Step-by-step explanation:
We have
1-cot²a + cot⁴a = sin²a(1+cot⁶a)
First, we can take a look at the right side. It expands to sin²a + cot⁶(a)sin²(a) = sin²a + cos⁶a/sin⁴a (this is the expanded right side) as cot(a) = cos(a)/sin(a), so cos⁶a = cos⁶a/sin⁶a. Therefore, it might be helpful to put everything in terms of sine and cosine to solve this.
We know 1 = sin²a+cos²a and cot(a) = cos(a)/sin(a), so we have
1-cot²a + cot⁴a = sin²a+cos²a-cos²a/sin²a + cos⁴a/sin⁴a
Next, we know that in the expanded right side, we have sin²a + something. We can use that to isolate the sin²a. The rest of the expanded right side has a denominator of sin⁴a, so we can make everything else have that denominator.
sin²a+cos²a-cos²a/sin²a + cos⁴a/sin⁴a
= sin²a + (cos²(a)sin⁴(a) - cos²(a)sin²(a) + cos⁴a)/sin⁴a
We can then factor cos²a out of the numerator
sin²a + (cos²(a)sin⁴(a) - cos²(a)sin²(a) + cos⁴a)/sin⁴a
= sin²a + cos²a (sin⁴a-sin²a+cos²a)/sin⁴a
Then, in the expanded right side, we can notice that the fraction has a numerator with only cos in it. We can therefore write sin⁴a in terms of cos (we don't want to write the sin²a term in terms of cos because it can easily add with cos²a to become 1, so we can hold that off for later) , so
sin²a = (1-cos²a)
sin⁴a = (1-cos²a)² = cos⁴a - 2cos²a + 1
sin²a + cos²a (sin⁴a-sin²a+cos²a)/sin⁴a
= sin²a + cos²a (cos⁴a-2cos²a+1-sin²a+cos²a)/sin⁴a
= sin²a + cos²a (cos⁴a-cos²a+1-sin²a)/sin⁴a
factor our the -cos²a-sin²a as -1(cos²a+sin²a) = -1(1) = -1
sin²a + cos²a (cos⁴a-cos²a+1-sin²a)/sin⁴a
= sin²a + cos²a (cos⁴a-1 + 1)/sin⁴a
= sin²a + cos⁶a/sin⁴a
= sin²a(1+cos⁶a/sin⁶a)
= sin²a(1+cot⁶a)
How to simplify fractions (please also right down rules when doing so, ((like x+x = x or axa=)
Question is
-2a(2b-3a)
Answer:
[tex] - 2a(2b - 3a) = - 2a2b + 2a3a \\ = - 4ab + 6 {a}^{2} \\ thank \: you[/tex]
2
Write the decimal equivalent for 43
Choose the correct answer below.
2
O A. 4= = 4.666667
3
2
OB. 4= = 4.67
3
2
OC. 4- = 4.6
3
2
OD. 45 = 4.66
3
Answer:
C
Step-by-step explanation:
as it goes 4.66666666... forever.
A is just a rounded answer.
B would mean 4.6767676767...
and D is just truncated.
What is the midpoint of segment AB?
Answer:
(-1, -3.5)
Step-by-step explanation:
Use the midpoint formula by finding the points of A and B.
A = (-5, -4)
B = (3, -3)
Add the x-values of both coordinates to get the following:
[tex]3_{1} + -5_{2} = -2\\-2/2 = -1[/tex]
Midpoint = (-1, y)
Now we find the y-value by doing the same as we did to the x-coordinates of A and B.
[tex]-3_{1} + -4_{2} = -7\\-7/2 = -3.5[/tex]
Midpoint = (-1, -3.5)
Can someone please help meee
Answer:
b
basically 5/8 goes to 1/2 0.8 times which is 4/5
A train travelling at 30km/hour reaches a tunnel which is 9 times as long as the train. If the train takes 2 minutes to completely clear the tunnel, how long is the train?
Answer: 111.1 m
Step-by-step explanation:
(30*2)/60 = 1 km ( the tunnel length is 1 Km.)
1 Km = 1000 m.
1000/9 = 111.1 m.
2. Damian is monitoring the temperature of
the swimming pool. It is currently 86.8° and
cooling 0.5° per minute. After how many
minutes will the swimming pool be 80.8°?
a. Equation:
I think 12 minutes will pass until the tempature reaches 80.8
The number of minutes when the temperature of the swimming pool is 80.8° will be 12 minutes.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Damian is monitoring the temperature of the swimming pool. It is currently 86.8° and cooling 0.5° per minute. Then the equation will be
y = 86.8 - 0.5x
The number of minutes when the temperature of the swimming pool be 80.8° will be
80.8 = 86.8 - 0.5x
0.5x = 6
x = 12
The number of minutes when the temperature of the swimming pool is 80.8° will be 12 minutes.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ2
a laptop computer is 1.05 centimeters thick
Answer:
yes and?
