Please help me with number 10 and 11!

Frank is having a raised rectangular platform built. He designed it so that the length of the platform is 4 feet longer than the

Anastaziya [24]

One system of equations would be
L = w+4
H = w-10
4H + 8(wL) = 1544
There is one viable solution; the width is 12, the length is 16, and the height is 2.

Using substitution with the system of equations, we have
4(w-10)+8(w(w+4))=1544
4w-40+8(w²+4w)=1544
4w-40+8w²+32w=1544

Combining like terms, we have
8w²+36w-40=1544

Factoring out a 4, we have
4(2w²+9w-10)=1544

Dividing both sides by 4 gives us
2w²+9w-10=386

Subtract 386 from both sides to get
2w²+9w-396=0

Using the quadratic formula, we have
$w=\frac{-9\pm \sqrt{9^2-4(2)(-396)}}{2(2)}
\\
\\=\frac{-9\pm \sqrt{81--3168}}{4}
\\
\\=\frac{-9\pm \sqrt{3249}}{4}=\frac{-9\pm 57}{4}
\\
\\=\frac{-9+57}{4}\text{ or }\frac{-9-57}{4}=\frac{48}{4}\text{ or }\frac{-66}{4}
\\
\\=12\text{ or }-16.5$

Since a negative width makes no sense, we know that w=12.

This means L=w+4=12+4=16 and H=w-10=12-10=2

5 0

4 years ago

Set up the integral that uses the method of cylindrical shells to find the volume V of the solid obtained by rotating the region

Ganezh [65]

Answer:

first exercise

V = 16 π

second exercise

V= 68π/15

Step-by-step explanation:

Initially, we have to plot the graph x = (y − 5)2 rotating around y = 3 and the limitation x = 4

<em>vide</em> picture 1

The rotation of x = (y − 5)2 intersecting the plane xy results in two graphs, which are represented by the graphs red and blue. The blue is function x = (y − 5)2. The red is the rotated cross section around y=3 of the previous graph. Naturally, the distance of "y" values of the rotated equation is the diameter of the rotation around y=3 and, by consequence, this new red equation is defined by x = (y − 1)2.

Now, we have two equations.

x = (y − 5)2

xm = (y − 1)2 (Rotated graph in red on the figure)

The volume limited by the two functions in the 1 → 5 interval on y axis represents a volume which has to be excluded from the volume of the 5 → 7 on y axis interval integration.

Having said that, we have two volumes to calculate, the volume to be excluded (Ve) and the volume of the interval 5 → 7 called as V. The difference of V - Ve is equal to the total volume Vt.

(1) Vt = V - Ve

Before start the calculation, we have to take in consideration that the volume of a cylindrical shell is defined by:

$(2) V=\int\limits^{y_{1} }_{y_{2}}{2*pi*y*f(y)} \, dy$

f(y) represents the radius of the infinitesimal cylinder.

Replacing (2) in (1), we have

$V= \int\limits^{5 }_{{3}}{2*pi*y*(y-5)^{2} } \, dy - \int\limits^{7 }_{{5}}{2*pi*y*(y-5)^{2} } \, dy$

V = 16 π

----

Second part

Initially, we have to plot the graph y = x2 and x = y2, the area intersected by both is rotated around y = −7. On the second image you can find the representation.

<em>vide</em> picture 2

As the previous exercise, the exclusion zone volume and the volume to be considered will be defined by the interval from x=0 and y=0, to the intersection of this two equations, when x=1 and y = 1.

The interval integration of equation y = x2 will define the exclusion zone. By the other hand, the same interval on the equation x=y2 will be considered.

Before start the calculation, we have to take in consideration that the volume of a cylindrical shell is defined by:

$(3) V=\int\limits^{x_{1} }_{x_{2}}{2*pi*x*f(x)} \, dx$

Notice that in the equation above, x and y are switched to facilitate the calculation. f(x) is the radius of the infinitesimal cylinder

Having this in mind, the infinitesimal radius of equation (3) is defined by f(x) + radius of the revolution, which is 7. The volume seeked is the volume defined by the y = x2 minus the volume defined by x=y2. As follows:

$V= \int\limits^{1 }_{{0}}{2*pi*x*(\sqrt{x} + 7) } \, dy - \int\limits^{1 }_{{0}}{2*pi*x*(x^{2}+7) } \, dy$

V= 68π/15

6 0

4 years ago

The tigers won 12 games last year.this year the tigers won 20 games. What is the percent increase in the number of games the tig

sergejj [24]

Its is 60% because 12/20 is 60%

4 0

4 years ago

Four friends are all working in summer jobs. Their names are LaTisha, Zack, Steve and Michelle. The jobs they have found this su

avanturin [10]

Answer:

LatTisha works as a Lifeguard

Zack works as a clerk at a grocery store

Steve works as a food server

Mitchel is a construction worker

Step-by-step explanation:

The parameters of the question are;

The names of the four friends are; LaTisha, Zack, Steve, and Michelle

The jobs found are; Food server, Lifeguard, Construction worker, and Clerk at a grocery store

1. The food server person likes his work

2. Zack and the lifeguard have known each other for years

3. Mitchel and the lifeguard are outside most of the time

4. LaTisha and the person working construction met on their job last summer

5. Neither Zack nor the food server worker worked last summer

We have;

Using known names,

Famale names are; LaTisha and Michelle

Male names are; Steve and Zack

Therefore

The food server worker is a guy, not Zack but likely Steve

Mitchel works outdoors, therefore, she works in the other outdoor employment which is construction

The remaining two occupations are;

Lifeguard and Clerk at a grocery store

Given that Zack is not the lifeguard, we have;

Zack is the clerk at a grocery store

LatTisha is the Lifeguard

6 0

3 years ago

There are 12 paperback mysteries on a shelf. This is 40% of the books on the shelf.

hjlf

Answer:

There are 30 books in the shelf.

Step-by-step explanation:

To solve this problem we can use a rule of three in such a way that 12 paperback mysteries are related to 40% of the books in the shelf in the same proportion that "x" total books are related to 100% of the books in the shelf. So we have:

12 -> 40%

x -> 100%

40*x = 12*100

40*x = 1200

x = 1200/40

x = 30 books

There are 30 books in the shelf.

6 0

4 years ago

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