The two triangles are similar since each triangle is the same shape of right triangle but different sizes. To find x, write a proportion between two equal ratios of side lengths.

$\frac{28}{20}=\frac{4x+2}{3x}$

Solve by cross multiplying.

28(3x) = 20(4x+2)

84x = 80x + 40

4x = 40

x=10

3 0

3 years ago

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Given the hyperbola y = 1/x, find the area under the curve between x = 5 and x = 33 to 3 sig. dig. namely: integral subscript 5

Shtirlitz [24]

Answer:

(b) ln(33/5)

Step-by-step explanation:

$\int\limits_{5}^{33} \frac{1}{x} \, dx = \ln(x) \Big|\limits_{5}^{33} = \ln(33) - \ln(5) \\\\= ln(33/5)$

Remember that in general

$\ln(a) - \ln(b) = \ln(a/b)$

4 0

2 years ago

A bank security camera is mounted on a wall. The camera is set at an angle of depression of 19 degrees so that it is focused on

777dan777 [17]

Answer:

8.95feet

Step-by-step explanation:

The set up is a right angled triangle where;

The camera's horizontal distance from the focus point = 26feet = Adjacent;

The height of the camera above the floor = Opposite = x

Angle of elevation = 19°

According to TOA in trig identity;

Tan theta = opp/adj

Tan 19 = x/26

x = 26tan 19

x = 26(0.3443)

X = 8.95feet

Hence the camera is placed at a height of 8.95feet above the floor

7 0

2 years ago