[tex]\large\underline{\sf{Solution-}}[/tex]
Given:
[tex] \rm \longmapsto x = a \sin \alpha \cos \beta [/tex]
[tex] \rm \longmapsto y = b \sin \alpha \sin \beta [/tex]
[tex] \rm \longmapsto z = c\cos \alpha[/tex]
Therefore:
[tex] \rm \longmapsto \dfrac{x}{a} = \sin \alpha \cos \beta [/tex]
[tex] \rm \longmapsto \dfrac{y}{b} = \sin \alpha \sin \beta [/tex]
[tex] \rm \longmapsto \dfrac{z}{c} = \cos \alpha[/tex]
Now:
[tex] \rm = \dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} } [/tex]
[tex] \rm = { \sin}^{2} \alpha \cos^{2} \beta + { \sin}^{2} \alpha \sin^{2} \beta + { \cos}^{2} \alpha [/tex]
[tex] \rm = { \sin}^{2} \alpha (\cos^{2} \beta + \sin^{2} \beta )+ { \cos}^{2} \alpha [/tex]
[tex] \rm = { \sin}^{2} \alpha \cdot1+ { \cos}^{2} \alpha [/tex]
[tex] \rm = { \sin}^{2} \alpha + { \cos}^{2} \alpha [/tex]
[tex] \rm = 1[/tex]
Therefore:
[tex] \rm \longmapsto\dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} } = 1[/tex]
Toby picks a 4-digit number.
It is larger than 2999 and it is a multiple of 2.
How many different numbers could he have picked?
Let’s reduce this question into easier terminology.
The number is a multiple of 2, meaning it is an even number. It is larger than 2,999 and less than 10,000 (since it is a 4 digit number).
Thus, Toby could have picked any even number from 3000 to 9,999. So this question is asking how many even numbers (multiples of 2) are between 3000 and 9,999.
For every thousand, there are 1000/2 = 500 multiples of 2:
500 multiples between 3,000 and 3,999
500 multiples between 4,000 and 4,999
and so on until 9,999. So there are
7*500 = 3500 multiples of 2 in this range.
Toby could have picked 3500 possible numbers.
Jimmy's Bike Rentals charges a $13 fixed fee plus $7 an
our for renting a bike. Amanda paid $55 to rent a bike. How
hany hours did she pay to have the bike checked out ?
Answer:
6 hours
Step-by-step explanation:
let the no. of hours she rent the bike be x
then,
13 + 7*x = 55
13 + 7x = 55
7x = 55 -13
7x = 42
x = 6
Kylie signed up for a streaming music service where there's a fixed cost for a monthly membership and a cost per song downloaded. Her total cost is given by the linear graph below. What does the slope of the line represent?
Answer:
we need the linear graph ._.
Step-by-step explanation:
What’s the perimeter of 4 feet long and 4 feet wide
4 times 4 so your awnser is 12
Hope that helps :)
Answer:
16
Step-by-step explanation:
4+4+4+4
Two people wrote a book together. They agreed to share the royalties so that the senior author received twice as much as the
junior author. What is each author's share of a $2400 royalty check?
Answer:
Junior author = $800
Senior author = $1600
Step-by-step explanation:
The check is split between the senior author and junior author in the ratio of 2:1
2:1 = $2400
Add the ratios together:
2 + 1 = 3
3 parts = $2400
Find one part of the total check by dividing both sides by 3:
1 part = $800
The junior author would get $800, and the senior author would get double, $1600pleaseeeee helpppppp <333
Step-by-step explanation:
64+72+4x+20=180(Sum of angles of a triangle )156+4x=1804x=180-1564x=24X=24/4X=6Therefore The value of X is 6 degree.
PLEASE HELP FAST WILL MARK BRANLIEST!!
