Answer:
Use Trigonometric formulae to simplify expressions
Step-by-step explanation:
Re-order to group the x and y,
Sin(y) / Sin(a+y) = x
to differentiate apply d/dx to both sides
[tex]\frac{d}{dx}[/tex]Sin(y) / Sin(a+y) = [tex]\frac{d}{dx}[/tex]x
use division rule on left side which will give
[tex]\frac{dy}{dx}[/tex]Cos(y)Sin(a+y) - [tex]\frac{dy}{dx}[/tex]Cos(a+y)Sin(y) / Sin²(a+y) = 1
Group them so dy/dx is on the left hand side:
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / Cos(y)Sin(a+y) - Cos(a+y)Sin(y)
Apply trigonometric sum formula to expand Sin(a+y) and Cos(a+y),
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / Cos(y)[Sin(a)Cos(y) + Cos(a)Sin(y)] - Sin(y)[Cos(a)Cos(y) - Sin(a)Sin(y)]
Simplify it
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (Cos²(y) + Sin²(y))(Sin(a))
[tex]\frac{dy}{dx}[/tex] = Sin²(a+y) / (1)(Sin(a))
The water depth of a pond is initially 36 inches and decreases at a rate of 0.2 inches per day through evaporation. Write a linear function that represents the depth of the pond at a given time.
Answer:
36-0.2d
Step-by-step explanation:
d refers to the number of days
This should work for your question if not I'm very sorry
The required expression for the decreasing depth of the pond is y = 36 - 0.2x, Where y is the depth of the pond after x days.
The equation is the relationship between variables and constants represented as y = ax + b is an example of a polynomial equation.
Here,
The water depth of a pond is initially 36 inches
The water depth of a pond decreases at a rate of 0.2 inches per day through evaporation.
Let the number of the days be x , and the depth left be y
According to the question,
Total depth in x days = 0.2x
Total remaining depth = 36 - 0.2x
or
y = 36 - 0.2x
Thus, the required expression for the decreasing depth of the pond is y = 36 - 0.2x, Where y is the depth of the pond after x days.
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A motorist drives for m hours at 120km/hr and n hours at 18km/hr. Altogether Somina drives 78km in 5 hours. Find m and n.
Answer:
(0.118, 4.882)
Step-by-step explanation:
If a motorist drives for m hours at 120km/hr, then the Distance of the motorist is expressed as;
Distance = Speed * time
da = 120m
If he drives n hours at 18km/hr;
db = 18 * n
db = 18n
Speed of the motorist altogether is expressed as;
Speed =78km/5hrs
Speed = 15.6km/hr
SInce the total distnce is 78km
120m + 18n = 78 ....1 ..... * 1
If total time is 5hrs
m + n = 5....2 ...*18
Solve simultaneously
120m + 18n = 78
18m + 18n = 90
Subtract
120m - 18m = 78-90
102m = -12
m = 0.118 hrs
m =
Since m + n = 5
n = 5 - m
= 5 - 12/102
n = 4.882
Hence (m,n) is (0.118, 4.882)
Someone help me
Right now.
Explain how to evaluate 34
Step-by-step explanation:
you can evaluate 3^4(3raise to the power of 4)by multiplying 3 four times and the answer is 81 (3*3*3*3) 81Answer:
Three to the fourth means multiply 3 together 4 times, so expanded form is 3 x 3 x 3 x 3. To evaluate the power, find the product of the factors in expanded form. 3 times 3 is 9, 9 times 3 is 27, and 27 times 3 is 81.
Step-by-step explanation:
A shipping company borrows £70 million at 5% compound
interest to build a new cruise ship. If it repays the debt
after three years, how much interest will the company pay?
Answer:
10.500.000 libras esterlinas
Step-by-step explanation:
70000000 x 0,05 = 3.500.000
3.500.000 x 3 = 10.500.000
45 degrees and 6 find each variable
Will mark brainliest
Answer:
[tex]x = y = 3\sqrt{ 2[/tex]
Step-by-step explanation:
Given
The attached triangle
Required
Find x and y
The given triangle has 45 degrees as one of its angles, and it is also a right angle triangle.
For this kind of parameter, the opposite = the adjacent
i.e. x = y
Apply Pythagoras theorem
[tex]x^2 + y^2= 6^2[/tex]
Substitute x for y
[tex]y^2 + y^2= 6^2[/tex]
[tex]2y^2= 36[/tex]
Divide by 2
[tex]y^2 = 18[/tex]
Take square root
[tex]y = \sqrt{18[/tex]
[tex]y = \sqrt{9 * 2[/tex]
Split
[tex]y = \sqrt{9} *\sqrt{ 2[/tex]
[tex]y = 3*\sqrt{ 2[/tex]
[tex]y = 3\sqrt{ 2[/tex]
[tex]x = y = 3\sqrt{ 2[/tex]
Willard F. Libby received his undergraduate degree from
.
After he completed his graduate work, he became a professor at
.
In 1960, he won a Nobel Prize in
Answer:
Berkley
Step-by-step explanation:
After he completed his graduate work, he became a professor at Berkley.
Answer:
Willard F. Libby received his undergraduate degree from
✔ University of California, Berkley
.
After he completed his graduate work, he became a professor at
✔ University of California, Berkley
.
In 1960, he won a Nobel Prize in
✔ chemistry
.
Step-by-step explanation:
My dad was painting our living room. He started with 5/9 of a can of paint.
He used 1/3 of the can. How much paint did he have left?
Answer:
0.2 rounded up or 1/5 (also rounded up)
Which of the following are perfect powers?
1
24
Answer:
Uhh, I guess 24? I don't understand this question
Question: Which of the following are perfect powers?
