A bird is nested on a tree top that is 14 feet above the ground. The bird looks down at a worm at a 30 angle of depression. How far is the worm from the base of the tree?

Answers

Answer 1

Applying the tangent ratio, the distance of the worm from the base of the tree is: 24.2 ft.

What is the Tangent Ratio?

Tangent ratio is part of the Trigonometry ratios, which is expressed as, tan ∅ = opposite side / adjacent side in a right triangle.

The information given would form a right triangle, where:

Reference angle = ∅ = 30°Opposite side = 14 ftAdjacent side = distance of the worm from the base of the tree = x

Applying the tangent ratio, we would have:

tan 30 = 14/x

x = 14/tan 30

x = 24.2 ft.

Therefore, applying the tangent ratio, the distance of the worm from the base of the tree is: 24.2 ft.

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Related Questions

which pair of pairs of polygons are congruent.

Answers

Answer:

bottom left. (arrow shaped)

Step-by-step explanation:

congruent shapes are the same size and shape

A number w minus 3 is less than or equals to 10

Answers

Answer:

Step-by-step explanation:

A number w minus 3 (w - 3) is less than or equal (≤) to 10

w - 3 ≤ 10

   + 3  + 3

w ≤ 13

Hope this helps!

The graph of f(x) = 8 - x and line l which is tangent to f at x =1 is
shown in the figure to the right. The equation for line l is y =-3x +10.
Region R is the shaded region between line l, the graph off and the
y-axis while S is the shaded region between line l, the graph off and
the x-axis.
(a) Find the area of the shaded region R.

Answers

By taking the integral of the difference between the two given lines, we will see that R = 0.75.

How to find the area of the region R?

Notice that the area will be given by the integral of the difference between the line L and our function on the interval [0, 1]

Then we just need to compute:

[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx[/tex]

Solving that we will get:

[tex]R = \int\limits^1_0 {-3x + 10 - (8 - x^3)} \, dx = \int\limits^1_0 ({-3x + 10 - 8 + x^3} )dx\\\\\R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\\\[/tex]

[tex]R = \int\limits^1_0 ({-3x + 2 + x^3} )dx\\\\R = \frac{-3}{2}*(1)^2 + 2*1 + \frac{1^4}{4} = 0.75[/tex]

So the area of region R is 0.75 square units.

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can someone solve what is n/n^3

Answers

Answer:

Alex = No B.

Step-by-step explanation:

1) Use Quotient Rule: [tex]\frac{x^{a} }{x^{b} } =x^{a-b}[/tex]

[tex]n^{1-3}[/tex]

2) Simplify 1 - 3 = 2

[tex]n^{-2}[/tex]

3) Use Negative Power Rule: [tex]x^{-a} =\frac{1}{x^{a} }[/tex]

[tex]\frac{1}{n^{2} }[/tex]


255, 250, 245, ...
Find the 40th term.

Answers

Answer:

so here we minus 5 from 255 to get to 250 and we do it again to get to 245. for reaching the 40th term we should do it 39 times.

so, 255+ (-5) (39) = 255 - 195 = 60

which is our 40th term.

The 40th term of  (255, 250, 245...) is 60.

What is arithmetic progression ?The difference between any two successive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers.There are three distinct progression kinds. As follows:Mathematical Progress (AP)Graphical Progress (GP)Rhythmic Progress (HP)It is feasible to find a formula for the nth term for a certain kind of sequence called a progression. The most popular mathematical progression, with simple formulas, is the arithmetic progression.

Calculations :

The formula to find the nth term = [tex]a_{n}[/tex]  =  -5n + 260

                                                      = [tex]a_{40}[/tex] x 5n = 260

                                                      = 260 - 200 = 60

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Rewrite the following without an exponent. (9/5)^-1

Answers

Answer:

5/9

Step-by-step explanation:

What we have here is the reciprocal of (9/5).  Inverting (9/5) results in (5/9), which is the desired result.

Help me out please, should be easy

Answers

Answer:

I'm pretty sure the points are plotted at (-1,-2) but I'm not exactly sure. Correct me if I'm wrong! :D


Solve for x. Round all answers to the nearest tenth.
11
11.7
10.2
11.9

Answers

11.9 - last one

Step-by-step explanation:

Adjacent + hypotenuse = Cos / Cah

Cos32 = x/14

x14

11.87... = x

So, 11.9 to nearest tenth

Hope this helps!

Find the distance between the two points (1, -4) and (5, 3). Give an exact answer in
terms of a square root.

