Recall that
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
cos(x - y) = cos(x) cos(y) + sin(x) sin(y)
If you subtract the first equation from the second one, you end up with
cos(x - y) - cos(x + y) = 2 sin(x) sin(y)
so that
sin(3x) sin(x) = 1/2 (cos(3x - x) - cos(3x + x)) = 1/2 (cos(2x) - cos(4x))
Then in the integral,
[tex]\displaystyle \int \sin(3x)\sin(x)\,\mathrm dx = \frac12 \int(\cos(2x)-\cos(4x))\,\mathrm dx \\\\ = \frac12 \left(\frac12 \sin(2x) - \frac14 \sin(4x)\right) + C \\\\ = \boxed{\frac14 \sin(2x) - \frac18 \sin(4x) + C}[/tex]
drag the expression to order them top to bottom from least to greatest.
-5 3/7. , -4 6/7, -4 3/7, 4 2/7 , 5 1/7
Answer:
A) - 5 3/7
B) - 4 6/7
C) - 4 3/7
D) 4 2/7
E) 5 1/7
Step-by-step explanation:
- 5 3/7 ≈ - 5.43
- 4 6/7 ≈ - 4.86
-4 3/7 ≈ - 4.43
4 2/7 ≈ 4.29
5 1/7 ≈ 5.14
what is -3(6x+4)+20x
Answer:
2x - 12
Step-by-step explanation:
Given:
-3(6x+4)+20x
Distribute:
-18x-12+20x
Combine like terms:
2x-12
Hope this helps, have a nice day :))
Answer:
3 8 + 1 2
i searched it
i neeed the answer now please
Answer:
D
Step-by-step explanation:
It is a positive gradient therefore the answers cannot be negative. Since it is an increase of 4 dollars it is option D.
Find the value of x in the isosceles triangle shown below.
Answer:
B) [tex]x = \sqrt{60}[/tex]
Step-by-step explanation:
1. As you can see from the image, there are two right triangles in the isosceles triangle. The base of each right triangle is 2 (because 4 ÷ 2 = 2), and the hypotenuse is 8.
2. Let's use Pythagorean Theorem to find the height of each right triangle, which will also give us the height of the isosceles triangle: [tex]a^2 + b^2 = c^2[/tex], where a = height, b = base, and c= hypotenuse.
[tex]a^2 + 2^2 = 8^2[/tex] [tex]a^2 + (2*2) = (8*8)[/tex] [tex]a^2 + 4 = 64[/tex] (Simplify both sides of the equation)[tex]a^2 + 4 - 4 = 64 - 4[/tex] (Subtract 4 from both sides)[tex]a^2 = 60[/tex] [tex]\sqrt{a^2} = \sqrt{60}[/tex] (Take square root of both sides[tex]a = \sqrt{60}[/tex]3. The√(60) is the height of each right triangle, and it's also the height of the isosceles triangle. Therefore, the answer is B) x = √60.
Bredt rides a bicycle 10 miles every 3 hours. At this rate, how many hours did Bredt ride if he rode 50 miles?
Answer:
15 hrs
Step-by-step explanation:
10 miles= 3hrs
50miles/10miles= 5
5(3hrs)=15 hrs
Answer:
10 miles = 3 hours
10 x 5 = 50
3 x 5 = 15
Bredt rode his bicy for 15 hours if he rode for 50 miles.
Step-by-step explanation:
Brain Builders
Trail
A
00
с
D
Processes
9. & Practices Model Math The
table shows the lengths of four trails
at a horseback riding camp. The
estimated length of all four trails is
12 miles. Find a possible length for
trail D. Show your work.
Length (mi)
2.6
1.8
4.2
What is y if 2y= 8x + 6
Answer:
[tex]y = \frac{8x + 6}{2}[/tex] = 4x + 3
Step-by-step explanation:
2y = 8x + 6
y = (8x + 6) / 2
y = 8x / 2 + 6 / 2
y = 4x + 3
ggj helpppppppp pls?
(i)To make 8 pancakes 250 ml milk is needed. So, to make 4 pancakes=
(250/8)×4=120 ml is needed!
(ii)To make 8 pancakes 5g butter is needed and to make 12 pancakes=
(5/8)×12=7.5 g butter is needed!
PLEASE HELP ITS MATH THANK YOUUUU
If 37 grams of pure drug are contained in 150 milliliters, how many grams are contained in 75 milliliter?
