If x = a sin α, cos β, y = b sin α.sin β and z = c cos α then (x²/a²) + (y²/b²) + (z²/c²) = ?
[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]
What is the common difference in the sequence?
The common difference is the amount between each number in an arithmetic sequence.
For example, the sequence 4,7,10,13,... has a common difference of 3.
When converting from inches to feet, the measurement in inches, m, of an object varies directly with its measurement in feet, f, with the constant of variation being 12.
What is the equation relating these two quantities?
How many inches would a 3.5-foot object measure?
inches
How many feet would a 27-inch object measure?
Step-by-step explanation:
wow, how complicated can one phrase this ...
the point being :
1 ft = 12 in and vice versa (1 in = 1/12 ft)
so, any measurements given in feet but needed in inches need to be multiplied by 12.
and any measurements given in inches but needed in feet need to be divided by 12.
so,
3.5 ft = 3.5×12 = 7/2 × 12 = 7×6 = 42 in
27 in = 27/12 = 9/4 = 2 1/4 or 2.25 ft
Answer:When converting from inches to feet, the measurement in inches, m, of an object varies directly with its measurement in feet, f, with the constant of variation being 12.
What is the equation relating these two quantities?
✔ m = 12f
How many inches would a 3.5-foot object measure?
✔ 42
inches
How many feet would a 27-inch object measure?
✔ 2.25
feet
Step-by-step explanation:
Find the area of this triangle.
Answer:
84 cm²
Step-by-step explanation:
Area triangle = 1/2(b x h)
Area = 1/2(21 x 8)
Area = 1/2(168)
Area = 84
84 cm²
-Chetan K
helpppppppp plzzzzzzzzzzzzzzzzz (ANSWER ONLY IF YOU KNOW)
Answer:
1/7 ( a+1 )
Step-by-step explanation:
1/7a + 1/7
1/7 ( a+1 )
the area of the floor of a cubical room is 49m .find the area of 4 walls of a room.
Answer: [tex]196m^2[/tex]
Step-by-step explanation:
since it's a cube the floor is in square shape
area of one wall = [tex]a^2[/tex] area of 4 walls = = [tex]4[/tex]×[tex]49[/tex] = [tex]196[/tex]Answer:
SINCE ITS A CUBE OF FLOOR SHAPE.
area of 1 wall=a²
=4
area of 4 wall=4x49
=169m²Ans.
Two sides of an equilateral triangle are labeled 12 inches and 3x - 6 inches. Find x.
Answer:
6
Step-by-step explanation:
In equilateral triangle, all the sides are congruent.
3x - 6 = 12
Add 6 to both sides
3x = 12 + 6
3x = 18
Divide both sides by 3
x = 18/3
x = 6
find the sum of the first seven terms -3,3,-3,3.
Show your work.
Directions: Follow the instructions for the following inequalities. Will give brainlist!
1. 4<7 Multiply both sides by 7, then by 6, then by 3, then by 10
2. 11>-2 Add 5 to both sides, then add 3, then add (-4)
3. -4<-2 Subtract 6 from both sides, then 8, and then 2
4. -8<8 Divide both sides by -4, then by -2
5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
1) 4<7
×7 ×7
28<49
×6 ×6
168<294
×3 ×3
504<882
×10 ×10
5040<8820
2) 11>-2
+5 +5
16> 3
+3 +3
19>6
+-4 +-4
15>2
3) -4<-2
-6 -6
-10<-8
-8 -8
-18<-16
-2 -2
-20<-18
4) -8<8
÷-4 ÷-4
2<-2
÷-2 ÷-2
-1< 1
5) ~The affect of the inequality sign didn't change. If you add or subtract the same positive or negative number to both sides of an inequality or an equation, the inequality stays the same. If you multiply or divide both sides of an inequality or an equation by the same positive number, the inequality stays the same. This is because when manipulating inequalities there are rules this if a < b then a + c < b + c so we get a new number that replaces a and b yet the inequality symbol stays the same so a still is smaller than b.
Hope this helped you- have a good day bro cya)
Please help!!
9.(05.02)
Solve the following system of equations: (5 points)
x - 2y = 5
2x - 4y = 10
Infinitely many solutions
No solutions
(0, 0)
(5, 10)
Answer:
Infinite solutions
Step-by-step explanation:
If you look at the equation, you will see that if you multiply everything by two (On the 1st equation), you get the 2nd equation. This means that the lines are the same, so infinite solutions.
