Recall that
• tan(x) = sin(x) / cos(x)
• sin(x) sin(y) = - 1/2 (cos(x + y) - cos(x - y))
• cos(x) cos(y) = 1/2 (cos(x + y) + cos(x - y))
Then we can write
tan(6x) tan(7x) = (sin(6x) sin(7x)) / (cos(6x) cos(7x))
tan(6x) tan(7x) = - (cos(13x) - cos(x)) / (cos(13x) + cos(x))
Make this replacement in the original equation and simplify:
tan(6x) tan(7x) = -1
- (cos(13x) - cos(x)) / (cos(13x) + cos(x)) = -1
(cos(13x) - cos(x)) / (cos(13x) + cos(x)) = 1
cos(13x) - cos(x) = cos(13x) + cos(x)
2 cos(x) = 0
cos(x) = 0
Solving for x gives
x = π/2 + nπ = (2n + 1)π/2
where n is any integer. However, since 2n + 1 is odd, for any odd multiple of π/2, we would end up with
tan(6 (2n + 1)π/2) = tan((2n + 1)×3π) = tan(odd multple of π/2)
since odd×odd = odd, and cos(odd multiplie of π/2) = 0, which would make tan(6x) undefined.
Therefore there are no solutions to this equation.
What is the coefficient
Answer:
B
Step-by-step explanation:
Using the Pascal's triangle
Pertaining to the 8th term the coefficients are;
1, 8, 28, 56, 70, 56,28, 8 and 1 in that order
Expanding this,
the coefficient of the term x^7y is 8
Solve for X ( 9th grade Algebra 1)
Answer:
x = 2
Step-by-step explanation:
(x+16)/3 = 3x
=> x+16 = 3x × 3
=> x+16 = 9x
=> 16 = 9x - x
=> 16 = 8x
=> 16/8 = x
=> 2 = x
An experiment to determine how many breaths a squirrel takes per minute yields this data: minute 1: 65 breaths;minute 2: 73 breaths; minute 3: 67 breaths; minute 4: 71 breaths; minute 5: 62 breaths. Calculate the average number of breaths per minute.
The average number of breaths per minute would be 67.6 breaths per minute.
Average can be calculated by dividing the sum of the observation by the number of observations,
[tex]Average = \frac{sum of observations}{number of observation}[/tex]
Step by step Explanation:
Over the course of 5 minutes, the squirrel takes
65 + 73 + 67+ 71+ 62 = 338 breaths in 5 minutes
So, the sum of observation = 338 and
the number of observations = 5
So If you take that number and divide it by the number of minutes, you will get the average.
[tex]=\frac{338}{5}[/tex]
67.6 breaths per minute.
Thus, the correct answer is - 67.6 breaths per minute.
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The zebras have been spotted in a
rectangular area of the Savannas that
is 1.4 kilometers by 2.4 kilometers. What
is the area of the rectangle?
Area of rectangle where Zebra spotted is 3.36 kilometer²
Step-by-step explanation:
Given that;
Zebras spotted in a rectangular area
Dimensions of area is 1.4 kilometers by 2.4 kilometers
Find:
Area of rectangle
Computation:
[tex]Area\ of\ rectangle = length \times width\\[/tex]
Area of rectangle = 1.4 x 2.4
Area of rectangle = 3.36 kilometer²
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Community Gym charges a $50 membership fee and a $50 monthly fee. Workout Gym charges a $190
membership fee and a $40 monthly fee. After how many months will the total amount of money paid to
both gyms be the same? What will the amount be?
Which of the following describes the correct process for solving the equation 2x − 6 = 22 and arrives at the correct solution?
Answer:
(01.07) Which of the following describes the correct process for solving the equation 2x + 6 = 22 and arrives at the correct solution? (1 point) Divide both sides by 6 and then add 2. The solution is x = 8. Subtract 6 from both sides and then divide by 2. The solution is x = 8.
mark me a brainlistAnswer:
2x-6=22
2x=22+6
2x=28
x=28/2
x=14
Which Canadian region continues to retain its French cultural influence from its beginnings as a colony called New France?
Group of answer choices
Alberta
Quebec
British Columbia
Northwest Territories
Answer:
I think it's Quebec
Step-by-step explanation:
because in canada's history, Canada remained a French territory until 1763 when it became the British colony of the Province of Quebec
of
Use>,<, or = to solve the
inequality below
4/1___5/2
Answer:
4/1>5/2 because
when solved 4>2.5
Find the perimeter and area of the figure.
5 cm
The perimeter of the figure is
centimeters
The area of the figure is
square centimeters.
PS: I got it wrong and I need help :)
Answer:
The perimeter is 20 cm.
The area is 25 cm^2.
Step-by-step explanation:
The perimeter is the distance around the figure.
This is a square, so each side is the same length.