Which is the graph of y = 2(x - 3)2 + 2
The graph will look like this
/Which of the following pairs consists of equivalent fractions? 8/16 and 3/4 5/3 and 3/5 12/18 and 10/15 12/20 and 10/25
Answer:
12/18 and 10/15
Step-by-step explanation:
12/18 = 2/3 (when the numerator and denominator are divided by 6)
10/15 = 2/3 (when the numerator and denominator are divided by 5)
∴ 12/18 and 10/15 are equivalent
10. Determine if the equation x - y = 1 defines y as a function of x.
Answer:
No.
Step-by-step explanation:
First solve for y:-
x - y^4 = 1
y^4 = x - 1
y = +/- (x - 1)^(1/4)
This is a one-to-many relation . For a given value of y there 2 values of x.
So this is NOT a function.
Please help with showing the points in the table
Answer:
attached
Step-by-step explanation:
Please try to create table yourself. just plug in the x value to calculate the y value, such as x=-5, y=-2; x=-6, y=-2... or x=-1, y=-1-3=-4 ...etc
Bill has two dollars and 2 cents. How much money does he have?
Answer:
He has $2.02
Step-by-step explanation:
You answered the question in the first sentance.
3y-6 = y+4 solve HELLLLKPPP
Please tell me the answer up to e no.
(I think you need a-e, if not let me know and I will edit accordingly)
a: Divide both sides by 4
cm -> 12:8
3:2
b: Convert and divide both sides by 3
cm -> 150:9
50:3
c: Convert and divide both sides by 20
cm -> 100:80
5:4
d: Convert and divide both sides by 4
months -> 4:12
1:3
e: Convert and divide both sides by 250
g -> 2000:250
8:1
Hope this helps, have a nice day :)
please please help with question ill give high points and brainliest
Answer:
Step-by-step explanation:
x over 32 = 3 over 16
Answer:
7/32 = 3/16
Step-by-step explanation:
Answer:
x=6
Step-by-step explanation:
We simplify the equation to the form, which is simple to understand
x/32=3/16
Simplifying:
+ 0.03125x=3/16
Simplifying:
+ 0.03125x=0.1875
We move all terms containing x to the left and all other terms to the right.
+ 0.03125x=0.1875
We simplify left and right side of the equation.
+ 0.03125x=0.1875
We divide both sides of the equation by 0.03125 to get x
( PLASE HELP ME) Solve the following equation.
5(x−4)=−10
Please provide both your answer AND your work. You will not receive full credit if you do not show your work for this question.
Answer:
x = 2
Step-by-step explanation:
5(x-4) =-10
Distribute 5 by multiplying x and -4 by 5
5x - 20 = -10
Add 20 to both sides
5x - 20 + 20 = -10 + 20
5x = 10
Divide both sides by 5
5x ÷ 5 = 10 ÷ 5
x = 2
-Chetan K
no need for explanation jsut answer
Answer:
y=4 because 8x4=32
32-2 =30
30+60=90
Answer:
the value of y is 4, so 8(4)-2 are 30 , then 30 degrees are the angle
A child's weight was 200% what it was at age 3. by what percent did the child's weight increase by
Answer:
The child's weight increase by 66.7%
How many solutions does this linear system have?
y = -6x+2
-12x - 2y = -4
one solution: (0,0)
O one solution: (1.4)
O no solution
O infinite number of solutions
Answer:
in finity
Step-by-step explanation:
Both provide ATP molecules, but only fermentation occurs when oxygen is present.
okokoo
The linear system have y = -6x+2 and -12x - 2y = -4 have infinite number of solutions.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given system of linear equations are y = -6x+2 and -12x - 2y = -4
To solve this system, we can substitute the expression for y from the first equation into the second equation, as follows.
-12x - 2y = -4
substitute y = -6x + 2 from first equation
-12x - 2(-6x + 2) = -4
Distribute the negative sign
-12x + 12x - 4 = -4
0 = 0
The equation 0 = 0 is a true statement, which means that the system has infinitely many solutions.
