A 45-foot tall tree is leaning towards a house, making an 86° angle with the ground. To stop the tree from leaning further, a cable is tied from the top of he tree and secured to a point on the ground 30 feet from the tree, opposite from the house. What angle does the cable make with the ground?
Answers
The angle (less than 90°) that the cable makes with the ground for this considered case is 59° approximately.
What is law of cosine?Let there is triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
[tex]a^2 + b^2 -2ab\cos(\theta) = c^2[/tex]
(c is opposite side to angle A)
Consider the diagram attached below.
In the diagram given, we have:
AB = tree with length of 45 ft
AC = cable, with length of 'x' ft (assume)
BC = distance of the base of the cable from the base of the tree of measurement 30 ft.
AD = vertical height of the point A (the top of the tree and cable) from the ground of 'h ft' (assume),
Using the cosine rule for the triangle ABC, taking:
|AC| = x = length of the side opposite to the known angle
|AB| = 45 ft and BC = 30 ft are rest of the two sides,
Angle opposite to AC is of 86°
Thus, we get:
[tex]45^2 + 30^2 -2(30)(45)\cos(86^\circ) = x^2\\\\2925 - 188.34 \approx x^2\\\\x \approx \sqrt{2736.66} \approx 52.31 \: \rm ft[/tex]
(took positive root because of x being length, which is a non-negative quantity).
For triangle ABD, using the sine ratio from the perspective of angle A, we get:
[tex]\sin(m\angle A) = \dfrac{\text{side opposite to A}}{\text{length of hypotenuse}} \\\\\sin(86^\circ) = \dfrac{h}{45}\\\\h = \sin(86^\circ) \times 45 \approx 44.89 \: \rm ft[/tex]
Now, for the triangle ACD, using the sine ratio from the perspective of angle C (smaller than 90°), we get:
[tex]\sin(m\angle C) = \dfrac{\text{side opposite to C}}{\text{length of hypotenuse}} \\\\\sin(\theta^\circ) = \dfrac{h}{x} \approx \dfrac{44.89}{52.31} \approx 0.858\\\\\theta =\sin^{-1}(0.858) \approx 59.09, 120.90[/tex]
Taking the angle smaller than 90°, we get:
[tex]\theta \approx 59.09^\circ \approx 59^\circ[/tex]
Thus, the angle (less than 90°) that the cable makes with the ground for this considered case is 59° approximately.
Learn more about law of cosines here:
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Answer:
That wasn't the correct answer
Step-by-step explanation:
c^2=45^2+30^2 - 2(45)(30)*Cos(94
c^2=2925+188.3425
c^2=3113.3425
take the square root:
c is approx. 55.8
sin86/55.8=sinx/45
55.8sinx=45sin94
divide both sides by 55.8
sinx=0.8045
sin^-1(0.8045)=53.6
Answer is 53.6 or "L" on the scavenger hunt worksheet
Related Questions
Please I need help and I'm struggling on this question
Answers
Answer:
D
Step-by-step explanation:
The combined expenses for year 3 and 4 are 600,000 + 700,000 which equal 1,300,000. The combined income for year 3 and 4 are 400,000 + 600,000 which equal 1,000,000. 1,300,000 (the combined expenses for year 3 and 4) is also 300,000 greater than 1,000,000 (the combined income for years 3 and 4)
Find the perimeter. Do not use decimals, units of measurement (ex. ft, mi,
yd, etc.) or commas in your answer.
Answers
76 yd
This is very simple
Perimeter is the sum of all the outer sides
22yd + 22yd + 16yd +16yd
This will give you
76yd
Answer: 76
Step-by-step explanation: Perimeter is 2(length +breadth)
2(22+16)
solve the inequality |x-1|+x<=5
Answers
Step-by-step explanation:
1st solution
When x-1 is positive
x-1+x≤5
2x-1≤5
2x≤6
x≤3
x-1≥0
x≥1
Solution: x€[1,3]
2nd solution
When x-1 is negative
-(x-1)+x≤5
-x-1+x≤5
-1≤5
0≤5
x-1<0
x<1
Solution: x€(-infinity, 1)
how many milliseconds are in a year
Answers
Answer:
3.154e+10
Step-by-step explanation:
The milliseconds unit number 31,536,000,000.00 ms converts to 1 yr, one calendar year.
