[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]
can you solve this for me step by step please!!!
Answer:
60 DEG
Step-by-step explanation:
Angle on a straight line = 180 DEG
Equation:
4x + 2x + 90 DEG = 180 DEG
6x = 90 DEG
x = 15 DEG
Therefore,
angle LMN = 15 * 4 = 60 DEG
Cantaloupes are four for $9, how many can you buy for $25?
The sum of 24 and 3 times a number y is equal to 56
Answer:
Step-by-step explanation:
24+3y=56 solve for y, subtract 24 from each side
3y=32 divide each side by 3
y=32/3
Answer:
y=32/3
Step-by-step explanation:
let the number be y, then
24+3y=56 solve for y, subtract 24 from each side
3y=32 divide each side by 3
y=32/3
The US dollar can be exchanged for other types of currency in the world the exchange rate is always changing suppose one eruro is equivalent to two dollars
HELP DUE TODAY! PLS HELPP
1. 2. 5. 10. Euro
2. ? ? ? US dollars
Answer:
$2, $4, $10, $20
Step-by-step explanation:
1*2=2
2*2=4
5*2=10
10*2=20
erome has an app that tracks his running times and distances. He records his distances and times in a table.
Time (secs) Distance (mi)
3
14.4
6
28.8
9
43.2
12
57.6
What is Jerome's speed in distance compared to time?
Enter only a number in the space provided. Do not enter words in the box.
Answer:
IM SMART
Step-by-step explanation:
factor:3x²-xy-4y²
pls help)):
Step-by-step explanation:
plz mark me as brainliest
[tex]3 {x}^{2} - xy - 4 {y}^{2} \\ = 3 {x}^{2} + 3xy - 4xy - 4 {y}^{2} \\ = 3x(x + y) - 4y(x + y) \\ = (3x - 4y)(x + y)[/tex]
Answer:(3x-4y)(x+y) or (x+y)(3x-4y)Hope it helps
ray4918 here to help
PLEASE HELP ME
The table shows the outputs, y, for different inputs, x:
Input (x) 1 2 3 4
Output (y) 5 5 7 9
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 2x − 8. Which relation has a greater value when x = 4? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 34? (5 points)
(10 points)
Answer:
See belowStep-by-step explanation:
Part AAccording to definition of the function, the data in the table is a function. Each input value has own output and no repeat inputs.Part BAt x = 4, y = 9 (table)At x = 4, f(4) = 2*4 - 8 = 8 - 8 = 0The relation in the table has greater value as 9 > 0
Part Cf(x) = 34, find x:
34 = 2x - 82x = 34 + 82x = 42x = 21What is w(53)is equal to
Answer:
Step-by-step explanation:
The question is slightly ambiguous. The problem is, do you find the first 40 hours using 10x and then the second equation using x >40. I don't think so, but it should be made clear. It turns out that the first 40 hours does equal 400 so that you can use the second expression with no worries.
w(53) = 15(53 - 40) + 400
w(53) = 15(13) + 400
w(53) = 195 + 400
w(53) = 595
It says find the product, then list the units. Please explain how to do this! Best explanation gets brainliest
Answer:
$72
Step-by-step explanation:
it is like how much someone earns for 8 hours of work at the rate of $9 per hour.
The rate of the answer is dollars since it's the money earned
Find the measure of the angles (S)
Please help out:/
Answer:
Step-by-step explanation:
The triangle’s angles add up to 180°
so 180 - (5x - 2) = the another one interior angle
180 - 5x + 2
182 - 5x
and then 2x + 76 + (182 - 5x) = 180
2x + 76 + 182 - 5x = 180
258 - 3x = 180
78 = 3x
x = 26
so 2x = (26)(2) = 52
5x - 2 = (5)(26) - 2 = 128
please give me a brainliest answer
Find the remainder when f(x) = 5x3 + 7x + 5 is divided by x + 2
A. -49
B. -7
C. 11
D. 59
Which sets are NOT closed under subtraction? Choose all that apply.
-Odd numbers
-Integers
-Prime numbers
-Natural numbers
-Irrational numbers
-Even numbers
Edward buys a bicycle online for 254.75$ if shipping and handling are an additional 24% of the price how much shipping and handiling will Edward pay
Answer:
315.89
Step-by-step explanation
7 pls pls pls help meeee!
Are these functions or not functions?
What is the equation of the line that passes through points (-3, 0.5) and (3, -0.5)?
Group of answer choices
=−6
y
=
−
6
x
=−16
y
=
−
1
6
x
=−6−17.5
y
=
−
6
x
−
17.5
=−16+1
Answer:
Remember that the slope is the change in y/the change in x
Step-by-step explanation:
1. The slope [tex]\frac{-0.5- 0.5}{3 - (-3)}[/tex]
= [tex]\frac{-1}{6}[/tex]
2. Find "b" which is the y-intercept. Pick one of the two point and the slope.
Let use (-3, 0.5) and the slope is -1/6
y = mx + b
0.5 = -1/6 (-3) + b Solve for b
3 = 3 + b Multiply each term by 6
0 = B
3. Write the equation of the line y = mx + b
y = -1/6x + 0
Solve for the variables shown in the steps simplifying the expression below:
2^5·8^4/16=2^5·(2^a)^4/2^4=2^5·2^b/2^4=2^c.
Answer:
a=3, b=12, c=13
Step-by-step explanation:
I need to show my work help
Answer:
it will take 90 minutes
Step-by-step explanation:
10 - 6 = 9
9 x 10 = 90
Answer:
give the other guy brainliest he deserves it
Step-by-step explanation:
Mario measured the depth of the river as a function of time and graphed his findings. Use this graph to answer the following question.
What is the maximum depth of the river?
1 meter
22 minutes
10 meters
9 minutes
Answer:
10 meters
Step-by-step explanation:
highest value on y-axis
A woman places a laser pointer on the ground and shines it at the top of a lamp post. She then
stands between the laser and the lamp post so the laser just barely touches the top of her head.
The woman, the lamppost, the laser, and the ground combine to form two similar right triangles.
She is standing 2.4 meters away from the lamppost and 2.1 meters from the laser. If the woman
is 1.8 meters tall, how tall is the lamppost?
I NEED HELP ON THIS QUICKLY
Answer:
B) Alternate Exterior Angles
Step-by-step explanation:
They are exterior (on the outside of the the lines) and they are alternate (opposite left and right).
Answer:
Alternate exterior angles
Step-by-step explanation:
Alternate exterior angles are outside angles that lies to the opposite side.
Help pls and show your work!
What is the equation of the line that is perpendicular to -2/5x-7 and passes through (4,-1)?
Step-by-step explanation:
maybe this is not the full expression, as you wrote the line equation in a funny way.
I understand the following :
the line is
y = (-2/5)×x - 7
perpendicular means crossing at a right angle (90 degrees).
the slope of the original line is -2/5.
as in every line equation, the slope is the factor of x. and it expresses the ratio y/x indicating the amount of units y is changing, when x changes a certain amount of units (e.g. when going from one point on the line to another).
the perpendicular slope turns the original y/x ratio upside-down, and also flips the sign.
so, it is 5/2.
the equation for the perpendicular line looks like
y = (5/2)×x + b
now what is b ?
for this we use the specified point on the line : (4, -1)
and we put these values as x and y into the equation :
-1 = (5/2)×4 + b = 5×2 + b = 10 + b
b = -11
and so, the full equation of the perpendicular line is
y = (5/2)×x - 11
helpppppppppppppppppppppppppppppp meeeeeeeeeeeeeeeeeee plsssssssssssssssssssssss there is more but plss help mee
Answer: The attachment is a bit difficult to read, and long. I'll make some suggestions and add some detail to a few of the problems, but would ask that these suggestions be applied to other problems to find the answers.
