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3 years ago

If the denominator is 10 and the numerator is 3, the fraction is

Mathematics

2 answers:

skelet666 [1.2K]3 years ago

7 0

3/10 is the answer to your question

arsen [322]3 years ago

6 0

Answer:

<h2>Fraction => 3/10 </h2>

<h3>hope that helps ✌</h3>

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He has a record contract that Pays him a base rate of $200 a month and then additional $12 for each album that he sells. Last mo

slavikrds [6]

Answer:

He sold a total of 37 albums last month.

Step-by-step explanation:

Given,

Total earned money = $644

Base payment = $200

Additional payment for each album = $12

We have to find the number of albums sold by him.

Solution,

Let the number of albums be 'a'.

Total earned money is the sum of base payment and additional payment for each album multiplied with number of albums sold.

So framing in equation form, we get;

$644=200+12a$

Subtracting both side by '200' using subtraction property, we get;

$200+12a-200=644-200\\\\12a=444$

Now dividing both side by '12' using division property, we get;

$\frac{12a}{12}=\frac{444}{12}\\\\a=37$

Hence he sold a total of 37 albums last month.

3 0

3 years ago

Simplify 1/4-7i to get a complex number in standard a + bi form.

Romashka [77]

Answer:

$\frac{1}{4-7i}=\frac{4}{65}+\frac{7}{65}i$

Step-by-step explanation:

we are given

$\frac{1}{4-7i}$

Firstly, we will get rid of imaginary term from denominator

so, we will multiply conjugate to both top and bottom term

$\frac{1}{4-7i}=\frac{1\times (4+7i)}{(4-7i)\times (4+7i)}$

$\frac{1}{4-7i}=\frac{4+7i}{4^2-(7i)^2}$

$\frac{1}{4-7i}=\frac{4+7i}{16+49}$

$\frac{1}{4-7i}=\frac{4+7i}{65}$

we can also write as

so, we get

$\frac{1}{4-7i}=\frac{4}{65}+\frac{7}{65}i$

7 0

3 years ago

a square figure with side 4 ft has a semicircle with radius 2ft at the top what is the perimeter of the figure ? what formula sh

andreyandreev [35.5K]

Answer:

~18.28 ft. / 12 + 2π ft. (Read explanation please!)

Step-by-step explanation:

<u>I) Find the square's perimeter:</u>

Obviously, a square's perimeter is its side length x 4. However, there would be a semicircle on top of it. So, to find it we use:

4 x 3 = 16 ft. (Since 1 of the sides is covered by the semicircle)

<u>II) Find the semicircle's perimeter:</u>

Finding the semicircle's perimeter is a bit more complicated, but no worries! We can use this formula:

<em>πr + 2r (pi x radius + radius x 2)</em>

But WAIT: We need to make sure we remove that one side of the square we mentioned earlier. So we would use:

<em>πr (pi x radius)</em>

In terms of π, the perimeter would be:

Or, if you used a standard approximation of π, let's say 3.14, it would be:

If we wanted to state the total perimeter using 3.14 as π, we would say the formula is:

2(3.14) + 4(3) = 18.28 ft.

Or in terms of π:

2π + 4(3) = 12 + 2π ft.

6 0

3 years ago

A giant tank in a shape of an inverted cone is filled with oil. the height of the tank is 1.5 metre and its radius is 1 metre. t

skad [1K]

The given height of the cylinder of 1.5 m, and radius of 1 m, and the rate

of dripping of 110 cm³/s gives the following values.

1) The rate of change of the oil's radius when the radius is 0.5 m is r' ≈ <u>9.34 × 10⁻⁵ m/s</u>

2) The rate of change of the oil's height when the height is 20 cm is h' ≈ <u>1.97 × 10⁻³ m/s</u>

3) The rate the oil radius is changing when the radius is 10 cm is approximately <u>0.175 m/s</u>

<h3>How can the rate of change of the radius & height be found?</h3>

The given parameters are;

Height of the tank, h = 1.5 m

Radius of the tank, r = 1 m

Rate at which the oil is dripping from the tank = 110 cm³/s = 0.00011 m³/s

$1) \hspace{0.15 cm}V = \frac{1}{3} \cdot \pi \cdot r^2 \cdot h$

From the shape of the tank, we have;

