Answer:
x = 2 y = -12
Step-by-step explanation:
x+ y = -10
2 + y = -10
y = -10 -2 = -12
Question in picture below.
If y=sin^3 x,prove that d^2y/dx^2 - 2 cot x dy/dx +3y=0
The proof of d^2y/dx^2 - 2 cot x dy/dx +3y = 0 is determined as 6cos²xsinx - 3sin³x - 6cos²xsinx + 3sin³x = 0
Equation of the derivativesThe equation is given as;
[tex]\frac{d^2y}{dx^2} - 2\ cotx \ \frac{dy}{dx} \ + 3y = 0 \ \ ---(1)[/tex]
y = sin³x
First derivative of yy = sin³x
let u = sinx (du/dx = cosx)
y = u³
dy/du = 3u²
[tex]\frac{dy}{dx} = \frac{dy}{du} \ .\ \frac{du}{dx} \\\\[/tex]
dy/dx = 3u² x cosx
dy/dy = 3sin²xcosx
y' = 3sin²xcosx
Second derivative of yy' = 3sin²xcosx
let u = sin²x (du/dx = 2sinxcosx)
v = cosx (dv/dx = -sinx)
[tex]y'' = \frac{d^2y}{dx^2} = V\frac{du}{dx} + U\frac{dv}{dx}[/tex]
y'' = 3[cosx(2sinxcosx) + sin²x(-sinx)]
y'' = 6cos²xsinx - 3sin³x
Substitute first derivative and second derivative of y in equation (1)
[tex]\frac{d^2y}{dx^2} - 2\ cotx \ \frac{dy}{dx} \ + 3y \\\\(6cos^2xsinx \ - \ 3sin^3x) \ - \ 2(\frac{cosx}{sinx} )(3sin^2xcosx) \ + 3(sin^3x) \\\\6cos^2xsinx \ - \ 3sin^3x \ - 6cos^2xsinx \ + \ 3sin^3x = 0 \ \ proved[/tex]
Learn more about differentiation here: https://brainly.com/question/25081524
Which expression is equivalent to 2(3 - x)?
Plsss help me with this answer this is due tmrw
Answer:
2
Step-by-step explanation:
13+7x=27
-13 -13
7x=14
÷7
x=2
Answer:
x = 2
Step-by-step explanation:
Given
13 + 7x = 27#1) Subtract 13 from each side.
13 + 7x - 13 = 27 - 137x = 14#2) Divide 7 from each side.
7x/7 = 14/7x = 2Pls help math easy will give brainlest
Answer(s)
Problem 9: 138.53
Problem 10: Function
Problem 11: Not A Function (Not Sure)
Edit; Problem 9 should've been right, I have no idea then.
please help (due tomorrow)
7:obtuse angle
8:right angle
9:FDE, AFB
Maya is building a model of her city's downtown area. She is constructing part of an office building, as shown below. Each cube has an edge length of 1/6 foot.
The height of the model building is foot?
A.3/4
B.1/2
C.1/6
D.3/18
E.1/4
Answer: the answer is 1 over 2 which is e
Step-by-step explanation: 4 and 2 and 3 equal 9 so 1 over 6 times 9 cubes equal 1.5 which is 1 over 2
What is the slope of
the line?
Give your answer as
a fraction in simplest
form.
Answer:
3/4
Step-by-step explanation:
two points are
(8,6) and (12,9)
formula :
(y2-y1)/(x2-x1)
(9-6)/(12-8) =
3/4
slope often means rate of change
in this graph
price changes as the number of lemon changes
in economics this graph is called the
supply curve
its called the law of supply
increases in price causes increase in the quantity supplied
if something is worth more, it will cause an increase in price which will cause people who want to make money to try supply more of it
quizlet
A store having a sale on chocolate chips
and walnuts. For 6 pounds of chocolate chips and 5 pounds of walnuts, the total cost Is $35. For 2 pounds of
chocolate chips and 3 pounds of walnuts, the total cost Is $15. Find the cost for each pound of chocolate chips and each pound of walnuts.
