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3 years ago

If 2x⁴ + 2y⁴ + 2z⁴ = 144, what is the mean of x⁴, y⁴ and z⁴

Mathematics

1 answer:

Margarita [4]3 years ago

5 0

Answer: 24

Step-by-step explanation:

Given

$2x^4+2y^4+2z^4=144$

dividing whole equation by 2, we get

$\Rightarrow x^4+y^4+z^4=72$

Mean is given by the sum of the value of entities divided by the total no of entities

$\Rightarrow \text{Mean}=\dfrac{x^4+y^4+z^4}{3}\\\\\Rightarrow \text{Mean}=\dfrac{72}{3}\\\\\Rightarrow \text{Mean}=24$

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Find the roots of h(t) = (139kt)^2 − 69t + 80

Sonbull [250]

Answer:

The positive value of $k$ will result in exactly one real root is approximately 0.028.

Step-by-step explanation:

Let $h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ , roots are those values of $t$ so that $h(t) = 0$ . That is:

$19321\cdot k^{2}\cdot t^{2}-69\cdot t + 80=0$ (1)

Roots are determined analytically by the Quadratic Formula:

$t = \frac{69\pm \sqrt{4761-6182720\cdot k^{2} }}{38642}$

$t = \frac{69}{38642} \pm \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$

The smaller root is $t = \frac{69}{38642} - \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ , and the larger root is $t = \frac{69}{38642} + \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ .

$h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ has one real root when $\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} = 0$ . Then, we solve the discriminant for $k$ :

$\frac{80\cdot k^{2}}{19321} = \frac{4761}{1493204164}$

$k \approx \pm 0.028$

The positive value of $k$ will result in exactly one real root is approximately 0.028.

7 0

2 years ago

Delicious bakeshop sells a ratio of 3 powdered donuts to 5 glazed donuts. Which of the follow represents the ratio of powdered d

kolezko [41]

Answer:

21 to 35

Step-by-step explanation

I aced the test

3 0

3 years ago

Read 2 more answers

ava picks a number greater than 3 tens 6 ones. the number is less than 52. it has more than 6 ones. what could the. number be?

Svetlanka [38]

Any where between 37 and 51

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3 years ago

Brandon decided to make his own hand sanitize. To be effective and sanitizer

icang [17]

Answer:

Step-by-step explanation:

The water has to be 100% - 60% = 40%

100% represents both water alcohol (I think that's what you meant).

40% of 250 = 40/100 * 250 = 10000/100 = 100 mL

So 100 mL = water

150 mL = alcohol.

4 0

2 years ago

P=2L+2W<br><br>solve for L <br>do the entire equation

VashaNatasha [74]

$HEY THEIR!!$

Taking commen 2 in RHS
p = 2 (L+W )

Divide by 2 on both sides.
p/2 = L+W

Subtract W on both sides.
p/2 - W = L

or L = p/2- W

HOPE IT HELPS YOU

6 0

3 years ago

If 2x⁴ + 2y⁴ + 2z⁴ = 144, what is the mean of x⁴, y⁴ and z⁴​

If 2x⁴ + 2y⁴ + 2z⁴ = 144, what is the mean of x⁴, y⁴ and z⁴