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SCORPION-xisa [38]
2 years ago
10

Work out the volume of this sphere.

Mathematics
1 answer:
navik [9.2K]2 years ago
3 0

Answer:

Volume of the sphere ( V ) = 1436.02 cm³

Step-by-step explanation:

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

Given that the radius of the sphere r = 7 cm

Volume of the sphere

                  V = \frac{4}{3} \pi r^{3}

                 V = \frac{4}{3} \pi (7)^{3}

                 V = \frac{4}{3} X3.14 X (7)^{3} = 1436.02

                 V = 1436.02 cm³

Volume of the sphere

                  V = 1436.02 cm³

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Answer:

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3 years ago
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a total of $9500 is invested, part at 10% simple interest and part at 9%. if the total annual return from the two investments is
Nutka1998 [239]

a total of $9500 is invested, part at 10% simple interest and part at 9%

if the total annual return from the two investments is $914.00

Amount invested = 9500

Total amount return means total yield = $914

Let x amount  is invested at 10% simple interest

Interest for first part =  10 % times x = 0.10x

Remaining part invested is 9500 -x

Interest for remaining amount = 9% (9500 -x) = 0.09(9500-x)

Total interest yield is 914. Now we frame an equation

0.10x + 0.09(9500-x) = 914

0.10x +855 - 0.09x = 914 (combine like terms)

0.01 x + 855 = 914 (subtract 855)

0.01x = 59 ( divide both sides by 0.01)

So x = 5900

$5900 is invested in 10% simple interest

9500 - 5900 = $3600 is invested in 9% simple interest


3 0
3 years ago
The diagonals of a rectangle are always
guapka [62]

Answer:

The diagonals of a rectangle are always congruent

7 0
2 years ago
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write the equation of a line that is perpendicular to the given line and that passes through the given point. y-4=5/2(x+3) ; (-7
faltersainse [42]
The gradient of the perpendicular line would be the negative reciprocal of the original line. Therefore the gradient of the perpendicular line would be -2/5x.
Since we know y=mx+c, ∴y=-2/5x+c. Sub in the x and y values of the given point and we get that c=26/5.

The perpendicular equation would be y=-2/5x+26/5.
I hope I got this right.
7 0
3 years ago
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A concession stand at an athletic event is trying to determine how much to sell cola and iced tea for in order to maximize reven
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Solution :

Demand for cola : 100 – 34x + 5y

Demand for cola : 50 + 3x – 16y

Therefore, total revenue :

x(100 – 34x + 5y) + y(50 + 3x – 16y)

R(x,y)  = $100x-34x^2+5xy+50y+3xy-16y^2$

$R(x,y) = 100x-34x^2+8xy+50y-16y^2$

In order to maximize the revenue, set

$R_x=0, \ \ \ R_y=0$

$R_x=\frac{dR }{dx} = 100-68x+8y$

$R_x=0$

$68x-8y=100$  .............(i)

$R_y=\frac{dR }{dx} = 50-32x+8y$

$R_y=0$

$8x-32y=-50$  .............(ii)

Solving (i) and (ii),

4 x (i)    ⇒       272x - 32y = 400

     (ii)   ⇒   (-<u>)     8x - 32y = -50   </u>

                        264x        = 450

∴   $x=\frac{450}{264}=\frac{75}{44}$

     $y=\frac{175}{88}$

So, x ≈  $ 1.70      and    y = $ 1.99

    R(1.70, 1.99) = $ 134.94

Thus, 1.70 dollars per cola

          1.99 dollars per iced ted to maximize the revenue.

Maximum revenue = $ 134.94

4 0
3 years ago
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