Answer:
17.5
Step-by-step explanation:
The ratio of "pure drug" to liquid is 35:150
Therefore to evaluate for 75 mls we get the ratio 75/2150 or simply 1/2
multiply 35 by the ratio 1/2
35/2=17.5
Check (24, 144, 145) is a Pythagorean triplet
Answer:
4, 144, 145 are not Pythagorean triplets
Step-by-step explanation:
According tp Pythagoras theorem,
Sum of squares of two sides must be equal to square of the third side.
By Pythagoras theorem,
24^2 + 144^2 = 145^2
576 + 20736 = 21025
21312 ≠ 21025
Numbers 24, 144, 145 does not satisfy the Pythagoras theorem.
So, 24, 144, 145 are not Pythagorean triplets.
Hence, checked.
Answer:
It is not a Pythagorean tripletWhat is the area of a triangle with a base of 6.5 inches and a height of 8 inches?
Answer: 26 inches
Step-by-step explanation: 6.5 x 8 = 52/2 = 26 area of a triangle
An online company is advertising a microwave oven on sale for 35% off the original price of $253.99. What is the sale price for the microwave oven? Round your answer to the nearest cent, if necessary.
Answer:
The answer is $88.90
Step-by-step explanation:
$253.99÷.35=88.896. Rounding up the 6 makes the 89 to 90.
factories
x²+6x+5-4y-y²
Step-by-step explanation:
−5y)(20y−23x)
x(6x−5y)−4(6x−5y)
2
=(6x−5y)(x−4(6x−5y))
=(6x−5y)(x−24x+20y)
=(6x−5y)(20y−23x)
What is the difference between a part to part ratio and a part to whole ratio. Use the example of a bowl that has two oranges and five bananas.
Part to part ratio
For 2 oranges and five bananas
2oranges:5bananas(2:5)
Part to whole ratio
2oranges:7pieces of fruit(2:7)
5bananas:7pieces of fruit (5:7)
All the best!
PLEASE HELP ITS MATH THANK YOUUUU HURRY
The answer is 8 centimeters
4cm=1 km
8cm=2 km
the answer is 8 centimeters
A rectangular photograph that is 5 inches wide and 7 inches long is enlarged to produce a photgraph that is 12 inches wide, if the enlarged photograph is in proportion to the original, what is the length in inches of the large photograph?
9514 1404 393
Answer:
16.8 inches
Step-by-step explanation:
The length is 7/5 = 1.4 times the width. The length of the enlargement will be ...
(12 in)×1.4 = 16.8 in
The large photo will be 16.8 inches long.
Of 100 students, 30 can speak French, 10 can speak German, and 6 can speak both French and German. If a student is picked at random, what is the probability that he or she can speak French or German? (Enter your probability as a fraction.)
Answer:
the correct answer would be 1,800
distance between the
points (3,7) (-5,16)
lets talk about the basics of pythagoras (maths)?
Answer:
Is there a question?
Step-by-step explanation:
The Pythagorean theorem states that for any right triangle with legs of length “a” and “b” and a hypotenuse of length “c,” the lengths of the sides always satisfy the relationship, “a^2 + b^2 = c^2.” In other words, the sum of the squares of the lengths of the two legs of a triangle is equal to the square of its hypotenuse. The formula is alternatively written with the hypotenuse length isolated (i.e., c = Sqrt(a^2 + b^2).
This is the definition.
