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3 years ago

A 96 foot tree casts a shadow that is 120 feet long. What is the angle of elevation of the sun? Round to the nearest degree.

Mathematics

1 answer:

zysi [14]3 years ago

4 0

Answer:

$\alpha \approx 39^{\circ}$

Step-by-step explanation:

Let assume that tree grows perpendicular to surface. The statement is geometrically represented in the attachment included below, which resembles a right-angled triangle. Lastly, the angle of elevation of the sun is determined with the help of the following trigonometric relationship:

$\tan \alpha = \frac{96\,ft}{120\,ft}$

$\tan \alpha = \frac{4}{5}$

$\alpha = \tan^{-1}\left(\frac{4}{5} \right)$

$\alpha \approx 38.660^{\circ}$

$\alpha \approx 39^{\circ}$

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The temperature of a weather station was 12.8 °F at midnight and fell 1.4 °F each hour for six hours. Which of the following sol

Len [333]

Answer:

Let's try to find a linear relation like:

T(h) = a*h + b

where a is the slope and b is the y-intercept.

h is the number of hours after midnight.

T is the temperature at the time defined by h.

We know that at midnight, the temperature is 12.8°F.

At midnight, we have h = 0, then:

T(0) = a*0 + b = 12.8°F

b = 12.8°F

Now we know that our function is:

T(h) = a*h + 12.8°F

We also know that the temperature fell 1.4 °F each hour for six hours.

Then the slope will be -1.4°F

We can write the linear relationship as:

T(h) = -1.4°F*h + 12.8°F (for 0 ≤ h ≤ 6)

Where we have a restriction in the possible values of h, because we know that this model only works for six hours after midnight,

3 0

2 years ago

Read 2 more answers

Find the equation of the axis of symmetry of the parabola.

Stolb23 [73]

Answer:

Just substitute 0 instead of f (x),therefore

$x { }^{2} - 12x + 36 \\ x = 6$

The answer option is C

7 0

3 years ago

Assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are n= 8 trials, each with

alina1380 [7]

Answer:

0.80589

Step-by-step explanation:

So all of the numbers of correct answers less than 4 are 0,1,2,3

We need to calculate the probability for each separately and then add them together.

To find the probability we have to first find the combination. We know that there’s n=8 trials and that p=0.3. So 1-0.3 gives us 0.7.

The combination formula is: ! / (!(−)!)

So the n would always =8, and the r would be 0,1,2,3. So you would have to calculate it for 0,1,2,3 Separately. This can be done by hand or you can use a simple combinations calculator online.

For 0;

The combination is 1,

1 x 0.3^0 x 0.7^8-0 =

0.057648

For 1;

The combination is 8,

8 x 0.3^1 x 0.7^8-1 =

0.19765

For 2;

The combination is 28

28 x 0.3^2 x 0.7^8-2 =

0.296475

For 3;

The combination is 56

56 x 0.3^3 x 0.7^8-3 =

0.254122

All that’s left is to add these four numbers;

0.057647 + 0.19765 + 0.296475 + 0.254122 = 0.80589

4 0

3 years ago

2. Consider the circle x² + y2 = 1, given in figure. Let OP makes an angle 30° with the x axis.

PolarNik [594]

The equation of the tangent line to the circle passing through the point P is; y = (1/√3)x ± 2/√3

<h3>How to find the equation of the tangent?</h3>

I) We are given the equation of the circle as;

x² + y² = 1

Since angle of inclination is 30°, then slope is;

m = tan 30 = 1/√3

Then equation of the tangent will be;

y = (1/√3)x + c

Put (√3)x + c into the given circle equation to get;

x² + ((1/√3)x + c)² = 1

x² + ¹/₃x² + (2/√3)cx + c² = 1

⁴/₃x² + (2/√3)x + (c² - 1) = 0

Since we need to find value of c for equation to become tangent, then the above quadratic equation must have real and equal roots.

Thus;

((2/√3)c)² - 4(⁴/₃)(c² - 1) = 0

⁴/₃c² - ¹⁶/₃(c² - 1) = 0

⁴/₃c² - ¹⁶/₃c² + ¹⁶/₃ = 0

4c² = ¹⁶/₃

c² = ⁴/₃

c = √⁴/₃

c = ±²/√3

Thus, equation of tangent is;

y = (1/√3)x ± 2/√3

II) Radius from the given equation is 1. Thus, we will use trigonometric ratio to find the x and y intercept;

x-intercept is at y = 0;

0 = (1/√3)x ± 2/√3

-(1/√3)x = ±2/√3

Intercept is positive. Thus;

x = (2/√3)/(1/√3)

x = 1

y - intercept is positive at x = 0;

y = (1/√3)0 ± 2/√3

y = 2/√3

Read more about Equation of tangent at; brainly.com/question/17040970

#SPJ1

6 0

1 year ago

Find the area of the circle with the given diameter.<br> d = 28 inches

alexdok [17]

Answer: 196pi in.^2

Step-by-step explanation:

Divide the diameter by two.

You would get 14, then square it, you would get 196.

4 0

3 years ago