Answers

Answer:

A lovely answer of : [tex]\sqrt{17}[/tex]

For those of you who use a dark theme : square root of (17)

And a short Explanation:

Use the Pythagorean theorem to find the result

Answer both Question 11 and 12. I will make Brainelist + 50 points ​

Answers

Answer:

#11. i) 5, ii) 6, iii) - 4, iv) 6#12- see below

Step-by-step explanation:

#11

Given equation for sum of the first n terms

[tex]S_n=7n-2n^2[/tex]

Using the equation solve the following

i)

The first term [tex]t_1[/tex], is same as the sum of the first 1 term, so n = 1

[tex]t_1=S_1=7(1)-2(1)^2=7-2=5[/tex]ii)

Sum of the first 2 terms, when n = 2

[tex]S_2=7(2)-2(2)^2=14-8=6[/tex]iii)

Common difference is the difference between two consequitive terms.

First, find the second term:

[tex]t_2=S_2-t_1=6-5=1[/tex]

Now find the difference between the first two terms:

[tex]d=t_2-t_1=1-5=-4[/tex]iv)

We need to find such n that [tex]S_n[/tex] = - 30

[tex]7n - 2n^2=-30[/tex][tex]2n^2 - 7n-30=0[/tex][tex]2n^2-12n+5n-30=0[/tex][tex]2n(n-6)+5(n-6)=0[/tex][tex](n-6)(2n+5)=0[/tex][tex]n=6[/tex] is the only positive root

So the answer is 6

#12

Simplifying in steps as below

a) i)[tex]\dfrac{5}{y-3} +\dfrac{2}{3-y}=[/tex][tex]\dfrac{5}{y-3}-\dfrac{2}{y-3}=[/tex][tex]\dfrac{5-2}{y-3}=[/tex][tex]\dfrac{3}{y-3}[/tex]ii)[tex]\cfrac{1}{m+3} +\cfrac{2m}{m^2-9} =[/tex][tex]\cfrac{1}{m+3} +\cfrac{2m}{(m-3)(m+3)} =[/tex][tex]\cfrac{m-3}{(m-3)(m+3)}+\cfrac{2m}{(m-3)(m+3)} =[/tex][tex]\cfrac{m-3+2m}{(m-3)(m+3)} =[/tex][tex]\cfrac{3m-3}{(m-3)(m+3)}[/tex]

Liam is a tyre fitter. it takes him 124 minuets to fit 4 tyre's to a lorry. how long would t take him to fit 6 tyre's to a lorry?
if he works for 93 minuets how many tyre's will he fit?

Answers

168 minutes or 2 hours 48 minutes

Step-by-step explanation:

Since 12 tyres is 3 times 4 tyres, it will take 3 times as long as 56 minutes.

3 * 56 minutes = 168 minutes

We can convert the answer to hours and minutes.

60 minutes = 1 hour

120 minutes = 2 hours

168 minutes – 120 minutes = 48 minutes

168 minutes = 2 hours 48 minutes

Answer: 168 minutes or 2 hours 48 minute

3 times as long as 56 minutes.
3 * 56 minutes = 168 minutes
We can convert the answer to hours and
minutes.
60 minutes = 1 hour
120 minutes = 2 hours
168 minutes - 120 minutes = 48 minutes
168 minutes = 2 hours 48 minutes
Answer: 168 minutes or 2 hours 48 minute

I need help on my work or I get 0 percent

Answers

Answer:

B and E

Step-by-step explanation:

E is 3/4 8 times (this is just simple multiplication) and B is 3/4 8 times just shorter. Simplified if you will.

Evan walked 2 1/8 miles to his aunts house. He has already walked 6/8 mile. How much farther does Evan have to go?

Answers

Rewrite 2 1/8 as 17/8

Now subtract:

17/8 - 6/8 = 11/8 = 1 3/8


answer : 1 3/8 miles left

pieces of chalk are stacked in a pile. part of the pile is shown. the bottom row has 15 pieces of chalk, and the top row has 6 pieces of chalk. each row has on less piece of chalk than the row below it. how many pieces of chalk are in the pile?

Answers

To answer the question, you need to count backwards from 15 to 6 and add up the pieces of chalk. 15+14+13+12+11+10+9+8+7+6=105. That means there are 105 pieces of chalk in the pile. Hope this helps.

SOMEONE PLSSSSSS HELP ME SOLVE THIS FAST
I WILL MARK BRAINLIEST

Answers

Answer:

D

Step-by-step explanation:

I calculated the area for 54 feet and then for 0.5 feet using the equation [tex]A=\sqrt{\frac{3}{4} }a^{2}[/tex] , where a is the size and then divided first area by second area

find measure of the missing angles and justify your answer with postulates and theorems.

