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3 years ago

8

The volume of the ice cream cone in the diagram is 12 cubic centimeters. 9 centimeters is the height of the ice cream cone, what

is the diameter of the opening of the cone?

2 answers:

algol [13]3 years ago

8 0

Answer:

Diameter = 8

Step-by-step explanation:

Cone volume formula = (pi)*r^2*h/3

V = (12pi)*r^2*(9/3)

V = (12pi)*r^2*3

12/3 = 4

V =(pi)*4^2*h/3

4*2 = 8

The Diameter is 8

Vlad1618 [11]3 years ago

4 0

Answer:

2.2568m

Step-by-step explanation:

volume= 12 π cm³

or, 1/3 πr²h = 12π cm³

or, πr² × 9 = 12π ×3

or, r²= 36π/9π

or, r²= 4

or, r= 2

d = 2r = 2× 2= 4 cm

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3 years ago

Evaluate the indefinite integral. (Use C for the constant of integration.) <br> ex 5 ex dx.

melisa1 [442]

Answer:

$5 e^{x} +C$

where C is constant of integration

Step-by-step explanation:

<u><em>Explanation:-</em></u>

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Now integrating with respective to 'x' , we get

I = $\int\limits {5 e^{x} } \, d x$

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3 years ago

Linear system please help 60 points * please please please help will give brainlist

bearhunter [10]

Answer:

1. a. b = - 8

b. x = 8

c. x = 11

d. x = 5

2. 12 soccer balls and 8 basketballs can be purchased.

Step by step explanation

a. $- 14 + 6b + 7 - 2b = 1 + 5b$

Calculate the sum

$- 7 + 6b - 2b = 1 + 5b$

Collect like terms

$7 + 4b = 1 + 5b$

Move variable to L.H.S and change it's sign

Similarly, Move constant to R.H.S and change its sign

$4b - 5b = 1 + 7$

Collect like terms

$- b = 8$

Change the signs on both sides of the equation

$b = - 8$

-----------------------------------------------------------------

b. $\frac{5x + 10}{ - 6} = - 5$

Apply cross product property

$5x + 10 = - 5 \times ( - 6)$

Multiply the numbers

$5x + 10 = 30$

Move constant to R.H.S and change its sign

$5x = 30 - 10$

Calculate the difference

$5x = 20$

Divide both sides of the equation by 5

$\frac{5x}{5} = \frac{20}{5}$

Calculate

$x = 4$

----------------------------------------------------------------

c. $- 15 = \frac{ - 8x - 17}{7}$

Apply cross product property

$- 15 \times 7 = - 8x - 17$

Multiply the numbers

$- 105 = - 8x - 17$

Swap the sides of the equation

$- 8x - 17 = - 105$

Move constant to R.H.S and change its sign

$- 8x = - 105 + 17$

Calculate

$- 8x = - 88$

Change the signs on both sides of the equation

$8x = 88$

Divide both sides of the equation by 8

$\frac{8x}{8} = \frac{88}{8}$

Calculate

$x = 11$

------------------------------------------------------------------

D. $5 = 6x + 5(x - 10)$

Distribute 5 through the parentheses

$5 = 6x + 5x - 50$

Collect like terms

$5 = 11x - 50$

Swap both sides of the equation

$11x - 50 = 5$

Move constant to R.H.S and change its sign

$11x = 5 + 50$

Calculate the sum

$11x = 55$

Divide both sides of the equation by 11

$\frac{11x}{11} = \frac{55}{11}$

Calculate

$x = 5$

------------------------------------------------------------------

2.

Solution,

No.of students in soccer = x

No.of students in basketball = y

Total no.of students = 20

i.e x + y = 20 → equation ( i )

Cost of soccer ball = $ 7

Cost of basketball = $ 10

Total budget = $ 164

i.e 7x + 10 y = 165 → equation ( ii )

In equation ( i ),

x + y = 20

Move 'y' to R.H.S and change its sign

x = 20 - y

Put the value of x in equation ( i )

$7(20 - y) + 10y = 164$

$140 - 7y + 10y = 164$

$3y = 164 - 140$

$3y = 24$

$y = \frac{24}{3}$

$y = 8$

Now, put the value of y in equation ( i ) ,

x + y = 20

$x + 8 = 20$

$x = 20 - 8$

$x = 12$

Hence, 12 soccer balls and 8 basketballs can be purchased.

Hope this helps...

Best regards!!

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