# Consider this multivariable function. f(x,y)=xy+2x+y−36 a) What is the value of f(2,−3)? b) Find all x-values such that f (x,x) = 0

Question
Multivariable functions
Consider this multivariable function. f(x,y)=xy+2x+y−36
a) What is the value of f(2,−3)?
b) Find all x-values such that f (x,x) = 0

2021-02-10
a) We find f(2,-3) be replacing x by 2 and by -3 in f(x,y)
f(2,-3)=2(-3)+2(2)+(-3)-36
f(2,-3)=-6+4-3-36=-41
b) Now, we solve f(x,x)=0 as follow.
f(x,x)=0
$$\displaystyle{x}^{{2}}+{2}{x}+{x}-{36}={0}$$
$$\displaystyle{x}^{{2}}+{3}{x}-{36}={0}$$
$$\displaystyle{x}=\frac{{-{b}\pm\sqrt{{{b}^{{2}}-{4}{a}{c}}}}}{{{2}{a}}}={\left(-{3}\pm\sqrt{{{3}^{{2}}-{4}{\left({1}\right)}{\left(-{36}\right)}}}\right)}\frac{{)}}{{{2}{\left({1}\right)}}}=\frac{{-{3}\pm\sqrt{{153}}}}{{2}}$$

### Relevant Questions

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Previous studies show that $$\sigma_1 = 19$$.
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The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
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At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant.
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Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.
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