Or for how many milliseconds is 365 days in a year?
The answer is one Year is equal to 31557600000 Milliseconds.
Answer:
3.154e+10, 30 billion milliseconds are in one calendar year.
Solve using the Elimination Method
5x + y = 4
6x - y = 7
Answers
Answer:
x=1,y=-1
Step-by-step explanation:
To use the elimination method, we make the coefficient of y the same:
But they are already the same just with different signs.
So we add the 2 equations to make equation 3:
5x + y = 4
+ + = +
6x - y = 7
11x = 11
Solve for x:
x = 1
Substitute the value of x into either equation 1 or 2 to find y:
I chose 1:
5(1)+y=4
5+y=4
y=4-5
y=-1
Our answer is x=1,y=-1
Substituting these values into equation 2 verifies our answer
if a thing is not a flower, then it is not a plant.
shorthand
Answers
Answer:
False, plants can be anything, take grass and trees and cacti, plant just need photosynthesis.
Step-by-step explanation:
You see, plants aren't based on if they are a flower or not
Explain how you would find 2/3 x 12 mentally. (help lol)
Answers
Answer: 8
You just need to multiply the numerator (top number) by the 12
2x12=24
so now its 24/3
24/3 simplified is 8
I’ll give brainiest
Answers
Answer:
If you taKE the pentagon and the hexagon she is wrong.
Step-by-step explanation:
hope this helped.
Answer:
nothing
Step-by-step explanation:
she is crazy, it fits perfectly, lol
8+4 please help me IM IN A HURRY
Answers
Answer:
12
Step-by-step explanation:
Just add 4 more to 8 and you get 12
Answer:
12
Step-by-step explanation:
if you simplify it, it becomes 1+1+1+1+1+1+1+1+1+1+1+1=12
you invest 5,000 in a bank for 2 years at a 3% interest rate.
Answers
Answer:
If simple interest: $5,300
If compounding interest: $5,304.50
Step-by-step explanation:
**As you haven't specified if the interest is simple or compounding, I have provided both**
Simple interest[tex]\sf Formula:A = P(1 + rt)[/tex]
where:
A = final amountP = principalr = interest rate (in decimal form)t = time (in years)Given:
P = 5000r = 3% = 0.03t = 2Substituting the given values into the formula and solving for A:
[tex]\implies \sf A = 5000(1 + 0.03 \cdot 2)[/tex]
[tex]\implies \sf A = 5000(1.06)[/tex]
[tex]\implies \sf A = 5300[/tex]
Compound interest[tex]\sf Formula:A=P(1+\frac{r}{n})^{nt}[/tex]
where:
A = final amountP = principalr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = 5000r = 3% = 0.03n = 1t = 2Substituting the given values into the formula and solving for A:
[tex]\implies \sf A=5000(1+\frac{0.03}{1})^2[/tex]
[tex]\implies \sf A=5000(1.03)^2[/tex]
[tex]\implies \sf A=5304.5[/tex]
Step-by-step explanation:
Let's say interest is I
Investment (deposit)is D=5000
Time T=2yrs
and rate R =3% thus
I=D×R/100×T
5000×3/100×2
I=300
point b has coordinates (3,1). the x-coordinate of point a is -6. the distance between point a and point b is 15 units. what are the possible coordinates of point a?
Answers
Answer:
(-6,-11).
Step-by-step explanation:
Hope this helps! Have a great day.
Let Tn, be the number of dots in figure.
How many dots are there in figure 30?
Look at the picture (don't mind of the highlighted ones).
