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2 years ago

50 POINTS!!!

Mathematics

1 answer:

r-ruslan [8.4K]2 years ago

8 0

housing: 900/4500 = 0.2 = 20%

transportation: 650 / 4500 = 0.14 = 14%

utilities: 120/4500 = 0.026 = 2.6% ( round to 3% maybe)

food: 475/4500 = 0.105 = 10.5% (round to 11% maybe)

savings: 1600 / 4500 = 0.355 = 35.5% (round to 36% maybe)

Student Loan: 270 / 4500 = 0.06 = 6%

Other expenses: 485 / 4500 = 0.107 = 10.7% (round to 11% maybe)

You didn't say if they needed to be rounded so I gave you the options on the ones that may need it.

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A tank has the shape of a surface generated by revolving the parabolic segment y = x2 for 0 ≤ x ≤ 3 about the y-axis (measuremen

Darina [25.2K]

Answer:

$100\pi\int\limits^9_0 {(\sqrt y)^2(14-y)} \, dy$ ft-lbs.

Step-by-step explanation:

Given:

The shape of the tank is obtained by revolving $y=x^2$ about y axis in the interval $0\leq x\leq 3$ .

Density of the fluid in the tank, $D=100\ lbs/ft^3$

Let the initial height of the fluid be 'y' feet from the bottom.

The bottom of the tank is, $y(0)=0^2=0$

Now, the height has to be raised to a height 5 feet above the top of the tank.

The height of top of the tank is obtained by plugging in $x=3$ in the parabolic equation . This gives,

$H=3^2=9\ ft$

So, the height of top of tank is, $y(3)=H=9\ ft$

Now, 5 ft above 'H' means $H+5=9+5=14$

Therefore, the increase in height of the top surface of the fluid in the tank is given as:

$\Delta y=(14-y)$ ft

Now, area of cross section of the tank is given as:

$A(y)=\pi r^2\\r\to radius\ of\ the\ cross\ section$

Radius is the distance of a point on the parabola from the y axis. This is nothing but the x-coordinate of the point.

We have, $y=x^2$

So, $x=\sqrt y$

Therefore, radius, $r=\sqrt y$

Now, area of cross section is, $A(y)=\pi (\sqrt y)^2$

Work done in pumping the contents to 5 feet above is given as:

$W=D\int\limits^{y(3)}_{y(0)} {A(y)(\Delta y)} \, dy$

Plug in all the values. This gives,

$W=100\int\limits^9_0 {\pi (\sqrt y)^2(14-y)} \, dy\\\\W=100\pi\int\limits^9_0 { (\sqrt y)^2(14-y)} \, dy\textrm{ ft-lbs}$

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2 years ago

Select the values that are solutions of the inequality X 3<4.

Rina8888 [55]

Answer:

x=12 if you divide you'll get 4

8 0

3 years ago

Simplify the expression (0.4)^3

mafiozo [28]

0.4^3 = 0.4 · 0.4 · 0.4 = 0.064

6 0

3 years ago

Read 2 more answers

The area of a triangle is 15x^4+3x^3+4x^2-x-3 square meters. The length of the base of the triangle is 6x^2-2 meters. What is th

MArishka [77]

Answer:

The height of the triangle is: $H = (5x^2 + x +3)$

Step-by-step explanation:

Here, the area the triangle is given as: $15x^4 + 3x^3 + 4x^2 - x - 3$

Also, base of the triangle = $(6x^2 -2)$

Let us assume the height of the triangle = H units

Now, AREA of TRIANGLE = $\frac{1}{2} \times B \times H$

$\implies (15x^4+3x^3+4x^2-x-3 ) = \frac{1}{2} \times ( 6x^2-2) \times H\\\implies H =\frac{ (15x^4+3x^3+4x^2-x-3 )}{(3x^2-1)}$

Solving by LONG DIVISION, we get:

$H = (5x^2 + x +3)$

Hence, the height of the triangle is: $H = (5x^2 + x +3)$

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3 years ago

27 x and 45y Find the GCF of the terms: b. 3 a. 1 d. 9xy b. 9

Luden [163]

Answer:

d. 9

Step-by-step explanation:

it can't be the rest... ion even know how to explain it.

3 0

3 years ago