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xxMikexx [17]
3 years ago
14

A person is purchasing a new golf club bag. The compartment for the golf balls is approximately the shape of a rectangular prism

with the dimensions of 8 inches by 11 inches by 5 inches. Assuming golf balls are spherical with a 1.68 inch diameter, how many golf balls should fit in the compartment bag?
Mathematics
1 answer:
Akimi4 [234]3 years ago
5 0

Answer:

The answer to your question is: 161 balls

Step-by-step explanation:

Data

rectangular prism = 8 in x 11 in x 5 in

diameter golf balls = 1.68 in     radius = 1.68/ 2 = 0.84 in

Formula

Volume rectangular prism = l x w x h

Volume sphere = (4/3)π r³

Process

Volume rectangular prism = 8 x 11 x 5 = 400 in³

Volume balls = (4/3) (3.1416) (0.84)³ = 2.48

# of balls in the compartment = volumen rectangular prism / volume balls

# of balls in the compartment = 400 / 2.48 = 161. 29

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2x^5-x^2+1=0<br> can you help me ?<br> slove it in details<br> thanks
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Move 1 to the left side of the equation by subtracting it from both sides.

\sqrt{2x -5 - 2 - 1 = 0 }

Subtract 1 from -2.

\sqrt{2x -5 - 3 = 0 }

Add 3 to both sides of the equation.

\sqrt{2x - 5 = 3}

To remove the radical on the left side of the equation, square both sides of the equation.

\sqrt{2x - 5^3 = 3^2}

Simplify each side of the equation.

Multiply the exponents in (( 2x - 5) ^\frac{1}{2})^2 .

Apply the power rule and multiply exponents, (a^m)^n = a^mn

(2x -5)^\frac{1}{2}.2 = 3^2

Cancel the common factor of 2.

(2x - 5)^1 = 3^2

Simplify.

2x - 5 = 3^2

Raise 3 to the power of 2.

2x - 5 = 9

Solve for x

Move all terms not containing x to the right side of the equation.

Add 5  to both sides of the equation.

2x = 9 + 5

Add 9 and 5.

2x = 14

Divide each term by 2  and simplify.

Divide each term in 2x = 14 by 2.

\frac{2x}{2} = \frac{14}{2}

Cancel the common factor of 2.

x = \frac{14}{2}

Divide 14 by 2.

x = 7

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Complete the equation so that it had infinitely many solutions
vova2212 [387]

Answer:

1 - z/3

Step-by-step explanation:

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I’m confused on this question help?
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Answer:

C

Step-by-step explanation:

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3 years ago
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A standard form of a parabola with points through (2, 0) (3, 2) (4, 6)
LenKa [72]

The standard form of a parabola with points through (2, 0) (3, 2) (4, 6)

is y = x² - 3x + 2 ⇒ 3rd answer

Step-by-step explanation:

The standard form of a parabola is y = ax² + bx + c, where a, b , c are constant

To find a , b , c

  • You must have 3 points lie on the parabola
  • Substitute the coordinates of each point in the equation to make system of equations of a , b and c
  • Solve the system of equation to find them

∵ The standard form of a parabola is y = ax² + bx + c

∵ The parabola passes through points (2 , 0) , (3 , 2) , (4 , 6)

- Substitute the coordinates of each point in the equation

Point (2 , 0)

∵ x = 2 and y = 0

∴ 0 = a(2)² + b(2) + c

∴ 0 = 4a + 2b + c

- Switch the two sides

∴ 4a + 2b + c = 0 ⇒ (1)

Point (3 , 2)

∵ x = 3 and 2 = 0

∴ 2 = a(3)² + b(3) + c

∴ 2 = 9a + 3b + c

- Switch the two sides

∴ 9a + 3b + c = 2 ⇒ (2)

Point (4 , 6)

∵ x = 4 and y = 6

∴ 6 = a(4)² + b(4) + c

∴ 6 = 16a + 4b + c

- Switch the two sides

∴ 16a + 4b + c = 6 ⇒ (3)

Subtract equation (1) from equations (2) and (3)

∴ 5a + b = 2 ⇒ (4)

∴ 12a + 2b = 6 ⇒ (5)

- Multiply equation (4) by -2 to eliminate b

∴ -10a - 2b = -4 ⇒ (6)

- Add equations (5) and (6)

∴ 2a = 2

- Divide both sides by 2

∴ a = 1

Substitute the value of a in equation (4) to find b

∵ 5(1) + b = 2

∴ 5 + b = 2

- Subtract 5 from both sides

∴ b = -3

Substitute the value of a and b in equation (1) to find c

∵ 4(1) + 2(-3) + c = 0

∴ 4 - 6 + c = 0

- Add like terms

∴ -2 + c = 0

- Add 2 to both sides

∴ c = 2

Substitute the values of a , b , c in the standard form above

∵ y = ax² + bx + c

∵ a = 1 , b = -3 , c = 2

∴ y = (1)x² + (-3)x + (2)

∴ y = x² - 3x + 2

The standard form of a parabola with points through (2, 0) (3, 2)

(4, 6) is y = x² - 3x + 2

There is another solution you can substitute the x-coordinate of each point in each answer to find the corresponding value of y, if the value of y gives the same value of the y-coordinate of the point for the three points then this answer is the standard form of the parabola

Learn more:

You can learn more about the parabola in brainly.com/question/8054589

#LearnwithBrainly

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Find the value of x. Round to the nearest tenth.
nordsb [41]

Step-by-step explanation:

here,,

a=3,b=10,C=120°

c^2=a^2+b^2-2ab cos120°

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=9+100-(-30)

=109+30

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