Answers
Answer:
4294967293 dots
Step-by-step explanation:
Figure 1 has 5 dots.
Figure 2 has 13 dots.
Figure 3 has 29 dots.
Subtract and find different of each term:
13-5 = 829-13 = 16Let [tex]\displaystyle \large{b_n}[/tex] be sequence of difference (and the sequence appears to be geometric.)
So for [tex]\displaystyle \large{b_n}[/tex], find the common ratio which is 2.
Hence, [tex]\displaystyle \large{b_n = 8(2)^{n-1}}[/tex] - recall geometric sequence formula below:
[tex]\displaystyle \large{a_n = a_1r^{n-1}}[/tex]
The sequence of difference [tex]\displaystyle \large{b_n=8(2)^{n-1}}[/tex] can be simplified to:
[tex]\displaystyle \large{b_n=2^3(2)^{n-1}}\\\displaystyle \large{b_n=2^{n+2}}[/tex]
Now to find the original sequence:
[tex]\displaystyle \large{a_n = a_1 + \sum_{k=1}^{n-1}b_k}[/tex]
Hence:
[tex]\displaystyle \large{T_n=5+\sum_{k=1}^{n-1}8(2)^{k-1}}[/tex]
Recall:
[tex]\displaystyle \large{\sum_{k=1}^{n-1} a_1r^{n-1} =a_1\left( \dfrac{1-r^{n-1}}{1-r}\right)}[/tex]
Therefore:
[tex]\displaystyle \large{T_n=5+\sum_{k=1}^{n-1}8(2)^{k-1}}\\\displaystyle \large{T_n=5+8\left(\dfrac{1-2^{n-1}}{1-2}\right)}\\\displaystyle \large{T_n=5+8\left(\dfrac{1-2^{n-1}}{-1}\right)}\\\\\displaystyle \large{T_n=5+8(-1+2^{n-1})}\\\displaystyle \large{T_n=5-8+8(2)^{n-1}}\\\displaystyle \large{T_n=2^{n+2}-3}[/tex]
Therefore, the sequence for 5,13,29 is [tex]\displaystyle \large{2^{n+2}-3}[/tex].
Therefore, in figure 30:
[tex]\displaystyle \large{T_{30}=2^{30+2}-3}\\\displaystyle \large{T_{30}=2^{32}-3}\\\displaystyle \large{T_{30}=4294967293}[/tex]
Therefore, there are 4294967293 dots in figure 30
What is the value of x?
Answers
Answer:
Step-by-step explanation:
Sum of all angles of triangle = 180°
15x + 3 + 3x - 1 + 52 = 180
15x + 3x + 3 - 1 + 52= 180
Combine like terms.
18x + 54 = 180
To find the vlaue of x, we have to islolate x
Step1: Subtract 54 from both sides
18x = 180 - 54
18x = 126
Step2: Divide both sides by 18
x = 126/18
x = 7
Answer:
x = 7 degrees
Step-by-step explanation:
See attached image.
If someone answers this question, the next one i'll ask with be 100 points
Answers
[tex]\text{The two angles are supplementary, so their sum is}~ 180^{\circ} \\\\m\angle A + m\angle B =180\\\\\implies 2x-14+3x-6 = 180\\\\\implies 5x -20 = 180\\\\\implies 5x = 180+20\\\\\implies 5x = 200\\\\\implies x =\dfrac{200}5\\\\\implies x = 40\\\\\text{Hence, the measure of angle A is}~ m\angle A = (2\cdot 40 -14)^{\circ} = 66^{\circ}[/tex]
Somebody pls help! Im really confused and this is due soon!!!
Answers
Luis forma una torre con seis dados normales colocados sobre una mesa, tal como se muestra en la figura. Considerando que él puede moverse alrededor de la mesa, ¿Cuántos puntos cómo mínimo son visibles para él?
Answers
El número de puntos visibles para el será de 84.
