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adoni [48]
3 years ago
11

3. find the domain and range of a) 3x-2y+7=0i think in y-intercept form it is y=3/2x + 7/2

Mathematics
1 answer:
bekas [8.4K]3 years ago
3 0
3x-2y+7=0\\\\The\ slope-intercept\ form:\\\\2y=3x+7\ \ \ \ \ /:2\\\\y=\frac{3}{2}x+\frac{7}{2}\\\\The\ domain:x\in\mathbb{R}\\\\The\ range:y\in\mathbb{R}

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State the missing reasons in this proof.<br><br><br> a. <br> b. <br> c.
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verify that the fucntion satisfies the three hypotheses of rolles theorem on the given interval . then find all numbers c that s
Ghella [55]

The roots of the polynomial <span><span>x^3 </span>− 2<span>x^2 </span>− 4x + 2</span> are:

<span><span>x1 </span>= 0.42801</span>

<span><span>x2 </span>= −1.51414</span>

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f'(x) = 3x^2 - 4x - 4

so we have:

3x^2 - 4x - 4 = 0

<span>x = ( 4 +- </span><span>√(16 + 48) </span>)/6

x_1 = -4/6 = -0.66

x_ 2 = 2

According to Rolle's theorem, we have one point in between:

x1 = 0.42801 and x2 = −1.51414

where f'(x) = 0, and that is <span>x_1 = -0.66</span>

so we see that Rolle's theorem holds in our function.

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What is the square root of negative four
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The work of a student to find the dimensions of a rectangle of area 6 + 8x and width 2 is shown below:
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A closed can, in a shape of a circular, is to contain 500cm^3 of liquid when full. The cylinder, radius r cm and height h cm, is
Gemiola [76]
To express the height as a function of the volume and the radius, we are going to use the volume formula for a cylinder: V= \pi r^2h
where
V is the volume 
r is the radius 
h is the height 

We know for our problem that the cylindrical can is to contain 500cm^3 when full, so the volume of our cylinder is 500cm^3. In other words: V=500cm^3. We also know that the radius is r cm and height is h cm, so r=rcm and h=hcm. Lets replace the values in our formula:
V= \pi r^2h
500cm^3= \pi (rcm^2)(hcm)
500cm^3=h \pi r^2cm^3
h= \frac{500cm^3}{ \pi r^2cm^3}
h= \frac{500}{ \pi r^2}

Next, we are going to use the formula for the area of a cylinder: A=2 \pi rh+2 \pi r^2
where
A is the area 
r is the radius 
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We know from our previous calculation that h= \frac{500}{ \pi r^2}, so lets replace that value in our area formula:
A=2 \pi rh+2 \pi r^2
A=2 \pi r(\frac{500}{ \pi r^2})+2 \pi r^2
A= \frac{1000}{r} +2 \pi r^2
By the commutative property of addition, we can conclude that:
A=2 \pi r^2+\frac{1000}{r}
7 0
3 years ago
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