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rodikova [14]
3 years ago
10

its 76 degrees fahrenheit at the 6000-foot level of a mountain, and 49 degrees Fahrenheit at the 12000-foot level of the mountai

n. write a liner equation to find the temperature T at an elevation x on the mountain, where x is in thousands of feet.
Mathematics
1 answer:
brilliants [131]3 years ago
5 0

T = \frac{-9}{2}x + 103 is the linear equation to find the temperature T at an elevation x on the mountain, where x is in thousands of feet.

<em><u>Solution:</u></em>

The linear equation in slope intercept form is given as:

T = cx + k ------ (i)

Where "t" is the temperature at an elevation x

And x is in thousands of feet

<em><u>Given that its 76 degrees fahrenheit at the 6000-foot level of a mountain</u></em>

Given, when c = 6 thousand ft and T = 76^{\circ} fahrenheit

This implies,

From (i)

76 = c(6) + k

76 = 6c + k

⇒ k = 76 - 6c  ----- (ii)

<em><u>Given that 49 degrees Fahrenheit at the 12000-foot level of the mountain</u></em>

Given, when c = 12 thousand ft and T = 49^{\circ} fahrenheit

This implies,

From (i)

49 = c(12) + k

49 = 12c + k

Substitute (ii) in above equation

49 = 12c + (76 - 6c)

49 = 12c + 76 - 6c

49 - 76 = 6c

6c = -27

c = \frac{-9}{2}

Substituting the value of c in (ii) we get

k = 76 - 6( \frac{-9}{2})\\\\k = 76 + 27 = 103

Substituting the value of c and k in (i)

T = \frac{-9}{2}x + 103

Where "x" is in thousands of feet

Thus the required linear equation is found

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Which expression is equivalent to n2 + 26n + 88 for all values of n?
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Option B is correct.

The expression which is equivalent to  n^2+26n+88  is; (n+22)(n+4)

Explanation:

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then,

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we see that (n+22) is common to both terms so, we have;

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Check:

(n+4)(n+22) = n\cdot n+ 22n+4n+88=n^2+26n+88   [ True]



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so, (6+7(1.732),0)\text{ and }(6-7(1.732),0) are the required points.

i.e. (18.124,0) and ( -6.124,0) are the required points.

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