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sveticcg [70]
3 years ago
6

In ΔQRS, the measure of ∠S=90°, the measure of ∠R=36°, and RS = 98 feet. Find the length of QR to the nearest tenth of a foot.

Mathematics
1 answer:
erica [24]3 years ago
5 0

The Length of the hypotenuse RQ is 121.1 feet

<u>Step-by-step explanation:</u>

Here angle SQR =(180-90-36)=54

through trigonometry we know that SINФ=Perpendicular/Hypotenuse

here SIN54 = RS/RQ

we know that SIN 54 =0.809

putting the values of SIN54 and RS

0.809 = 98/X

applying cross multiplication

X = 98/0.809

X = 121.1

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7^x=3^[x+4] solve x using logarithmic
Andrei [34K]

By taking advantage of the definition of <em>exponential</em> and <em>logarithmic</em> function and their inherent relationship we conclude that the solution is x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3).

<h3>How to solve an exponential equation by logarithms</h3>

<em>Exponential</em> and <em>logarithmic</em> functions are <em>trascendental</em> functions, these are, functions that cannot be described <em>algebraically</em>. In addition, <em>logarithmic</em> functions are the <em>inverse</em> form of <em>exponential</em> functions. In this question we take advantage of this fact to solve a given expression:

  1. 7ˣ = 3ˣ⁺⁴     Given
  2. ㏒ 7ˣ = ㏒ 3ˣ⁺⁴      Definition of logarithm
  3. x · ㏒ 7 = (x + 4) · ㏒ 3     ㏒ aᵇ = b · ㏒ a
  4. x · ㏒ 7 = x · ㏒ 3 + 4 · ㏒ 3     Distributive property
  5. x · (㏒ 7 - ㏒ 3) = 4 · ㏒ 3      Existence of additive inverse/Modulative and associative properties
  6. x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3)     Existence of multiplicative inverse/Modulative property/Result

By taking advantage of the definition of <em>exponential</em> and <em>logarithmic</em> function and their inherent relationship we conclude that the solution is x = 4 · ㏒ 3/(㏒ 7 - ㏒ 3).

To learn more on logarithms: brainly.com/question/20785664

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4 0
2 years ago
Jenna drew irregular quadrilateral ABCD inscribed in circle P. She knows that: m∠3=2⋅m∠1, and m∠2=2⋅m∠4, and m∠2+m∠3=360°. What
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Answer:

The generalisation she can make from her work is that the other two angles of the quadrilateral are supplementary i.e their sum is 180°

Step-by-step explanation:

We are given the following from what she knows

m∠3=2⋅m∠1... 1

m∠2=2⋅m∠4 ... 2

m∠2+m∠3=360 ... 3

From what is given, we can substitute equation 1 and 2 into equation 3 as shown:

From 3:

m∠2+m∠3=360

Substituting 1 and 2 we will have:

2⋅m∠4 + 2⋅m∠1 = 360

Factor out 2 from the left hand side of the equation

2(m∠4+m∠1) = 360

Divide both sides by 2

2(m∠4+m∠1)/2 = 360/2

m∠4+m∠1 = 180°

Since the sum of two supplementary angles is 180°, hence the generalisation she can make from her work is that the other two angles of the quadrilateral are supplementary i.e their sum is 180°

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Answer:

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