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2 years ago

A traveler comes upon a fork in the road on the path to the travelers right a sign reads Mercer 24 km

Mathematics

2 answers:

Mariana [72]2 years ago

8 0

Answer:

a=25.km

Step-by-step explanation:

A traveler comes upon a fork in the road on the path to the travelers right a sign reads Mercer 24 km

The concluding part could be the following:

On the path to the traveler's left, a sign reads "Turtle Lake: 17km." The traveler also observes that the angle between the paths is 1.3 radians. Assuming both paths are perfectly straight, what is the distance between Mercer and Turtle Lake? km Round your answer to the nearest kilometer

since the angle between them is actually 1.3 rad

lets convert to degrees

74.48 degrees

using cosine of angle we can find the distance between the two destinations

$a^{2} =b^{2} +c^{2} -2bcCos\alpha$

$\alpha$ =74.48 deg

a^2=17^2+24^2-(2*17*24)cos74.48

a^2=646.65

find the square root of both sides

a=25.42km

approximately=25Km

trapecia [35]2 years ago

3 0

Answer: this is not a question

Step-by-step explanation:

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Sketch the region of integration for the following integral. ∫π/40∫6/cos(θ)0f(r,θ)rdrdθ

solong [7]

Answer:

The graph is sketched by considering the integral. The graph is the region bounded by the origin, the line x = 6, the line y = x/6 and the x-axis.

Step-by-step explanation:

We sketch the integral ∫π/40∫6/cos(θ)0f(r,θ)rdrdθ. We consider the inner integral which ranges from r = 0 to r = 6/cosθ. r = 0 is located at the origin and r = 6/cosθ is located on the line x = 6 (since x = rcosθ here x= 6)extends radially outward from the origin. The outer integral ranges from θ = 0 to θ = π/4. This is a line from the origin that intersects the line x = 6 ( r = 6/cosθ) at y = 1 when θ = π/2 . The graph is the region bounded by the origin, the line x = 6, the line y = x/6 and the x-axis.

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2 years ago

Which number, when substituted for x, makes the equation 4x+8=164x+8=16 true?

ra1l [238]

X = 2

4x + 8 = 16
-8 -8
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4x= 8
-- --
4 4
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7 0

2 years ago

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The degree measure of angle a is 135°. which expression below is equivalent to the radian measure of angle a?

Kazeer [188]

It is given that $\angle a=135^{\circ}$ .

Now, know that in 180 degrees there are $\pi$ radians. This can be written as:

$180^{\circ}=\pi$ radians

$\therefore 1^{\circ}=\frac{\pi}{180}$ radians (dividing both sides by 180)

Thus, to find the measure of the given angle of $135^{\circ}$ in radians, we will have to multiply the above equation by 135. Thus, we get:

$135^{\circ}=\frac{\pi}{180}\times 135$ radians

$135^{\circ}\approx2.356$ radians

Thus, equivalent to the radian measure of angle a is 2.356

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2 years ago

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Which transformations have been applied to the graph of f(x) = x2 to produce the graph of g(x) = –5x2 + 100x – 450? Select three

RSB [31]

Answer:

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

Step-by-step explanation:

we have

$f(x)=x^{2}$

This is a vertical parabola open upward

The vertex is a minimum

The vertex is the origin (0,0)

$g(x)=-5x^{2}+100x-450$

This is a vertical parabola open downward

The vertex is a maximum

The first thing to note is that fx) is a parabola that opens up and g(x) opens down, so a reflection across the x-axis must have been applied.

Find the vertex of g(x)

Convert to vertex form

$g(x)=-5x^{2}+100x-450$

Complete the square

$g(x)=-5(x^{2}-20x)-450$

$g(x)=-5(x^{2}-20x+100)-450+500$

$g(x)=-5(x^{2}-20x+100)+50$

$g(x)=-5(x-10)^{2}+50$

The vertex is the point (10,50)

To translate the vertex of (0,0) to (10,50)

The rule of the translation is

(x,y) ------> (x+10,y+50)

That means ----> The translation is 10 units at right and 50 units up

therefore

The transformations are

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

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2 years ago

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Given ΔADC and ΔAEB, What is AE?

chubhunter [2.5K]

Answer:

AE = 43.2 units

Step-by-step explanation:

As per the given question image, it can be seen that in the $\triangle ADC \text { and }\triangle AEB :$

1. $\angle B = \angle C = 90^\circ$

2. $\angle A$ is common to both the triangles.

3. Two angles are common, so the third angle $\angle E$ is also equal to $\angle D$ .

All the three angles in the $\triangle ADC \text { and }\triangle AEB$ are equal to each other, hence the triangles are similar.

As per the property of similar triangles, the ratio of their sides will be equal.

AB : AC = AE : AD

AC = 88 units

BC = 55 units

AB = AC - AB = 33 units

Let side AE = $x$ units

Side AD = AE + ED

So, AD = $x + 72$

Using the ratio:

$\dfrac{AB}{AC} = \dfrac{AE}{AD}\\\Rightarrow \dfrac{33}{55} = \dfrac{x}{x+72}\\\Rightarrow 55x = 33 \times 72\\\Rightarrow x = \dfrac{3\times 72}{5}\\\Rightarrow x = 43.2\ units$

So, AE = 43.2 units

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2 years ago