y-b)(c-a)=(x-a)(d-b)


Check that you understand why both (a,b) and (c,d) are on this line.


Here our indepedent variable, instead of x, is T, temperature. Our dependent variable is v, velocity. Substituting,


(v - 355)(49 - 40) = (T - 40)(360 - 355)


9(v - 355) = 5(T - 40)


v-355 = \frac 5 9 T - \frac{200}{9}


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That's our answer; let's check it.


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