Cost for each pound ( chocolate chips: $
X
0
Cost for each pound of walnuts: $[
Answer:
chocolate chips: $3.75
walnuts: $2.5
Step-by-step explanation:
lets say chocolate chips cost x dollars and walnuts cost y dollars. we then have
6x + 5y = 35
2x + 3y = 15
multiply the second equation by 3 to get 6x + 9y = 45
subtract the 1st equation from the new equation to get 4y = 10, so y=$2.50
plug this value into the 2nd equation to get x=$3.75
The product of two positive integers is 20. Find the two numbers
Answer:
1 and 20 or 2 and 10 or 4 and 5
Step-by-step explanation:
the divisors of 20 are 1 , 2 , 4 , 5 , 10 , 20
Then
20 = 1 × 20
= 2 × 10
= 4 × 5
find the area of each plane figure 10.5 km 3.7 km
Answer:
28.4
Step-by-step explanation:
10.5x2= 21
3.7x2= 7.4
21+7.4 = 28.4
A set of books sits on a shelf at a store. This line plot shows the thickness of each book. Jessica buys one of the second thinnest books on the shelf. Jada buys the second thickest book on the shelf.
How much thicker is Jada's book than Jessica's book?
Enter your answer in the Box as a mixed number in simplest form.
Please help.
Answer:
2 inches
Step-by-step explanation:
if there are 2 books that are 1 1/2 thick, the second thinnest book would be 1/12... the second thickest book im guessing would be 3 1/2, so you'd have 2 inches in between
Answer: the answer is, 2 and one half
Step-by-step explanation: I took the test. Please give brainliest
What is the discriminant of the polynomial below?
2x^2 + 3x - 7
A. -5
B. -47
C. 23
D. 65
Answer:
2x^2 + 3x - 7 (a= 2 , b= 3 , c= -7)
discriminant= b^2 - 4ac
= (3)^2 - 4(2)(-7)
= 9 + 56 = 65
The answer is D. 65
Hope this helps :)
Cindy counted 8,723 blue beads, 4,632 red beads, 3,512 green beads, and 5,971 white beads.
Doris counted 6,802 blue beads, 3,162 red beads, 987 green beads, and 2,689 white beads.
How many did Cindy and Doris count in all.
Answer:
36,478 beads
Step-by-step explanation:
8723+4632+3512+5971=22,838
6,802+3,162+987+2,689=13,640
22,838+13,640= 36,478
So Cindy and Doris have 36,478 beads in total.
Pls help word problem how many hours?
This answer was deemed incorrect, so sorry for posting this!
Pls help easy math will give brainlest
Answer:
Problem 17
Independent -- T
dependent -- D
_________________________
Problem 16
Independent -- X
dependent -- Y
_________________________
Problem 18
Independent -- R
dependent -- Q
Step-by-step explanation:
17/3x+17-2/3x-15 what is the solution
Answer:
Step-by-step explanation:
[tex]\sf \dfrac{17}{3}x+17-\dfrac{2}{3}x-15 = \dfrac{17}{3}x-\dfrac{2}{3}x+17-15[/tex]
[tex]=\dfrac{17-2}{3}x + 2\\\\\\=\dfrac{15}{3}x+2[/tex]
Express as a sum of logarithms.
[tex] log_{2}(16 \times 24) [/tex]
Use the vectors v = (3,-4) and w =(1,2) to answer the following questions:
a. Find v. w
b. Find the angle between v and w. Round to the nearest degree.
We will see that for the given vectors:
a) v.w = -5b) The angle between the vectors is 116.57°How to find the dot product?
Remember that the dot product between two vectors:
a = (x₁, y₁) and b = (x₂, y₂) the dot product is:
a.b = x₁*x₂ + y₁*y₂ = |a|*|b|*cos(θ).
a) We have:
v = (3,-4) and w = (1,2)
The dot product will give:
v.w = 3*1 + (-4)*2 = 3 - 8 = -5
b) We will have:
|v|*|w|*cos(θ) = -5
Where:
|v| = √(3^2 + (-4)^2) = 5|w| = √(1^2 + 2^2) = √5Then we have:
5*√5*cos(θ) = -5
cos(θ) = -1/√5
θ = Acos(-1/√5) = 116.57°
The angle between the two vectors is 116.57°.
