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3 years ago

Express this equation in logarithmic form.bx = n

Mathematics

2 answers:

Usimov [2.4K]3 years ago

7 0

It will be written like <span>log (base b) N = x . </span>

jeyben [28]3 years ago

5 0

Answer:

logarithmic form is x = $log_{b}(n)$ .

Step-by-step explanation:

Given : $b^{x} = n$ .

To find : Express this equation in logarithmic form.

Solution : We have given that $b^{x} = n$ .

By the Logarithmic rule : If $p^{q} = r$ in which case one writes q = $log_{p}(r)$ .

On comparing p = b , q =x , r = n .

Plugging the values

$b^{x} = n$ : x = $log_{b}(n)$ .

Therefore, logarithmic form is x = $log_{b}(n)$ .

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What is the length of the leg in a right triangle whose hypotenuse is 13 and other leg is 12.

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It is 5 because you have to do 12 squared minus 13 squared and then square root that which equals 5

3 0

3 years ago

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Find parametric equations and symmetric equations for the line. (Use the parameter t.) The line through (4, −5, 2) and parallel

Nataliya [291]

Answer:

Step-by-step explanation:

From the given information, the symmetric equations for the line pass through(4, -5, 2) i.e ( $x_o, y_o, z_o$ ) and are parallel to $\dfrac{x+5}{1} = \dfrac{y}{2}= \dfrac{z-3}{1}$

The parallel vector to the line i + zj+k = ai + bj + ck

Hence, the equation for the line is :

$x = x_o + at \\ \\ x = y_o + bt \\ \\ x = z_o + ct$

x = 4 + t

y = -5 + 2t

z = 2 + t

Thus, x, y, z = ( 4+t, -5+2t, 2+t )

The symmetric equation can now be as follows:

$\begin {vmatrix} x = 4+ t \\ \\ \dfrac{x-4}{1} = t \begin {vmatirx} \end {vmatrix}$ $\begin {vmatrix} y = - 5+2t \\ \\ \dfrac{y+5}{2} =t \end {vmatrix}$ $\begin {vmatrix} z =2+t \\ \\ \dfrac{z-2}{1} =t \end {vmatrix}$

∴

$\dfrac{x-4}{1}= \dfrac{y+5}{2}=\dfrac{z-2}{1}$

8 0

3 years ago

6 points

kodGreya [7K]

Answer:

$y=-2\,(x+3)^2-3$

Step-by-step explanation:

Notice that they are asking you to write the equation of the parabola in vertex form, that is using the coordinates of the vertex $(x_v,y_v)$ in the expression:

$y-y_v=a\,(x-x_v)^2\\y=a\,(x-x_v)^2+y_v$

we can start by directly replacing the given vertex coordinates (-3, -3) in the expression, and then using the extra info on the point the parabola goes through in order to find the parameter $a$ :

$y=a\,(x-x_v)^2+y_v\\y=a\,(x+3)^2+(-3)\\y=a\,(x+3)^2-3\\-5=a\,(-2+3)^2-3\\-5=a\,(1)-3\\a=-5+3\\a=-2$

So, now we can write the full expression for the parabola:

$y=a\,(x+3)^2-3\\y=-2\,(x+3)^2-3$

8 0

3 years ago

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nasty-shy [4]

Answer:

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Step-by-step explanation:

5 0

3 years ago

A function is expressed by the equation y=0.3x−6. For what value of the independent variable will the value of the function be e

Anna11 [10]

Answer:

0; 10; 20

Step-by-step explanation:

x is the independent variable

y is the dependent variable

y is dependent on x

a) For what value of the independent variable will the value of the function be equal to −6

y=0.3x−6

-6 = 0.3x-6

0=0.3x

x = 0

Therefore, if the independent variable is 0, the value of the function will be -6.

b) For what value of the independent variable will the value of the function be equal to −3

y=0.3x−6

-3 = 0.3x-6

0.3x = -3+6

0.3x = 3

x = 3/0.3

x = 10

Therefore, if the independent variable is 10, the value of the function will be -3.

c) For what value of the independent variable will the value of the function be equal to 0.

y=0.3x−6

0=0.3x-6

6 = 0.3x

x = 6/0.3

x = 20

Therefore, if the independent variable is 20, the value of the function will be 0.

7 0

3 years ago