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abruzzese [7]
3 years ago
9

How do you join the bar you left weighs 45 pounds you add weight to the bar that are 10 pounds each if you add six weights to th

e bar how many pounds will you left
Mathematics
1 answer:
tigry1 [53]3 years ago
4 0
Hello!

45 + 10 + 6 = 61

So, your answer is 61.

I hope that was helpful! c:
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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
4x - 6 = 30 can you solve it
olya-2409 [2.1K]

Answer:

x = 9

Step-by-step explanation:

take -6 to the other side so you add it to 30 = 36

equation is now 4x = 36

divide 4/4 and 36/4

x = 9

6 0
3 years ago
Nicole buys envelopes for her home office that come in boxes of 125 envelopes. If she buys 18 boxes, how many envelopes will she
yawa3891 [41]

Answer:

➩ 2,250 envelopes.

Step-by-step explanation:

Given that, Nicole buys 125 envelopes per box for her home office.

Therefore, She will have 18*125 envelopes in all

So, 18*125 is 2,250 envelopes

6 0
3 years ago
A pound of cherries is normally $5.00. Today there is a 20% discount. What is the sale price
Kruka [31]
The Answer Is $4.00
Hope This Helps!

6 0
3 years ago
Read 2 more answers
The budget for a remake of a movie is 100 times the budget of the original movie. The original movie's budget was 10^5 dollars.
Arte-miy333 [17]

Answer:

100,000,000

Step-by-step explanation:

10*10=100*10=1000*10=10000*10=100000*10=1000000*100=100,000,000

4 0
3 years ago
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