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3 years ago

25 letters in 4 days

Mathematics

1 answer:

pentagon [3]3 years ago

5 0

In order to write 25 letters in 4 days you would need to write 6.25 a day

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Among all right triangles whose hypotenuse has a length of 12 cm, what is the largest possible perimeter?

Veronika [31]

Answer:

Largest perimeter of the triangle =

$P(6\sqrt{2}) = 6\sqrt{2} + \sqrt{144-72} + 12 = 12\sqrt{2} + 12 = 12(\sqrt2 + 1)$

Step-by-step explanation:

We are given the following information in the question:

Right triangles whose hypotenuse has a length of 12 cm.

Let x and y be the other two sides of the triangle.

Then, by Pythagoras theorem:

$x^2 + y^2 = (12)^2 = 144\\y^2 = 144-x^2\\y = \sqrt{144-x^2}$

Perimeter of Triangle = Side 1 + Side 2 + Hypotenuse.

$P(x) = x + \sqrt{144-x^2} + 12$

where P(x) is a function of the perimeter of the triangle.

First, we differentiate P(x) with respect to x, to get,

$\frac{d(P(x))}{dx} = \frac{d(x + \sqrt{144-x^2} + 12)}{dx} = 1-\displaystyle\frac{x}{\sqrt{144-x^2}}$

Equating the first derivative to zero, we get,

$\frac{dP(x))}{dx} = 0\\\\1-\displaystyle\frac{x}{\sqrt{144-x^2}} = 0$

Solving, we get,

$1-\displaystyle\frac{x}{\sqrt{144-x^2}} = 0\\\\x = \sqrt{144-x^2}}\\\\x^2 = 144-x^2\\\\x = \sqrt{72} = 6\sqrt{2}$

Again differentiation P(x), with respect to x, using the quotient rule of differentiation.

$\frac{d^2(P(x))}{dx^2} = \displaystyle\frac{-(144-x^2)^{\frac{3}{2}}-x^2}{(144-x)^{\frac{3}{2}}}$

At x = $6\sqrt{2}$ ,

$\frac{d^2(V(x))}{dx^2} < 0$

Then, by double derivative test, the maxima occurs at x = $6\sqrt{2}$

Thus, maxima occurs at x = $6\sqrt{2}$ for P(x).

Thus, largest perimeter of the triangle =

$P(6\sqrt{2}) = 6\sqrt{2} + \sqrt{144-72} + 12 = 12\sqrt{2} + 12 = 12(\sqrt2 + 1)$

7 0

3 years ago

Sigmund wrote four checks last month, and these were the only transactions for his checking account. According to his check regi

Lady bird [3.3K]

Answer:

The Check that hasn't been cleared yet is for $372.15.

Step-by-step explanation:

168.48+ 168.93+ 177.78+ 177.93= 693.12

887.79- 693.12= 194.67

1,065.27- 887.79= 177.48

194.67+ 177.48= 372.15

To check your answer:

372.15+ 693.12= 1,065.27

Hope this helped you!! (:

7 0

3 years ago

Read 2 more answers

Solve for h: -2/3h-4=4/3

Sindrei [870]

Isolate the variable by dividing each side by factors that don't contain the variable.

h = −8

3 0

2 years ago

in the diagram,transversal t intersects parallel lines m and n. Classify the given angle pair. then determine each measures.

professor190 [17]

Answer:

Step-by-step explanation:

Corresponding angles: ∠2=∠ 6 ; ∠1 = ∠5 ; ∠4 = ∠8; ∠3 =∠7

Vertically opposite angles: ∠1 = ∠3; ∠2 = 4; ∠5 = ∠7 ; ∠6 = ∠8

Interior angles : ∠4, ∠3 , ∠6, ∠7

alternate interior angles are equal: ∠3 = ∠5 ; ∠4 = ∠6

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3 years ago

Emma drank 1/4 of a milk shake in 1/12 of a minute. How many minutes will it take her to drink a full milk shake?

zaharov [31]

i think it would take about three minutes

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3 years ago