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2 years ago

Find the volume of the following figure. Round the answer to the nearest hundredth if necessary.

Mathematics

1 answer:

telo118 [61]2 years ago

8 0

Answer:

48 yd^3.

Step-by-step explanation:

Volume of a pyramid = 1/3 * height * area of the base.

The area of the triangular base = 1/2 * height * base = 1/2*6*8

= 24 yd^2.

So the volume of the figure

= 1/3 * 6 * 24

= 2*24

= 48 yd^3.

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On a cold February morning, the radiator fluid in Stanley’s car is -18 degrees When the engine is running, the temperature goes

Rasek [7]

Remark

This is an arithmetic progression. You have the first and last terms and the difference.

Givens

a = - 18

L = 60

d = 4.5

Equation

L = a + (n - 1)d

Solve

60 = -18 + (n - 1) * 4.5 Add 18 to both side

60 + 18 = (n - 1) * 4.5

78 = (n - 1) * 4.5 Divide both sides by 4.5

78/4.5 = n - 1

17.3333 = n - 1 Add 1 to both sides.

18.3333 = n

Conclusion

It will that 18 1/3 or 18.33333 minutes to get the from -18 to 60 degrees.

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3 years ago

Whats (14-7) multiplied by (40-32) plz gib right answer!

jenyasd209 [6]

Answer:

Step-by-step explanation:

(14-7) x (40-32) = 7 x 8

= 56

Hope you understood :)

6 0

2 years ago

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Solve by factoring: x^4-12x^2= 64

USPshnik [31]

The final solution is all the values that make (x+4)(x−4)(x2+4)=0x+4⁢x-4⁢x2+4=0 true.x=−4,4,2i,−2i

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3 years ago

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Rationalise the denominator of: 1/(√3 + √5 - √2)

Paul [167]

Step-by-step explanation:

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm :\longmapsto\:\dfrac{1}{ \sqrt{3} + \sqrt{5} - \sqrt{2} }$

can be re-arranged as

$\rm :\longmapsto\:\dfrac{1}{ \sqrt{3} - \sqrt{2} + \sqrt{5} }$

$\rm \: = \: \dfrac{1}{( \sqrt{3} - \sqrt{2} ) + \sqrt{5} }$

On rationalizing the denominator, we get

$\rm \: = \: \dfrac{1}{( \sqrt{3} - \sqrt{2} ) + \sqrt{5} } \times \dfrac{( \sqrt{3} - \sqrt{2} ) - \sqrt{5} }{( \sqrt{3} - \sqrt{2} ) - \sqrt{5} }$

We know,

$\rm :\longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}$

So, using this, we get

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{ {( \sqrt{3} - \sqrt{2} )}^{2} - {( \sqrt{5}) }^{2} }$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{3 + 2 - 2 \sqrt{6} - 5}$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{5 - 2 \sqrt{6} - 5}$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{ - 2 \sqrt{6}}$

$\rm \: = \: \dfrac{ - ( - \sqrt{3} + \sqrt{2} + \sqrt{5}) }{ - 2 \sqrt{6}}$

$\rm \: = \: \dfrac{- \sqrt{3} + \sqrt{2} + \sqrt{5}}{2 \sqrt{6}}$

On rationalizing the denominator, we get

$\rm \: = \: \dfrac{- \sqrt{3} + \sqrt{2} + \sqrt{5}}{2 \sqrt{6}} \times \dfrac{ \sqrt{6} }{ \sqrt{6} }$

$\rm \: = \: \dfrac{- \sqrt{18} + \sqrt{12} + \sqrt{30}}{2 \times 6}$

$\rm \: = \: \dfrac{- \sqrt{3 \times 3 \times 2} + \sqrt{2 \times 2 \times 3} + \sqrt{30}}{12}$

$\rm \: = \: \dfrac{- 3\sqrt{2} + 2 \sqrt{3} + \sqrt{30}}{12}$

Hence,

$\boxed{\tt{ \rm \dfrac{1}{ \sqrt{3} + \sqrt{5} - \sqrt{2} } =\dfrac{- \sqrt{3 \times 3 \times 2} + \sqrt{2 \times 2 \times 3} + \sqrt{30}}{12}}}$

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<h3>More Identities to know:</h3>

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$\pink{\boxed{\tt{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}}}$

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3 years ago

Solve for x. 2x^2-4x=0 A. 0, -4 B. 0, -2 C. 0, 2 D. 2, 4

madam [21]

Step-by-step explanation:

2x²-4x=0

2x²=4x

2x=4

x=2

option C

7 0

3 years ago

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