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3 years ago

In which of the following units is acceleration expressed? A. Newtons B. Kilograms C. Foot-pounds D. Meters per second squared

Mathematics

1 answer:

ELEN [110]3 years ago

3 0

Answer:

D. Meters per second

Step-by-step explanation:

here's why the answer is D even though they arent the best explanations but none the less the answer is still right.

1. Newton = force

2.kilo = mass

3. foot-pound = force

4. Meters Per sec = speed/acceleration

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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,

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

7 0

3 years ago

6x-12=2x-6 Also,how do you check your answer?

taurus [48]

6x-12 = 2x-6

get like terms on the same side by adding/subtracting.

6x - 12 = 2x - 6
+ 12, -2x on both sides

6x - 2x = -6 + 12

4x = 6

divide all by 4

x = 1.5

to check your answer, plug in 1.5 for x and see if they are equal to one another.

6(1.5) - 12 = -3
2(1.5) - 6 = -3

7 0

3 years ago

What mixed number between is 1 and 1 1/2?

EastWind [94]

1 1/4

Pretty easy. For me at least.

6 0

3 years ago

Read 2 more answers

Pleas evelp im scared i fail

igomit [66]

Answer:

z=4

y=6

q=13

a=36

r=21

m=15

Step-by-step explanation:

hopefully this helps :)

5 0

3 years ago

A concession stand sold ice cream cones, salted pretzels, and tacos at a basketball game. Ice cream cones were sold for $3.00, s

WITCHER [35]

Answer:

51 salted pretzels were sold.

Step-by-step explanation:

Step 1: Write the data

Number of Ice cream cones sold: x

Cost of ice cream cones sold: 3x

Number of Salted pretzels sold: y

Cost of salted pretzels sold: 2.5y

Number of tacos sold: z

Cost of tacos sold: 2z

Step 1: Make equation 1

Total money made: $359.5

Money made from tacos: $70

Money made from ice cream cones and salted pretzels: 359.5-70 = $289.5

Equation 1:

3x + 2.5y = 289.5

Step 3: Make equation 2

Cost per tacos: $2

Total number of tacos sold: z

Money made from total tacos: $70

2z = 70

z = 35 tacos were sold

Total number of ice cream cones and salted pretzels sold: 140-35 = 105

Equation 2:

x + y = 105

Step 4: Find the unknown value by substitution

3x + 2.5y = 289.5

x + y = 105

Find x in terms of y from equation 2

x + y = 105

x = 105 - y

Substitute x in equation 1

3x + 2.5y = 289.5

3(105-y) + 2.5y = 289.5

315 - 3y + 2.5y = 289.5

0.5y = 25.5

y = 51

y represents the number of salted pretzels sold. Therefore, 51 salted pretzels were sold.

4 0

3 years ago