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3 years ago

Angles 4, 5, and 6 are in the ratio 2:5:3. Find the measure of each angle

Mathematics

1 answer:

garri49 [273]3 years ago

4 0

Answer:

The angles 4, 5 and 6 are 36, 90 and 54 respectively.

Step-by-step explanation:

First, let's find the total number of parts:

2 + 5 + 3 = 10

The amount of degrees per part is 180 / 10 = 18.

Now, we multiply that factor to the ratio:

$2*18 : 5*18 : 3*18//36:90:54$

Thus, the angles 4, 5 and 6 are 36, 90 and 54 respectively.

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“encontrar la integral indefinida y verificar el resultado mediante derivación”

Oliga [24]

$I=\displaystyle\int\frac x{(1-x^2)^3}\,\mathrm dx$

Haz la sustitución:

$y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx$

$\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{y^3}=\frac1{4y^2}+C=\frac1{4(1-x^2)^2}+C$

Para confirmar el resultado:

$\dfrac{\mathrm dI}{\mathrm dx}=\dfrac14\left(-\dfrac{2(-2x)}{(1-x^2)^3}\right)=\dfrac x{(1-x^2)^3}$

$I=\displaystyle\int\frac{x^2}{(1+x^3)^2}\,\mathrm dx$

Sustituye:

$y=1+x^3\implies\mathrm dy=3x^2\,\mathrm dx$

$\implies I=\displaystyle\frac13\int\frac{\mathrm dy}{y^2}=-\frac1{3y}+C=-\frac1{3(1+x^3)}+C$

(Te dejaré confirmar por ti mismo.)

$I=\displaystyle\int\frac x{\sqrt{1-x^2}}\,\mathrm dx$

Sustituye:

$y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx$

$\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{\sqrt y}=-\frac12(2\sqrt y)+C=-\sqrt{1-x^2}+C$

$I=\displaystyle\int\left(1+\frac1t\right)^3\frac{\mathrm dt}{t^2}$

Sustituye:

$u=1+\dfrac1t\implies\mathrm du=-\dfrac{\mathrm dt}{t^2}$

$\implies I=-\displaystyle\int u^3\,\mathrm du=-\frac{u^4}4+C=-\frac{\left(1+\frac1t\right)^4}4+C$

Podemos hacer que esto se vea un poco mejor:

$\left(1+\dfrac1t\right)^4=\left(\dfrac{t+1}t\right)^4=\dfrac{(t+1)^4}{t^4}$

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3 years ago

What is the length of PQ , rounded to the nearest tenth.

Assoli18 [71]

Answer:

10.8 units

Step-by-step explanation:

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3 years ago

At a cake sale, David bought 3 cakes and paid $10.50. At the same price, Lisa bought 4 cakes and 8 cookies and paid $14.80. What

Olin [163]

Price of a Cake

10.5/3= 3.5

1 Cake = $3 and 5 cents, 3.5

Price of a cookie

3.5*4=14

14 out of 14.80 was the cost of 4 cakes

Which leaves us with 0.8

8/0.8= 0.1

The Price of 1 cookie is 0.1

1 Cake: 3.5

1 Cookie: 0.1

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3 years ago

Using the information in the customer order, determine the length and width of the garden. Enter the dimensions. ↓

SashulF [63]

Answer:

Length: 14 feet Width: 1 foot

Step-by-step explanation:

This is the only way to have a rectangle that has a perimeter of 30 feet, and an area of 14 feet.

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14 + 14 = 28

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2 + 28 = 30

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14 x 1 = 14

These dimesnions also have an area of 14.

So, 14 and 1 are the correct dimensions!

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2 years ago

What is 5 8/12 as a mixed number in its simplest form

Elena-2011 [213]

Answer:

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Step-by-step explanation:

Just keep simplifying 8/12 until you end up with 2/3

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Just to make it clear 8/12 = 2/3

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3 years ago