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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

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

rosijanka [135]

Answer:

48

Step-by-step explanation:

7 0

3 years ago