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3 years ago

What is the exact volume of the cone

Mathematics

1 answer:

Vitek1552 [10]3 years ago

7 0

Answer:

V≈418.88

Step-by-step explanation:

Volume formula: V=πr^2h /3

R= radius

H= height

R= 5 ft

H= 16 ft

Formula= V=π5^2(16/3)

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Steve is turning half his backyard into a chicken fan. His backyard is a 24 m x 45 m rectangle. He wants to put a chicken wire f

Phoenix [80]

Answer:

51 meters

Step-by-step explanation:

Steve is turning half his backyard into a chicken fan. His backyard is a 24 m x 45 m rectangle. He wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner. How many meters of fencing will Steve need?

We are to find the meters of fencing for the diagonal.

We solve the question using Pythagoras Theorem

= c² = a² + b²

Where

c = Diagonal

a = Width

b =Length

Diagonal² = Width² + Length ²

Hence:

Diagonal ² = 45² + 24²

Diagonal = √45² + 24²

Diagonal = √(2601)

Diagonal = 51 m

Therefore, the meters of fencing for the diagonal that Steve would be needing = 51 meters

7 0

3 years ago

10. An arithmetic sequence has this recursive formula. What is the explicit formula?

Mrrafil [7]

Answer:

$a_{n}=45-3n$

Step-by-step explanation:

Method 1:

Arithmetic sequence is in the form

$a_{n} =a_{1} +(n-1)d\\$

d is the common difference, can be found by:

$d=a_{n}-a_{n-1}=-3$

Subtituting the $a_{1}$ and $d$

You get:

$a_{n}=42+(-3)(n-1)=45-3n$

Method 2 (Mathematical induction):

Assume it is in form $a_{n}=45-3n$

Base step: $a_{1} =45-3(1)=42$

Inducive hypophesis: $a_{n}=45-3n$

GIven: $a_{n+1} =a_{n}-3$

$a_{n+1}=45-3n-3=45-3(n+1)$

Proved by mathematical induction

$a_{n}=45-3n$

5 0

3 years ago

In a triangle, one of the angle measures 70°

Tanya [424]

Answer:

the two angles are 55° each

Step-by-step explanation:

Let the two equal angles be y each

Therefore,

70° + y + y = 180°

Collect like terms

2y = 180 — 70

2y = 110

Divide both side by the coefficient of y i.e 2

y = 110/2

y = 55°

Therefore, the two angles are 55° each

4 0

3 years ago

Can any one help me in this please any math genius

andriy [413]

It is 10 to 1 significant figures

3 0

2 years ago

Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)

DiKsa [7]

Answer:

The standard equation of the sphere is $(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Let the first endpoint be represented as $(x_{1}, y_{1}, z_{1})$ and the second endpoint be $(x_{2}, y_{2}, z_{2})$ .

Hence,

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Midpoint = $(\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})$

Midpoint = $(\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\$

Midpoint = $(5, 5, 4)$

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

$d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }$

$d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}$

$d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}$

$d = \sqrt{16 +196 + 0$

$d =\sqrt{212}$

$d = 2\sqrt{53}$

This is the diameter

To find the radius, r

From $Radius = \frac{Diameter}{2}$

$Radius = \frac{2\sqrt{53} }{2}$

∴ $Radius = \sqrt{53}$

r = $\sqrt{53}$

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is $(5, 5, 4)$

Radius of the sphere is $\sqrt{53}$

The equation of a sphere of radius r and center $(h,k,l)$ is given by

$(x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}$

Hence, the equation of the sphere of radius $\sqrt{53}$ and center $(5, 5, 4)$ is

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}$

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

This is the standard equation of the sphere

6 0

3 years ago