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3 years ago

In the figure below, Z is the center of the circle. Suppose that OR=4, ST= 4, UZ= 6, and VZ=4x-6. Find the following.

Mathematics

1 answer:

Ann [662]3 years ago

3 0

Answer:

x = 3 units

SV = 2 units

Step-by-step explanation:

In $\odot Z$ QR and ST are chords such that:

QR = ST = 4

That is both the chords are equal in measure.

Equal chords are at equal distance from the center of the circle. Therefore,

VZ = UZ

4x - 6 = 6

4x = 6 + 6

4x = 12

x = 12/4

x = 3 units

Since, perpendicular dropped from the center of the circle bisects the chord.

$\therefore SV = \frac{1}{2} ST$

$\therefore SV = \frac{1}{2} \times 4$

$\therefore SV = 2\: units$

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Answer:

The height of the tree is approximately 21.4 feet

Step-by-step explanation:

We list out the question parameters first as follows;

The distance from the base of the tree where the angle of elevation is measured, d = 10 feet

The angle of elevation to the top of the tree from 10 feet from the base, θ = 65°

Let 'h' represent the height of the tree, then we have;

The line formed by the angle 65° angle, the height of the tree, 'h', and the distance 'd', form a right triangle with 'h' being the opposite leg to the given reference angle, 65°, and 'd' being the adjacent leg

By trigonometric ratio, we have;

$tan(\theta) = \dfrac{Opposite \ leg \ length}{Adjacent\ leg \ length} = \dfrac{h}{d}$

∴ h = d × tan(θ)

Plugging in the given values, we get;

h = 10 feet × tan(65°) = 21 feet $5\frac{11}{32}$ inches

∴ By rounding to the nearest tenth of a foot, the height of the tree, h ≈ 21.4 feet.

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3 years ago

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Gelneren [198K]

Answer:

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Step-by-step explanation:

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Elenna [48]

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Read 2 more answers

Suppose you are climbing a hill whose shape is given by the equation z = 1400 − 0.005x2 − 0.01y2, where x, y, and z are measured

Anarel [89]

Answer: You start to ascend

Explanation:

Since you are walking due south and the positive y-axis points north, the y-coordinate decreases.

Let

$y'$ = y-coordinate after walking due south
$z'$ = z-coordinate (or the height) after walking due south

So, the point where you stand after walking due south has a coordinate of $(100, y', z')$ . Moreover,

$z' = 1,400 - 0.05(100)^2 - 0.01(y')^2
\\ \boxed{z' = 1350 - 0.01(y')^2}$

Since the y-coordinate decreases after walking due south and $z' = 1350 - 0.01(y')^2$ ,

$y' \leq 120\\ \Rightarrow (y')^2 \leq 120^2 = 14,400\\ \Rightarrow -0.01(y')^2 \geq -0.01(14,400) = -144\\ \Rightarrow z' = 1,350 - 0.01(y')^2 \geq 1,350 - 0.01(14,400) = 1,206\\ \Rightarrow \boxed{z' \geq 1,206}$

So, the height after walking due south exceeds 1,206 meters, which is the previous height before walking due south. Therefore, if you walk due south from point with coordinates (100, 120, 1206), you are ascending.

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