$\dfrac{h}{r} = \dfrac{1.5}{1}$

Which gives;

h = 1.5·r

$V = \mathbf{\frac{1}{3} \cdot \pi \cdot r^2 \cdot (1.5 \cdot r)}$

$\dfrac{d}{dr} V =\dfrac{d}{dr} \left( \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot (1.5 \cdot r)\right) = \dfrac{3}{2} \cdot \pi \cdot r^2$

$\dfrac{dV}{dt} = \dfrac{dV}{dr} \times \dfrac{dr}{dt}$

$\dfrac{dr}{dt} = \mathbf{\dfrac{\dfrac{dV}{dt} }{\dfrac{dV}{dr} }}$

$\dfrac{dV}{dt} = 0.00011$

Which gives;

$\dfrac{dr}{dt} = \mathbf{ \dfrac{0.00011 }{\dfrac{3}{2} \cdot \pi \cdot r^2}}$

When r = 0.5 m, we have;

$\dfrac{dr}{dt} = \dfrac{0.00011 }{\dfrac{3}{2} \times\pi \times 0.5^2} \approx 9.34 \times 10^{-5}$

The rate of change of the oil's radius when the radius is 0.5 m is r' ≈ <u>9.34 × 10⁻⁵ m/s</u>

2) When the height is 20 cm, we have;

h = 1.5·r

$r = \dfrac{h}{1.5}$

$V = \mathbf{\frac{1}{3} \cdot \pi \cdot \left(\dfrac{h}{1.5} \right) ^2 \cdot h}$

r = 20 cm ÷ 1.5 = $13.\overline3$ cm = $0.1\overline3$ m

Which gives;

$\dfrac{dr}{dt} = \dfrac{0.00011 }{\dfrac{3}{2} \times\pi \times 0.1 \overline{3}^2} \approx \mathbf{1.313 \times 10^{-3}}$

$\dfrac{d}{dh} V = \dfrac{d}{dh} \left(\dfrac{4}{27} \cdot \pi \cdot h^3 \right) = \dfrac{4 \cdot \pi \cdot h^2}{9}$

$\dfrac{dV}{dt} = \dfrac{dV}{dh} \times \dfrac{dh}{dt}$

$\dfrac{dh}{dt} = \dfrac{\dfrac{dV}{dt} }{\dfrac{dV}{dh} }$ <em />

$\dfrac{dh}{dt} = \mathbf{\dfrac{0.00011}{\dfrac{4 \cdot \pi \cdot h^2}{9}}}$

When the height is 20 cm = 0.2 m, we have;

$\dfrac{dh}{dt} = \dfrac{0.00011}{\dfrac{4 \times \pi \times 0.2^2}{9}} \approx \mathbf{1.97 \times 10^{-3}}$

The rate of change of the oil's height when the height is 20 cm is h' ≈ <u>1.97 × 10⁻³ m/s</u>

3) The volume of the slick, V = π·r²·h

Where;

h = The height of the slick = 0.1 cm = 0.001 m

Therefore;

V = 0.001·π·r²

$\dfrac{dV}{dr} = \mathbf{ 0.002 \cdot \pi \cdot r}$

$\dfrac{dr}{dt} = \mathbf{\dfrac{0.00011 }{0.002 \cdot \pi \cdot r}}$

When the radius is 10 cm = 0.1 m, we have;

$\dfrac{dr}{dt} = \dfrac{0.00011 }{0.002 \times \pi \times 0.1} \approx \mathbf{0.175}$

The rate the oil radius is changing when the radius is 10 cm is approximately <u>0.175 m</u>

Learn more about the rules of differentiation here:

brainly.com/question/20433457

brainly.com/question/13502804

3 0

3 years ago

How to solve (including answer) x^2+8x+7=0 by factoring

sesenic [268]

Since the first term in the equation is $x^{2}$ , you know that each group you make will have to have an x in it. Now, you need to figure out what times what equals 7 and adds up to 8. You can list all of the numbers that multiply to seven until you find the right numbers.

-1 x -7
1 x 7

1 and 7 add to eight and multiply to seven, so those will be the numbers in your groups. This makes your factored groups (x + 1)(x + 7).

3 0

4 years ago

If the denominator is 10 and the numerator is 3, the fraction is ​

If the denominator is 10 and the numerator is 3, the fraction is