Step-by-step explanation:
PLS HELP ME ON THIS QUESTION!!!
George has a storage unit already occupied by a large container that is the same height of the whole unit. How much space is left for storage?
Answer:
945 m³
Step-by-step explanation:
Space left for storage = Volume of storage unit - volume of the container
Storage unit:
length = l = 15.3 m
Height = h = 10 m
Width = w = 7 m
Volume of storage unit = l * w *h
= 15.3 *7* 10
= 1071 m³
Container:
length = l =4.2 m
Height = h = 10 m
Width = w = 3 m
Volume of container = l * w *h
= 4.2 *3* 10
= 126 m³
Space left = 1071 - 126 = 945 m³
Choose the graph below that represents the following system of inequalities: y is greater than and equal -3x + 1 and y is greater than and equal 1/2x + 3
Answer:
Step-by-step explanation:
Choose the graph below that represents the following system of inequalities: y is greater than and equal -3x + 1 and y is greater than and equal 1/2x + 3
What is 3x^2-5x-13=0
Answer:
D. 58
Step-by-step explanation:
Given, 3x+8x+4x=6x+63
⇒15x=6x+63
⇒9x=63
⇒x=7
Then 5x+23=5(7)+23
=35+23
=58
HELLLPPPPP!!!!!!!!!!!!!!!!!!
Answer:
1}6 times
Step-by-step explanation:
The highest number of president born in Virginia minus the highest number of president born in Texas2}Yes.New York and Mast has the same number of president which is four
3}Yes,this can be done using piechart.
4}I am still working on this question
2+ (-3)^2 - (-1)
please explain! :3
Answer:
12
Step-by-step explanation:
Hello!
First of all you have to understand the order of operations.
PEMDAS
Parenthesis, Exponent, Multiplication/Divison, Addition, Subtraction.
From this you can see that we first have to deal with the exponent, then multiplication, then the addition.
So we get 2+9-(-1)
The 9 is from -3^2
2+9+1
11+1
12.
Hope this helps!
1) Lisa took a trip to Kuwait. upon leaving she decided to convert all of her dinars back into dollars . how many dollars did she receive if she exchanged 13 dinars at a rate of 1 dinar for every $3?
2) Willie bought one bunch of asparagus for $2. how many bunches of asparagus can Daniel buy if he has $12?
round your answer to the nearest whole number!!!
The function f(x) is graphed below. What is the value of f(-2)?
Answer:
f(-2) = 4
Step-by-step explanation:
Looking at the graph, at -2 the graph is at the point (-2,4). Therefore, the value of f(-2) is 4.
Write the fraction as a decimal.
What is Three-Quarters of Three-Quarters?
You will be marked brainliest if you tell me how step by step.
A. 92x + 280 < 1,108
B. 280x + 92 > 1,108
C. 280x + 92 < 1,108
D. 92x + 280 > 1,108
Answer:
whats the question
Step-by-step explanation:
for me to help
Please help me anyone please and thank you
Answer:
Step-by-step explanation:
x^2 - 6x = -156 Next step is:
x^2 - 6x + (-3)^2 = -156 + (-3)^2
in right triangle abc below where ac=2 and angle BAC is theta find y in terms of theta
please ignore my work!
Answer:
2tanθ -2 = y
Step-by-step explanation:
First, to make things a little simpler, we can say that the point between C and B is D, so BD = y
We are given that ∠ADC = 45° , and ∠ACD = 90°. Because the angles of a triangle add up to 180 degrees, we can say
∠CAD + ∠ACD + ∠ADC = 180°
∠CAD + 90 + 45 = 180
∠CAD = 45°
In a 45/45/90 degree triangle, we can say that the two non-hypotenuse sides are the same. The hypotenuse is opposite of the right angle, so in this triangle, it would be AD. Therefore, we can say that AC = CD = 2
Because BC = CD + DB , we can say that
BC = CD + DB
BC = 2 + y
y = BC -2
Therefore, if we know BC, we can solve for y.
We want to solve for BC given
- the angle opposite of it (θ)
- the side adjacent to the angle (AC).
One equation that fits this is
tanθ = opposite/adjacent
tanθ = BC/AC
tanθ = (2+y)/2
multiply both sides by 2 to remove a denominator
2 tanθ=2+y
subtract 2 from both sides to isolate th y
2tanθ -2 = y
Simplify the expression.