Step-by-step explanation:
infinitely many solutions :)
I NEED HELP PLEASE!!!!
Answer:
the answer is x=15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
since angles 84 and 5x + 9 are alternate interior angles they both are equal
i.e
5x +9 = 84
5x = 84 -9
5x = 75
x = 75/5
therefore x = 15
keep smiling
01.01 LC)Look at the following numbers: −4, −5, 0, 5 Which pair of numbers has a sum of zero? 5, −5 −5, 0 −4, 5 −4, 0
Answer:
5, -5
hope this helps
Answer:
Train to BaDussy
Step-by-step explanation:
A box is pulled to the right with a force of 65 N at an angle of 58 degrees to the horizontal. The surface is frictionless. The free body diagram is shown.
A free body diagram with 3 force vectors. The first vector is pointing north, labeled F Subscript N Baseline, the second vector is pointing south labeled F Subscript g Baseline = 30 N, and the third pointing 58 degrees north of east labeled F Subscript g Baseline = 65 N.
What is the net force in the x-direction?
30 N
34 N
55 N
65 N
Answer:
34 N.
Step-by-step explanation:
Net force in x direction = 65 cos 58
= 34 N.
Answer:
34N is the answer :)
Step-by-step explanation:
write an inequality whose solutions are represented by the shaded part of the graph
Answer:
x > 3
Step-by-step explanation:
A flock of birds perched on a tree. In the morning, each bird perched 1 tree and 1 bird left. In the afternoon, 2 chicks perched, 1 tree left over. Ask how many birds, how many trees?
Answer:
2 birds 1 tree
Step-by-step explanation:
I think only not sure
The domine of definition of the function
[tex]f(x) = \frac{1}{ \sqrt{ |\cos(x)| + \cos(x) }} \: is \\ [/tex]
[tex]\large\underline{\sf{Solution-}}[/tex]
Given function is
[tex]\rm \longmapsto\:f(x) = \dfrac{1}{ \sqrt{ |cosx| + cosx} } [/tex]
Now,
[tex]\rm \longmapsto\:f(x) \: is \: defined \: if \: |cosx| + cosx > 0[/tex]
We know,
[tex]\begin{gathered}\begin{gathered}\bf\: \rm \longmapsto\: |x| = \begin{cases} &\sf{ - x \: \: when \: x < 0} \\ \\ &\sf{ \: \: x \: \: when \: x \geqslant 0} \end{cases}\end{gathered}\end{gathered}[/tex]
So,
[tex]\begin{gathered}\begin{gathered}\bf\: \rm \longmapsto\: |cosx| + cosx = \begin{cases} &\sf{ \: \: 0 \: \: when \: cosx \leqslant 0} \\ \\ &\sf{ \: \: 2 \: cosx \: \: when \: cosx > 0} \end{cases}\end{gathered}\end{gathered}[/tex]
So,
[tex]\rm\implies \:f(x) \: is \: defined \: when \: cosx > 0[/tex]
So, from graph we concluded that cosx > 0 in the following intervals.
[tex]\begin{gathered}\boxed{\begin{array}{c|c} \bf cosx & \bf \: x \: \in \: \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf + ve & \sf \bigg( - \dfrac{\pi}{2} ,\dfrac{\pi}{2} \bigg) \\ \\ \sf + ve & \sf \bigg(\dfrac{3\pi}{2} ,\dfrac{5\pi}{2} \bigg) \\ \\ \sf + ve & \sf \bigg(\dfrac{7\pi}{2} ,\dfrac{9\pi}{2} \bigg) \end{array}} \\ \end{gathered}[/tex]
So, if we generalized this we get
[tex]\rm\implies \:cosx > 0 \: when \: x \: \in \: \bigg(\dfrac{(4n - 1)\pi}{2} ,\dfrac{(4n + 1)\pi}{2} \bigg) \: \forall \: n \in \: Z[/tex]
Hence,
Domain of the function is
[tex]\red{\rm\implies \boxed{\tt{ \: x \in \: \bigg(\dfrac{(4n - 1)\pi}{2} ,\dfrac{(4n + 1)\pi}{2} \bigg) \: \forall \: n \in \: Z}}}[/tex]
[tex]\textsf{More to know :-} \\[/tex]
[tex]\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c} \bf T-eq & \bf Solution \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf sinx = 0 & \sf x = n\pi \: \forall \: n \in \: Z\\ \\ \sf cosx = 0 & \sf x = (2n + 1)\dfrac{\pi}{2}\: \forall \: n \in \: Z\\ \\ \sf tanx = 0 & \sf x = n\pi\: \forall \: n \in \: Z\\ \\ \sf sinx = siny & \sf x = n\pi + {( - 1)}^{n}y \: \forall \: n \in \: Z\\ \\ \sf cosx = cosy & \sf x = 2n\pi \pm \: y\: \forall \: n \in \: Z\\ \\ \sf tanx = tany & \sf x = n\pi + y \: \forall \: n \in \: Z\end{array}} \\ \end{gathered}\end{gathered}[/tex]
If a line has a slope of 4 and a y-intercept of 3, what is the equation of that line in slope-intercept from???
