SOLUTION: Please Help. Show work Thanks in advance. A person's systolic blood pressure, which is measured in millimeters of mercury (mm Hg), depends on a person's age, in years. The equ

Algebra ->  Equations -> SOLUTION: Please Help. Show work Thanks in advance. A person's systolic blood pressure, which is measured in millimeters of mercury (mm Hg), depends on a person's age, in years. The equ      Log On


   

Question 1016995: Please Help. Show work Thanks in advance.

A person's systolic blood pressure, which is measured in millimeters of mercury (mm Hg), depends on a person's age, in years. The equation:
P=0.007y^2−0.03y+122
P=0.007y^2-0.03y+122

gives a person's blood pressure, P
P
, at age y
y
years.
A.) Find the systolic pressure, to the nearest tenth of a millimeter, for a person of age 40 years.


B.) If a person's systolic pressure is 132.54 mm Hg, what is their age (rounded to the nearest single year)?

Found 2 solutions by rothauserc, macston:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
A) P = 0.007(40)^2 -0.03(40) + 122
P = 132.0
***********************************************
Systolic blood pressure for age 40 is 132.0mm Hg
***********************************************
:
B) 132.54 = 0.007y^2 -0.03y +122
0.007y^2 -0.03y -10.54 = 0
:
use quadratic formula to solve for y
;
y = (-(-0.03) + sqrt((0.03)^2−4*0.007*(−10.54))) / (2(0.007)) = 41.005514286
y = (-(-0.03) - sqrt((0.03)^2-4*0.007*(-10.54))) / (2(0.007)) = −36.7198
:
Note that * means multiply
:
we accept the positive value for y and reject the negative value
:
**************************************************************
The person's age for 132.54mm Hg systolic pressure is 41 years
**************************************************************

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
P=0.007y^2-0.03y+122
.
A.) Find the systolic pressure, to the nearest tenth of a millimeter, for a person of age 40 years.
.
Replace y with 40 and solve for P.
.
P=0.007(40^2)-0.03(40)+122
.
B.) If a person's systolic pressure is 132.54 mm Hg, what is their age (rounded to the nearest single year)?
.
Replace P with 132.54 and solve for y:
.
P=0.007y^2-0.03y+122
132.54=0.007y^2-0.03y+122 . Subtract 132.54 from each side.
0=0.007y^2+0.03y-10.54 . Multiply each side by 1000.
0=7y^2+30y-10540 .
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 7y%5E2%2B30y%2B-10540+=+0) has the following solutons:

y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2830%29%5E2-4%2A7%2A-10540=296020.

Discriminant d=296020 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-30%2B-sqrt%28+296020+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%2830%29%2Bsqrt%28+296020+%29%29%2F2%5C7+=+36.719800028893
y%5B2%5D+=+%28-%2830%29-sqrt%28+296020+%29%29%2F2%5C7+=+-41.0055143146072

Quadratic expression 7y%5E2%2B30y%2B-10540 can be factored:
7y%5E2%2B30y%2B-10540+=+7%28y-36.719800028893%29%2A%28y--41.0055143146072%29
Again, the answer is: 36.719800028893, -41.0055143146072. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7%2Ax%5E2%2B30%2Ax%2B-10540+%29

.
Since negative age does not work, the person's age is 36.7 years.
.
ANSWER B: The person is 37 years old.
.