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2 years ago

13

You buy a quart of ice cream that comes in a cylindrical tub. A quart has a volume about 58 cubic inches. The tub has a height o

f 5 inches. What is the radius of the ice cream tub?

1 answer:

max2010maxim [7]2 years ago

4 0

The answer is 72 because ice cream has a lot of sugar in it

You might be interested in

A straight slide in a playground design makes an isosceles triangle with the

julia-pushkina [17]

Answer:

Option D.

Step-by-step explanation:

First, the you need ti understand that the triangle is an isosceles right angled triangle. In other words, the base and height are equal in length. The third side is the slide. This is the longest side.
Next, we know that the formula for calculating the area of a right angled triangle is given by:

A = 1/2 (base × perpendicular height)

The perpendicular height is equal to the base. Let's say the base is <em>x</em>. It means that the height is also x, since height = base.
Therefore, the formula will be:

A = 1/2 (x.x)

=1/2 (x²)

32 = 1/2 (x²)

Multiplying both sides by 2 gives:

32×2 = x²

64 = x²

8 = x

To find the third side, we use the Pythagoras theorem:

C² = A² + B²

= 8² + 8²

= 128

C = √128

= 8√2

However, the answer will not be exact, so we multiply the length of the base and height by 2. This gives x = 16 (Length of base = length of height)

Repeating the steps above gives C = √ (16)² + (16)²

= √256

This corresponds to option D.

3 0

2 years ago

emmainna [20.7K]

Use the given recursion and starting value of $x_0 = 2.4$ to find $x_1$ :

$x_1 = \dfrac{x_0 + \frac6{x_0}}2 = \dfrac{2.4 + \frac{6}{2.4}}2 = 2.45$

Do the same for $x_2$ and $x_3$ :

$x_2 = \dfrac{x_1 + \frac6{x_1}}2 = \dfrac{2.45 + \frac6{2.45}}2 \approx 2.44949$

$x_3 = \dfrac{x_2+\frac6{x_2}}2 \approx \dfrac{2.44949 + \frac6{2.44949}}2 \approx \boxed{2.44949}$

(That's not a mistake. This just tells you that the 2nd and 3rd iterates are very close together and have at least the same first 5 digits after the decimal.)

5 0

1 year ago

Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$

Viktor [21]

When $n=0$ , we have

$5^{3^0} + 1 = 5^1 + 1 = 6$

$3^{0 + 1} = 3^1 = 3$

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for $n=k$ , that

$3^{k + 1} \mid 5^{3^k} + 1$

Now for $n=k+1$ , we have

$5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)$

so we know the left side is at least divisible by $3^{k+1}$ by our assumption.

It remains to show that

$3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1$

which is easily done with Fermat's little theorem. It says

$a^p \equiv a \pmod p$

where $p$ is prime and $a$ is any integer. Then for any positive integer $x$ ,

$5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3$

Furthermore,

$5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3$

which goes all the way down to

$5^{3^k} \equiv 5 \pmod 3$

So, we find that

$\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3$

QED

5 0

1 year ago

Working as a waiter, Michael earns $7.50 per hour plus tips Last night he received $43.50 in tips and earned a total of $88.50.

vredina [299]

Answer: 6 hours

Step-by-step explanation:

$7.50per hour

$43.50 in tips

$88.50 total

88.50-43.50=45

45 divided by 7.50 equals 6

So your answer is 6 hours

Hope this helped:))

3 0

2 years ago

The top piece from a model of city hall is shown below.

alexandr402 [8]

Answer:

The area that she painted = 896 mm^2

Step-by-step explanation:

Given:

The given figure is a pyramid with square base.

Here we need to find the surface area of the figure that need to be painted.

Surface area of a square pyramid = (S×S) + 2×S×L square.units

Where, S = side of the base L = slant height of the pyramid.

Now we have to plug in the given values.

Here S = 14, L =25

Plug in these values into the formula

= (14*14) + 2*14*25

= 196 + 700

= 896 mm^2

The area that she painted = 896 mm^2

Hope this will helpful.

Thank you.

4 0

2 years ago

Read 2 more answers