Answer:
24
Step-by-step explanation:
p/2 = 12.
To leave the p alone, multiply 2 from both sides.
p = 24
1-cot^2a+cot^4a=sin^2a(1+cot^6a) prove it.
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)
The sum of 30 terms of series in A.P, whose last term is 98, is 1635. Find the first term and the common difference.
Let a(n) denote the n-th term in the sequence. Because the terms are in arithmetic progression, there is a fixed number d that separates consecutive terms, so that starting with a(1) = a, the next few terms are
a(2) = a(1) + d = a + d
a(3) = a(2) + d = a + 2d
a(4) = a(3) + d = a + 3d
and so on, up to
a(n) = a + (n - 1) d
We're given that the 30th term is 98, so
a(30) = a + 29d = 98
The sum of the first 30 terms is 1635, so that
[tex]\displaystyle \sum_{n=1}^{30}a(n) = \sum_{n=1}^{30}(a+(n-1)d) \\\\ 1635 = a\sum_{n=1}^{30}1 + d\sum_{n=1}^{30}(n-1) \\\\ 1635 = 30a + d\sum_{n=0}^{29}n \\\\ 1635 = 30a + d\sum_{n=1}^{29}n \\\\ 1635 = 30a + \frac{d\times29\times30}2[/tex]
so that
30a + 435d = 1635
Solve the equations in boldface for a and d. I'll eliminate a and solve for d first.
-30 (a + 29d) + (30a + 435d) = -30 (98) + 1635
-30a - 870d + 30a + 435d = -2940 + 1635
-435d = -1305
d = 3
Then
a + 29 (3) = 98
a + 87 = 98
a = 11
Instructions: Find the missing side. Round your answer to the nearest tenth.
Answer:
x = 24.9
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 43 = x /34
34 cos 43 = x
x=24.86602
To the nearest tenth
x = 24.9
Four students are playing a multi-level video game. Leo is playing the first level in the game.
Ralph is six levels above Leo.
Mike is two levels below Ralph.
Don, who is playing the last level of the game, is five levels above Mike.
How many levels does the game have?
Answer:
10 levels
Step-by-step explanation:
Ralph is on level 7
Mike level 5
Don level 10 and is playing the last one of game
The game has 10 levels
Leo is playing the first level and Ralph is sex levels above Leo. This means that Ralph is playing level:
= 1 + 6
= 7
Mike is two levels below Ralph which means that Mike is playing level:
= 7 - 2
= 5
Don is playing the last level and is five levels above Mike which means that Don is playing level:
= 5 + 5
= 10
Don is playing level 10 which is the last level so the game has 10 levels.
Find out more at https://brainly.com/question/23623247.
Please help explanation if possible
Answer:
y=-3x+5
Step-by-step explanation:
concepts: y=mx+b is slope intercept equation formula
m=slope
b= y intercept
Therefore we need to find the slope and y intercept
first find slope
m=[tex]\frac{y2-y1}{x2-x1}[/tex]
let y2 be 2
let y1 be -4
let x2 be 1
let x1 be 3
[tex]\frac{2-(--4)}{1-3}[/tex]
6/-2 = -3
m=-3
slope is -3
y= -3x+ b
we need find y intercept now
just plug in (1,2) into that equation
2=-3(1)+b
b=5
y=-3x+5
Find the slope of the line that passes through (1, 13) and (4,9)?
Geometry, please answer question ASAP
Answer:
66
Step-by-step explanation:
since BD and BC are congruent, angle C and angle D are equal. this means 6x-9=3x+24. If you solve this equation you get x=11. If you plug it into either 6x-9 or 3x+24 you get 57. 180-(57+57)=66
how many tens are in the number 15?
Answer:
1 tens and 5 ones
Which regular polygon can be used to form a tessellation?
I need help
Answer: Option 4 (Hexagon)
Step-by-step explanation:
A equilateral triangle, square and hexagon can be used to form a tessellation.