There are four sides, so
5 + 5 + 5 + 5 = 20 cm
The area of the figure is
s^2
where s is a side
so 5 * 5 = 25 cm^2
How would I solve this problem
After t hours, the first truck covers a distance of (70 km/h) t while the second truck covers a distance of (80 km/h) t. So the distance between them is
(70 km/h) t + (80 km/h) t = (150 km/h) t
They are 900 km apart after
(150 km/h) t = 900 km ===> t = (900 km) / (150 km/h) = 6 h
Please help I have my maths tutor tomorrow.
when the tank had 8000 litres in it. Ron said it was 2/3 full. How much did it hold when it was full?
Answer:
12000
plss mark brainliest
Step-by-step explanation:
8000÷2/3
Explanation:
x = full tank capacity
2/3 of x = (2/3)*x = 8000 which is the amount Ron states when its 2/3 full
To solve for x, we will multiply both sides by 3 and then divide both sides by 2 like so
(2/3)x = 8000
2x = 8000*3
2x = 24000
x = 24000/2
x = 12000 liters is the full capacity
Note that,
2/3 of 12000 = (2/3)*12000 = 8000
which confirms our answer.
need help on #4 !!!!
Step-by-step explanation:
What other numbers are of this form have exactly four factors?
8 = 2³ has 4 factors 1, 2, 2², 2³
For any prime p, p³ has 4 factors 1, p, p², p³
Do all the perfect cubes have exactly four factors?
If p is not prime, then it is not true anymor
For instance, 8³ has more than 4 factors 1, 2², 2³,:
Is it true that all numbers that have exactly four factors are perfect cubes?
6 has 4 factors : 1, 2, 3, 6 but this is not a perfect cube.
PLEASE HELP I WILL GIVE YOU A BRAINLY AND ALOT OF POINTS I HAVE A VERY LIMITED AMOUNT OF TIME PLSS
3x
x+3
x-3
x/3
x³
3^x (write the x small and above the 3 the same way as the 3 is written with the x above)
Answer:
3xx + 33 - x3/xx^33^xStep-by-step explanation:
2)
product means multiply 3*xSum means add x + 3Difference between means subtract. The first number is written first 3-xQuotient means divide 3/x. The first number is the numerator.Third power means x raised to the 3 x^3the xth power means 3^xExplain the properties of following shapes in detail -
(a) Parallelogram
(b) Trapezium
(c) Rhombus
Satisfied answerer will get thanks and brainliest.
Answer:
The Properties of parallelogram are
a) Opposite sides are equal
b) All angles are not 90°
The Properties of trapezium are
a) One pair of opposite side is parallel
b) side of adjacent angle and non parallel side
of trapezium is 180°
The Properties of rhombus are
a) All sides are equal
b) All angles are not 90°
measure of angle JKM if measure of angle JKL = 42° and measure of angle LKM = 28°
Answer:
80 degrees
Step-by-step explanation:
add both the angles
Hannah went to the school store to buy supplies and spent $16. She bought four more pencils than pens and two fewer erasers than pens. Pens cost $1.25 each, pencils cost $0.55 each, and erasers cost $0.75 each. If x represents the number of pens Hannah bought, write an equation in terms of x that can be used to find how many of each item she bought. Use your equation to determine algebraically how many pens Hannah bought.
The algebaraic equation required is :
2.55x + 0.7 = 16
The number of pens Hannah bought is 6
If :
x = number of pens
4 more pencils Than pens ; Number of pencils = x + 4
2 fewer erasers than pens ; number of erasers = x - 2
Total amount spent = $16
The total number of items bought is :
(x) + (x + 4) + (x - 2)
Multiplying by the cost of each :
1.25x + 0.55(x+4) + 0.75(x-2)
Hence, Total amount spent can be represented as :
1.25x + 0.55(x+4) + 0.75(x-2) = 16
1.25x + 0.55x + 2.2 + 0.75x - 1.50 = 16
2.55x + 0.7 = 16
The algebraic equation is : 2.55x + 0.7 = 16
The number of pens Hannah bought can be calculated thus :
2.55x + 0.7 = 16
2.55x = 16 - 0.7
2.55x = 15.30
x = 15.30 / 2.55
x = 6
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Answer:
Step-by-step explanation: x = the number of pens Hannah bought
(x + 4) = the number of pencils Hannah bought
(x - 2) = the number of erasers Hannah bought
The equation to solve would be 1.25x + 0.55(x + 4) + 0.75(x - 2) = 16
1.25x + 0.55(x + 4) + 0.75(x - 2) = 16.00
1.25x + 0.55x + 4 * 0.55 + 0.75x - 2 * 0.75 = 16.00
1.25x + 0.55x + 2.20 + 0.75x - 1.50 = 16.00
1.25x + 0.55x + 0.75x = 15.30
2.55x = 15.30
x = 6
Note: if you didn't get a Whole Number, you know that you must've made a mistake. You can't buy part of a pen or pencil or eraser.
x = the number of pens Hannah bought = 6
(x + 4) = the number of pencils Hannah bought = 6 + 4 = 10
(x - 2) = the number of erasers Hannah bought = 6 - 2 = 4
You can check your work: 1.25(6) + 0.55(6 + 4) + 0.75(6 - 2) = 1.25(6) + 0.55(10) + 0.75(4) = 16 (check!)
