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Korvikt [17]
2 years ago
12

a simple dart target has two concentric circles. the larger circle has a radius of 4. the smaller circle has a radius of 2. the

scoring should correspond to the relative difficulty of hitting the inner circle and the outer ring. how many more points should a player receive for landing a dart in the inner circle, as opposed to the outer ring? the player should receive 2 π times as many points. the player should receive 3 times as many points. the player should receive 9 times as many points. the player should receive 4 π times as many points.
Mathematics
1 answer:
Inessa05 [86]2 years ago
7 0

The points awarded for striking the inner circle ought to be tripled.

What is the inner circle?

  • The face region of the circle determines the likelihood of landing an outrage there.
  • The formula for calculating a circle's area is: inner circle for the exterior circle, apply the formula to subtract the inner circle's value to determine the remaining area.

The formula for the area of a(one) circle is an inner circle for the external circle, use the formula also abate the value of the inner circle, to find the remaining area, which means that the area of the external circle is 3( three) times larger, making it 3( three) times more likely to hit the external circle.

Thus, The points awarded for striking the inner circle ought to be tripled.

\pi r^2 A =\pi  2^2 = 12.566 A\\

so,

\pi   4^2 - 12.566 = 3(three)

Learn more about inner circle here: brainly.com/question/22340654

#SPJ4

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Can some one explain how to answer this and what the answer is 8+4(s-4)t
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4 years ago
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Area of the bounded curves y=x^2, y=√(7+x)
N76 [4]

Answer:

\displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = 5.74773

General Formulas and Concepts:

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Addition/Subtraction]:                                                         \displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]  

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Integration

  • Integrals

Integration Rule [Reverse Power Rule]:                                                               \displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C

Integration Rule [Fundamental Theorem of Calculus 1]:                                     \displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)

Integration Property [Addition/Subtraction]:                                                       \displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx

U-Substitution

Area of a Region Formula:                                                                                     \displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx

Step-by-step explanation:

<u>Step 1: Define</u>

\displaystyle \left \{ {{y = x^2} \atop {y = \sqrt{7 + x}}} \right.

<u>Step 2: Identify</u>

<em>Graph the systems of equations - see attachment.</em>

Top Function:  \displaystyle y = \sqrt{7 + x}

Bottom Function:  \displaystyle y = x^2

Bounds of Integration: [-1.529, 1.718]

<u>Step 3: Integrate Pt. 1</u>

  1. Substitute in variables [Area of a Region Formula]:                                   \displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx
  2. [Integral] Rewrite [Integration Property - Addition/Subtraction]:               \displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{1.718}_{-1.529} {\sqrt{7 + x}} \, dx - \int\limits^{1.718}_{-1.529} {x^2} \, dx
  3. [Right Integral] Integration Rule [Reverse Power Rule]:                             \displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{1.718}_{-1.529} {\sqrt{7 + x}} \, dx - \frac{x^3}{3} \bigg| \limits^{1.718}_{-1.529}
  4. Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:           \displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{1.718}_{-1.529} {\sqrt{7 + x}} \, dx - 2.88176

<u>Step 4: Integrate Pt. 2</u>

<em>Identify variables for u-substitution.</em>

  1. Set <em>u</em>:                                                                                                             \displaystyle u = 7 + x
  2. [<em>u</em>] Basic Power Rule [Derivative Rule - Addition/Subtraction]:                 \displaystyle du = dx
  3. [Limits] Switch:                                                                                               \displaystyle \left \{ {{x = 1.718 ,\ u = 7 + 1.718 = 8.718} \atop {x = -1.529 ,\ u = 7 - 1.529 = 5.471}} \right.

<u>Step 5: Integrate Pt. 3</u>

  1. [Integral] U-Substitution:                                                                               \displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx= \int\limits^{8.718}_{5.471} {\sqrt{u}} \, du - 2.88176
  2. [Integral] Integration Rule [Reverse Power Rule]:                                       \displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = \frac{2x^\Big{\frac{3}{2}}}{3} \bigg| \limits^{8.718}_{5.471} - 2.88176
  3. Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:           \displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = 8.62949 - 2.88176
  4. Simplify:                                                                                                         \displaystyle \int\limits^{1.718}_{-1.529} {\sqrt{7 + x} - x^2} \, dx = 5.74773

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

5 0
3 years ago
Given the system
wariber [46]

Answer:

1.Therefore the solution of given system is (3,4)

2.Therefore the solution of given system is (-1,2)

Step-by-step explanation:

1.

Given the system

2x +3y =18...........(1)

-2x+5y =14...........(2)

Adding the equation (1) and (2)

2x+3y-2x+5y= 18+14

⇔8y = 32

⇔y = \frac{32}{8}

⇔y = 4

Putting the value of y in equation (1)

2x + 3. 4=18

⇔2x+12 =18

⇔2x = 18-12

⇔2x = 6

⇔x =3

Therefore the solution of given system is (3,4)

2.

Given the system

3x +4y = 5..........(a)

2x +7y =12...........(b)

Equation (a) ×2 - equation (b)×3

2(3x+4y)- 3(2x+7y) = 2.5 -12.3

⇔6x + 8y -6x -21y = 10-36

⇔ -13y = -26

⇔y=\frac{-26}{-13}

⇔y = 2

Putting the value of y in equation (a)

3x +4.2 =5

⇔3x = 5 -8

⇔3x = -3

⇔x = -1

Therefore the solution of given system is (-1,2)

6 0
3 years ago
May I get help on this question please?
nata0808 [166]

Answer:2.50

Step-by-step explanation:

6 0
3 years ago
Can someone plz answer this question
nata0808 [166]
So you basically add all the numbers together multiply them by 100& divide by 54
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