MATHEMATICS HIGH SCHOOL

Find the radius of a sphere with a volume of 589 cubic centimeters

Answers

Answer 1

Answer:

Answer: The radius of a sphere is 5.20 cm.

Step-by-step explanation:

Volume of sphere = $(4)/(3)\pi r^3$ , where r = radius of sphere.

Given : Volume of sphere : 589 cubic centimeters

As per formula , we have

$(4)/(3)\pi r^3=589 \n\n\Rightarrow\ r^3=(589*3)/(4\pi)=(441.75)/(\pi)=(441.75)/(3.14)\n\n\Rightarrow\ r^3=140.684713376\approx140.68\n\n\Rigghtarrow\ r=\sqrt[3]{140.68} \approx5.20$

Thus , the radius of a sphere is 5.20 cm.

Answer 2

Answer: volume of sphere = $\pi$ r³

if volume of this sphere = 589 cm³

then πr³ = 589 cm³
r³ = $(589cm^(3) )/( \pi )$

∛r³ = ∛187.485 cm³

∴ r = 5.72 cm

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What is 80 divided by 6?

Answers

80 divided by 6 is equal to 13, with 2 remaining.

We have,

To divide 80 by 6, we perform the division operation and determine the quotient.

When we divide 80 by 6, we can think of it as finding out how many times 6 can fit into 80.

Starting with the largest possible multiple of 6 that is less than or equal to 80, we see that 6 times 13 equals 78.

Since 78 is the largest multiple of 6 which is less than 80, we know that 13 is the largest whole number quotient we can obtain.

However, there is a remainder of 2 when we divide 80 by 6.

This means that after dividing as many times as possible, we have 2 left over.

Therefore, the result of dividing 80 by 6 is:

80 ÷ 6 = 13 with a remainder of 2.

Thus,

80 divided by 6 is equal to 13, with 2 remaining.

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13.33 with a little line over the last three. Which makes it known that it is continuous. Or the fraction answer.. 40/3!

Is 4,400 is 10 times as much as 440

Answers

to do question we have to multiply 10 and 440: ("x times as much" is x Multiplied by", so "twice as much as 4 is 8", or "3 times 4 is 12),

this is 4400 or 4,400 - this is true!

The length of a rectangle is 2 inches more than a number. The width is 1 inch less than twice the same number. If the area of the rectangle is 42 in2 find the dimensions of the rectangle

Answers

Answer:

length: 6 inches

width: 7 inches

Step-by-step explanation:

Let n represent the number. Then the length is (n+2) and the width is (2n-1). The product of these dimensions is the area:

42 = (n+2)(2n -1) = 2n^2 +3n -2

2n^2 +3n -44 = 0 . . . . subtract 42

(n -4)(2n +11) = 0 . . . . . factor

n = 4 . . . . . . . . we aren't interested in the negative solution

Length = 4+2 = 6 . . . inches

Width = 2·4 -1 = 7 . . . inches

Final answer:

The dimensions of the rectangle given that its area is 42 square inches, the length is 2 inches more than a number, and the width is 1 inch less than twice the same number, are 6 inches by 7 inches.

Explanation:

To solve this problem, let's define the unknown number as

x. According to the problem, the length of the rectangle is 2 inches more than x (so it's x + 2), and the width is 1 inch less than twice the number x (which makes it 2x - 1).

Now, we'll use the formula for the area of a rectangle, which is length times width: (x + 2) * (2x - 1) = 42.

Solve this equation by expanding the parentheses (2x^2 + 4x - x - 2 = 42), simplifying (2x^2 + 3x - 2 - 42 = 0), and rearranging (2x^2 + 3x - 44 = 0).

Using the quadratic formula, we find that the possible values of x are 4 and -5.5. However, a negative size doesn't make sense in this context, so x = 4 inches. That makes the length = 4 + 2 = 6 inches, and the width = 2*4 - 1 = 7 inches. Therefore, "the dimensions of the rectangle are 6 inches by 7 inches".

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1.12g of platinum is in the necklace.

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