Answer:
•cos(s+t) = cos(s)cos(t) - sin(s)sin(t) = (-⅖).(-⅗) - (√21 /5).(⅘) = +6/25 - 4√21 /25 = (6-4√21)/25
•cos(s-t) = cos(s)cos(t) + sin(s)sin(t) = (-⅖).(-⅗) + (√21 /5).(⅘) = +6/25 + 4√21 /25 = (6+4√21)/25
cos(t) = ±√(1 - sin²(t)) → -√(1 - sin²(t)) = -√(1 - (⅘)²) = -⅗
sin(s) = ±√(1 - cos²(s)) → +√(1- cos²(s)) = +√(1 - (-⅖)²) = √21 /5
WILL GIVE BRAINLIEST, PLEASE HELP! Given the foci and vertices of an ellipse, complete the following steps.
Answer:
a) The location of the center of the ellipse is [tex](4,-6)[/tex]. It is determine by knowing the location of foci and Midpoint formula.
b) The standard equation of the ellipse is [tex]\frac{(x-4)^{2}}{31}+\frac{(y+6)^{2}}{81} = 1[/tex].
c) Major semiaxis ([tex]a[/tex]): [tex]a = 9[/tex], Minor semiaxis ([tex]b[/tex]): [tex]b = \sqrt{31}[/tex]
Step-by-step explanation:
a) Foci are located in the major axis of the ellipse, given the locations of ends of the major axis and locations of the foci. We can determine the location of the center of the ellipse by Midpoint formula:
[tex](h,k) = \frac{1}{2}\cdot F_{1}(x,y) + \frac{1}{2}\cdot F_{2} (x,y)[/tex] (1)
Where [tex]F_{1} (x,y)[/tex] and [tex]F_{2} (x,y)[/tex] are the locations of the foci.
If we know that [tex]F_{1}(x,y) = (4, -6-5\sqrt{2})[/tex] and [tex]F_{2} (x,y) = (4,-6+5\sqrt{2})[/tex], then the location of the center of the ellipse is:
[tex](h,k) = (4, -6)[/tex]
The location of the center of the ellipse is [tex](4,-6)[/tex]. It is determine by knowing the location of foci and Midpoint formula.
b) Now we need to determine the length of each semiaxis:
Major semiaxis ([tex]a[/tex])
[tex]a = \sqrt{[V_{2}(x,y)-(h,k)]\,\bullet\,[V_{2}(x,y)-(h,k)]}[/tex] (2)
[tex]V_{2}(x,y)-(h,k) = (4,3)-(4,-6)[/tex]
[tex]V_{2}(x,y) - (h,k) = (0, 9)[/tex]
[tex]a = 9[/tex]
Please notice that [tex]V_{2}(x,y)[/tex] is one of the vertices of the ellipse in the major axis.
Distance between focus and center ([tex]c[/tex])
[tex]c = \sqrt{[F_{2}(x,y)-(h,k)]\,\bullet\,[F_{2}(x,y)-(h,k)]}[/tex]
[tex]F_{2}(x,y) -(h,k) = (4-4,-6+5\sqrt{2}+6)[/tex]
[tex]F_{2}(x,y) - (h,k) = (0, 5\sqrt{2})[/tex]
[tex]c = 5\sqrt{2}[/tex]
Minor semiaxis ([tex]b[/tex])
[tex]c^{2} = a^{2}-b^{2}[/tex] (3)
[tex]b = \sqrt{a^{2}-c^{2}}[/tex]
If we know that [tex]a = 9[/tex] and [tex]c = 5\sqrt{2}[/tex], then the length of the minor semiaxis is:
[tex]b = \sqrt{31}[/tex]
In this case, the standard equation of the ellipse is defined by this formula:
[tex]\frac{(x-h)^{2}}{b^{2}}+\frac{(y-k)^{2}}{a^{2}} = 1[/tex]
If we know that [tex]a = 9[/tex], [tex]b = \sqrt{31}[/tex] and [tex](h,k) = (4, -6)[/tex], then the standard equation of the ellipse is:
[tex]\frac{(x-4)^{2}}{31}+\frac{(y+6)^{2}}{81} = 1[/tex]
The standard equation of the ellipse is [tex]\frac{(x-4)^{2}}{31}+\frac{(y+6)^{2}}{81} = 1[/tex].
c) The lengths of the axes are, respectively:
Major semiaxis ([tex]a[/tex]): [tex]a = 9[/tex]
Minor semiaxis ([tex]b[/tex]): [tex]b = \sqrt{31}[/tex]
Answer:
a) The location of the center of the ellipse is . It is determine by knowing the location of foci and Midpoint formula.
b) The standard equation of the ellipse is .
c) Major semiaxis (): , Minor semiaxis ():
Step-by-step explanation:
Help me again??????????????
