Vaccine design : most vaccine protect only against pathogens that within a certain region of atigenic space. suppose that a vaccine protects gainst any strain falling within a sphere of radious 2 centered at the point(2,1,0) in antigenic space. for each strain, determine whether this vaccine will be effective (a) astrain located at (0,0,0) in a antigenic space (b) astrain located at (1,0,3) in a antigenic space (c) astrain located at (1,0,1) in a antigenic space (d) astrain located at (1/4,2,1) in a antigenic space

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

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step-by-step explanation:

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