7(5 +t) - 4(t + 4)
7(5 + t) - 4(t + 4) = [
7(5 + t) - 4(t + 4) =
= 35 + 7t - 4t - 16 =
= 7t - 4t + 35 - 16 = 3t + 19
2a²-2ab-3b²+9 when a=3 and b=2
[tex]\\ \sf\longmapsto 2a^2-2ab-3b^2-9[/tex]
[tex]\\ \sf\longmapsto 2(3)^2-2(3)(2)-3(2)^2-9[/tex]
[tex]\\ \sf\longmapsto 2(9)-12-3(4)-9[/tex]
[tex]\\ \sf\longmapsto 18-12-12-9[/tex]
[tex]\\ \sf\longmapsto 6-18[/tex]
[tex]\\ \sf\longmapsto -12[/tex]
Answer:
3
Step-by-step explanation:
2(3)^2 - 2(3)(2) - 3(2)^2 + 9
2(9) - 12 - 3(4) + 9
18 - 12 - 12 + 9
= 3
Answer from Gauth math
(2x + 3y)² + 2(2x + 3y) + 1
Answer:
Here is your answer . hope this helps you.
Picture shown!
Complete the remainder of the table for the given function rule
y= -3x+4
x | -8 -4 0 4 8
y | 28 ? ? ? ?
Answer:
see below
Step-by-step explanation:
y= -3x+4
Let x = -4
y= -3(-4) +4 = 12 +4 = 16
Let x = -0
y= -3(0) +4 = 0 +4 = 4
Let x = 4
y= -3(4) +4 = -12 +4 = -8
Let x = 8
y= -3(8) +4 = -24 +4 = -20
If f(x) = x4 + 2x3 – 5x2-x + 6,
what would be the list of
q
possible rational roots?
Arrange your list from smallest to
largest
P =
= [?], [ ], [ ], [ ],[],[],[],[]
Qlo
Enter the number that belongs in the green box.
Enter
Answer:
Hello,
Step-by-step explanation:
possible rational roots are:
-6/1
-3/1
-2,/1
-1/1
1/1
2/1
3/1
6/1
Find the approximate side length of a square game board with an area of 128 in2. HELP PLZ
Answer:
The side length is approximately 11.3 inches
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
128 = s^2
Take the square root of each side
sqrt(128) = sqrt(s^2)
11.3137085= s
The side length is approximately 11.3 inches
Answer:
11.3
Step-by-step explanation:
Formula for square: x^2 = A
Plug in:
x^2 = 128
√x^2 = √128
x = 11.3
Hope this helped.
what does the rational form of the ratio a:b look like
Answer:
a/b
Step-by-step explanation:
The rational form of a:b or simply a/b is in the simplest form.
Answer:
Step-by-step explanation:
the answer is option 2 from the above sheet
I need help with this question...
Q: Five days last month it rained 6.5 inches. It rained 3.5 inches in 7 days last month. How many inches did it rain those 12 days?
Answer:
57 inches
Step-by-step explanation:
It rained 5*6.5+7*3.5=32.5+34.5=57 inches in the past 12 days
If 6x^3 - (k+6)x^2 + 2kx - 25 is divided by 2x-5 remainder is o find the value of k.
Answer:
25
Step-by-step explanation:
6x³-(k+6)x²+2kx-25
2x-5=0
2x=5
x=5÷2=2.5
6(2.5³)-(k+6)(2.5²)+2(2.5)k -25=0
(6×15.625)-(6.25k+37.5)+(5k)-25=0
93.75-6.25k-37.5+5k-25=0
93.75-37.5-25=6.25k-5k
31.25=1.25k
k=25
Mathematical Connections The triangle shown
is isosceles. Find the length of each side and the
perimeter.
#14
--------------------------------------
If a triangle is isosceles, it means that two sides have equal measures.The perimeter of a polygon is the sum of the lengths of all its sides.--------------------------------------
Value of n:
The two legs have the same length.One is [tex]5n - 17[/tex], and the other is [tex]2n + 1[/tex], thus:[tex]5n - 17 = 2n + 1[/tex]
[tex]5n - 2n = 1 + 17[/tex]
[tex]3n = 18[/tex]
[tex]n = \frac{18}{3}[/tex]
[tex]n = 6[/tex]
--------------------------------------
Lengths:
The lengths are given as functions of n, since n = 6:
[tex]5n - 17 = 5(6) - 17 = 30 - 17 = 13[/tex][tex]2n + 1 = 2(6) + 1 = 12 + 1 = 13[/tex][tex]n = 6[/tex]The length of the sides are: 13 cm, 13 cm and 6 cm.
--------------------------------------
Perimeter:
The perimeter is the sum of the lengths of all sides, so: 13 + 13 + 6 = 32 cm.
A similar question is given at https://brainly.com/question/6139098
Jonathan took 5 minutes to walk to the bus-stop, then spent 63 minutes waiting for the bus. If the bus journey to his school took 10 minutes, how much time did he take to reach his school?
Answer:
78 minutes or 1 hour and 18 minutes
Step-by-step explanation:
Add 5 and 63 and 10
