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WITCHER [35]
3 years ago
9

Cora takes a sheet of paper and cuts from one corner to the opposite corner, making two triangles. If the piece of paper is 15 i

nches long and 8 inches wide, how long is the diagonal cut that Cora made? (This is pythagorean theorem btw)
​
Mathematics
1 answer:
Bogdan [553]3 years ago
7 0
Answer: 17 inches

Explanation: so we have a triangle with the two side lengths 8 and 15 and we’re trying to find the hypotenuse. so using the pythagorean theorem, we have 8^2 + 15^2 = c^2. when we solve we get 64 + 225 = c^2, which is 289 = c^2. next, we find the square root of both sides and c = 17 inches.

hope this helped!
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Not equivalent

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Distribute the negative in the parentheses. It basically multiplying everything inside by -1.

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I need to find the derivative. I’m not very good at this so I am answer asap would be sosososo helpful
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Answer:

See below.

Step-by-step explanation:

First, notice that this is a composition of functions. For instance, let's let f(x)=\sqrt{x} and g(x)=7x^2+4x+1. Then, the given equation is essentially f(g(x))=\sqrt{7x^2+4x+1}. Thus, we can use the chain rule.

Recall the chain rule: \frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x). So, let's find the derivative of each function:

f(x)=\sqrt{x}=x^\frac{1}{2}

We can use the Power Rule here:

f'(x)=(x^\frac{1}{2})'=\frac{1}{2}(x^{-\frac{1}{2}  })=\frac{1}{2\sqrt{x}}

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g(x)=7x^2+4x+1

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g'(x)=(7x^2+4x+1)'=(7x^2)'+(4x)'+(1)'=14x+4

Now, we can put them together:

y'=f'(g(x))\cdot g'(x)=\frac{1}{2\sqrt{g(x)}} \cdot (14x+4)

y'=\frac{14x+4}{2\sqrt{7x^2+4x+1} } =\frac{7x+2}{\sqrt{7x^2+4x+1} }

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15. The height and yolume of a cylinder are 4cm and 616cm respectively. Calculate the diameter of the base. (take t = 27 쪽 A. 7c
irakobra [83]

Step-by-step explanation:

Given that,

  • Height of cylinder = 4 cm
  • Volume of cylinder = 616 cm³

To find,

  • Diameter of the base = ?

Firstly we'll find the base radius of the cylinder.

\longmapsto\rm{V_{(Cylinder)} = \pi r^2h}\\

<u>Accordi</u><u>ng</u><u> </u><u>to</u><u> </u><u>the</u><u> </u><u>qu</u><u>estion</u><u>,</u>

\longmapsto\rm{616= \dfrac{22}{7} \times r^2 \times 4}\\

\longmapsto\rm{616 \times 7 = 22 \times r^2 \times 4}\\

\longmapsto\rm{4312 = 88 \times r^2 }\\

\longmapsto\rm{\cancel{\dfrac{4312}{88}} =  r^2 }\\

\longmapsto\rm{49 =  r^2 }\\

\longmapsto\rm{\sqrt{49} =  r }\\

\longmapsto\rm{7 \; cm =  r }\\

Now,

\longmapsto\rm{Diameter = 2r }\\

\longmapsto\rm{Diameter = 2(7 \; cm) }\\

\longmapsto\bf{Diameter = 14 \; cm}\\

The required answer is 14 cm.

4 0
3 years ago
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