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belka [17]
1 year ago
10

Solve the following equation for X. Round your answer to four decimal places.

Mathematics
1 answer:
strojnjashka [21]1 year ago
4 0

ANSWER

x = 1.2226

EXPLANATION

To solve this equation we have to apply the property of the logarithm of the base,

\log _bb=1

Thus, we can apply the natural logarithm - whose base is e, to both sides of the equation,

\ln e^{4x}=\ln 133

Now we apply the property of the logarithm of a power,

\log a^b=b\log a

In our equation,

\begin{gathered} 4x\ln e^{}=\ln 133 \\ 4x^{}=\ln 133 \end{gathered}

Then divide both sides by 4 and solve,

\begin{gathered} \frac{4x^{}}{4}=\frac{\ln 133}{4} \\ x\approx1.2226 \end{gathered}

The solution to this equation is x = 1.2226, rounded to four decimal places.

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pickupchik [31]

Answer:

I agree that this question can be confusing:

Apparently point A and point B must be on the same straight line (measured from the light house or the question would be nonsensical)

tan 13 = H / DA      where H is height of lighthouse

tan 8 = H / DB       tangent measured from point B

tan 13 / tan 8 = DB / DA

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3 0
2 years ago
A portrait has dimensions of 30“ x 60“ and is surrounded by a frame of uniform width. If the total area (Portrait plus frame) is
Law Incorporation [45]

Answer:

The width of the is 4 inches

Step-by-step explanation:

Assume that the width of the frame is x

∵ The width of the fame is x inches

→ That means each dimension will increase by 2x ⇒ x from each side

∵ The portrait has dimensions of 30“ x 60“

∴ Its dimensions including the frame = (30 + 2x) × (60 + 2x)

∴ The total area of the portrait plus frame = (30 + 2x)(60 + 2x)

→ Multiply the brackets

∵ (30 + 2x)(60 + 2x) = 30(60) + 30(2x) + 2x(60) + (2x)(2x)

∴ (30 + 2x)(60 + 2x) = 1800 + 60x + 120x + 4x²

→ Add the like terms

∴ (30 + 2x)(60 + 2x) = 1800 + 180x + 4x²

∴ The total area of the portrait plus frame = 4x² + 180x + 1800

∵ The total area of the portrait plus frame = 2584 square inches

→ Equate the two right sides of the area

∴ 4x² + 180x + 1800 = 2584

→ Subtract 2584 from both sides

∴ 4x² + 180x + 1800 - 2584 = 0

→ Add the like terms in the left side

∴ 4x² + 180x - 784 = 0

→ Divide all terms by 4 to simplify

∴ x² + 45x - 196 = 0

→ Factorize it to find the value of x

∵ x² + 45x - 196 = (x - 4)(x + 49)

→ Equate the right side by 0

∴ (x - 4)(x + 49) = 0

→ Equate each factor by 0

∵ x - 4 = 0  

→ Add 4 to both sides to find x

∴ x = 4

∵ x + 49 = 0

→ Subtract 49 from both sides to find x

∴ x = -49 ⇒ refused it x can not be -ve (no negative dimensions)

∴ The width of the is 4 inches

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-2 pretty sure hope this helps
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