Answer:
The answers on Edge are 27, 81, and 100. These are perfect powers.
the slope of a line is 1, and the y-intercept is -1. what is the equation of the line written in slope-intercept form?
Answer:
y=x-1
Step-by-step explanation:
A university law school accepts 3 out of every 13 applicants. If the school accepted 243 students, find how many applications they received.
Thank you anyone who helps =)
Answer:
1,053 applications
Step-by-step explanation:
hope this helps!! please mark brainliest :))
Answer:lol figure it out Step-by-step explanation:
Hi, can I send a screenshot for my math 110 class?
Answer:
go on
Step-by-step explanation:
¯\_(ツ)_/¯
Find the value of x.
Answer:
x = 1.8
Step-by-step explanation:
7x = 17x - 18
bring all x values to a side
7x -17x = -18
-10x = -18
divide by -10
x = 9/5 = 1.8
The value of x is 6.
We know from Mid point theorem
The Midpoint Theorem, also known as the Midsegment Theorem, states that in a triangle, the line segment connecting the midpoints of two sides is parallel to the third side and is half its length.
So, from the figure we can write
7x = 1/2 (17x - 18)
7x (2) = 17x - 18
14x = 17x - 18
By subtracting 17x from both sides to eliminate the x term on the right side:
14x - 17x = 17x - 17x - 18
-3x = -18
Next, divide both sides of the equation by -3 to solve for x:
(-3x) / -3 = (-18) / -3
x = 6
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multiplication: 2x12=__________
Answer:24
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
12+12=24
quick answer please!!!
Answer:
a. it has reflectional symmetry with 16 line of symmetry
1
This quilt is made up of cloth pieces shaped like isosceles right triangles.
The hypotenuse of each triangle is 16 centimeters long. Find the area of one
cloth triangle. *choose one
32 square centimeters
16 square centimeters
42 square centimeters
64 square centimeters
Answer:
Its 64 cm
Step-by-step explanation:
Determine the value of the first term and write a recursive definition for the following
sequence.
{10,15,20,25,30,35,…}
PLEASE SHOW YOUR WORK!
50! POINTS! HELP QUICK!
Which of the following is the equation for the graph shown?
y squared over 4 minus x squared over 12 equals 1
y squared over 16 minus x squared over 12 equals 1
x squared over 4 minus y squared over 12 equals 1
x squared over 16 minus y squared over 12 equals 1
50 points!
Solve this equation-5/2=3/4+n
What is n ?
Answer:
n = -(13/4) or -3.25(In decimal form)
Step-by-step explanation:
-(5/2) = (3/4) + n
-(5/2) - (3/4)
n = -(13/4)
Adice is thrown once. Find the probability
of getting an even number .
Answer:
50%
Step-by-step explanation:
There are 6 sides on a normal dice 2,4,6 are even numbers making it 3/6 or 1/2 of the numbers are even so there is a 50% chance an even number will be rolled.
how can making a table or graph help you decide whether a rule is a function
Answer:
It is possible to know whether the rule is a function or not through the graph by drawing a straight line parallel to the Y axis.If the straight line cuts the graph of the relationship at more than one point, then it is not a function. If it breaks it in one point, then it becomes a function.
Step-by-step explanation:
If you need any explanation on math you can communicate with me on Whats on this number +201557831028 or in email or face
Find the equation of this line.
Simplify the fractions.
Answer:
Step-by-step explanation:
Where's the line?
Solve: 64-3x-3 .64+22=38
4.0/5
136
The answer is x = -8/9.
Hope you have a good rest of your day. :)
Answer:
B. [tex]x=-\frac{8}{9}[/tex]
Step-by-step explanation:
edge 2021
:) Good luck, loves!
The diameter of a cylindrical vessel is 42 cm and its height is 50 cm. Find the
volume of the vessel. ( π = 22 / 7 )
Answer:
I have made it in above picture
What is equivalent to the equation y=3x+z/4?
How many solutions does this equation have?
–9 − 5p = –2 − 5p
Answer:
no solutions
Step-by-step explanation:
welp me someone this iready is for a grade.
Answer: 1920 cubic centimeter
Step-by-step explanation:
L*W*H for both and add
8*10*10=800
8*10*14=1120
800+1120=1920 cubic centimeters
Pls help with math ASAP due tonight
Answer:
The equation of the line is y=-1/2x-3.5
Step-by-step explanation:
Given the two points on the line, (1, -4) and (3, -5), find the slope of the line with the equation [tex]m=\frac{y2-x2}{y1-x1}[/tex].
[tex]m=\frac{-5-(-4)}{3-1} =\frac{-5+4}{3-1} =\frac{-1}{2}[/tex]
After you find the slope of the line, substitute x and y with either point given to you. For me, I'll use point (1, -4) to solve for the y-intercept.
[tex]-4=\frac{-1}{2} (1)+b[/tex]
[tex]\frac{1}{2} -4=\frac{-1}{2} +\frac{1}{2} +b[/tex] add both sides by 1/2 so that b is alone
[tex]\frac{-7}{2} =b[/tex]
You can rewrite -7/2 as -3.5.
Help I’ll give brainly
i really want to say 648 but it might be 27 or 15552
Select the correct answer.
Which expression is equivalent to?
Step-by-step explanation:
[tex]4 {x}^{2} \sqrt{ {5x}^{4} } \times 3 \sqrt{5 {x}^{8} } [/tex]
[tex]4 {x}^{2} \times \sqrt{5} \times {x}^{2} \times 3 \sqrt{5} \times x ^{4} [/tex]
[tex]4 {x}^{2} \times {x}^{2} \times {x}^{4} \times \sqrt{5} \times 3 \sqrt{5} [/tex]
= 4x⁸ × 5 × 3
= 60x⁸