Answers
You may need to input the number only without the "degrees".
=============================================================
Explanation:
First we'll focus on triangle DEH. Ignore the other points and values.
We have the sides of EH = 32 and DH = 49. Let x be the measure of angle DHE, which is one of the pieces of angle DHG. We'll use the cosine rule to find x.
cos(angle) = adjacent/hypotenuse
cos(H) = EH/DH
cos(x) = 32/49
x = arccos(32/49)
x = 49.227195
The value is approximate and rounded to 6 decimal places. Make sure your calculator is in degree mode. Arccos is the same as inverse cosine.
We'll come back to this value later.
---------------------
Now focus on triangle HFG. Ignore the other points.
We have the sides of FG = 38 and GH = 43
Let y be the measure of angle FHG, which is the missing piece to form angle DHG. Based on how x and y are set up, we can say x+y = angle DHG.
To find y, we'll need the sine rule this time
sin(angle) = opposite/hypotenuse
sin(H) = FG/GH
sin(y) = 38/43
y = arcsin(38/43)
y = 62.094527 which is approximate to 6 decimal places
---------------------
The last step is to add the values of x and y we found earlier
angle DHG = (angle DHE) + (angle FHG)
angle DHG = (x) + (y)
angle DHG = (49.227195) + (62.094527)
angle DHG = 111.321722
angle DHG = 111 degrees after rounding to the nearest whole degree.
----------------------
If you wanted to do this all in one step, you could say:
arccos(32/49)+arcsin(38/43) = 111.3217 which rounds to 111 degrees.
Related Questions
Find the centroid of ABC if
A = (2, 2), B = (-1,0), and C = (8,4).
([?], [ ])
Answers
Answer:
The centroid of ABC is (3 , 2).
Step-by-step explanation:
The steps are :
[tex]centre = ( \frac{x1 + x2 + x3}{3} \: , \: \frac{y1 + y2 + y3}{3} )[/tex]
[tex]centre = ( \frac{2 + ( - 1) + 8}{3} \: , \: \frac{2 + 0 + 4}{3} )[/tex]
[tex]centre = ( \frac{9}{3} \: , \: \frac{6}{3} )[/tex]
[tex]centre = (3 \: , \: 2)[/tex]
Answer:
The centroid of ∆ABC is (3 , 2).
Step-by-step explanation:
Solution :
Here's the required formula to find the centroid of ∆ABC :
[tex]{\star{\footnotesize{\purple{\underline{ \boxed{\sf{\pink{Centroid = \bigg( \dfrac{x_1 + x_2 + x_3}{3} \: , \: \dfrac{y_1 + y_2 + y_3}{3} \bigg)}}}}}}}}[/tex]
Where :
[tex]\rightarrow\rm{x_1}[/tex] = 2[tex]\rightarrow\rm{x_2}[/tex] = -1[tex]\rightarrow\rm{x_3}[/tex] = 8[tex]\rightarrow\rm{y_1}[/tex] = 2[tex]\rightarrow\rm{y_2}[/tex] = 0[tex]\rightarrow\rm{y_3}[/tex] = 4Substituting all the given values in the formula to find the centroid of ∆ABC
[tex]{\implies{\small{\sf{Centroid = \bigg( \dfrac{x_1 + x_2 + x_3}{3} \: , \: \dfrac{y_1 + y_2 + y_3}{3} \bigg)}}}}[/tex]
[tex]{\implies{\small{\sf{Centroid = \bigg( \dfrac{2 + ( - 1) + 8}{3} \: , \: \dfrac{2 +0 + 4}{3} \bigg)}}}}[/tex]
[tex]{\implies{\small{\sf{Centroid = \bigg( \dfrac{2 - 1 + 8}{3} \: , \: \dfrac{2 +0 + 4}{3} \bigg)}}}}[/tex]
[tex]{\implies{\small{\sf{Centroid = \bigg( \dfrac{10 - 1}{3} \: , \: \dfrac{2 + 4}{3} \bigg)}}}}[/tex]
[tex]{\implies{\small{\sf{Centroid = \bigg( \dfrac{9}{3} \: , \: \dfrac{6}{3} \bigg)}}}}[/tex]
[tex]{\implies{\small{\sf{Centroid = \bigg( \cancel\dfrac{9}{3} \: , \: \cancel\dfrac{6}{3} \bigg)}}}}[/tex]
[tex]{\implies{\small{\sf{Centroid = \Big( 3\: , \: 2 \Big)}}}}[/tex]
[tex]\star{\underline{\boxed{\rm{\red{Centroid = \Big( 3\: , \: 2 \Big)}}}}}[/tex]
Hence, the centroid of ∆ABC is (3 , 2).
[tex]\rule{300}{1.5}[/tex]
Find the derivative of (3+tan X )( 4+3 Cos X)
Answers
The derivative of [tex]f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)[/tex] is [tex]f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}[/tex].
In this question we shall use the following derivative rules:
Derivative of a sum of functions
[tex]\frac{d}{dt}(f(t) + g(t)) = \frac{df(t)}{dt} + \frac{dg(t)}{dt}[/tex] (1)
Derivative of a product of functions
[tex]\frac{d}{dt}(f(t)\cdot g(t)) = \frac{df(t)}{dt}\cdot g(t) + f(t)\cdot \frac{dg(t)}{dt}[/tex] (2)
Derivative of a constant
[tex]\frac{d}{dt}(k) = 0[/tex], [tex]\forall k \in \mathbb{R}[/tex] (3)
Derivative of a function multiplied by a constant
[tex]\frac{d}{dt}(c\cdot f(t)) = c\cdot \frac{df(t)}{dt}[/tex], [tex]\forall\, c\in \mathbb{R}[/tex] (4)
Derivative of the cosine function
[tex]\frac{d}{dt} \cos t = -\sin t[/tex] (5)
Derivative of the tangent function
[tex]\frac{d}{dt}\tan t = \sec^{2} t[/tex] (6)
Chain rule
[tex]\frac{d}{dt}f[u(t)] = \frac{df(u)}{du}\cdot \frac{du(t)}{dt}[/tex] (7)
Let be [tex]f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)[/tex], then the derivative of [tex]f(x)[/tex] is:
[tex]f'(x) = \sec^{2}x\cdot (4 + 3\cdot \cos x) + (3+\tan x)\cdot (-3\cdot \sin x)[/tex]
[tex]f'(x) = 4\cdot \sec^{2}x+3\cdot \sec x -9\cdot \sin x -3\cdot \sin x\cdot \tan x[/tex]
[tex]f'(x) = \frac{4+3\cdot \cos x}{\cos^{2}x} -\frac{9\cdot \sin x \cdot \cos x+3\cdot \sin^{2}x}{\cos x}[/tex]
[tex]f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}[/tex]
The derivative of [tex]f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)[/tex] is [tex]f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}[/tex].
We kindly invite to check this question on derivatives: https://brainly.com/question/21202620
PLEASE HELP!!!!
A farmer is building a chicken coop/ She digs some hole for the support poles. The bottom of the first hole is -6 1/4 ft from ground level. The bottom of the second hole is 1/3 as far from ground level as the first hole.
What is the position of the bottom of the second hole, relative to ground level?
A. 18 3/4 ft
B. 2 1/12 ft
C. -2 1/12 ft
B. -18 3/4 ft
Answers
3x - 4 + 2(-3 - 6x).
Answers
Answer:
-9x - 10
Step-by-step explanation:
Answer:
x=9/2
Step-by-step explanation:
So in this equation we have to solve using PEMDAS, or parentheses, exponents, multiplication, division, addition, then subtraction, going from left to right. So first, i deal with whats in the parentheses, but since it cannot be subtracted, I next go on to the next step. Since there are no exponents, our next step is to multiply or distribute 2 into (-3-6x). In other words, i multiply 2 by -3 and 2 by -6x. This is going to be -6 -12x. After that, i add and subtract common factors, so 3x-12x is -9x, and -4-6 is -10. This leaves us with -9x-10=0. I add 10 to each side according to addition property of equality. Thus, the equation is -9x=-10. Divide both sides by -9, by the division property of equality, and u get 10/9. If you want a decimal answer, type it into a calculator.
I need help with this.
Answers
Answer:
h
Step-by-step explanation
12 inches in 1 foot.
2.54 cm in 1 inch.
5x 12=60 inches
60 +4=64inches.
64 x 2.54=162.56 cm
Answer:
H. 162.56 cm
Step-by-step explanation:
12 inches in 1 foot.
2.54 cm in 1 inch.
5x 12=60 inches
60 +4=64inches.
64 x 2.54=162.56 cm
what does 9a^2 + 2b^2 if a=4 and b=7?
Answers
Answer:
242
Step-by-step explanation:
Answer:
242
Step-by-step explanation:
Given
9a² + 2b² ← substitute a = 4 and b = 7
= 9(4)² + 2(7)²
= 9(16) + 2(49)
= 144 + 98
= 242
Allison is saving to buy a $500 bicycle by working during
summer vacation,
• The job pays her $8 for every 1 hour worked.
• Allison works exactly 20 hours each week.
If she works for 4 weeks and buys the bicycle, how much
money will she have left over?
Answers
Answer:
140.00
Step-by-step explanation:
20 x 4 = 80 hours worked
80 x 8.00 = $640.00
640.00 - 500.00 = 140.00
Can someone do both plzzzz
Answers
Answer:
Answer to question 7: -2x+5y+9
Answer to question 8: 2x-6y+1
Answer:
7.) -2x + 5y + 9 ; 8.) 2x - 6y + 1
Step-by-step explanation:
7.)
7 + 2x + 5y - 4x + 2 ⇒ -2x + 5y + 9
2x - 4x ⇒ -2x
5y ⇒ 5y
7 + 2 ⇒ 9
8.)
-4y + 2x - 2y + 1 ⇒ 2x - 6y + 1
2x ⇒ 2x
-4y - 2y ⇒ -6y
1 ⇒ 1
help me pls and show work 8th grade math
Answers
Answer:
Find the slope this way Hanna,
Step-by-step explanation:
slope = m
m = (y2-y1) / (x2-x1)
you are given the two points
P1 = (-2,-6) in the form (x1,y1)
P2 = (2,2) in the form (x2,y2)
plug those into the slope formula above
m = (2-(-6) ) / (2 - (-2) )
m = (2 +6) / (2+2)
m = 8 / 4
m = 2
if you need more explanation just leave a comment, it will show up and I'll come look at your question
PLEASE HELP ASAP! DO IN 5 MINUTES! WILL MARK BRAINLIEST!
Answers
Answer:
15
Step-by-step explanation:
Given
Hypotenuse (h) = 17 cm
perpendicular (p) = 8 cm
base (b) = ?
we know by using Pythagoras theorem
b = √h² - p²
= √ 17² - 8²
= √ 225
= 15 cm
or
YZ = 15 cm
Hope it will help :)❤
A hospital has to be patrolled by security guards 24 hours a day. Seven security guards are ordered to split each day’s guard duty equally. How long will each security guard spend on guard duty in one day? Record your answer in hours rounded to the nearest tenth.
Answers
Answer:
3 hours
Step-by-step explanation:
24/7 = 3.42 hours and rounded that will be 3 hours
Does a rotation preserve congruence
Answers
80% or 7/9 which is greater
Answers
Answer:
80% is greater
Step-by-step explanation:
Answer:
The number 80% is greater than 7/9
Step-by-step explanation:
You have a balance of $4,600 on your credit card. The interest rate is 12% (1% per month). The late payment fee is $40.
You miss a payment. What are your fees plus interest for the month?
Answers
Answer:
$86
Step-by-step explanation:
first you gotta find the interest
4,600 * 1% = 46
so the interest is $46
then you add the interest and late fees together to get the payment for the month
46 + 40 = $86
your total cost is $86
The fess plus interest of the month will be $86 after missing a payment.
Given:
Balance = $4600
Interest rate = 0.01
Step 1: Calculate the interest for the month.
Interest for the month = Balance × Monthly Interest Rate
Substituting the value back to the formula
Interest for the month= $4,600 × 0.01
= $46
Step 2: Add the late payment fee.
Late payment fee = $40
Step 3: Total fees plus interest for the month.
Total = Interest for the month + Late payment fee
Total = $46 + $40
Total = $86
So, fees plus interest for the month when you miss a payment amount to $86.
Learn more about interest here:
https://brainly.com/question/28272078
#SPJ6
Find the gradient of the line segment between the points (8,6) and (10,12)
Answers
Answer:
3.
Step-by-step explanation:
The gradient = (12-6/(10-8)
= 6/2
= 3.
Equivalent ratio
44:99=
108:36=
33:9=
49:14=
Answers
Answer:
44:99 = 4:9
108:36 = 3:1
33:9 = 11:3
49:14 = 7;2
hope it helps
Given the equation x + 2y = 0, which equation will form a system of linear equations without a solution?
Please help
Answers
Answer:
2.5 and -0.75
The price of the shirt is 40$ the sale. tax is 8%
What is the total price for the shirt
A. 36.80
B. 33.20
C. 48.00
D 43.20
Answers
the correct answer is D 43.20
Answer:
A is the answer
Step-by-step explanation:
8% is the same same as 3.20$
So subtract that from 40$
Hope I could help !
A person standing on level ground is 3020 feet away from the foot of a building. If the height of the building is 2534 feet, find the angle of elevation formed at the point where the person is standing to the nearest degree
Answers
Answer:
40°
Step-by-step explanation:
Base length, b = adjacent = 3020 feets
Height of building, h = opposite = 2534 feets
The angle of elevation formed :
Using the trigonometry relation:
Tan θ = opposite / Adjacent
Tan θ = 2534 / 3020
Tan θ = 0.8390728
θ = tan^-1(0.8390728)
θ = 39.999
= 40°
Find the difference using fraction bars or a paper and pencil. Write your answer in simplest form. 7/10 - 1/2 help asap!! im on a test
Answers
Step-by-step explanation:
7/10 - 1/2 = 7/10 - 5/10 = 2/10
Answer:
4/4
Step-by-step explanation:
If I live in the United States and I send 100 dollars to someone who lives in Mexico, how much are 100 dollars in Mexican money
I'm conscious
Answers
Answer:
2935 Mexican pesos
Step-by-step explanation:
First, it's worth noting that at current exchange rates, your $100 will equal upwards of 2,395 pesos in Mexico.
Help plzzzzzzzzzzzzzzzzzzzz
Answers
Answer:
B
Step-by-step explanation:
Y is the total cost, 22x is how many tickets bought, and 10 is the parking cost
Use the information in the figure. Find mZD. 106 D Drawing not to scale 37° 53
Answers
Answer: Its B
Step-by-step explanation: Hope this was helpful I am not to sure this is the right answer but let me know if it is
PLEASE HELP MEEEEE!!!!!
Answers
Answer:
Tan ∠E = 63/16 = 3.9375
Step-by-step explanation:
Tan ∠E = 63/16 = 3.9375
Answer:
Try 63/16 which is 4.0625
Step-by-step explanation:
Again im sorry if its incorrect. XD hope it helps tho. doing the rest o ur question noe .. tehe
Yassar has purchased a $30,000 car for his business. The car depreciates at 30%
every year. {Depreciation means the value of the car decreases by that percent each
year).Calculate the value of the car to the nearest cent at the end of the 5th
year.
A. $5,042.10
B. $111.387.90
C. $21.000.00
D. $39,346.85
Answers
Answer:
A
Step-by-step explanation:
30% of 30000 is 9000, 30000-9000=21000 (1 year)
30% of 21000 is 6300, 21000-6300=14700 (2 years)
30% of 14700 is 4410, 14700-4410= 10290 (3 years)
30% of 10290 is 3087, 10290-3097= 7203 (4 years)
30% of 7203 is 2160.9, 7203-2160.9= 5042.1 (5 years)
Posted the next question!
Answers
Answer:
angle 3 and angle 2 are complementary angle.
Help me with this pls 10 points
Answers
Answer:
48
Step-by-step explanation:
Add 84+48 to get 132. subtract 180 the total to the 132 to get 48.
Answer:
its not 10 points its says 8
Step-by-step explanation:
Draw a parallel line to line PQ, Start the line with point R
Answers
Answer:It’s a long triangle
^^^^^^^^^^^^^^^^^^^^^^^^^^
Answer:Howwwwwwww!!!!!!.”?.?....?.??.??.
PLEASE HELP ASAP I HAVE 10 MINUTES
Answers
Answer:
4, -3
Step-by-step explanation:
I believe it'd be 4, -3 due to the shape moving seven units downwards, though I've only messed with triangles so I may be wrong. Sorry if I am.
Find the value of x.
Answers
Answer:
Step-by-step explanation:
Remark
Since the chords of the circle are equal and non intersecting, The 2 bisecting perpendiculars are going to be equal.
Equation
5x = 7x - 8 Subtract 7x from both sides
5x - 7x = - 8
-2x = - 8 Divide by - 2
x = - 8/-2
x = 5