A walker on a trail travels along the path described by the parametric equations

Using the Pythagorean Theorem, find the length of a leg of a right triangle if the other leg is 8 feet long and the hypotenuse i

iren [92.7K]

The <span>Pythagorean Theorem tells us that $a^{2}+b^{2}=c^{2}$ where c is the </span><span>hypotenuse and a and b are the other two sides. To solve for one of the shorter sides we need to rearrange:

$b=\sqrt{c^{2}-a^{2}}$

We can then substitute known values, and solve:
</span> $b=\sqrt{10^{2}-8^{2}}$
$b=\sqrt{100-64}$
$b=\sqrt{36}$
$b=6 feet$

8 0

3 years ago

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A gumball has a diameter that is 66 mm. The diameter of the gumball's spherical hollow core is 58 mm. What is the volume of the

grigory [225]

Answer:

Volume of gumball without including its hollow core is 48347.6 cubic mm.

Step-by-step explanation:

Given:

Diameter of Gumball = 66 mm

Since radius is half of diameter.

Radius of gumball = $\frac{diameter}{2}=\frac{66}{2} =33 \ mm$

Now We will first find the Volume of Gumball.

To find the Volume of Gumball we will use volume of sphere which is given as;

Volume of Sphere = $\frac{4}{3}\pi r^3$

Now Volume of Gumball = $\frac{4}{3}\times3.14 \times (33)^3 = 150456.24 \ mm^3$

Also Given

Diameter of gumball's spherical hollow core = 58 mm

Since radius is half of diameter.

Radius of gumball's spherical hollow core = $\frac{diameter}{2}=\frac{58}{2} =29 \ mm$

Now We will find the Volume of gumball's spherical hollow core.

Volume of Sphere = $\frac{4}{3}\pi r^3$

So Volume of gumball's spherical hollow core = $\frac{4}{3}\times3.14 \times (29)^3 = 102108.61 \ mm^3$

Now We need to find volume of the gumball without including its hollow core.

So, To find volume of the gumball without including its hollow core we would Subtract Volume of gumball spherical hollow core from Volume of Gumball.

volume of the gumball without including its hollow core = Volume of Gumball - Volume of gumball's spherical hollow core = $150456.24\ mm^3 - 102108.61\ mm^3 = 48347.63\ mm^3$

Rounding to nearest tenth we get;

volume of the gumball without including its hollow core = $48347.6\ mm^3$

Hence Volume of gumball without including its hollow core is 48347.6 cubic mm.

8 0

2 years ago

What does a sample space look like?

grin007 [14]

Answer:

A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment

Hope this helps even a little bit:)

6 0

1 year ago

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Un dirigible que está volando a 800 m de altura, distingue un pueblo con un ángulo de depresión de 12°. ¿A qué distancia del pue

alexira [117]

Answer:

3764 m

Step-by-step explanation:

Resolvemos usando la función trigonométrica de tangente.

tan θ = Opuesto / Adyacente

θ = Ángulo de depresión = 12 °

Opuesto = 800m

Adyacente = Distancia de la ciudad = x

Cruz multiplicar

bronceado 12 = 800 / x

Cruz multiplicar

bronceado 12 × x = 800

x = 800 / tan 12

x = 3763.7040876 m

Aproximadamente = 3764 m

6 0

2 years ago

Can anyone help me choose the correct answer?!

lara [203]

Answer:

f(x)=x-6 is your answer.

when x=0

f(0)=0-6=-6

similarly other too

7 0

2 years ago