Find the value of each variable. Please help! 25 points!

[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]

Answer:

y=3x-4

Step-by-step explanation:

Answer:

31 cm

Step-by-step explanation:

the scatterplot is rising, so based on an assumption of where a line going through the scatterplot is going to go, you get 41

Answer:

2 birds 1 tree

Step-by-step explanation:

I think only not sure

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

Answer:

10d

Step-by-step explanation:

6d+5 =11d

2-3d = -1d

11d-1d= 10d

Up 8 Units, Hope this helps :)

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

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

Cost:-

[tex]\\ \sf\longmapsto f(15)[/tex]

[tex]\\ \sf\longmapsto 1.19(15)[/tex]

[tex]\\ \sf\longmapsto 17.89[/tex]

Answer:

x²(x - y)

Step-by-step explanation:

x³ - x²y ( x² is common to both terms so factor it out )

= x²(x - y)

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

Answer:

1. The powers include: budgeting and appropriation of funds for all county activities; building and maintaining county roads; making and enforcing civil and criminal resolutions and ordinances not in conflict with state law, including those for land use and building construction; supporting and implementing.

2. Serves as a licensed peace officer and is responsible for enforcing the criminal laws of the state. Manages and operates the county jail. Provides security for the courts.

3. County governments perform essential administrative functions such as registering voters, supervising elections, keeping records, providing police protection, and administrating health and welfare services.

Step-by-step explanation:

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

295 x 3 = 885

885-104 = 781

781 pebbles

Answer:

ik this

Step-by-step explanation:

i believe its 180

Answer: B) 115

Step-by-step explanation: i hop this help if not sorry :(

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)

Answer:

this problem is  Non-proportional

Step-by-step explanation:

hope this helps

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!

[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]

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.

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.

Answer :- Yes, x = - 4 is a solution of x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8.

__________________

Hope it'll help you!

ℓu¢αzz ッ

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 :)

Answer:

1/7 ( a+1 )

Step-by-step explanation:

1/7a + 1/7

1/7 ( a+1 )

Answer:

The blur of the photo I do not understand sorry

Step-by-step explanation:

ty for the points

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

Answer:

$20

Step-by-step explanation:

12.6x-2.1x=210

10.5x=210

x=210/10.5

x=20

Answer:

5, -5

hope this helps

Answer:

Train to BaDussy

Step-by-step explanation: