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Marianna [84]
2 years ago
14

A bird flying at an altitude of 50 feet spies a worm in the ground up ahead. How far must the bird travel to the worm if the ang

le of depression from the bird to the worm is 56°?
Mathematics
1 answer:
Blababa [14]2 years ago
7 0

Answer:

33.7 ft

Step-by-step explanation:

We solve the above question using Trigonometric function of Tangent

tan θ = opposite/adjacent

θ = 56°

Opposite = 50 ft

Adjacent = x

Cross Multiply

tan 56 = 50 ft/x

Cross Mulitiply

tan 56 × x = 50ft

x = 50ft/tan 56

x = 33.725425842 ft

Approximately = 33.7 ft

The bird must travel 33.7 ft to meet the worm

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Explain how to do this please show your work
madreJ [45]

Answer:

(x-  5)(x - 3)

x(x - 3) -5(x - 3)

x^2 - 3x - 5x + 15

x^2 - 8x + 15

4 0
2 years ago
A box of pencils is 5 1/4 inches wide. Seven pencils, laid side by side, take up 2 5/8 inches of the width. How many inches of t
Andre45 [30]

Answer:   Width of box is not taken up by pencils =  2\dfrac58\text{ inches}

Width of each pencil =\dfrac38\text{ inches}

Step-by-step explanation:

Given: Width of pencil box = 5\dfrac14\text{ inches}=\dfrac{21}{4}\text{ inches}

Width of seven pencils = 2\dfrac58\text{ inches}=\dfrac{16+5}{8}\text{ inches}=\dfrac{21}{8}\text{ inches}

Width of box is not taken up by pencils =  Width of pencil box  - Width of seven pencils

\left \{ {{y=2} \atop {x=2}} \right. \dfrac{21}{4}-\dfrac{21}{8}\\\\=\dfrac{21\times2-21}{8}\\\\=\dfrac{21}{8}\text{ inches}=2\dfrac58\text{ inches}

Width of box is not taken up by pencils =  2\dfrac58\text{ inches}

Width of each pencil = (Width of seven pencils ) ÷ 7

=\dfrac{21}{8}\div7\\\\=\dfrac{21}{8}\times\dfrac17\\\\=\dfrac38\text{ inches}

Width of each pencil =\dfrac38\text{ inches}

3 0
2 years ago
Read 2 more answers
Georgia’s scores in six subjects are 89, 75, 92, 68, 78, 75, and 80. If she finds a single value that summarizes all the values
posledela
It would be mean. The mean is the average that is you are looking for, since she wants a summerization of all the values in the data set. To find the mean (average) add all the numbers and then divide by the amount of numbers.
5 0
2 years ago
Assume that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles
OverLord2011 [107]

Answer:

Final answer is approx 6.644 years.

Step-by-step explanation:

Given that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles is 16% every year and that of cars is 25% every year.

So we can use growth formula:

A=P\left(1+r\right)^t

Then we get equation for motorcycles and cars as:

A=5.75\left(1+0.16\right)^t

A=3.5\left(1+0.25\right)^t

Now we need to find about when the sale of cars will be more than the sale of motorcycles. So we get:

3.5\left(1+0.25\right)^t>5.75\left(1+0.16\right)^t

3.5\left(1.25\right)^t>5.75\left(1.16\right)^t

3.5\left(1.25\right)^t>5.75\left(1.16\right)^t

\frac{\left(1.25\right)^t}{\left(1.16\right)^t}>\frac{5.75}{3.5}

\left(\frac{1.25}{1.16}\right)^t>1.64285714286

t\cdot\ln\left(\frac{1.25}{1.16}\right)>\ln\left(1.64285714286\right)

t>\frac{\ln\left(1.64285714286\right)}{\ln\left(\frac{1.25}{1.16}\right)}

t>6.6436473051

Hence final answer is approx 6.644 years.

7 0
2 years ago
Is the inequality true for all values of x? <br> (3x+8)^2 &gt; 3x(x+16)
emmainna [20.7K]

Answer:

Yes

Step-by-step explanation:

yes

6 0
2 years ago
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