If <em>x</em> = -1, you have
2(-1) + 3 cos(-1) + <em>e</em> ⁻¹ ≈ -0.0112136 < 0
and if <em>x</em> = 0, you have
2(0) + 3 cos(0) + <em>e</em> ⁰ = 4 > 0
The function <em>f(x)</em> = 2<em>x</em> + 3 cos(<em>x</em>) + <em>eˣ</em> is continuous over the real numbers, so the intermediate value theorem applies, and it says that there is some -1 < <em>c</em> < 0 such that <em>f(c)</em> = 0.
Answer:
The rate of change is "-3". Which means the rate at which the tractor uses fuel.
Step-by-step explanation:
The equation describes a line and any line follows the equation:
y = m*x + c
Where "m" is the rate of change and "c" is the shift on the line. Comparing the equation for the fuel and the equation from the line, the rate of change must be "-3". The rate of change in this context describes the speed at which the tractor uses fuel, at a rate of 3 gallons per hour.
I'm sorry but the solution you proposed was a bit hard to follow, so I'll just post my solution: we convert "2 and 1/2" to a single fraction:
So, we know that 5/2 gallons cost 60 dollars, which means
To find the cost of a single gallon, we have to solve the equation for g:
Answer: 
Step-by-step explanation:
Given
The sprinkler can water the area up to 
i.e. is the radius
If the screw leads to a reduction of 25% in radius, then the new radius is
So, the area corresponding to this radius
Thus, the maximum area that can be covered is
Answer:
Equation 1
6*a = 360°
Equation 2
2*a + 2*b = 360°
a = 60°
b = 120°
Step-by-step explanation:
From the first picture we can see that 6 angles a° made a complete circle, that is, 360°. So:
6*a = 360°
a = 360°/6 = 60°
From the second picture we can see that 2 angles a° and 2 angles b° made a complete circle, then:
2*a + 2*b = 360°
2*b = 360° - 2*60°
b = 240°/2 = 120°
