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3 years ago

Q1

Mathematics

1 answer:

Nady [450]3 years ago

6 0

Answer:

Step-by-step explanation:

The square root of the number is 4.

because she is thinking number 16.

She is thinking of √256;

then the square root of √256 is being asked.

√(√256) = √ 16 = 4

another way of answering the question:

let x be the number she is thinking

x² = 256

x = √256

x = 16

then square root of 16 is 4.

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an inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a

viktelen [127]

Answer:

the rate of change of the water depth when the water depth is 10 ft is; $\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t

Then the similar triangles ΔOCD and ΔOAB is as follows:

$\dfrac{h}{r}= \dfrac{20}{8}$ ( similar triangle property)

$\dfrac{h}{r}= \dfrac{5}{2}$

$\dfrac{h}{r}= 2.5$

h = 2.5r

$r = \dfrac{h}{2.5}$

The volume of the water in the tank is represented by the equation:

$V = \dfrac{1}{3} \pi r^2 h$

$V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h$

$V = \dfrac{1}{18.75} \pi \ h^3$

The rate of change of the water depth is :

$\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

$\dfrac{dv}{dt}= - 4 \ ft^3/sec$

Therefore,

$-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

the rate of change of the water at depth h = 10 ft is:

$-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}$

$100 \pi \dfrac{dh}{dt} = -4 \times 6.25$

$100 \pi \dfrac{dh}{dt} = -25$

$\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}$

Thus, the rate of change of the water depth when the water depth is 10 ft is; $\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

4 0

4 years ago

A beverage distributor has a facility that bottles beer. Beer bottles are supposed to be filled to 12 oz but there are slight va

-BARSIC- [3]

The associated z score for filling to 10.98 oz. is -1.16.

<h3>Z score</h3>

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (x - μ) / σ

where x is the raw score, μ is the mean and σ is the standard deviation.

Given that μ = 12.01, σ = 0.89, hence:

For x = 10.98:

z = (10.98 - 12.01)/0.89 = -1.16

The associated z score for filling to 10.98 oz. is -1.16.

Find out more on Z score at: brainly.com/question/25638875

4 0

3 years ago

3. Simplify the following<br>a)[(116)3 x 114]x 1212

Fiesta28 [93]

Answer:

48082464 is the answer

Step-by-step explanation:

=[(116)3×114] × 1212

=[348×114] × 1212

=39672 × 1212

=48082464 is the answer

hope it will help :)

7 0

4 years ago

Read 2 more answers

A pair of shoes usually sells for $64. If the shoes are 20% off, and sales tax is 8%, what is the total price of the shoes, incl

Marina86 [1]

Answer:

$55.30

Step-by-step explanation:

4 0

3 years ago

What is the 13th term of the geometric sequence with this formula

adell [148]

Answer:

Step-by-step explanation:

You plug in 13 to n-1. to get -2^12. This equates to 4096, and you multiply that by 3

8 0

4 years ago