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Rasek [7]
3 years ago
11

For any linear function f(x) = mx + b, when does kf(x) = f(kx)?

Mathematics
1 answer:
iogann1982 [59]3 years ago
4 0

Only when <em>b</em> = 0 or <em>k</em> = 1<em>.</em>

If <em>f(x)</em> = <em>mx</em> + <em>b</em>, then

<em>f</em> (<em>kx</em>) = <em>m</em> (<em>kx</em>) + <em>b</em> = <em>mkx</em> + <em>b</em>

while

<em>k</em> <em>f(x)</em> = <em>k</em> (<em>mx</em> + <em>b</em>) = <em>kmx</em> + <em>kb</em>

The two expression are identical only if

<em>kb</em> = <em>b</em>   ===>   <em>kb</em> - <em>b</em> = 0   ===>   <em>b</em> (<em>k</em> - 1) = 0   ===>   <em>b</em> = 0 or <em>k</em> = 1

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A sphere with radius 16 m is cut by a plane that is 9 m below its center. what is the best approximation of the area of the circ
alexdok [17]
The complete question in the attached figure

we know that
the equation of a sphere is
(x-h)²+(y-k)²+(z-l)²=r²

<span>let's assume that the center of the sphere is at the origin
</span>so
(h,k,l)-------> (0,0,0)
for r=16 m
(x-h)²+(y-k)²+(z-l)²=r²-------->  (x)²+(y)²+(z)²=16²

for z=9 m
(x)²+(y)²+(9)²=16²--------> (x)²+(y)²=256-81--------> (x)²+(y)²=175
the radius of the circle is r=√175 m
so the area of the circle A=pi*r²-----> A=pi*175-----> A=549.5 m²

the answer is 
the area of the circle is 549.5 m²

6 0
3 years ago
Suppose △JMN≅△KQR .
zvonat [6]
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4 0
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Solve the following:<br>a) 2(5x – 3) = 24<br>b) 5(2x + 1) = 50​
likoan [24]

Answer:

x = 3 and x = \frac{9}{2}

Step-by-step explanation:

(a)

2(5x - 3) = 24 ( divide both sides by 2 )

5x - 3 = 12 ( add 3 to both sides )

5x = 15 ( divide both sides by 5 )

x = 3

(b)

5(2x + 1) = 50 ( divide both sides by 5 )

2x + 1 = 10 ( subtract 1 from both sides )

2x = 9 ( divide both sides by 2 )

x = \frac{9}{2}

3 0
3 years ago
The equation of the line that is parallel<br> to 4x+2 and passing through (5,15)
Mila [183]

Answer:

y=4x-5.

Step-by-step explanation:

slop-interception form of the required line is y=kx+b, where k - slop, b - intercept;

1) to find value of k:

if the required line is parallel to the given line, then slop of the given line = slop of the required line, it means k=4 and the required line is y=4x+b;

2) to find the value of 'b':

if to substitute the given coordinates into the equation of the given line, then:

15=4*5+b, b= -5.

3) finally, y=4x-5

8 0
2 years ago
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