The functions are illustrations of composite functions.
<em>The soil temperature at 2:00pm is 67</em>
The given parameters are:
---- the function for sun intensity
-- the function for temperature
At 2:00pm, the value of h (number of hours) is:
![\mathbf{h = 2:00pm - 6:00am}](https://tex.z-dn.net/?f=%5Cmathbf%7Bh%20%3D%202%3A00pm%20-%206%3A00am%7D)
![\mathbf{h = 8}](https://tex.z-dn.net/?f=%5Cmathbf%7Bh%20%3D%208%7D)
Substitute 8 for h in
, to calculate the sun intensity
![\mathbf{I(8) =\frac{12 \times 8 - 8^2}{36}}](https://tex.z-dn.net/?f=%5Cmathbf%7BI%288%29%20%3D%5Cfrac%7B12%20%5Ctimes%208%20-%208%5E2%7D%7B36%7D%7D)
![\mathbf{I(8) =\frac{32}{36}}](https://tex.z-dn.net/?f=%5Cmathbf%7BI%288%29%20%3D%5Cfrac%7B32%7D%7B36%7D%7D)
![\mathbf{I(8) =\frac{8}{9}}](https://tex.z-dn.net/?f=%5Cmathbf%7BI%288%29%20%3D%5Cfrac%7B8%7D%7B9%7D%7D)
Substitute 8/9 for I in
, to calculate the temperature of the soil
![\mathbf{T(8/9) =\sqrt{5000 \times 8/9}}](https://tex.z-dn.net/?f=%5Cmathbf%7BT%288%2F9%29%20%3D%5Csqrt%7B5000%20%5Ctimes%208%2F9%7D%7D)
![\mathbf{T(8/9) =\sqrt{4444.44}}](https://tex.z-dn.net/?f=%5Cmathbf%7BT%288%2F9%29%20%3D%5Csqrt%7B4444.44%7D%7D)
![\mathbf{T(8/9) =66.67}](https://tex.z-dn.net/?f=%5Cmathbf%7BT%288%2F9%29%20%3D66.67%7D)
Approximate
![\mathbf{T(8/9) =67}](https://tex.z-dn.net/?f=%5Cmathbf%7BT%288%2F9%29%20%3D67%7D)
Hence, the soil temperature at 2:00pm is 67
Read more about composite functions at:
brainly.com/question/20379727
Answer:
(a) The unit circle is centered at (0,0) with a radius of 1.
(b) The equation of a circle of radius <em>r</em>, with a center located at (0,0):
<em>x</em>²<em>+ y</em>² <em>= r</em>².
(c) (i) P(1,0)
(ii) P(0,1)
(iii) P(-1,0)
(iv) P(0,-1)
Step-by-step explanation:
Answer:
![a_n=-7+4(n-1)](https://tex.z-dn.net/?f=a_n%3D-7%2B4%28n-1%29)
or
![a_n=-7+(n-1)(4)](https://tex.z-dn.net/?f=a_n%3D-7%2B%28n-1%29%284%29)
Step-by-step explanation:
-7,-3,1,5,... is a arithmetic sequence.
Arithmetic sequences have a common difference. That is, it is going up by 4 each time.
When you see arithmetic sequence, you should think linear equation.
The point-slope form of a line is
.
m is the common difference, the slope.
Any they are using the point at x=1 in the point slope form. So they are using (1,-7).
So let's put this into our point-slope form:
![y-(-7)=4(x-1)](https://tex.z-dn.net/?f=y-%28-7%29%3D4%28x-1%29)
![y+7=4(x-1)](https://tex.z-dn.net/?f=y%2B7%3D4%28x-1%29)
Subtract 7 on both sides:
![y=-7+4(x-1)](https://tex.z-dn.net/?f=y%3D-7%2B4%28x-1%29)
So your answer is
![a_n=-7+4(n-1)](https://tex.z-dn.net/?f=a_n%3D-7%2B4%28n-1%29)
Answer:
The height of the building is of 244.95 feet.
Step-by-step explanation:
We use the Pythagorean Theorem to solve this question.
We have that:
The shadow of 50 feet is one side of the right triangle, while the height h is other side.
The hypotenuse is the distance from the end of the shadow to the top of the building, which is 250 feet.
So
![50^2 + h^2 = 250^2](https://tex.z-dn.net/?f=50%5E2%20%2B%20h%5E2%20%3D%20250%5E2)
![h^2 = \sqrt{250^2 - 50^2}](https://tex.z-dn.net/?f=h%5E2%20%3D%20%5Csqrt%7B250%5E2%20-%2050%5E2%7D)
![h = 244.95](https://tex.z-dn.net/?f=h%20%3D%20244.95)
The height of the building is of 244.95 feet.