SumasDado que Luis forma una torre con seis dados normales colocados sobre una mesa, para determinar cuántos puntos cómo mínimo son visibles para él se debe realizar el siguiente cálculo:
La suma de la cara del dado ubicada boca abajo, más su contraria, siempre dará 7. Por ende, en tanto 1 + 2 + 3 + 4 + 5 + 6 - 7 = 14, y 14 x 6 es igual a 84, el número de puntos visibles para el será de 84.
Aprende más sobre sumas en https://brainly.com/question/16620242
Answer:El número de puntos visibles para el será de 84.
Step-by-step explanation:
13. Namir purchased fuel for his farm truck that cost $79.17. He gave the clerk a $100 bill. How much change should Namir receive?
Answers
Answer:
$20.83
Step-by-step explanation:
cost of fuel purchased =$79.17
amount given to the clerk= $100
amount of change she should receive= 100-79.17
= $20.83
13 The diagram shows a square photo being placed right in the middle of a rectangular frame with an area of (x2 + 10x + 24) cm2. Given the length of the photo is x cm. 2 cm ? ? 2 cm The empty spaces on both sides of the photo have the same length. Find the length of each empty space.
Answers
Answer:
Length of empty space=3cm
Step-by-step explanation:
YOU CAN FIND THE COMPLETE SOLUTION IN THE GIVEN ATTACHMENT
I HOPE IT HELPED YOU
1.24$
6.43$
2.13$
with these numbers i need to round to the nearest dollar (SHOW WORK PLS) estimate total cost.
Answers
Answer:
$10
Step-by-step explanation:
1.24+6.43+2.13= 9.8
9.8 rounded to the nearest dollar is $10.
You can do it a different way, rounding the numbers before adding.
this would be:
1.3+6.4+2.1= 9.8
Either way, you get the same number. 9.8
And 9.8 rounded to the nearest dollar is $10
All the best, -Crispin
Answer:
$1.00
$6.00
$2.00
The estimated cost is $9.00
Step-by-step explanation:
1.24 = The 2 in 1.24 is smaller than 5 so you round down
6.43 = The 4 in 6.43 is smaller than 5 so you round down
2.13 = The 1 in 2.13 is smaller than 5 so you round down
Mya and Ashley are buying tickets to the art show. Adult
tickets cost $3 more than the student tickets. Mya buys 7
tickets and 6 adult tickets. Ashley buys 15 student tickets and
1 adult ticket. They both spend the same amount of money
on their tickets. What is the price of one adult ticket?
Answers
Answer:
$8
Step-by-step explanation:
a: adult tickets
s: student tickets
Mya: 7s + 6(3+s)
Ashley: 15s + 1(3+s)
Mya: 7s + 6(3+s) –> 7s + 18 +6s –> 13s +18
Ashley: 15s + 1(3+s) –> 15s + 3 + s –> 16s +3
13s + 18 = 16s +3
15 = 3s, divide 3 from both sides so s = 5
so students tickets cost $5
since adult tickets cost $3 more than student tickets:
($3 + $5) = $8 for an adult ticket.
Answer:
the answer is $8
Step-by-step explanation:
Pls give ana brainiliest she deserves it.:)
write an equation for each hyperbola.
vertices (0,2),(0,-2)
foci (0, +/- square root of 5)
Answers
Check the picture below, so the hyperbola looks more or less like so, hmmm so is a vertical one, so is opening towards the y-axis, meaning the fraction that is positive is the one with the y-variable, its traverse axis length is 4 units, from +2 to -2, meaning that a = 2, and the distance either focus to the center is √5, so
[tex]\textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ a=2\\ c=\sqrt{5} \end{cases}\qquad \cfrac{(y- 0)^2}{ 2^2}-\cfrac{(x- 0)^2}{ b^2}=1[/tex]
[tex]\sqrt{5}=\sqrt{2^2+b^2}\implies 5=4+b^2\implies 1=b^2\implies \sqrt{1}=b\implies 1=b \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(y- 0)^2}{ 2^2}-\cfrac{(x- 0)^2}{ 1^2}=1\implies \cfrac{y^2}{4}~~ - ~~x^2~~ = ~~1[/tex]
What is the answer to 3²x9
Answers
Answer:
81
Step-by-step explanation:
[tex]3^{2} =9[/tex]
[tex]9(9)=81[/tex]
10. A museum gift shop sells hats with embroidered logos of the museum.
The hats are available in small, medium, and large sizes. They are available
in the colors red and green.
