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castortr0y [4]
3 years ago
12

College calculus: volume of a solid

Mathematics
1 answer:
Oliga [24]3 years ago
3 0
First, start by graphing the given region.
You should get a parabolic shape with min at (0,6) and end points intersecting with y=7.
When you rotate this around y=5, it will look like a vertical doughnut.
The cross-section of a doughnut is circular and looks like a washer.

Hence, we will use the 'washer method'
V = \pi  \int\limits^a_b {R^2 - r^2} \, dx
R is radius of outer ring from center which is y=5. The max value of region is y=7, giving a distance of 2 for our radius.
R = 2
'r' is radius of inner ring, this is point along curve f(x)=5+sec(x).
The distance from y=5 would be f(x) - 5.
r = sec(x)

V = \pi  \int\limits^{\pi/3}_{-\pi/3} {4 - sec^2 (x)} \, dx  \\  \\  \\ V = \pi |_{-\pi/3}^{\pi/3}(4x - tan x) \\  \\  \\ V = \frac{8\pi^2}{3} - 2\sqrt{3} \pi
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A bat and a ball cost one dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?
Aleks04 [339]
Set up an algebraic equation: b=cost of ball
1.10=1+b+b
1.10=1+2b
subtract 1 from both sides
.10=2b
divide by 2 on both sides
ball=5 cents
6 0
3 years ago
For a function p(x)= x^2-9, what is the inverse function for the domain [0, infinity\
kkurt [141]
An inverse function is a function that reverses another function, so we have a function called:

p(x)

Then, the inverse function will be as follows:

p^{-1}(x)

Given that y = p(x), we need to isolate x in terms of y:

y =  x^{2} -9
∴ y+9 = x^{2}

So:

x=+\sqrt{y+9} and x=-\sqrt{y+9}

therefore, exchanging variables x and y:

y=+\sqrt{x+9} and y=-\sqrt{x+9}
p^{-1}(x)=+\sqrt{x+9} and p^{-1}(x)=-\sqrt{x+9}

Which are the figures shown below.

7 0
3 years ago
Mikheal wanted to rewrite the conversion factor "1 yard = 0.914 meters" to create a conversion factor to convert meters to yards
Levart [38]
Divide both 1 yard and 0.914 meters by 1. 1x = 0.914y
Now, since you want 1 meter = "variable"
1 meter times 1 yard divided by 0.914 meters. 
1 meter = 1.094 yards
7 0
3 years ago
The price of a 5-minute phone call is $1.75. What is the price of a 12-minute phone call?
Ksju [112]

Answer:

$4.20

Step-by-step explanation:

you first do 1.75 divided by 5 which gives you .35

so you do .35 times 12 which gives you 4.2

6 0
3 years ago
H(x) = x2 1 k(x) = x – 2 (h k)(2) = (h – k)(3) = Evaluate 3h(2) 2k(3) =.
natima [27]

Quadratic equation is the equation in which only one variable is unknown. The highest power of the variable is 2.The value of the given functions are,

(h+k)(x)=5

(h-k)(x)=9

3h(2)+2k(3)=17

<h3>Given information-</h3>

The given function is,

h(x)=x^2+1

k(x)=x-2

<h3>Quadratic equation</h3>

Quadratic equation is the equation in which only one variable is unknown. The highest power of the variable is 2.

1) The value of the function (h+k)(2),

(h+k)(x)=h(x)+k(x)

(h+k)(x)=x^2+1+x-2

(h+k)(2)=2^2+1+2-2

(h+k)(x)=5

2)The value of the function (h-k)(3),

(h-k)(x)=h(x)-k(x)

(h-k)(x)=x^2+1-x+2

(h-k)(3)=3^2+1-3+2

(h-k)(x)=9

3) The value of the function 3h(2)+2k(3)

3h(x)+2k(x)=3x^2+3+2x-2\times 2

3h(2)+2k(3)=3\times2^2+3+2\times2-2\times 2

3h(2)+2k(3)=17

Hence the value of the given functions are,

(h+k)(x)=5

(h-k)(x)=9

3h(2)+2k(3)=17

Learn more about the quadratic equation here;

brainly.com/question/2263981

4 0
2 years ago
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