The quadratic equation f(x) = - x² + 3 · x + 13 evaluated at x = 10 is equal to - 57.
<h3>How to find the value associated with a quadratic equation</h3>
In this case we have a quadratic equation (f(x) = - x² + 3 · x + 13) that has to be evaluated at a value of x, that is, x = 10. Now we proceed to show the solution of the exercise step by step:
- x² + 3 · x + 13, x = 10 Given
- 10² + 3 · 10 + 13 Previous step
- 100 + 30 + 13 Definition of power / Definition of multiplication
- 57 Definition of addition and subtraction
The quadratic equation f(x) = - x² + 3 · x + 13 evaluated at x = 10 is equal to - 57.
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Answer:
3 gallons
Step-by-step explanation:
35 minutes = -1 gallon
5 x 60 = 300
300 + 15 = 315
315 ÷ 35 = 9
12 - 9 = 3
The area of the shaded region is 40π/3 square cm if the radius of the small circle r is 3 cm and the radius of the large circle R is 7 cm.
<h3>What is a circle?</h3>
It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have a circle in which the shaded region is shown.
The radius of the small circle r = 3 cm
The radius of the large circle R = 3+4 = 7 cm
The area of the shaded region:
= area of the large circle sector - an area of the small circle sector
= (120/360)[π7²] - (120/360)[π3²]
= 49π/3 - 3π
= 40π/3 square cm or
= 13.34π square cm
Thus, the area of the shaded region is 40π/3 square cm if the radius of the small circle r is 3 cm and the radius of the large circle R is 7 cm.
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Answer:
c. 55.4 ft/s
Step-by-step explanation:
Speed of the object is represented by the function:
where x represents the number of feet the object has fallen. We have to find the speed of the object after it has fallen 48 feet. This means we have to find f(x) for x = 48. Substituting x = 48 in above equation we get:
Thus, rounded to nearest tenth, the speed of the object after it has fallen 48 feet would be 55.4 ft/s