If you want to learn more about vectors, you can read:
https://brainly.com/question/3184914
mrs. matthews gave a test to her 120 science students. if she gives 5 bonus points to each test grades , how will this affect the mean , median , and mode scores?
How many solutions does this
system have?
=
-x + 3y = 3
2x – 6у = 30
If the total amount of a loan, $24,000 is paid off in 3 years with an interest rate of 3.70%, compounded monthly, what was the principal rounded to the nearest cent? Provide only a numerical value for your answer (For example, if your amount came to $5,704.97, then you would type in 5704.97 as your answer).
Answer:
21482.20
Step-by-step explanation:
A = P(1+r/m)^mt
A = Total Amount, P = Principal, r = rate. m = number of months, t = time
24000 = P(1 + 0.037/12)^12*3
24000 = P(1.003083333)^36 --- I added 1 to 0.037 divied by 12, then multiplied 12*3 on the outside of the parentheses
24000 = 1.117204101(P)
24000/1,117204101 = 1.117204101P/1.1177204101
P = 21482.20
Good luck! :)
Charlotte has a peice of string that is 14 feet long. She cuts it into pieces that are each 1/3 foot long. How many cut pieces of string does charlotte have?
Answer:
42
Step-by-step explanation:
Since each cut is 1/3 of a foot, you can tell that it will take 3 pieces to make 1 foot. Based on that ratio, you can do 14*3, which is 42 pieces.
Can somebody please help me I will mark u brilliant
Answer:
2/7 + (-3/4) + (-2/7) + 4/3
If we look at 2/7 and (-2/7), we can see that both of them combined will get you a result of 0, so let's do that first.
2/7 + (-2/7) = 0
Now we're left with;
(-3/4) + 4/3
Make sure to convert both fractions into having a common denominator,
[They both have a common denominator of 12], so:
(-3/4) = (-9/12)
4/3 = 16/12
Add them:
(-9/12) + 16/12
16/12 - 9/12
= 7/12, which cannot further be simplified.
1. The width of a rectangular table is 7 - 2x feet and the length is 5x + 2 feet. Write a polynomial that represents the perimeter.
2. Base from problem number 10, what is the perimeter of the rectangular table if x is 3.
Answer:
perimeter is 36
Step-by-step explanation:
if x=3
then it turns into
Width 7-2(3)
length 5(3)+2
which equals
width 1
length 17
since it's a perimeter you add all four corners
which is 1+1+17+17=36
Evaluate the sum of the finite geometric series -5- 10 - 20 - 40 - . . . - 2560
Answer:
-5015
Step-by-step explanation:
Sum of a Geometric Series (finite)
Sₙ = a(rⁿ - 1) / (r - 1)Step 1 : Finding n
aₙ = -2560r = -10/-5 = 2a = -5aₙ = arⁿ⁻¹ -2560 = -5(2)ⁿ⁻¹512 = (2)ⁿ⁻¹2⁸ = (2)ⁿ⁻¹8 = n - 1n = 9Step 2 : Substitute the values in the Sₙ formula
S₉ = -5(2⁹ - 1) / 2 - 1S₉ = -5 x 1023S₉ = -5015Joan believes the best way to play roulette is to place a bet on a 6 block of numbers as her probability of winning is 638. She decides to place a $20 bet with this probability. She will win $100 (and keep her bet!) if one her numbers come up but she will lose if any other number is shown, a probability of 3238. What is the expected value for Joan? Round to the nearest cent. Do not round until your final calculation.
Answer:
-1.05
Step-by-step explanation:
Pls answerrrrrrrrrrrrrrrrrrrrrrrrrrr
Answer:
The answer should be 2
Step-by-step explanation:
P
r
=
n
!
(
n
−
r
)
!Subtract
1
from
2
.Simplify
2
!
(
1
)
!
.
pls help pls help pls help
Answer: 336ft²
Step-by-step explanation:
The polygon in the image provided is a trapezoid.
