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3 years ago

Please help me answer this!

Mathematics

1 answer:

Tomtit [17]3 years ago

5 0

Answer:

x = 3

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of a right triangle is called the hypotenuse and the other two sides are the legs.

The tangent ratio relates the opposite leg with the adjacent leg. Please note the given side is the opposite leg to 60° and x is the adjacent leg to 60°, thus we apply the tangent ratio:

$\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}$

$\displaystyle \tan 60^\circ=\frac{3\sqrt{3}}{x}$

Solving for x:

$\displaystyle x=\frac{3\sqrt{3}}{\tan 60^\circ}$

Since:

$\tan 60^\circ=\sqrt{3}:$

$\displaystyle x=\frac{3\sqrt{3}}{\sqrt{3}}$

Simplifying:

x = 3

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A toy ball in the shape of a sphere expands and contracts. When it is completely closed, it has a diameter of 12.5 inches.Find

lana [24]

The volume of the sphere is $1022.65 \ in^3$

Explanation:

Given that the diameter of the toy ball is 12.5 inches

We need to determine the volume of the toy ball.

The radius of the toy ball is given by

$r=\frac{d}{2}$

$r=\frac{12.5}{2}$

$r=6.25 \ in$

Thus, the radius of the toy ball is 6.25 in

The volume of the sphere can be determined using the formula,

$V=\frac{4}{3} \pi r^{3}$

Substituting the values, we get,

$V=\frac{4}{3} \pi(6.25)^{3}$

Multiplying, we get,

$V=\frac{976.5625 \pi}{3}$

Substituting $\pi=3.14$ , we have,

$V=\frac{976.5625 (3.14)}{3}$

Simplifying, we get,

$V=1022.65 \ in^3$

Thus, the volume of the sphere is $1022.65 \ in^3$

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3 years ago

Find the standard form of the equation of the parabola with a focus at (-2, 0) and a directrix at x = 2.

krok68 [10]

Answer:

$y^2=\frac{1}{8}x$

Step-by-step explanation:

The focus lies on the x axis and the directrix is a vertical line through x = 2. The parabola, by nature, wraps around the focus, or "forms" its shape about the focus. That means that this is a "sideways" parabola, a "y^2" type instead of an "x^2" type. The standard form for this type is

$(x-h)=4p(y-k)^2$

where h and k are the coordinates of the vertex and p is the distance from the vertex to either the focus or the directrix (that distance is the same; we only need to find one). That means that the vertex has to be equidistant from the focus and the directrix. If the focus is at x = -2 y = 0 and the directrix is at x = 2, midway between them is the origin (0, 0). So h = 0 and k = 0. p is the number of units from the vertex to the focus (or directrix). That means that p=2. We fill in our equation now with the info we have:

$(x-0)=4(2)(y-0)^2$