Please click thanks and mark brainliest if you like
write the equation in point -slope form using this graph
Step-by-step explanation:
Step 1: Write the equation using point-slope form
Point-Slope Form: [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
[tex]y-0=m(x-3)[/tex]
[tex]y = m(x-3)[/tex]
Step 2: Find the slope
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{-2-0}{-2-(-3)}[/tex]
[tex]m=\frac{-2}{1}[/tex]
[tex]m=-2[/tex]
Step 3: Combine them together
[tex]y = m(x - 3)[/tex]
y = -2(x - 3)
IF NEEDED: Completely factor
[tex]y = (-2 * x) + (-2 * -3)[/tex]
y = -2x + 6
Inverse trigonometry functions I need help finding the answers everything I’ve tried says it’s wrong
Answer:
see below
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hypotenuse
cos x = 13/20
Taking the inverse cos of each side
arccos ( cos x ) = arccos( 13/20)
x = arccos ( 13/20)
x =49.45839
x = 49 to the nearest whole number
sin theta = opp/ hyp
sin y = 13/20
Taking the inverse sin of each side
arcsin ( sin y ) = arcsin( 13/20)
y = arcsin ( 13/20)
y=40.5416
y = 41 to the nearest whole number
I need help really bad does can I contact anyone for help I need to complete or I fail really bad.
Step-by-step explanation:
45 >= 4x + 5
40 >= 4x
10 >= x (x <= 10)
and
53 > 4x + 5
48 > 4x
12 > x (x < 12)
so, both conditions need to be true (that is the meaning of "and").
how can that be achieved ? well, the harder, narrower condition beats any other.
so, when x <= 10, then it is automatically also smaller than 12.
so, the solution (inequality notation) is
x <= 10
and the graph just shows a line that starts at 10 (with a full, black dot at 10, as the point is included) and goes all the way to the left (to infinity and beyond ...)
Helpppppppppppppppppp What does the statement ∣
Answer:
b is 7 units from 0.
Step-by-step explanation:
[tex]|b|[/tex] = 7 means that the absolute value of b is 7. This means that b can be -7 or 7, so it will always be 7 units from 0.
Hope this helps!
What number line shows Point A at -4, Point B at 2.5, Point C at -2 1/2, and Point D, which is the opposite of Point A.
Answer: Choice A
Explanation:
Since -3/5 > -0.8, this means -3/5 is to the right of -0.8
Larger stuff is to the right of smaller stuff. Another example would be 10 > 7, meaning we have 10 to the right of 7 since 10 is larger.
Any negative value is always to the left of 0, so -3/5 is to the left of 0.
That's why the answer is choice A.
On Saturday, the fruit and juice bar was selling 22 glasses of fruit punch an hour. By 4 p.m., they had sold 132 glasses. If their goal was to sell more than 264 glasses of fruit punch, which inequality can be used to find h, the number of hours they must stay open to make their goal?
A. 132 + 22h > 264
B. 22h < 264 + 132
C. 132 + 22h < 264
D. 132 + 264 > 22h
Answer:
A. 132 + 22h > 264
Step-by-step explanation:
Hourly sales = 22 glasses of fruit punch
Sales by 4 p.m = 132 glasses
Goal = more than 264 glasses
h = number of hours they must stay open to make their goal
The inequality:
132 + 22h > 264
22h > 264 - 132
22h > 132
h > 132/22
h > 6 hours
This means, the number of hours they must stay open to make their goal of more than 264 glasses is more than 6 hours
pls help asap no wrong answers------------
Answer:
0.75, 1.25
Step-by-step explanation:
first we bring the line equation into the same format as the parabola equation (y = ...)
3x - y = 1
=>
y = 3x - 1
now we can say for the intersection points both equations must have the same result.
4x² - 1 = 3x - 1
4x² - 3x = 0
x(4x - 3) = 0
there are only 2 possible cases to make this true :
x = 0
and 4x - 3 = 0
4x = 3
x = 3/4 = 0.75
for the y value let's use the easier equation (line) :
y = 3×3/4 - 1 = 9/4 - 4/4 = 5/4 = 1.25
simplify 4x^2-3xy+2xy+9x^2
Answer:
13x^2 - xy
Step-by-step explanation:
4x^2-3xy+2xy+9x^2
=13x^2-xy
solve this questions
Answer:
3 a) solution:-
Discount=Rs 1,200
S .P =RS 4,000
M P=?
we know that,
Discount= M.P - S.P
or, Rs 1,200= M.P - Rs 4,000
or, M.P = RS (4,000-1,200 )
M.P = RS 2,800
In no. 3 all we have to make like this .........
Hope it helps
Answer:
Step-by-step explanation:
2)a) M.P =₹ 5000
S.P = ₹4000
Discount amount = M.P - S.P
= 5000 - 4000
= ₹1000
Discount percent = [tex]\frac{discount \ amount}{M.P}*100[/tex]
[tex]= \frac{1000}{5000}*100\\[/tex]
= 20%
3)a) Discount = ₹ 1200
S.P = ₹ 4000
M.P = S.P + discount
= 4000 + 1200
= ₹ 5200
4)a ) Discount rate = 15%
S.P= ₹ 4000
[tex]M.P = \frac{100+Discount rate}{100}*S.P\\\\=\frac{115}{100}*4000[/tex]
= ₹ 4600
Gregg’s phone plan charges $.50 per text message plus $.70 a day. Howard’s plan charges $.30 a text plus $2.50 a day. For what number of texts, a day are the cost of the phone plans the same? Show work.
Answer:
x=9
Step-by-step explanation:
.5x+.7 = .3x+2.5
-.7 -.3x
.2x=1.8
/.2 /.2
x=9
.5(9)+.7=5.2
.3(9)+2.5=5.2
[tex]\sqrt{a} +\sqrt{b} =\sqrt{a+b}[/tex]CHO A,B THUỘC R, khẳng định sau đúng hay sai
Answer:
Hello,
Step-by-step explanation:
Le théorème est faux
since a=9 and b=16 then
[tex]\sqrt{9} +\sqrt{16} =3*4=7 \\\sqrt{9+16} =\sqrt{25} =5\\[/tex]
Does anyone know the answer for this?
Answer:
I'm pretty sure it's the 3rd option
Answer:
first option is correct
Step-by-step explanation:
because there are less no. on negative side than on positive one
A. 83°
B. 90°
C. 97°
D. cannot be determined
Answer:
90
Step-by-step explanation:
c is perpendicular to b
That means angles 5,6,7,8 are 90 degrees
a is parallel to c
That means b is perpendicular to a
That means that 1,2,3,4 are 90 degrees
<1 = 90 degrees
Answer:
the answer is 90
Step-by-step explanation:
simpliy because c and b make a right angle
GEOMETRY QUESTION- Find m < h
9514 1404 393
Answer:
m∠H = 38°
Step-by-step explanation:
External angle GFD is the sum of internal angles G and H.
14x +1 = 89° +(5x -7)
9x = 81°
x = 9°
Then the measure of angle H is ...
angle H = 5(9°) -7° = 38°
the function h(x) is a transformation of the square root parent function
Answer:
h(x)=\sqrt(x+6)
Step-by-step explanation:
I just did the test for a p e x
Help plz and thanks
Answer:
6b
Step-by-step explanation:
create another show real life multi-step function problems with Solutions in quadratics
Answer:
Kazan also SOS jz zks zj sj aka always zks. aiwow
Pls I need help!!!Question 6 (Essay Worn 6 points) (06.03) 9(5x + 1) = 37 From the expression above, pronde an example of each of the following: sum, term, product, factor, quotient, and coefficient. If any are not present, write 'not present."
Answer:
5x+1=6.136
5x=6.136-1
5x=5.136
x=5.135/5
x=1.03
x=1
Graph the function
Is it a, b, c or d?
Answer:
D
Step-by-step explanation:
(the line is a / shape, so the slope is positive)
(the line crosses the y axis at (0,-2))
(using the above information, we can conclude that the equation is y=2x-2)
or
slope = m = rise/run = 2/1 = 2
y=mx+b
y=2x+b
Choose any point on the line) (1,0)
0=2(1)+b
b=-2
y=2x-2
What is the translation from the preimage to the image in the graph?
Answer:
(x, y ) → (x + 7, y + 5 )
Step-by-step explanation:
Consider the coordinates of R and R'
R (- 5, 0 ) and R' (2, 5 )
x- direction : - 5 → 2 is + 7 units
y- direction : 0 → 5 is + 5 units
Translation rule is (x, y ) → (x + 7, y + 5 )
10,4,7
The above set 4 numbers have a mean of 8
what could the mystery number
11 is the mystery number
Answer:
The mystery number is 11
Step-by-step explanation:
→ Set up an equation
( 10 + 4 + 7 + x ) ÷ 4 = 8
→ Multiply both sides by 4
21 + x = 32
→ Minus 21 from both sides
x = 11