Answer:
Part A is no because after subtracting it is 6/10 and 6/10 is not equal to 1/2
Step-by-step explanation:
First you make the fraction's denominator equal
2/5 = 4/10
Camen's water bottle is 1 8/10
Jorge's water bottle is 2 4/10
1/2 = 5/10
Make the fractions into a improper fraction
Camen's is 18/10
Jorge's is 24/10
subtract it
24 - 18 = 6
So Part A is no because after subtracting it is 6/10 and 6/10 is not equal to 1/2
Hey i need help with this question. I need it to be solved and I need to see the length of the diagonal. Please put a proper answer or Branly will just take the points away from you. Thanks
Answer:
x = 40.25 mStep-by-step explanation:
Use Pythagorean
x² = 36² + 18² x² = 1620x = √1620x = 40.25 mAnswer:
in right angled triangle BCD
by using Pythagoras law
P²+B²=H²
A²+B²=C²
36²+18²=x²
x=√1620=18√5m
x=18√5 m is your answer
Evaluate the expression when x=6 and y=4 Explain how you calculated your answer
10y+x 2nd power
Answer:
Ans = 76
Step-by-step explanation:
10y + [tex]x^{2}[/tex]
=> 10 * 4 + [tex]6^{2}[/tex]
=> 40 + 36
=> 76
Hope it helps :)
Is - 51/2 rational or irrational? Explain your reasoning.
Answer:
Step-by-step explanation:
It's rational because it doesn't have a continuous decimal. -51/2 is -25.5
Answer:
I believe it is ration since a rational number is any interger, fraction, or repeating decimal.
Step-by-step explanation:
The Pizza Barn sells one customer 3 large pepperoni pizzas and 2 orders of breadsticks for $30. They sell another customer 4 large pepperoni pizzas and 3 orders of breadsticks for $41. How much does the Pizza Barn charge for each pepperoni pizza and each order of breadsticks
Answer:
Pizzas: $8, Breadsticks: $3
Step-by-step explanation:
1. Write an equation.
Let the variables p = price of pizzas, and b = price of breadsticks
The equation: 3p + 2b = $30 for the first customer. The equation: 4p + 3b = $41 for the other customer.
2. Use the Elimination Method.
(4p+3b=41) x3 = 12p+9b=123
- (3p+2b=30) x4 = 12p+8b = 120
------------------------------------------------
8b = 3
Pizzas: $8
Breadsticks: $3
Find the missing length. The triangles are similar.
Can someone help me?
Need to show the work
Answer:
AB = [tex]\frac{108}{7}[/tex]
Step-by-step explanation:
Δ ALM and Δ ACB are similar, then the ratios of corresponding sides are equal, that is
[tex]\frac{AM}{AB}[/tex] = [tex]\frac{AL}{AC}[/tex] , substitute values
[tex]\frac{12}{AB}[/tex] = [tex]\frac{14}{18}[/tex] = [tex]\frac{7}{9}[/tex] ( cross- multiply )
7AB = 108 ( divide both sides by 7 )
AB = [tex]\frac{108}{7}[/tex] ( = 15 [tex]\frac{3}{7}[/tex] )
Distribute and evaluating
(X + 6) (x - 3)
Answer:
x^2+3x-18
Step-by-step explanation: hoped I helped
Answer: [tex]x^{2} +3x-18[/tex]
Step-by-step explanation:
First, let's take our given (x+6)(x-3)
Now distribute
[tex]x^{2} -3x+6x-18\\combine\\x^{2} +3x-18[/tex]
A diver went 24 feet below the surface of the ocean, and then 47 feet down. What is the diver's new position relative to the surface?
Write an expression to represent the problem, and solve.
Answer:
71 feet below the water.
Step-by-step explanation:
x=the divers position relative to the surface
when x=0, the diver is at the surface.
when x=-24, the diver is 24 feet below the surface, therefore -24-47=-71.
