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4 years ago

Solve the following equations. 3 ⋅ 62^x = 648

Mathematics

1 answer:

gayaneshka [121]4 years ago

7 0

Answer:

$x=1.56861$

Step-by-step explanation:

$62^x=648$

By using logarithms it becomes easier to solve this question because of the properties they have

From the property of logarithms

$loga^x=xloga$

Take logarithms on both sides

$log62^x=log648$

$\Rightarrow xlog62=log648$

$\Rightarrow x=\frac{log648}{log62}$

$\Rightarrow x=1.56861$

$x=1.56861$

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What operation comes first?

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Suppose you want to place a shelf that is 30 1/3 inches long in the center of a wall that is 45 3/4 inches wide. About how fare

mrs_skeptik [129]

Answer:

7.71 inches far from each edge of the wall you should place the shelf.

Step-by-step explanation:

Given:

$\textrm{size of a shelf}=30\frac{1}{3} =\frac{91}{3}=30.33\ inches\\\textrm{size of a wall}=45\frac{3}{4} =\frac{183}{4}=45.75\ inches\\$

Let,

AB = distance between the edges or distance of wall.

ED = size of the shelf.

C is the centre of the wall.

To Find:

Distance from the edge of the wall to the shelf, when the shell is placed at the center of the wall.

AE = DB = ?

Solution:

As we need to place the shelf exactly in the center.

First we will calculate the distance from the center of the wall to the edge.

So the distance from the centre of the wall to the edge will be exactly half of the size of the wall.

$CB = \frac{1}{2}\times AB\\ =\frac{1}{2}\times 45.75\\\therefore CB=22.875\ inches$

now the distance from the centre to the end of the shelf will be exactly half of the size of the shelf.

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Now we want to calculate the distance from the edge of the wall to the shelf,that is the distance from the end of the shelf to the edge of the wall.

$AE=BD= BC-CD\\=22.875-15.165\\=7.71\ inches\\\therefore AE = BD = 7.71\ inches$

Therefore, 7.71 inches far from each edge of the wall you should place the shelf.

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15+ Points for Best Answers!!

Bogdan [553]

1) mesure of an arc= R.Ф, where R is the radius & Ф the angle <span>IN RADIAN

32</span>°===>8π/45 OR 0.5585, So mes of Arc CD = 6x0.5585 = 3.35 cm

2) DAC = 31° & CAD =27° , these 2 angles being adjacent I can write that

Angle(DAC +CAB=DCB) ==>Angle DCB =(31°+27°=58°)

To remember that any vertex of an angle on the circles, its sides intercept an arc which mesure is twice the angle,

Hence since mes Angle DCB=58°, that means the ARC intercepted, namely DB has a length of 2x 58 = 116°

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