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Sergio039 [100]
2 years ago
8

Find the VOLUME of this composite solid.

Mathematics
1 answer:
Black_prince [1.1K]2 years ago
8 0

Answer:

  (294π +448) cm³ ≈ 1371.6 cm³

Step-by-step explanation:

The half-cylinder at the right end has a radius of 7 cm, as does the one on top. Together, the total length of these half-cylinders is 8 cm + 4cm = 12 cm. That is equivalent in volume to a whole cylinder of radius 7 cm that is 6 cm long.

The cylinder volume is ...

  V = πr²h = π(7 cm)²(6 cm) = 294π cm³

__

The cuboid underlying the top half-cylinder has dimensions 4 cm by 8 cm by 14 cm (twice the radius). So, its volume is ...

  V = LWH = (4 cm)(8 cm)(14 cm) = 448 cm³

Then the total volume of the composite figure is ...

  (294π +448) cm³ ≈ 1371.6 cm³

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Write an exponential function in the form y=ab^x that goes through points (0,12) and (3,6144)
skad [1K]

Given:

An exponential function goes through points (0,12) and (3,6144).

To find:

The exponential function.

Solution:

The general exponential function is:

y=ab^x           ...(i)

The function goes through point (0,12). Substituting x=0,y=12, we get

12=ab^0

12=a

The function goes through point (3,6144). Substituting a=12, x=3,y=6144 in the general exponential function, we get

6144=12b^3

\dfrac{6144}{12}=b^3

512=b^3

512^{\frac{1}{3}}=b

8=b

Putting a=12,b=8 in (i), we get

y=12(8)^x

Therefore, the required exponential function is y=12(8)^x.

3 0
2 years ago
PLEASE HELP!!! It would be amazing if you could show the steps!!
r-ruslan [8.4K]

Answer:

A:

|7-x|

B:

With absolute value equations, you can make two equations.

|7-x|-4\\xx>11

5 0
3 years ago
A spring has a natural length of 7 m. If a 4-N force is required to keep it stretched to a length of 11 m, how much work W is re
bezimeni [28]

Answer:

18 J is the work required to stretch a spring from 7 m to 13 m.

Step-by-step explanation:

The work done is defined to be the product of the force F and the distance d  that the object moves:

W=Fd

If F is measured in newtons and d<em> </em>in meters, then the unit for is a newton-meter, which is called a joule (J).

This definition work as long as the force is constant, but if the force is variable like in this case, we have that the work done is given by

W=\int\limits^b_a {f(x)} \, dx

Hooke’s Law states that the force required to maintain a spring stretched x    units beyond its natural length is proportional to

f(x)=kx

where k is a positive constant (called the spring constant).

To find how much work W is required to stretch it from 7 m to 13 m you must:

Step 1: Find the spring constant

We know that the spring has a natural length of 7 m and a 4 N force is required to keep it stretched to a length of 11 m. So, applying Hooke’s Law

4=k(11-7)\\\\\frac{k\left(11-7\right)}{4}=\frac{4}{4}\\\\k=1

Thus F=x

Step 2: Find the the work done in stretching the spring from 7 m to 13 m.

Recall that the natural length is 7 m, so when we stretch the spring from 7 m to 13 m, we are stretching it by 6 m beyond its natural length.

Work needed to stretch it by 6 m beyond its natural length

W=\int\limits^6_0 {x} \, dx \\\\\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1\\\\\left[\frac{x^{1+1}}{1+1}\right]^6_0\\\\\left[\frac{x^2}{2}\right]^6_0=18

18 J is the work required to stretch a spring from 7 m to 13 m.

5 0
2 years ago
Find the product, give an answer in standerd form <br> (3x2+6x+2)(2x2-8+1)
Aleks [24]
-18x-24 Hope this helps
8 0
2 years ago
What number should replace the question mark?
TiliK225 [7]

Answer:

Just a guess but I think 5

Step-by-step explanation:

The top right square on all boxes is the difference of the second box and the first box which equals the third box. This rule is applied to all of the other boxes so if I'm not wrong the question mark should be 5

3 0
3 years ago
Read 2 more answers
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