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2 years ago

7

If you were in a hot air balloon 500 m above the ground, at what angle of depression would you look at a point on the ground 800

m horizontally from the balloon

1 answer:

liubo4ka [24]2 years ago

3 0

Set up trig ratio using tangent.
Tan theta = opp/adj
Tan theta = 500/800
Tan^-1 (500/800) = 32 degrees

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56. How many tangent lines to the curve <img src="https://tex.z-dn.net/?f=y%3Dx%20%2F%28x%2B1%29" id="TexFormula1" title="y=x /(

PIT_PIT [208]

There are 2 tangent lines that pass through the point

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

Explanation:

Given:

$y=\frac{x}{x+1}$

The point-slope form of the equation of a line tells us that the form of the tangent lines must be:

$y=m(x-1)+2$ $[1]$

For the lines to be tangent to the curve, we must substitute the first derivative of the curve for $m$ :

$\frac{dy}{dx} =\frac{d(x)}{dx}(x+1)-x^\frac{d(x+1)}{dx} \\ \\$

$\frac{dy}{dx} =\frac{x+1-x}{(x+1)^2}$

$\frac{dy}{dx}= \frac{1}{(x+1)^2}$

$m=\frac{1}{(x+1)^2}$ $[2]$

Substitute equation [2] into equation [1]:

$y=\frac{x-1}{(x+1)^2}+2$ $[1.1]$

Because the line must touch the curve, we may substitute $y=\frac{x}{x+1}:$

$\frac{x}{x+1}=\frac{x-1}{(x+1)^2}+2$

Solve for x:

$x(x+1)=(x-1)+2(x+1)^2$

$x^2+x=x-1+2x^2+4x+2$

$x^2+4x+1$

$x\frac{-4±\sqrt{4^2-4(1)(1)} }{2(1)}$

$x=-2$ ± $\sqrt{3}$

$x=-2$ ± $\sqrt{3}$ <em> </em> $and$ $x=-2-\sqrt{3}$

There are 2 tangent lines.

$y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2$

and

$y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2$

8 0

2 years ago

The slope distance between two points was measured with an EDM and found to be 1223.88 ft. If the zenith angle (the angle from t

Serjik [45]

Answer:

Horizontal distance = 1218.41 ft

Step-by-step explanation:

Given data:

Slope distance = 1223.88 ft

Zenith angle is = 95°25'14"

converting zenith angle into degree

Zenith angle is $= 95 +\frac{25}{60} + \frac{14}{3600} =$ 94.421°

Horizontal distance $= S\times sin(Z)$

putting all value to get horizontal distance value

Horizontal distance $= 1223.88\times sin(95.421)$

Horizontal distance = 1218.41 ft

3 0

2 years ago

For what values of y:is the value of the fraction 7−2y /6 greater than the value of the fraction 3y−7 /12 ?

Fynjy0 [20]

Let's start by plugging in 1 for y. You get 7-2/6, which is 5/6. The other equation is 3-7/12, which equals -1/3. Now let's try 10. You get 7-2(10)/6, which is -13/6. The other equation is 3(10)-7/12, which is 23/12, and is larger!

1 is a value of y that could work!

Hope this helps!! :)

8 0

2 years ago

Read 2 more answers

Shelley is making a rectangular blanket with dimensions 8 1/2 feet by 5 1/2 feet. She purchases 10 yards of ribbon to put a bord

scoray [572]

Answer:

there are no options listed, but some statements that are true about this question are:

total perimeter = (8.5 x 2) + (5.5 x 2) = 28 feet = 9¹/₃ yards
since Shelley purchased 10 yards of ribbon, it should be enough
after finishing the blanket, Shelley will have 2 feet of ribbon left

6 0

2 years ago

What are the missing numbers?

n200080 [17]

2^2. 2 and 2. Because 2 and 2

8 0

2 years ago