The graph of the logarithmic function f(x) = loga(x) passes through the points and . The graph lies the y-axis.

2 answers:

8 0

The question is incomplete. But this explanation will help you very much.

1) Regarding the function $log_ax$ , its graph always passes through the points (1,0) and (a,1).

That is due to the properties of logarithm function:

a) $log_a1=0$

b) $log_aa=1$

That in turn is due to the properties of the exponential functions.

a^0 = 1 and a^1 = a

2) Regarding the y-axis.

The function $log_ax$ will never touch the y-axis, because the logaritm of zero is not defined. So the graph lies to the righ of the y-axis (i.e. the domain of the function is x > 0)

lesya692 [45]2 years ago

3 0

Answer:

(1, 0)

Step-by-step explanation:

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What is the proof the formula for cos(A+B)=cosAcosB-sinAsinB?

brilliants [131]

Given data, cos(A - B) = cosAcosB + sinAsinB
let, A=60' and B=30' ( here the ' sign bears degree) 
L.H.S = cos(A - B) 
=cos (60'-30) ( using value of A and B ) 
=cos30' 
= sqrt3/2 
R.H.S= cosAcosB + sinAsinB 
=cos60' cos30' + sin60' sin30' 
= 1/2* sqrt3/2+ sqrt3/2*1/2 
= sqrt3/4 + sqrt3/4 
=2 sqrt3/4 
= sqrt3/2 
so L.H.S =R.H.S or cos(A - B) = cosAcosB + sinAsinB

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2 years ago

Given directed line segment QS , find the coordinates of R

Degger [83]

Answer:

The answer is below

Step-by-step explanation:

The question is not complete, what are the coordinates of point Q and R. But I would show how to solve this.

The location of a point O(x, y) which divides line segment AB in the ratio a:b with point A at ( $x_1,y_1$ ) and B( $x_2,y_2$ ) is given by the formula:

$x=\frac{a}{a+b}(x_2-x_1)+x_1\\ \\y=\frac{a}{a+b}(y_2-y_1)+y_1$

If point Q is at ( $x_1,y_1$ ) and S at ( $x_2,y_2$ ) and R(x, y) divides QS in the ratio QR to RS is 3:5, The coordinates of R is:

$x=\frac{3}{3+5}(x_2-x_1)+x_1=\frac{3}{8}(x_2-x_1)+x_1\\ \\y=\frac{3}{3+5}(y_2-y_1)+y_1=\frac{3}{8}(y_2-y_1)+y_1$

Let us assume Q(−9,4) and S(7,−4)

$x=\frac{3}{8}(7-(-9))+(-9)=\frac{3}{8}(16)-9=-3\\\\y=\frac{3}{8}(-4-4)+4=\frac{3}{8}(-8)+4=1$

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2 years ago

How many intersections are there of the graphs of the equations below? x + 5y = 6 3x + 30y = 36 none one two infinitely many Mar

denpristay [2]

I believe the answer would be the second option. The equations given above when graph would intersect only once with each other. They intersect at only point (0,6/5). These are the values of x and y that will agree to the equation. Two equations in a set will always intersect at only one point.

5 0

1 year ago

Read 2 more answers

Which equation can be used to find the length of Line segment A C? Triangle A B C is shown. Angle A C B is 90 degrees and angle

taurus [48]

Answer:

AC = 10sin(40°)

Explanation:

The diagram representing the question is shown in the attached image

Since the given triangle is a right-angled triangle, we can apply the special trig functions

These functions are as follows:

sin(θ) = opposite / hypotenuse