I REALLY NEED HELP

Mathematics

1 answer:

garri49 [273]3 years ago

4 0

Look at the picture.

1.
$y=mx+b\\\\m=\dfrac{9}{3}=3\\\\b=4\\\\\boxed{f(x)=3x+4}$

2.
$f(x)=-2x+3\\\\for\ x=-2\to f(-2)=-2\cdot(-2)+3=4+3=7\to(-2;\ 7)\\for\ x=-1\to f(-1)=-2\cdot(-1)+3=2+3=5\to(-1;\ 5)\\for\ x=0\to f(0)=-2\cdot0+3=3\to(0;\ 3)\\for\ x=1\to f(1)=-2\cdot1+3=-2+3=1\to(1;\ 1)$

3.
$y=mx+b\\\\m=\dfrac{3}{6}=\dfrac{1}{2}=0.5\\\\b=-3\\\\\boxed{f(x)=0.5x-3}$
$for\ x=-6\to f(-6)=-6\\for\ x=-2\to f(-2)=-4\\for\ x=0\to f(0)=-3\\for\ x=6\to f(6)=0$

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6. Sketch the region enclosed by the graphs of x =0, 6y-5x=0 and x+3y=21. Find the area

kow [346]

We can see that revolving the region formed by intersecting 3 lines, we will get 2 cones that are connected their bases.
Volume of the cone V=1/3 *πr²*h

1) small cone has r=5, and h=5
Volume small cone V1= 1/3 *π*5²*5 = 5³/3 *π
2) large cone has r=5, and h=21-6=15, h=15
Volume large cone V2= 1/3 *π*5²*15 = 5³*π
3) whole volume
5³/3 *π + 5³*π=5³π(1/3+1)=((5³*4)/3)π=(500/3)π≈166.7π≈523.6

Area
we see 2 right triangles,
Area of the triangle=1/2*b*h, where b -base, h -height
1) small one, b=5, h=5
A1=(1/2)*5*5=25/2
2)large one, b=5, h=15
A2=(1/2)*5*15=75/2
3) whole area=A1+A2=25/2+75/2=100/2=50