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2 years ago

14

Solve 4^(2x) = 7^(x−1).

1 answer:

sweet [91]2 years ago

3 0

To solve for x in the given equation, use natural logarithms. Getting the natural logarithms of both sides, will be ln 4^(2x) = ln 7^(x-1). This is also equal to 2x ln 4 = (x-1) ln 7. Rearranging the equation, 2x/(x-1) = ln 7/ln 4. The right side is equal to 1.4037. Thus, the value of x is -2.3539.

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the length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58 degre

Anarel [89]

Answer:

The height of the pole is 167 m

Step-by-step explanation:

The given parameters are;

Increase in the length of the shadow = 90 m

Initial angle of elevation of the Sun = 58°

Final angle of elevation of the Sun = 36°

We have a triangle formed by the change in the length of the shadow and the rays from the two angle of elevation to the top of the pole giving an angle 22° opposite to the increase in the length of the shadow

We have by sin rule;

90/(sin (22°) = (Initial ray from the top of the pole to the end of the shadow's length)/(sin(122°)

Let the initial ray from the top of the pole to the end of the shadow's length = l₁

90/(sin (22°) = l₁/(sin(122°)

l₁ = 90/(sin (22°) ×(sin(122°) = 283.3 m

Therefore;

The height of the pole = 283.3 m × sin(36°) = 166.52 m

The height of the pole= 167 m to three significant figures.

3 0

3 years ago

Read 2 more answers

Find cot theta if csc theta = <br><br>sqrt17/4 and tan theta >0.

Lorico [155]

Answer:

$tan \theta = 4$

Step-by-step explanation:

We know that

$cosec \theta = \frac{hypotenuse }{opposite }$

Given :

$cosec \theta =\frac{\sqrt{17}}{4}\\$

So 4 is the opposite side of theta.

$tan \theta = \frac{opposite}{adjacent}$

We use the Pythagorean theorem to find for the adjacent side.

$a = \sqrt{17 - 4^2} = \sqrt{17-16} = 1$

$Therefore, \ tan \theta = \frac{4}{1} = 4$

7 0

3 years ago

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Anarel [89]

A and D are 85 degrees

4 0

2 years ago

Which sequence is arithmetic?

MissTica

Answer:

11, 14, 17, 20

Step-by-step explanation:

An arithmetic sequence has a common difference d between consecutive terms.

Consider 2, 6, 18, 54

6 - 2 = 4, 18 - 6 = 12, 54 - 18 = 36 ← no common difference, not arithmetic

Consider 3, 6, 12, 24

6 - 3 = 3, 12 - 6 = 6, 24 - 12 = 12 ← no common difference, not arithmetic

Consider 11, 14, 17, 20

14 - 11 = 3, 17 - 14 = 3, 20 - 17 = 3 ← common difference of 3, so arithmetic

Consider 7, 11, 13, 18

11 - 7 = 4, 13 - 11 = 2, 18 - 13 = 5 ← no common difference, not arithmetic

The arithmetic sequence is 11, 14, 17, 20

3 0

3 years ago

Julie was given a new map of New Hampshire to calculate some distances. The scale is 1 inch = 50 miles. How far is Conway from L

Aloiza [94]

Answer:

Conway is 312.50 miles from Littleton

Step-by-step explanation:

Given

$Scale: 1\ in = 50\ mi$

See attachment

Required

Distance between Conway and Littleton

The scale distance between Conway and Littleton is 6.25 inches.

So, the actual distance is calculated as:

$1\ in = 50\ mi$

Multiply both sides by 6.25

$6.25 * 1\ in = 50\ mi * 6.25$

$6.25\ in = 312.50\ mi$

<em>Hence, Conway is 312.50 miles from Littleton</em>

7 0

2 years ago