8.12394 rational or irrational
Answer:
rational
Step-by-step explanation:
if it does not terminate nor become periotic it is irrational other wise it is rational
Pamela's parakeet is currently in a rectangular bird cage that has a length of 3 feet, a width of 2 feet, and a height of 3 feet. Since the parakeet has gotten larger, Pamela is looking to buy a new rectangular bird cage. She wants the new cage to have a volume that is 4 times the volume of the parakeet's current cage. If Pamela wants to keep the length of the new cage the same, how must the other dimensions change?
Answer:
The volume of existing cage = length x widht x height = 3 x 2 x 3 = 18 cubic ft
Now she wants cage with volume four times of this cage
New Volume = V1 = 18 x 4 = 72 cubic ft
Keeping length same = 3 ft
Length x width x height = V1
3 x Width x height = 72
Width x height = 72 /3
Width x height = 24
Now multiple of 24 must be the width and height.
Taking width = 6 ft and height = 4 ft, we will get our answer
Proof:
Length x width x height = V1
3 x 6 x 4 = 72
Please help. Find the area of the composite figure
Okay so multiple 17 times 8 and 16 times 33 and then add the answers together and you should get 664!
Step-by-step explanation:
here's your solution
=> Firstly divide above picture in two parts
=> 1st = traingle
=> 2nd = trapezium
=> area of traingle = 1/2*base*height
=> height = 8
=> we need to find out base by using Pythagoras formula
=> base^2 = 17^2 - 8^2
=> base^2 = 289 - 64 = 225
=> base = √225
=> base of traingle = 15
=> now, area of traingle = 1/2*15*8
=>60sq.units
=> area of trapezium = 1/2(sum of p. sides ) *
distance between them
=> area = 1/2*(33 + 15)*16
=> area = 1/2*16*48
=> area = 384sq.units
=> area of whole figure = 384 + 60
= 444 sq.units
Plz help with my math!
Answer:
(-2, 6)
Step-by-step explanation:
Plug in one of the equations into the y-variable (doesn't matter which):
2x + 10 = -4x - 2
Combine like terms by adding the 4x to both sides. This makes it cancel out on the right side, and 2x + 4x on the right side is 6x:
6x + 10 = -2
Combine like terms by subtracting 10 from both sides, making it cancel out on the left side, and on the right: -2 - 10:
6x = -12
Then isolate the x-variable by dividing both sides by 6:
x = -2
Taking the -2, plug it into an x-variable in either of the equations:
y = 2x +10
y = 2(-2) + 10
y = -4 + 10
y = 6
Which term has the definition "A conclusion based on evidence"?
a. Data
b. Bias
c. Inference
d. Sample
Answer:
The answer would be C. Inference
Simplify x + 4x + 6x
answer:
11x
step-by-step explanation:
just add them since they are like termsx + 4x + 6x
= 11x
Answer:
11x
Step-by-step explanation:
just add them all together
x + 4x = 5x
5x + 6x = 11x
hope this helps :)
Solve for the missing arcs
Answer:
Step-by-step explanation:
arc KL = 60°
arc LNK = 360° - 60°
arc NJK = 180°
angle JQN = 60°
arc JN = 60°
arc JM = 60°+55° = 115°
arc MN = 55°
arc MKN = 360° - 55° = 305°
arc JML = 180°
angle MQL = 180° - 55° - 60° = 65°
arc ML = 65°
arc LN = 55° + 65° = 120°
Which product is greater than 3/5
Look at the picture ☺️
Pls answer ASAP✨
Answer:
C. 3/5*5/3
Step-by-step explanation:
because you multiply across and get:
3 5 15
_ * _ = _
5 3 15
Which is 1 whole
I hope this helps!!!
Solve: 7x = 6x -9
plsss
Answer:
x = -9
Step-by-step explanation:
which statement is incorrect?
Where exactly are the alleged statements?
what's the answer to -1.3g + 1.9 = -11.1
Answer:
g = 10
Step-by-step explanation:
-1.3g + 1.9 = -11.1
-1.3g = -11.1 - 1.9
-1.3g = -13
g = 10
PLS HELP the LAST QUESTION, please...
Answer:
280 Cubic inches
Step-by-step explanation:
When finding the volume, the equation is V=l*w*h
Therefore, the equation should be:
10.1*3.9*6.8
This is equal to exactly 267.852
However, the answer is 280 cubic in. because it's a larger number and it's about 13 from the actual answer. On the other hand, 250 cubic in. is about 17 from the actual number.
The numbers 1 - 30 are written down on pieces of paper and placed in a hat for
students to to randomly select.
Answer:
Event A = 1/3
Event B = 1/6
Step-by-step explanation:
The probability of drawing a number between 1 and 10 (Event A) is approximately 0.3333 or 33.33%.
To calculate the probability of Event A, we need to determine the total number of favorable outcomes (numbers between 1 and 10) and divide it by the total number of possible outcomes (all numbers from 1 to 30).
Counting the favorable outcomes:
Event A consists of numbers between 1 and 10. So, there are 10 favorable outcomes: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
Counting the total possible outcomes:
The hat contains numbers from 1 to 30. So, there are 30 possible outcomes: {1, 2, 3, ..., 30}.
Calculating the probability of Event A (P(A)):
The probability of an event is given by the formula:
P(A) = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes).
In this case,
P(A) = 10 (favorable outcomes) / 30 (total possible outcomes)
P (A) = 1/3 ≈ 0.3333 or 33.33%.
To know more about probability here
https://brainly.com/question/11234923
#SPJ2
The equation y = 25x can be used to predict the height in feet, y, of the elevator after
1 seconds.
Find the height of the elevator when the time is 0 seconds.
Time (s), «
0 5 10 15
Height (ft), y
Answer:
y = 0 feet
Step-by-step explanation:
Given equation:
y = 25x
Where,
y = height (feet)
x = time (seconds)
25 = constant
Find the height of the elevator when the time is 0 seconds
y = 25x
y = 25(0)
y = 0 feet
9 ( x + 4 ) = 63
Solving 2 step equations
Answer:
The answers is x=3
Step-by-step explanation:
Divide both sides by the numeric factor on the left side then solve.
Hope this helps.
May i please have a brainless Thank you.
PLEASE HELP
WORTH 30 PTS!!
Choose the step that shows where a mistake is made (if there is one).
-2(x + 4) + 4x = 16
Step 1 -2x + 8 + 4x = 16
Step 2 2x + 8 = 16
Step 3 2x = 8
Step 4 x = 4
a Step 1
b Step 2
c Step 3
d Step 4
e No mistakes were made. The steps are correct and the answer is x = 4.
Answer:
The mistake is in step 1 when you do -2(x+4) you do the distributive property first -2 times x is -2x that's correct but -2 times 4 is not 8 it is -8
when you multiply by negatives the answer will always be a negative unless your multiply 2 negative number together then itll be positive ex. 4 × -4 = -16 (negative) but -4 × -4 = 16 (positive)
What is the value of x? please help
Which of the following is an example of simple harmonic motion?
A. The motion of a rotating beacon
B. A ball bouncing on a sidewalk
C. Calculating the angle of elevation for a building
D. A police car shining a spotlight into buildings as it drives by
Answer:
The motion of a rotating beacon.
Step-by-step explanation:
A rectangular room is 12-1/2 feet long and 10-1/3 feet wide. What is the area of the room?
Answer:
the length of room is 24 feet
Step-by-step explanation:
Let the breadth be x .
Then, Length, l = x + 9
According to the question,
Area of rectangle = length × breadth
Putting the values of length and breadth, we get:
360 = ( x + 9 ) x
360 = x² + 9x
x² + 9x - 360 = 0
x² + 24x - 15x - 360 = 0
x( x + 24) - 15(x + 24) = 0
( x + 24 ) = 0 or ( x - 15 ) = 0
x = - 24 or x = 15 [ Negative number is ignored ]
Now,
Length, l = x + 9 = 15 + 9 = 24 feet
Thus, the length of room is 24 feet .
A football team took possession of the ball on the 50 yard line. They lost 5 yards on the first down, and lost another 6 yards on the play. What yard line does the team hike the ball on the third down of their possession?
Answer: The answer should be 39 yard line
Step-by-step explanation: If you start at the 50 and remove 11 yards you will have 39 yards left
A ratio of two numbers is equal to 3:8. If the smaller number is 12,find the greater number.
The other no. is:
32
As you can see that in the ratio given, 3 is the smaller no. and 12 too.
So when we divide 12 by 3, we get 4
Then to find the other no. we need to multiply 4 with 8 (which is the other no. in the ratio given)
Therefore, we get the other no. as 32
And also when you divide 12 by 32,
You get the answer as 3 by 8 (which is the given ratio)
Hope you found this helpful!
THANK YOU!!
∝ Sidhdi