Answers

Answer:

Step-by-step explanation:

Carrie uses her phone primarily to take a lot of selfies. The storage space on her phone is limited, so Carrie needs to keep track of how many selfies she takes.
There is a proportional relationship between the number of selfies Carrie takes, x, and the amount of storage (in megabytes) she uses taking selfies, y.
x (selfies) y (megabytes)
10 20
12 24
21 42
22 44
Write an equation for the relationship between x and y. Simplify any fractions.
y=

Answers

Answer:   y = 2x

Explanation:

A direct proportion is of the form y = kx

To find k, pick any row to divide the y over x value

k = y/x = 20/10 = 2k = y/x = 24/12 = 2k = y/x = 42/21 = 2k = y/x = 44/22 = 2

No matter which row you go for, the constant of proportionality is 2. Meaning that we double the x value to get to y.

Therefore, we go from y = kx to y = 2x

Please help me with this!!

Answers

Answer:

A, B, D, F

Step-by-step explanation:

Given expression: [tex]8^{\frac23}[/tex]

Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]

[tex]\implies 8^{\frac23}=(8^2)^{\frac13}[/tex]

Apply exponent rule [tex]a^{\frac{1}{n}}=\sqrt[n]{a}[/tex]

[tex]\implies (8^2)^{\frac13}=\sqrt[3]{8^2}[/tex]

Therefore, option A

Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]

[tex]\implies 8^{\frac23}=(8^{\frac13})^2[/tex]

Apply exponent rule [tex]a^{\frac{1}{n}}=\sqrt[n]{a}[/tex]

[tex]\implies (8^{\frac13})^2=(\sqrt[3]{8})^2[/tex]

Therefore, option B

Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]

[tex]\implies 8^{\frac23}=(8^{\frac13})^2[/tex]

As [tex]8^{\frac13}=2[/tex]

[tex]\implies (8^{\frac13})^2=2^2[/tex]

Therefore, option D

Apply exponent rule [tex]a^{bc}=(a^b)^c[/tex]

[tex]\implies 8^{\frac23}=(8^{\frac13})^2[/tex]

As [tex]8^{\frac13}=2[/tex]

[tex]\implies (8^{\frac13})^2=2^2[/tex]

[tex]\implies 2^2=4[/tex]

Therefore, option F

how many one third cup servings are in 16 cups

Answers

it’s 48 because you need 3, 1/3 cups to make 1 full cup so 3 times 16 is 48!

LOTS OF POINTS + BRAINLIEST

Suppose p and q are both prime numbers with p > q. Prove that p-q and p+q cannot both be positive perfect squares.

FULL PROOF REQUIRED.

Answers

Answer:

The list od prime number is a quadratic sequence, each time going up by n + 2. for example, 1, 4, 9, 16, 25. they are going up by 3, then + 2 and add 2 every step. The sequence is always going up by an odd number. a negative number take away a negative number always gives you a positive number, likewise, adding does too. Therefore, you can not get both of them to fit into the sequence of increasing odd numbers.

Round to the nearest tenth, I will give brainlyest PLEASE

Answers

1. cos B= a/x

x= 11/cos 37°

x= 13.77

2. tan A= a/x

x= 4/tan 41°

x= 4.60

3. sin B = x/c

x= sin 37° × 10.3

x= 6.20

4. tan A= a/b

tan A= 4/13

A= tan-1(0.31)

A= 17°6'10"

5. cos A= b/c

cos A= 12/13

A= cos -¹(0.92)

A= 22°37'12"

6. tan B= a/b

tan B= 3/3

tan B= 1

B= tan‐¹(1)

B= 45°

The number 1 is a factor of _________.
A) all odd numbers
B) all even numbers
C) all whole numbers

Answers

Answer:

The number 1 is a factor of C)all whole numbers.

hello!

1 is a factor of all whole numbers.

Every single number, including odd numbers and even numbers, is divisible by 1 (evenly, without any remainders)

Remember, whole numbers include odd numbers, even numbers, and 0.

note:-

Hope everything is clear; if you need any more explanation and/or clarification, kindly let me know, and I will comment and/or edit my answer.

What is the Area of this shape?

Answers

14 * 12 = 168

(12*8) / 2 = 48

216 cm ^2

Answer:

1,344 cm counting the side shape or 168 cm counting only the rectangle.

Step-by-step explanation:

14 cm x 12 cm = 168cm

168 x 8 = 1,344 cm

100 Points ! ! !
Exploiting points will be reported.

Brain deposited $9,824 into a savings account for which interest is compounded daily at a rate of 3.62%. How much interest will he earn after 8 years?

