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2 years ago

Which of the following statements are true

Mathematics

1 answer:

Shkiper50 [21]2 years ago

8 0

Answer: B , c, E

Step-by-step explanation:

Given that ,

∡J=90° , ∡k=30° , ∡L=60°

In the triangle ΔJKL,

tan ∠L = tan 60°

⇒ JK÷JL= √3

⇒JK = √3JL

Thus, A is incorrect and B is correct

Again,

cos ∠L = cos60° =0.5

⇒JL/KL = 1÷2

⇒ JL = (1÷2)KL

⇒JL×2= KL

⇒ KL=2JL

Hence, F & D are incorrect and C is correct

Earlier we got,

JK = √3.JL

⇒JL=JK÷√3

and JL= (1÷2).KL

So, JK÷√3=(1÷2)KL

⇒JK÷√3×2 = KL

⇒2.JK= √3KL

⇒JK = (√3÷2).KL

hence E is correct

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Answer:

The dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)

Step-by-step explanation:

Let the length of garden be x

Let the breadth of garden be y

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We are given that the area of the garden is 122 square feet

So, $xy=122$ ---A

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So, cost of brick along length x = 20 x

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So, Other three side s = x+2y

So, cost of brick along the other three sides= 10(x+2y)

So, Total cost = 20x+10(x+2y)=20x+10x+20y=30x+20y

Total cost = 30x+20y

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Total cost = $30x+20(\frac{122}{x})$

Total cost = $\frac{2440}{x}+30x$

Now take the derivative to minimize the cost

$f(x)=\frac{2440}{x}+30x$

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Equate it equal to 0

$0=-\frac{2440}{x^2}+30$

$\frac{2440}{x^2}=30$

$\sqrt{\frac{2440}{30}}=x$

$9.018 =x$

Now check whether it is minimum or not

take second derivative

$f'(x)=-\frac{2440}{x^2}+30$

$f''(x)=-(-2)\frac{2440}{x^3}$

Substitute the value of x

$f''(x)=-(-2)\frac{2440}{(9.018)^3}$

$f''(x)=6.6540$

Since it is positive ,So the x is minimum

Now find y

Substitute the value of x in A

$(9.018)y=122$

$y=\frac{122}{9.018}$

$y=13.528$

Hence the dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Read 2 more answers

Which of the following statements are true​

Which of the following statements are true