Make a tree diagram or a table to represent all possible varieties of hats sold at
the museum.
Answers
About 1.37x10^7 people in South America speak English.
English is the primary language for about 3.7 x 10^6 of the
people. About how many times as much people speak
English as their primary language?
Answers
Answer:
1 x 106
Step-by-step explanation:
What is the measure of angle x?
Enter your answer in the box.
m∠x=
°
Answers
Answer:
x = 61°
Step-by-step explanation:
x = 180 - (37 + 82)
Angles in a triangle add up to 180°.
x = 180 - 119
x = 61°
What is the median of set A
Answers
Answer:
30
Step-by-step explanation:
10,10,20,20,20,20,30,30,30,30,40,50,50,60
The two numbers in the middle are 30 and 30.
30 + 30=60
60/2=30
Hope it Helps
ten less than 40% of a number is -4
Answers
Answer:
Number is "n" (.40* n)-10=-4
Step-by-step explanation:
i found this off of the Internet hope this helps
What is 26.375% written as a decimal number?
Answers
Answer: 263.75
Step-by-step explanation:
because i know
The decimal form of 26.375% is 0.26375.
How to convert percentage into decimal ?
Let, x be a number.
Now, if we want to convert x% to decimal, then we have to divide x by 100.
How to find decimal form of 26.375% ?To convert the given percentage into decimal, we have to divide the given percentage by 100.
∴ 26.375% = [tex]\frac{26.375}{100}[/tex] = 0.26375
Hence, 26.375% = 0.26375
Learn more about percentage here :
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Jeff drinks 2/3 of a glass of juice write A fraction that is equivalent to 2/3
Answers
Answer:
4/6 , 8/12, etc
Step-by-step explanation:
A fraction that can be equivalent to 2/3 is 4/6 or 8/12
This is because if you were to multiply 2/3 by 2/2 you multiplied by the same amount and also the product of that can be simplified to 2/3s.
A lender estimates the closing costs on a home loan of $90,000 as listed below. closing cost charge loan origination $180 title insurance $365 attorney’s fees $795 inspection $300 recording fees $120 escrow $980 the actual closing costs were: closing cost charge loan origination $180 title insurance $340 attorney’s fees $830 inspection $375 recording fees $150 escrow $1,000 evaluate the lender's good faith estimate as a percentage of the loan amount. a. the lender made a very good estimate; it was within 0.25% of the actual closing costs. b. the lender made a fairly good estimate; it was between 0.25% and 0.5% from the actual closing costs. c. the lender made a somewhat poor estimate; it was between 0.25% and 0.5% from the actual closing costs. d. the lender made a very poor estimate; it was between 0.5% and 0.75% from the actual closing costs.
Answers
Based on the details above, the lender's good faith estimate is one that is within 0.25% of the actual closing costs.
What is good faith estimate?A Good Faith Estimate commonly referred to as GFE, is known to be a kind of situation where a lender is given to a person as one request or apply for a form of reverse mortgage.
Note that the Lenders often needs a Good Faith Estimate (GFE) for about a period of three business days one getting the loan application. This will explain your loan terms and costs linked with the loan.
From the above, , the lender's good faith estimate is one that is within 0.25% of the actual closing costs and thus can tell the costs linked with the loan.
Learn more about good faith from
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Answer:
is D. the lender made a very poor estimate; it was between 0.5% and 0.75% from the actual closing cost
Step-by-step explanation:
I saw the answer on quizlet