SHOW WORK AND WILL GIVE BRAINLIST

Answers

$3299.62

compounded daily interest : [tex]\sf A = P(1 + \dfrac{r}{n})^{nt}[/tex]

[tex]\sf 9,824.00(1 + \dfrac{3.62\%}{365})^{(365)(8)}[/tex]

[tex]\sf \$13,123.62[/tex]

total money he will have : $13,123.62

amount earned : $13,123.62 -  $9,824 = $3299.62

Answer:

Interest = $3,299.64 (nearest cent)

Step-by-step explanation:

Compound interest formula:  [tex]\sf I=P(1+\frac{r}{n})^{nt}-P[/tex]

where:

I = total interest earned over time periodP = initial principal balancer = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsed

Given:

P = $9,824r = 3.62% = 0.0362n = 365t = 8 years

Substituting given values into the formula and solving for I:

[tex]\sf \implies I=9824(1+\frac{0.0362}{365})^{365 \times8}-9824[/tex]

[tex]\sf \implies I=13123.62461-9824[/tex]

[tex]\sf \implies I=3299.62 \ (nearest \ hundredth)[/tex]

convert 5'5 into meters​

Answers

It will be around 1.6metres

hope it helps

Answer:

1.65 meters

Step-by-step explanation:

1 ft = 0.3048 meters

just multiply

Part A: Given sine of theta is equal to radical 3 over 2 comma determine three possible angles θ on the domain [0,∞).


Part B: Given θ = 675°, convert the value of θ to radians and find sec θ.


(Picture below is equation stated in Part A)

Answers

Answer:

  A.  {60°, 120°, 420°}

  B.  θ = 15π/4; sec(θ) = √2

Step-by-step explanation:

A.

The sine function is periodic with period 360°, and it is symmetrical about the line θ = 90°. The reference angle for the given value of sin(θ) is ...

  θ = arcsin(√3/2) = 60°

The next larger angle with the same sine is (2×90°) -60° = 120°. Any multiple of 360° added to either one of these angles will give an angle with the same sine. A possible set of 3 angles is ...

  {60°, 120°, 420°}

__

B.

One degree is π/180 radians, so the given angle in radians is ...

  θ = 675° = 675(π/180) radians = 15π/4 radians

This angle has the same trig function values as 7π4, a 4th-quadrant angle with a reference angle of π/4, or 45° The secant of that angle is

  sec(45°) = √2

The 4th-quadrant angle has the same sign, so ...

  sec(675°) = sec(15π/4) = √2


A rare species of insect was discovered in the rain forest. In order to protect the species,
environmentalists declare the insect endangered and transplant the insects into a protected area.
The population of the insect t months after being transplanted is given by P(t).
P(t) =
60(1+0.4)
0.01t+3
a. How many insects were discovered? In other words, what was the population when t = 0?
b. What will the population be after 5 years? Round to the nearest whole insect.

Answers

Using the given function, it is found that:

a) 20 insects were discovered.

b) The population after 5 years will be of 417 insects.

What is the function for the number of insects after t months?

As stated in the exercise, it is given by:

[tex]P(t) = \frac{60(1 + 0.4t)}{0.01t + 3}[/tex]

Item a:

[tex]P(0) = \frac{60[1 + 0.4(0)]}{0.01(0) + 3} = \frac{60}{3} = 20[/tex]

20 insects were discovered.

Item b:

5 years = 60 months, hence:

[tex]P(60) = \frac{60[1 + 0.4(60)]}{0.01(60) + 3} \approx 417[/tex]

The population after 5 years will be of 417 insects.

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The cards below have a mean of 25. What is the missing number?: ? 19, 22, 31

Answers

Answer: Its 28.

Step-by-step explanation:

The missing number in the card s 28

How to determine the missing number?

Represent the missing number with x.

So, we have:

x, 19, 22 and 31

The mean of a dataset is:

Mean = Sum/Count

So, we have:

25 = (x + 19 + 22 + 31)/4

Multiply both sides by 4

100 = x + 19 + 22 + 31

Evaluate the sum

100 = x + 72

Subtract 72 from both sides

x = 28

Hence, the missing number is 28

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3(2x + 1) = 7x-2
What is x

Answers

Answer:

x=-5

Step-by-step explanation:

3(2x+1)=7x-2

6x+3=7x-2

6x-7x=-2-3

x=-5

3(2x + 1) = 7x-2

3*2x+3*1=7x-2

6x+3=7x-2

6x-7x=-3-2

-1x=-5

x=5

Determine the value of y, if x is -1. y= | x |-4

Answers

y=|-1|-4
The absolute value of -1 is 1
y=1-4
y=-3
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