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A vertical pole, of height b, casts a shadow onto the ground. The angle of elevation from the tip of the shadow on the ground to

slega [8]

Answer: $b=47.5$

Step-by-step explanation:

Draw a Rigth triangle as the one attached, where "b" is the height in feet of the pole.

IFor this exercise you need to use the following Trigonometric Identity:

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

In this case, you can identify that:

$\theta=30\°\\\\opposite=b\\\\hypotenuse=95$

Then, knowing these values, you can substitute them into $sin\theta=\frac{opposite}{hypotenuse}$ , as below:

$sin(30\°)=\frac{b}{95}$

Finally, you must solve for "b" in order to find its value. You get that this is:

$95*sin(30\°)=b\\\\b=47.5$

6 0

3 years ago

Find the domain and range of f(x). Please explain your answer.<br> f(x) = √(x^2+5x+6)

timama [110]

Answer:

Domain:— [ x ≥ -2, x ≤ -3 ]

Range:— [ y ≥ 0 ]

Step-by-step explanation:

You may use graphing calculator to draw a graph and examine the graph’s domain and range. However, I’ll explain further about the graph of quadratic in a surd.

First, factor the quadratic expression in the surd:—

$\displaystyle \large{f(x)=\sqrt{(x+3)(x+2)}}$

We can find the x-intercepts by letting f(x) = 0.

I’ll be separating in two parts — one for finding x-intercept and one for finding y-intercept.

__________________________________________________________

Finding x-intercepts

Let f(x) = 0.

$\displaystyle \large{0=\sqrt{(x+3)(x+2)}}$

Solve for x, square both sides:—

$\displaystyle \large{0^2 = (\sqrt{(x+3)(x+2)})^2}\\\displaystyle \large{0=(x+3)(x+2)}$

Simply solve a quadratic equation:—

$\displaystyle \large{x=-3,-2}$

Therefore, x-intercepts are:—

$\displaystyle \large{\boxed{x=-3,-2}}$

__________________________________________________________

Finding y-intercept

Let x = 0.

$\displaystyle \large{f(x)=\sqrt{(0+3)(0+2)}}\\\displaystyle \large{f(x)=\sqrt{3 \cdot 2}}\\\displaystyle \large{f(x)=\sqrt{6}}$

Therefore, y-intercept is:—

$\displaystyle \large{\boxed{\sqrt{6}}}$

__________________________________________________________

However, I want you to focus on x-intercepts instead. We know that the square root only gives you a positive value. That means the range of function can only be y ≥ 0.

For domain, first, we have to know how or what the graph looks like. You can input the function in a graphing calculator as you’ll see that when x ≥ -2, the graph heads to the right while/when x ≤ -3, the graph heads to the left. This means that the lesser value of x-intercept gets left and more value get right.

See, between -3 < x < -2, there is no curve, point or anything between the interval. Therefore, -3 < x < -2 does not exist in function.

Hence, the domain is:—

x ≥ -2, x ≤ -3

4 0

2 years ago

15 Points

lakkis [162]

Answer:

y = 22⅘

Step-by-step explanation:

5x = 4

x = 0.8

y + 62(0.8) - 3y = 4

2y = 49.6 - 4

2y = 45.6

y = 22.8

4 0

3 years ago

How do you write 2x-3y=-15 In slope intercept form?

Vadim26 [7]

First, you subtract 2x on both sides
$- 3y = - 2x - 15$

divided on both sides by -3
$y = \frac{ - 2}{ - 3} x - \frac{15}{ - 3}$

$y = \frac{2}{3} x + 5$

8 0

3 years ago

Read 2 more answers

Which mark on the tape measure is closest to 2.23607 inches?

Lapatulllka [165]

Answer:

5.7 cm or 2 1/4 in

Step-by-step explanation:

Your tape measure is not shown.

On my tape measure, 5.7 cm is the closest mark. On the inch scale, 2 1/4 inches is the next-closest mark.

_____

On a tape measure graduated in 1/32 inch between 2 and 3 inches, you can find the closest mark by rounding to the nearest 32nd:

2.23607 × 32 ≈ 71.55 ≈ 72 --- 32nds of an inch

72/32 = 2 1/4 . . . . the closest mark on an inch ruler graduated in 32nds

__

For a ruler graduated in millimeters, you can find the closest millimeter in the same way. There are 25.4 mm to the inch.

2.23607 in × 25.4 mm/in ≈ 56.80 mm ≈ 57 mm

57 mm = 5.7 cm . . . closest mark on metric scale

__

When we check the error, we find the metric mark is closer than the inch mark.

5.7 cm ≈ 2.24409 in . . . . error of 0.00802 in

2 1/2 in = 2.25000 in . . . error of 0.01393 in

5 0

3 years ago