The formula for the area of a trapezoid is [tex]A=(\frac{a+b}{2} )(h)[/tex]
Where
A is the area
a is one of the bases (24 for this)
b is the other base (32 for this)
and h is the height (12 for this)
Sub the values into the formula and solve
[tex]A=(\frac{24+32}{2} )(12)\\A=(\frac{56}{2} )(12)\\A=(28)(12)\\A=336[/tex]
Answer:
336
Step-by-step explanation:
24 x 12 = 288. 12 x 8 = 96 divided by 2 is 48. 288 + 48 = 336
Suppose that each person sitting in an enclosed room that measures 10 ft x 15 ft x 12 ft produces about 600 BTUs of
body heat per hour. Which statements are correct?
A)
3 people will produce approximately 8.33 BTUs/ft3 in a 9 hour period.
B)
4 people will produce approximately 13.33 BTUs/ft3 in a 10 hour period.
C)
5 people will produce approximately 3.33 BTUs/ft? in a 2 hour period.
D)
6 people will produce approximately 7.33 BTUs/ft3 in a 4 hour period.
E)
7 people will produce approximately 9.33 BTUs/ft3 in a 4 hour period.
The volume of a cuboid is the product of its length, width, and height. Out of the five statements B, C, and E are correct.
What is the volume of a cuboid?The volume of a cuboid is the product of its length, width, and height. It is formulated as:
[tex]\rm \text{Volume of Cuboid} = Length \times Width \times Height[/tex]
As the dimensions of the room are given and a room is mostly in the shape of a cuboid. Therefore, the volume of the room can be written as,
The volume of the room = 10ft × 15ft × 12ft = 1800 ft³
A.)
The heat produced by 3 people in a period of 9 hours will be
= 600 BTU × 3 people × 9 hour
= 16,200 BTU
We already know the volume of the room is 1800 ft³. Therefore, the heat produced per unit volume can be written as:
[tex]\rm \text{Heat produced per unit volume}= \dfrac{16,200\ BTU}{1800\ ft^3} = 9\ BTU/ft^3[/tex]
Hence, the statement that 3 people will produce approximately 8.33 BTUs/ft³ in a 9 hour period is wrong.
B.)
The heat produced by 4 people in a period of 10 hours will be
= 600 BTU × 4 people × 10 hours
= 24,000 BTU
We already know the volume of the room is 1800 ft³. Therefore, the heat produced per unit volume can be written as:
[tex]\rm \text{Heat produced per unit volume}= \dfrac{24,000\ BTU}{1800\ ft^3} = 13.334\ BTU/ft^3[/tex]
Hence, the statement that 4 people will produce approximately 13.334 BTUs/ft³ in a 10 hour period is correct.
C.)
The heat produced by 5 people in a period of 2 hours will be
= 600 BTU × 5 people × 2 hours
= 6,000 BTU
We already know the volume of the room is 1800 ft³. Therefore, the heat produced per unit volume can be written as:
[tex]\rm \text{Heat produced per unit volume}= \dfrac{6,000\ BTU}{1800\ ft^3} = 3.334\ BTU/ft^3[/tex]
Hence, the statement that 5 people will produce approximately 3.334 BTUs/ft³ in a 2 hour period is correct.
D.)
The heat produced by 6 people in a period of 4 hours will be
= 600 BTU × 6 people × 4 hours
= 14,400 BTU
We already know the volume of the room is 1800 ft³. Therefore, the heat produced per unit volume can be written as:
[tex]\rm \text{Heat produced per unit volume}= \dfrac{14,400\ BTU}{1800\ ft^3} = 8\ BTU/ft^3[/tex]
Hence, the statement that 6 people will produce approximately 7.334 BTUs/ft³ in a 4 hour period is wrong.
E.)
The heat produced by 7 people in a period of 4 hours will be
= 600 BTU × 7 people × 4 hours
= 16,800 BTU
We already know the volume of the room is 1800 ft³. Therefore, the heat produced per unit volume can be written as:
[tex]\rm \text{Heat produced per unit volume}= \dfrac{16,800\ BTU}{1800\ ft^3} = 9.334\ BTU/ft^3[/tex]
Hence, the statement that 7 people will produce approximately 9.334 BTUs/ft³ in a 4 hour period is correct.
Learn more about the Volume of a Cuboid:
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