The factorisation of 10xᴧ2 – 18xᴧ3 + 14xᴧ4 is
Answer:
2x^2 (5 - 9x + 7x^2)
Step-by-step explanation:
use the smallest exponent (x^2) and number (10) to factor
2 and x^2 could be factored from all
when factoring put exponents, you subtract them
2x^2 (5 - 9x + 7x^2)
what is the vertex and where is the x-intercept(s)?
Answer:
Vertex (-2,-9)
x-intercepts -5 and 1
y-intercept -5
Step-by-step explanation:
6m + 3z + 4m + 2w - 5z
Step-by-step explanation:
6m + 3z + 4m + 2w - 5z
6m + 4m + 3z - 5z + 2w
10m - 2z + 2w
Therefore the answer is 10m -2z + 2w
A soda company has determined that it's profit during lunch on a given day
could be modeled by the function P(s)=-1/3s^2+ 10s + 8 where P is the profit
and s is the number of sodas sold. Determine the amount of sodas that would
maximize profit and how much the company would earn.
9514 1404 393
Answer:
15 sodas will give a maximum profit of 83
Step-by-step explanation:
For quadratic ax^2 +bx +c, the maximum occurs at x = -b/(2a). Here, we have ...
a = -1/3, b = 10
x = -b/(2a) = -10/(2(-1/3)) = 15
The profit for sale of 15 sodas is ...
P(15) = (-1/3s +10)s +8 = (-1/3(15) +10)(15) +8 = 5(15) +8 = 83
The company would earn a maximum of 83 from sale of 15 sodas.
PQ is an example of what?
Answer:
PQ=
Step-by-step explanation:
Performance Qualification
(regarding business or acquiring a job)
Hi, I need help on the question that is listed on the photograph below: Thanks In Advance!
Answer:
first ma 8x+4y and bic ma 6x +5y last ma -2x+y
HELP HELP HURRYYY the product of two numbers is rational. The first number is 3 sqrt2. What is the possible value of the other number?
The possible value of the other number will be 7√32. The correct option is D.
What is a rational number?A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. For instance, every integer and 3/7 are rational numbers.
It is given that the first number is 3√2 the value of the second number will be:-
Rational number = 3√2 x 7√32
Rational number = 21√64
Rational number = 21√( 8 x 8 )
Rational number = 21 x 8
Rational number = 168
Therefore, the possible value of the other number will be 7√32. The correct option is D.
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A car is traveling at a rate of 54 kilometers per hour. What is the car's rate in kilometers per minute?
How many kilometers will the car travel in 15 minutes? Do not round your answers.
Answer: 3.6
Step-by-step explanation: What i did was determined how many minutes are in a hour which are 60 minutes. so due to the fact that you're looking for the travel in (15) "minutes" I had to divide 54 by 15. Which gives you 3.6
I need help on this I'll give brainiest whoever is right
how many students are good in mathematics only and how many students are not good in any of the three courses
Answer:
do you have a graph to go along with this?
Write the chemical formula for this molecule:
N—N
O
O
(NO)²
[tex]\huge\mathfrak\red{hope \: it \: helps}[/tex]
I need help on what to do I would gladly appreciate if you can help
Answer:
9.89 or 7 radical 2
Step-by-step explanation:
Which fraction on number lin is equal to 3
Answer:
12/4
Step-by-step explanation:
12/4
= 3/1
= 3
So, 12/4 = 3
In a three-person tug-of-war, three ropes are tied at a point. Gary is pulling due East with a force of 650 Newtons, June is pulling due North with a force of 450 Newtons, and Levi is pulling the third rope. The knot in the middle is not moving. What is the magnitude of Levi's effort?
A) 34.7 Newtons
B) 55.3 Newtons
C) 550 Newtons
D) 790.6 Newtons
Answer:
Its D) 790.6
Step-by-step explanation:
All I can say is that I aced the test so.
The answer to the question what is the magnitude of Levi's effort is D 790.6 N
Since Gary is pulling due East with a force of 650 Newtons, June is pulling due North with a force of 450 Newtons, the force due to Levi will be equal to the resultant force from Gary and June.
Since both Gary and June pull due East and due North respectively and these directions are perpendicular to each other, their resultant force is
R = √[(650 N)² + (450 N)²]
R = √[422500 N² + 202500 N²]
R = √[625000 N²]
R = 790.57 N
R ≅ 790.6 N
Since the resultant force due to Gary and June is 790.6 N, this is equal to the magnitude of Levi's effort since the knot does not move.
So, the magnitude of Levi's effort is 790.6 N
So, the answer to the question what is the magnitude of Levi's effort is D 790.6 N
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