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2 years ago

Can someone help me and solve the following equation showing work please? thank you!

Mathematics

1 answer:

dsp732 years ago

3 0

The angle made by an arc at the centre of the circle is double the angle made by the same arc at any point on the circle. The measure of the angle θ will be 45°.

<h3>What are an arc and subtended angle theorem?</h3>

According to the arc and subtended angle theorem, The angle made by an arc at the centre of the circle is double the angle made by the same arc at any point on the circle.

The angle made by an arc at the centre of the circle is double the angle made by the same arc at any point on the circle. Therefore, the measure of the angle θ will be half the measure of the ∠P.

As it can be observed the measure of the angle ∠P is 90°, therefore, the measure of the angle θ can be written as,

∠P = 2 × ∠θ

90° = 2 × ∠θ

∠θ = 45°

Hence, the measure of the angle θ will be 45°.

Learn more about Arc and Subtended angle Theorem:

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Answer:

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Step-by-step explanation:

When adding fractions, you must ensure the denominator is the same in both fractions.

In this case, the 3 can be multiplied by 2 to equal 6, the other denominator.

When multiplying fractions to create a common denominator, you must multiply the both the numerator and the denominator by the same value, to ensure that the fraction is still equivalent.

2/3 × 2/2 = (2×2)/(3×2) = 4/6

Replace 2/3 with its equivalent 4/6.

Now you will add the numerators together.

1/6 + 4/6 = (1+4)/6 = 5/6

Your final answer is 5/6

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3 years ago

If a toy rocket is launched vertically upward from the ground level with an initial velocity of 128 feet per second, then its he

natta225 [31]

Answer:

The maximum height of the rocket is 256 feet

Step-by-step explanation:

The vertex form of the quadratic function f(x) = ax² + bx + c is

f(x) = a(x - h)² + k, where

(h, k) is the vertex point

h = $\frac{-b}{2a}$ and k = f(h)

(h, k) is a minimum point if a > 0 and a maximum point if a < 0

Let us use these rules to solve the question

∵ h(t) = -16t² + 128t

→ Compare it by the form of the quadratic function above

∴ a = -16 and b = 128

∵ a < 0

∴ The vertex (h, k) is a maximum point

∴ The maximum height of the rocket is the value of k

→ Use the rule of h above to find it

∵ h = $\frac{-128}{2(-16)}$ = $\frac{-128}{-32}$

∴ h = 4

→ Substitute x in the equation by the value of h to find k

∵ k = h(h)

∴ k = -16(4)² + 128(4)

∴ k = -256 + 512

∴ K = 256

∴ The maximum height of the rocket is 256 feet

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3 years ago