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Fantom [35]
3 years ago
8

Heather can rake and fill 6.8 bags of leaves each hour how many bags of leaves will heather rake and fill in 17 hours

Mathematics
1 answer:
Sergeu [11.5K]3 years ago
6 0

Answer:

115.6

Step-by-step explanation:

115.6, this would be your answer because 17 hours × 6.8 would get you 115.6

so 17 × 6.8 = 115.6

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An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per second. The pyramid, at the top, h
UNO [17]

Answer:

\frac{225}{16} cm/s

Step-by-step explanation:

We are given that

\frac{dV}{dt}=25cm^3/s

Side of base=4 cm

l=w=4 cm

Height,h=12 cm

We have to find the rate at which the water level rising when the water level is 4 cm.

Volume of pyramid=\frac{1}{3}lwh=\frac{1}{3}l^2h

\frac{l}{h}=\frac{4}{12}=\frac{1}{3}

l=\frac{1}{3}h

Substitute the value

V=\frac{1}{27}h^3

Differentiate w.r.t t

\frac{dV}{dt}=\frac{3}{27}h^2\frac{dh}{dt}

Substitute the values

25=\frac{1}{9}(4^2)\frac{dh}{dt}

\frac{dh}{dt}=\frac{25\times 9}{16}=\frac{225}{16} cm/s

5 0
3 years ago
The indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Th
Fantom [35]

Answer:

∫6x^5(x^6-2)\,dx = \frac{1}{2}(x^6-2)^2+C

Step-by-step explanation:

To find:

∫6x^5(x^6-2)\,dx

Solution:

Method of substitution:

Let x^6-2=t

Differentiate both sides with respect to t

6x^5\,dx=dt

[use (x^n)'=nx^{n-1}]

So,

∫6x^5(x^6-2)\,dx = ∫ t\,dt = \frac{t^2}{2}+C_1 where C_1 is a variable.

(Use ∫t^n\,dt=\frac{t^{n+1} }{n+1} )

Put t=x^6-2

∫6x^5(x^6-2)\,dx = \frac{1}{2}(x^6-2)^2+C_1

Use (a-b)^2=a^2+b^2-2ab

So,

∫6x^5(x^6-2)\,dx = \frac{1}{2}(x^6-2)^2+C_1=\frac{1}{2}(x^{12}+4-4x^6)+C_1=\frac{x^{12} }{2}-2x^6+2+C_1=\frac{x^{12} }{2}-2x^6+C

where C=2+C_1

Without using substitution:

∫6x^5(x^6-2)\,dx = ∫6x^{11}-12x^5\,dx = \frac{6x^{12} }{12}-\frac{12x^6}{6}+C=\frac{x^{12} }{2}-2x^6+C

So, same answer is obtained in both the cases.

7 0
2 years ago
The area of the shaded region in the shape to the right
larisa86 [58]
Oof this one is hard I think it’s 20 mm but I’m not sure
3 0
3 years ago
The surface area of a cube is 600 cm. what is its volume? 200 1000 600 800​
Studentka2010 [4]

Answer:

1000 cm^3

Step-by-step explanation:

First, Find the side length of the cube. The surface area is all the area on the surface of a 3-dimensional object. Since a square has 6 congruent faces the formula for surface area is 6s^2 where s is the side length. Since we know the surface area we can solve for the side length.

600=6s^2- DIvide by 6

100=s^2- Take the square root of both sides.

10=s

The volume of a cube is s^3.

10^3=V

1000=V

3 0
2 years ago
Tools -
rosijanka [135]

Answer:

48

Step-by-step explanation:

7 0
3 years ago
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