Answer:
y=3x-4
Step-by-step explanation:
Factorize; x cubed - x squared y ?
ASAP, please
Answer:
x²(x - y)
Step-by-step explanation:
x³ - x²y ( x² is common to both terms so factor it out )
= x²(x - y)
Freddy bought 3 bags of pebbles to put in his fish tank. Each bag contains 295 pebbles. After he put the right amount of pebbles in his fish tank, he had 104 pebbles left over. How many pebbles did he put in his fish tank?
295 x 3 = 885
885-104 = 781
781 pebbles
HELP PLS MARKING BRAINLEIST
Answer:
1
Step-by-step explanation:
5/5=1
Answer:
4/5
Step-by-step explanation:
You move up four on the y-axis and over 5 on the x-axis and it would meet the next point
Hope this Helps
Use the remainder theorem to determine whether x=-4 is a solution of x^6+5x^5+5^4+5^3+2x^2-10x-8.
Hello haohaoxNienie!
[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
Use the remainder theorem to determine whether x = - 4 is a solution of x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8.
[tex] \large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}[/tex]
Refer to the attached picture.
Steps :-First find the divisor using the given information (x = - 4).Now, divide x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8 by x + 4.We'll get the remainder as 0.Using the remainder theorem & solving it, we'll get LHS & RHS as 0.Hence proved.Answer :- Yes, x = - 4 is a solution of x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8.
__________________
Hope it'll help you!
ℓu¢αzz ッ
Find the slope of the line that passes through (1, 2) and (10, 10).
You are buying bottles of a sports drink mix for a softball team. Each bottle costs $1.19. What function rule models the total cost of a purchase? Evaluate the function for 15 bottles
Answer: f(x) = 1.19x, where f(x) is the total cost, and x is the cost per bottle
Cost of 15 bottles: $17.85
Step-by-step explanation:
This question describes a straightforward relation between cost per bottle, and cost for all the bottles. As such, simply equate one variable to the value of one bottle, and f(x) as the value of every bottle.
Hope it helps :) and let me know if you want me to elaborate.
P.S. f(x) can simply be substituted for "y"
Let
no of bottles be x
.The function is given by
[tex]\\ \sf\longmapsto f(x)=1.19x[/tex]
Now
Bottles=15Cost:-
[tex]\\ \sf\longmapsto f(15)[/tex]
[tex]\\ \sf\longmapsto 1.19(15)[/tex]
[tex]\\ \sf\longmapsto 17.89[/tex]
Describe the translation of the point to its image. (-2,-3) to (-2,4)
Up 8 Units, Hope this helps :)
can someone pls help me
Answer:10 & 12
Step-by-step explanation:
Answer:
The 5th step will need 32 blocks, and the 6th step will need 64 blocks.
Step-by-step explanation:
Each step requires the blocks to be doubled. The first step has two, 2x2 is 4. There are 4 blocks in the next step. 4x2 is 8. There are 8 blocks in the next step, and so on and so forth. Just multiply by 2. Hope this helped!
Use the Pythagorean Theorem to find the distance between the point (1,4) and (-5,-4) on the coordinate plane? (FREE RESPONSE)
PLZ I NEED IT RIGHT NOW
Answer:
hope this helps
(6d+5)−(2−3d) find the difference
Answer:
10d
Step-by-step explanation:
6d+5 =11d
2-3d = -1d
11d-1d= 10d
Questions linked below
Answer:
The blur of the photo I do not understand sorry
Step-by-step explanation:
ty for the points
Help pls and show your work!
neeeeeeed heeeeeelp pleaseeeeeeeee
Answer:
D
Step-by-step explanation:
Hope this is correct and helps
Answer:
D
Step-by-step explanation:
I'm not completely sure but A is constant cuz it don't move B is increasing C is same as A and D Is decreased