Step-by-step explanation:
9. Coinciding lines line on top of each other. I.e., they are the same equation. If we take A, for example, we can reduce the second expression by dividing by 2: (2x+4y=6)/2 = (x + 2y = 3). This matches the first expression (x + 2y = 3). ! Whoa, that went fast.
10. (x+8)(x-8) = x² +8x -8x - 64 = x² - 64
11. I don't have the time to explain how one can factor, but practice is important. And I don't know if this is completely factored, but it matches one of the options. Try (n-2)(n²+2n + 4) [n³ +2n² +4n - 2n² -4n -8 = n³ - 8. It works.
12. The denominators are the same, so add the numerators and keep the denominator. (7x+4y)/x²y
13. The slope is the "Rise" over the "Run." (3,4), (8,-1) Rise = (-1 - 4) = -5. Run = (8-3) = 5 Slope = -(5/5) = -1
14. A line with a positive slope will move upwards as x increases. We can eliminate options C and D immediately. That leaves A and B. The line we are looking for is y = 5x + b. We are not given b, the y-intercept, so determine the slopes of both lines: I get 4 for A and 5 for B. To confirm B is correct, we could calculate b for y=5x+b by using given point, (2,3). 3 = 5*2 + b, b = -7. We can't see this point (0,-7) on the graph, but it appears correct. B is the best answer.
15. The line will have the form of y=mx+b. Calculate m, the slope, from the two points (3,1) and (4,7). Rise = 6, Run = 1 Slope = 6. y=6x+b. Find b by using either of the given poins and solving for b. I'll choose (3,1). y=6x+b; 1 = 18 + b; b = -17. The equation is y=6x-17. Rearrange option A (y =6x - 17).
16. The second value in each factor must, when multiplied together, equal the final term of the original expression, -9y². I see only one option for which that is true, C. Multiply the two factors in C to be certain, and you'll find they result in the correct expression.
Carla and Ben earn commission every time they sell soemthing. Carla sold 3 suits and 1 pair of shoes, and earned 47$ in commission. Ben sold 7 suits and 2 pairs of shoes, and earned 107$ in commision. how much commission do they get from selling suits, and how much do they get from selling shoes
Answer:
$13
Step-by-step explanation:
Please tell me if i'm wrong.
John has 4 milligrams of copper and 0.76 milligram of lead.
How much more copper does he have than lead?
A
3.24 milligrams
B 32.4 milligrams
C 4.76 milligrams
Answer:
A 3.24 milligrams
Step-by-step explanation:
4 milligrams of copper - 0.76 milligrams of lead = 3.24 milligrams.
brainliest please. . . .
A farmer owns a total of 8 acres of land. The land is separated into (3)1/3 equally sized sections. How many acres are in each section?
Write your answer as a mixed number in simplest form.
Answer:
each section is 2 2/3 or 2.66666666
Step-by-step explanation:
LY!
Fill in the missing numbers to complete the pattern:
2.6, 3.1,
4.6, 5.1
find the slope with the given numbers
Answer:
[tex]m=-\frac{1}{26}[/tex]
Step-by-step explanation:
Formula:
[tex]Slope:m=\frac{y_2-y_1}{x_2-x_1}\\[/tex]----------------------------------------------------------------------------------------------------------------
Work:
[tex]m=\frac{-15-(-16)}{-7-19}\\\\m=-\frac{1}{26}[/tex]
Plz help and explain the answer
Hey there!
If she bought 3 LBS (pounds) of bananas and they cost 54¢ per lb, then your equation should look like this: 3 × 0.54 = t and you should be able to find the answer from there!
t = result / how much he spent in total
Equation:
t = 3 × 0.54
3 × 0.54 = t
SIMPLIFY IT
t = 1.62
Therefore, Erin spent ≈ $1.62 (1 dollar & 62 cents)
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)