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3 years ago

If x = √3 − √2 , find the value of ( −1/x)root 2

Mathematics

1 answer:

makkiz [27]3 years ago

8 0

hello

$\dfrac{-1}{x}\sqrt{2}=\dfrac{-\sqrt{2}}{\sqrt{3}-\sqrt{2}}=\dfrac{-\sqrt{2}(\sqrt{3}+\sqrt{2})}{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2})}\\\\=\dfrac{-\sqrt{2}(\sqrt{3}+\sqrt{2})}{3-2}\\\\=-\sqrt{6}-2$

hope this helps

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A rectangular garden of area 208 square feet is to be surrounded on three sides by a brick wall costing $ 8 per foot and on one

vova2212 [387]

Answer:

Therefore the dimensions of the garden is 16 feet by 13 feet.

Step-by-step explanation:

Let the length of the garden be x and the width of the garden be y.

Given that the area of the rectangular garden is 208 square feet.

Therefore,

xy =208

$\Rightarrow y = \frac{208}{x}$

Again given that,

The garden is to be surrounded on three sides by a brick wall costing $ 8 per feet and the remaining sides by a fence costing $5 per feet.

The perimeter of the rectangle is = 2(length+ breadth)

= 2(x+y)

=2x+2y

The total cost of fence

$C= [ (2x\times 8)+(y\times 8)+(y\times 5)]$

= (16x+ 8y +5y)

$=16x+13y$

$=16x+\frac{13\times 208}{x}$

$=16x +\frac{2704}{x}$

To find the maximum or minimum point, we need to find out $\frac{dC}{dx}$ and set $\frac{dC}{dx}$ =0.

$\frac{dC}{dx}=16 -\frac{2704}{x^2}$

Then

$16 -\frac{2704}{x^2}=0$

$\Rightarrow \frac{2704}{x^2}=16$

$\Rightarrow x^2 =\frac{2704}{16}$

$\Rightarrow x=\pm \sqrt{169}$

$\Rightarrow x=\pm 13$

Again $\frac{d^2C}{dx}= \frac {8112}{x^3}$

$\therefore\left| \frac{d^2C}{dx}\right |_{x=13}= \frac {8112}{13^3}>0$

Therefore at x= 13 , the cost is minimum.

Therefore x = 13 feet.

The other side of the garden is $=\frac{208}{13}$ feet = 16 feet.

Therefore the dimensions of the garden is 16 feet by 13 feet.

4 0

3 years ago

What is the height of the tree to the nearest tenth of a foot?

Ugo [173]

Answer:

The height of the tree is approximately 21.4 feet

Step-by-step explanation:

We list out the question parameters first as follows;

The distance from the base of the tree where the angle of elevation is measured, d = 10 feet

The angle of elevation to the top of the tree from 10 feet from the base, θ = 65°

Let 'h' represent the height of the tree, then we have;

The line formed by the angle 65° angle, the height of the tree, 'h', and the distance 'd', form a right triangle with 'h' being the opposite leg to the given reference angle, 65°, and 'd' being the adjacent leg

By trigonometric ratio, we have;

$tan(\theta) = \dfrac{Opposite \ leg \ length}{Adjacent\ leg \ length} = \dfrac{h}{d}$

∴ h = d × tan(θ)

Plugging in the given values, we get;

h = 10 feet × tan(65°) = 21 feet $5\frac{11}{32}$ inches

∴ By rounding to the nearest tenth of a foot, the height of the tree, h ≈ 21.4 feet.

3 0

2 years ago

Please help me complete this !! 12points

Svet_ta [14]

Answer:

x1=1

x2=3

y1=5

y2=1

midpoint= (x1+x2/2, y1+y2/2)=(1+3/2,5+1/2)=(2,3)

x1=2

x2=4

y1=4

y2=6

midpoint= (x1+x2/2, y1+y2/2)=(2+4/2,4+6/2)=(3,5)

x1= -2

x2=4

y1=4

y2= -6

midpoint= (x1+x2/2, y1+y2/2)=(-2+4/2,4-6/2)=(1,-1)

x1=0

x2=0

y1=3

y2=5

midpoint= (x1+x2/2, y1+y2/2)=(0/2,3+5/2)=(0,4)

x1= -2

x2=2

y1= -6

y2=6

midpoint= (x1+x2/2, y1+y2/2)=(-2+2/2,-6+6/2)=(0,0)

x1=1

x2=4

y1=4

y2=5

midpoint= (x1+x2/2, y1+y2/2)=(1+4/2,4+5/2)=(5/2,9/2)

x1=-3

x2=-4

y1=5

y2=5

midpoint= (x1+x2/2, y1+y2/2)=(-3-4/2,5+5/2)=(-7/2,5)

x1=5

x2= -4

y1=2

y2=6

midpoint= (x1+x2/2, y1+y2/2)=(5-4/2,2+6/2)=(1/2,4)

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2 years ago

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Answer:

Step-by-step explanation:

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Inga [223]

Answer:

1/20 of 2 minutes = 6 seconds

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2 years ago

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