Solve equation for 5(x - 3) + 2 = 5(2x - 8) - 3
Answer:
[tex]\boxed {\sf x=6}[/tex]
Step-by-step explanation:
[tex]\sf 5(x - 3) + 2 = 5(2x - 8) - 3[/tex]
Use the Distributive property :
[tex]\boxed { \sf Multiply\: 5\: by \:x\: and \:5\: by\: 3:}[/tex]
→ [tex]\sf 5x-15+2[/tex]
→ [tex]\sf -15+2[/tex]
[tex]\sf =-13[/tex]
[tex]\sf 5x-13[/tex]
______________________
[tex]\sf 5\left(2x-8\right)-3[/tex]
[tex]\boxed {\sf Multiply\: 5 \: by \: 2x \: and \: 5\: by\: -8:}[/tex]
→ [tex]\sf 10x-40-3[/tex]
→ [tex]\sf -40-3=-43[/tex]
[tex]\sf 10x-43[/tex]
_______________
[tex]\sf 5x-13=10x-43[/tex]
[tex]\boxed {\sf Add\: 13 \:to\: both\: sides:}[/tex]
[tex]\sf 5x-13+13=10x-43+13[/tex]
[tex]\sf 5x=10x-30[/tex]
[tex]\boxed{\sf Subtract\: -10x\: from\: both\: sides:}[/tex]
[tex]\sf 5x-10x=10x-30-10x[/tex]
[tex]\sf -5x=-30[/tex]
[tex]\boxed{\sf Divide \:both \:sides\: by \:-5:}[/tex]
[tex]\sf \cfrac{-5x}{-5}=\cfrac{-30}{-5}[/tex]
[tex]\sf x=6[/tex]
___________________________
Answer:
x = 6
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightDistributive Property
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
5(x - 3) + 2 = 5(2x - 8) - 3
Step 2: Solve for x
(Parenthesis) Distribute: 5x - 15 + 2 = 10x - 40 - 3Simplify [Order of Operations]: 5x - 13 = 10x - 43[Subtraction Property of Equality] Subtract 10x on both sides: -5x - 13 = -43[Addition Property of Equality] Add 13 on both sides: -5x = -30[Division Property of Equality] Divide -5 on both sides: x = 6Jon has to pay $5.00
admission for the skating rink
and $2.50 per hour to rent
rollerblades. How many
hours can he skate for $15?
Answer: 4 hours
Step-by-step explanation: 15-5=10 10/2.50 =4
Answer:
4 hours
Step-by-step explanation:
$15 is our initial value, and we have a flat fee of $5
15-5=10
We have a remaining $10 left to be divided by the $2.50 per hour
10÷2.50=4
4 tells us the number of hours
claim less than 50%of students like chocolate. Data: In a sample of 12 students 2 of them like chocolate. Calculate the p value to at least 4 digits of accuracy.
Mike's grandmother opened a savings account in Mike's name and deposited some money into the account. The account pays an annual simple interest rate of 11%. After 14 years, the interest earned on the account was $3,080. How much money did Mike's grandmother deposit in the account?
Answer:
Step-by-step explanation:
Bà của Mike đã mở một tài khoản tiết kiệm đứng tên Mike và gửi một số tiền vào tài khoản. Tài khoản trả lãi suất đơn giản hàng năm là 11%. Sau 14 năm, tiền lãi thu được trên tài khoản là $ 3,080
this is a CALCULUS question, "Derivatives As A function"
I want to know the answer and how did u get it, I'm really lost in this subject
Derivative Functions
The derivative function gives the derivative of a function at each point in the domain of the original function for which the derivative is defined. We can formally define a derivative function as follows.
Definition:
let f be a function. The derivative function, denoted by f', is the function whose domain consists of those values of x such that the following limit exists:
[tex]f'(x)= \lim_\\ \ \\ \frac{f(x+h)-f(x)}{h} {h \to 0}[/tex]
f(x)=-x^2-9x-7
f(x)=−x
2
−9x−7
f = 3
Answer:
Assuming the question posed is to find the values of x thtat satisfy the equation f(x) = x^2 - 9x - 7, this is a quadratic equation of the form Ax^2 + Bx + C which has the closed-form solution x = (-b +/- Sqrt[b^2 - 4 ac])/(2a) - widely known as the "quadratic equation."
Step-by-step explanation:
By applying the quadratic equation, we find that the solutions to this equation are
x = 1/2 * (9-Sqrt[109])
x = 1/2 * (9+Sqrt[109])
Pablo elp meeeeeee vvvv wwwwww ww w w
Answer:
pablo and lakaka vvvvvvvvvvvvvv
Step-by-step explanation:
A population numbers 11,000 organisms initially and grows by 7.7% each year.
Answer:
84,700 is the answer. If I multiply
To the nearest hundredth:
4.15
0.07
7000 1 + 0.07/4 ) ^ 4 x 15
Answer:
4.15 is same 4.15
0.07 is also same
Last one is 5.08 x 10^290
what the answer to this math problom
Step-by-step explanation:
S=b*h/2=8*10/2=40m2
40*4=160m²
Answer:
60 m2
Step-by-step
i did that before hope this helps :)