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.Com
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)   (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)   (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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=296020 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 36.719800028893, -41.0055143146072. Here's your graph:

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

Please help me with this problem. The answer I came up with was 36.7mm A person's... (answered by ikleyn)
A person's systolic blood pressure, which is measured in millimeters of mercury (mm Hg),... (answered by Boreal)
A person's systolic blood pressure, which is measured in millimeters of mercury (mm Hg),... (answered by ikleyn)
An experiment was set up to find a relationship between weight and systolic blood... (answered by htmentor)
4. The data below are the ages and systolic blood pressure (measured in millimeters of... (answered by Fombitz)
The mean systolic blood pressure of adult males is normally distributed with a mean of... (answered by stanbon)
The mean systolic blood pressure of adult males is normally distributed with a mean of... (answered by stanbon)
A person’s blood pressure, P(t), in millimeters of mercury (mm Hg), is modeled by the... (answered by stanbon)
Systolic blood pressure, the upper number in a blood pressure reading, is measured as... (answered by robertb)