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2 years ago

What is the volume of this cylinder?

Mathematics

1 answer:

tatiyna2 years ago

4 0

Answer:

The volume of the cylinder is 792

Step-by-step explanation:

3.14*6^2*7= 791.68 then when you round it up to the nearest whole number it's 792

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Write 8256 correct to 3 significant figures.

konstantin123 [22]

Answer:

8260 line over 6

Step-by-step explanation:

4 0

2 years ago

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

2 years ago

A patient who originally weighed 340 pounds lost 60 pounds. What percent of his original weight did he lose?

Semenov [28]

Answer:

82.35%

Step-by-step explanation:

60 divided by 340=0.17647058823

Multiply that by 100 and you get 17.647058823

Next, round and you get 17.65

100-17.65=82.35

4 0

2 years ago

Lindsay's soccer team won 4 games last month. This month they won 7. What is the percent increase of the amount of games that th

uysha [10]

Answer: 3%

Step-by-step explanation:

5 0

2 years ago

Find the number b such that the line y = b divides the region bounded by the curves y = 36x2 and y = 25 into two regions with eq

Gemiola [76]

Answer:

b = 15.75

Step-by-step explanation:

Lets find the interception points of the curves

36 x² = 25

x² = 25/36 = 0.69444

|x| = √(25/36) = 5/6

thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).

The area of the bounded region is given by the integral

$\int\limits^{5/6}_{-5/6} {(25-36 \, x^2)} \, dx = (25x - 12 \, x^3)\, |_{x=-5/6}^{x=5/6} = 25*5/6 - 12*(5/6)^3 - (25*(-5/6) - 12*(-5/6)^3) = 250/9$

The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.

$125/18 = \int\limits^{\sqrt{b}/6}_0 {(b - 36 \, x^2)} \, dx = (bx - 12 \, x^3)\, |_{x = 0}^{x=\sqrt{b}/6} = b^{1.5}/6 - b^{1.5}/18 = b^{1.5}/9$

125/18 = b^{1.5}/9

b = (62.5²)^{1/3} = 15.75

8 0

3 years ago