Hence, the linear system have y = -6x+2 and -12x - 2y = -4 have infinite number of solutions.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ7
The product of twice a number and four is the same as the difference of seven times the number and 2/7 Find the number.
Answer:
the number is -2/7
Step-by-step explanation:
let the number be x
2x ×4= 7x-2/7
8x = 7x-2/7
collect like terms
8x-7x = -2/7
X= -2/7
(7g - 6) - (-3n – 4) =
Answer:
7g + 3n - 2
Step-by-step explanation:
when you subtract you 'add the opposite'; subtracting a negative is the same as adding a positive
for example, using the above statement we can rewrite the problem as:
7g - 6 + 3n + 4
we can combine -6 and 4 to get -2
7g + 3n - 2 or 7g + 3n + (-2)
The points (18,21) and (42,49) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.
Answer: 5/2
Step-by-step explanation: 49 - 42/ 21 - 18
the length of a rectangular field three times of it's breath.if the area of the field is 675 m2, find the perimeter
with full solution
L/W = 3/1 or L = 3*W
A = L*W = (3*W)*W = 3*W^2 = 675 m^2
W^2 = (675 m^2)/3 = 225 m^2
W = sqrt(225 m^2) = 15 m
L = 3*W = 3*(15 m) = 45 m
Someone plz help me :(
Answer:
28 miles
Step-by-step explanation:
12:3
7:x
12÷3=4
4 miles per hour
7•4=28
helpppppppppppppppppppppppppppppppppppppppp
Answer:
12/12=1
2.5/2.5=1
5/_=1
mysterty number is 5
5.5./_=1
mystery number is 5
Step-by-step explanation:
Raquel y Beatriz van a montar a caballo Raquel lo hace cada 3 días y Beatriz cada 4 días. Si coinciden el 24 de febrero
Si el año es ordinario, entonces Raquel y Beatriz se encontrarán el 8 de febrero, más si el año es bisiesto, entonces se encontrarán el 7 de febrero.
El período de coincidencia es el tiempo que pasa entre dos fechas en las que Raquel y Beatriz coinciden y queda determinado por el mínimo común múltiplo de los tiempos de frecuencia de cada una. En este caso, el período de coincidencia corresponde a 12 días.
Si tenemos que coincidieron el 24 de febrero, debemos considerar dos posibilidades: (i) Año ordinario, (ii) Año bisiesto.
Si el año es ordinario, entonces Raquel y Beatriz se encontrarán el 8 de febrero, más si el año es bisiesto, entonces se encontrarán el 7 de febrero.
Invitamos cordialmente a ver esta pregunta sobre mínimo común múltiplo: https://brainly.com/question/21756809
Nota - El enunciado se encuentra incompleto, la forma completa se describe a continuación:
Raquel y Beatriz van a montar a caballo. Raquel lo hace cada 3 días y Beatriz cada 4 días. Si coinciden el 24 de febrero, ¿cuando volverán a coincidir?
Find the interval(s) on which the function is negative.
y = x^2 - 6x - 16
I. (-∞, -2)
II. (-∞, 3)
III. (-2, 8)
IV. (8,∞)
A. III only
B. I only
C. II only
D. I,II
Answer:
I am going to say that it is option A.
Step-by-step explanation:
I hope this helped out a lot!
Adam is scuba diving. He descends 5 feet below sea level. He then descends the same distance 4 more times. What integer represents Adam's new DISTANCE from sea level?
O -25ft
O 20ft
O 9ft
0 -20 ft
Answer:
-20 ft
-5×4= -20
-5ft×4= -20ft
Simplify 2x2 + 3x2 + 3x
Answer:
10+3x
Step-by-step explanation:
2(2) = 4
3(2) = 6
4+6 = 10
10+3x
Answer:
Step-by-step explanation:
i need the answer to the bottom question please help !!!!!!!!!!!!!!
Answer:
y = 9/17 x - 28/17
Step-by-step explanation:
