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3 years ago

What happens to the value of the expression m-10 as m decreases?

Mathematics

1 answer:

elena-14-01-66 [18.8K]3 years ago

6 0

Answer:

As m decreases value of the given expression $m^{-10}$ also decreases because the value of the given expression $m^{-10}$ depends only on the value of m.

Step-by-step explanation:

Given expression is $m^{-10}$

<h3>To check what happens to the value of the expression m-10 as m decreases :</h3>

From the given expression $m^{-10}$

we have that as m decreases value of the given expression $m^{-10}$ also decreases because the value of the given expression $m^{-10}$ depends only on the value of m

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3 years ago

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Simplify (Are all division)<br><br>2+4i<br>3i<br><br>3+2i<br>4+i<br><br>2i^11

Alla [95]

$We\ know:\ i=\sqrt{-1}\to i^2=-1$

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$\dfrac{3+2i}{4+i}=\dfrac{3+2i}{4+i}\cdot\dfrac{4-i}{4-i}=\dfrac{(3+2i)(4-i)}{4^2-i^2}\\\\=\dfrac{(3)(4)+(3)(-i)+(2i)(4)+(2i)(-i)}{16-(-1)}=\dfrac{12-3i+8i-2i^2}{16+1}\\\\=\dfrac{12+5i-2(-1)}{17}=\dfrac{12+5i+2}{17}=\dfrac{14+5i}{17}=\dfrac{14}{17}+\dfrac{5}{17}i$

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3 years ago

Santos is a lifeguard and spots a drowning child 50 meters along the shore and 60 meters from the shore to the child. Santos run

Amanda [17]

Answer:

Santos should run approximately 36.145 meters along the shore

Step-by-step explanation:

The given parameters are;

The distance along the shore of the child = 50 meters

The distance from the shore of the child = 60 meters

The rate at which Santos can run = 4 m/s

The rate he can swim = 0.9 m/s

Let 'x' represent the distance he runs along the shore

We have;

The time he spends running on the shore, t₁ = x/4

The time he spends swimming, t₂ = (√(60² + (50 - x)²)/0.9

The total time, T = t₁ + t₂ = x/4 + (√(60² + (50 - x)²)/0.9

To find the maximum, we have;

dT/dx = 0 = d(x/4 + (√(60² + (50 - x)²)/0.9)/dx = 1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0

1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0

Simplifying using a graphing calculator gives;

$\dfrac{x - 2000}{9} = \sqrt{x^2-100\cdot x+6,100}$

1519·x² - 151900·x + 3505900 = 0

x = (151900 ± √((-151900)² - 4×1519×3505900))/(2 × 1519)

x ≈ 63.86 m or x ≈ 36.145 m

We note that the distance from a point x = 63.83 meters and 36.145 meters from where Santos spots the girl to the location of the girl are the same

Therefore, Santos should run approximately 36.145 meters along the shore before jumping into to the water in order to save the child

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2 years ago

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Lunna [17]

Answer:

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Step-by-step explanation:

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x = 59°

Step-by-step explanation:

8 0

3 years ago