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3 years ago

the hypotenuse and a side of a right angled triangle are 13cm and5cm respectively. fined the length of the third side

Mathematics

2 answers:

alexgriva [62]3 years ago

8 0

Answer:

<h2>Lenght of the third side =12</h2>

Step-by-step explanation:

$hypotenuse = 13 \\ opposite = 5 \\ adjacent = x \\ {hyp}^{2} = {opp}^{2} + {adj}^{2} \\$

${13}^{2} = {5}^{2} + {x}^{2} \\ 169 = 25 + {x}^{2} \\ 169 - 25 = {x}^{2} \\ 144 = {x}^{2}$

$\sqrt{144} = \sqrt{ {x}^{2} } \\ 12 = x$

eduard3 years ago

5 0

Answer:

If the third side is the hypotenuse, then (using the Pythagorean Theorem) the square of its length is the sum of the squares of the other two sides: 132+52 , so the length of the hypotenuse is √194=13.92838827718412...

However, it is also possible to have a right triangle with a hypotenuse of 13 cm and one side of 5 cm, in which case the third side would be: √132−542=12.

Of course, the second answer may seem “nicer” but both are correct and the question is ambiguous.

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during a softball game kay hit a fly ball the function f(x) = -16t^2 + 64t + 4 describes the height of the softball in feet. mak

STatiana [176]

<h2>Hello!</h2>

The graph is attached.

To graph a parabola we need to know the following:

- If the parabola is open upwards or downwards

- They axis intercepts (if they exist)

- The vertex position (point)

We are given the function:

$f(t)=-16t^{2}+64t+4$

Where,

$a=-16\\b=64\\c=4$

For this case, the coefficient of the quadratic term (a) is negative, it means that the parabola opens downwards.

Finding the axis interception points:

Making the function equal to 0, we can find the x-axis (t) intercepts, but since the equation is a function of the time, we will only consider the positive values, so:

$f(t)=-16t^{2}+64t+4\\0=-16t^{2}+64t+4\\-16t^{2}+64t+4=0$

Using the quadratic equation:

$\frac{-b+-\sqrt{b^{2}-4ac } }{2a}=\frac{-64+-\sqrt{64^{2}-4*-16*4} }{2*-16}\\\\\frac{-64+-\sqrt{64^{2}-4*-16*4} }{2*-16}=\frac{-64+-\sqrt{4096+256} }{-32}\\\\\frac{-64+-\sqrt{4096+256} }{-32}=\frac{-64+-(65.96) }{-32}\\\\t1=\frac{-64+(65.96) }{-32}=-0.06\\\\t2=\frac{-64-(65.96) }{-32}=4.0615$

So, at t=4.0615 the height of the softball will be 0.

Since we will work only with positive values of "x", since we are working with a function of time:

Let's start from "t" equals to 0 to "t" equals to 4.0615.

So, evaluating we have:

$f(0)=-16(0)^{2}+64(0)+4=4\\\\f(1)=-16(1)^{2}+64(1)+4=52\\\\f(2)=-16(2)^{2}+64(2)+4=68\\\\f(3)=-16(3)^{2}+64(3)+4=52\\\\f(4.061)=-16(4.0615)^{2}+64(4.0615)+4=0.0034=0$

Finally, we can conclude that:

- The softball reach its maximum height at t equals to 2. (68 feet)

- The softball hits the ground at t equals to 4.0615 (0 feet)

- At t equals to 0, the height of the softball is equal to 4 feet.

See the attached image for the graphic.

Have a nice day!

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3 years ago

the hypotenuse and a side of a right angled triangle are 13cm and5cm respectively. fined the length of the third side​

the hypotenuse and a side of a right angled triangle are 13cm and5cm respectively. fined the length of the third side