Answer:
[tex]\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )[/tex].
Step-by-step explanation:
We need to find all the points on the curve x=4cos(t),y=4sin(t) that have the slope of 1/2.
[tex]x=4cos (t)[/tex]
[tex]\dfrac{dx}{dt}=-4sin (t)[/tex]
[tex]y=4sin (t)[/tex]
[tex]\dfrac{dy}{dt}=4cos (t)[/tex]
Now,
[tex]\dfrac{dy}{dx}=\dfrac{dy}{dt}\times \dfrac{dt}{dx}[/tex]
[tex]\dfrac{dy}{dx}=4cos (t)\times \dfrac{1}{-4sin (t)}[/tex]
[tex]\dfrac{dy}{dx}=-\cot t[/tex]
So, slope of the curve is [tex]-\cot t[/tex].
[tex]-\cot t=\dfrac{1}{2}[/tex]
[tex]-\tan t=2[/tex]
[tex]\tan t=-2[/tex] ...(1)
Using [tex]\sec^2t=1+\tan^2t[/tex], we get
[tex]\sec^2t=1+(-2)^2[/tex]
[tex]\sec^2t=1+4[/tex]
[tex]\sec t=\pm \sqrt{5}[/tex]
[tex]\cos t=\pm \dfrac{1}{\sqrt{5}}[/tex]
Now,
[tex]\sin^2t=1-cos^2t[/tex]
[tex]\sin t=\pm \sqrt{1-\dfrac{1}{5}}[/tex]
[tex]\sin t=\pm \sqrt{\dfrac{4}{5}}[/tex]
[tex]\sin t=\pm \dfrac{2}{\sqrt{5}}[/tex]
It equation (1), tan(t) is negative. So, sin and cos have different signs.
If [tex]\sin t= \dfrac{2}{\sqrt{5}}[/tex], then [tex]\cos t=- \dfrac{1}{\sqrt{5}}[/tex].
[tex]x=4cos (t)=-\dfrac{4}{\sqrt{5}}[/tex]
[tex]y=4sin (t)=\dfrac{8}{\sqrt{5}}[/tex]
If [tex]\sin t=- \dfrac{2}{\sqrt{5}}[/tex], then [tex]\cos t= \dfrac{1}{\sqrt{5}}[/tex].
[tex]x=4cos (t)=\dfrac{4}{\sqrt{5}}[/tex]
[tex]y=4sin (t)=-\dfrac{8}{\sqrt{5}}[/tex]
Therefore, the two points are [tex]\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )[/tex].
what is 1 1/3 divided by 3/5
Answer:
6.11
Step-by-step explanation:
First divide 11by 3 and 3by 5.And divide the answer of 11by 3 by 3by5
14 – (2y + 5) = -2y + 9
Answer:
The answer is all real numbers
Step-by-step explanation:
Simpify both sides of the equation: 14−(2y+5)=−2y+9
14+−1(2y+5)=−2y+9(Distribute the Negative Sign)
14+−1(2y)+(−1)(5)=−2y+9
14+−2y+−5=−2y+9
(−2y)+(14+−5)=−2y+9(Combine Like Terms)
−2y+9=−2y+9
−2y+9=−2y+9
Then add 2y to each side. −2y+9+2y=−2y+9+2y
9=9. Then subtract 9 from each side. 9-9=9-9=0. That means that all real numbers is the answer.
Hey there!
[tex]Answer:\boxed{\text{All are solutions}}[/tex]
[tex]Explanation:[/tex]
[tex]14-(2y+5)=-2y+9[/tex] Equation
14−(2y+5)=−2y+9 Simplify both sides
14 + -1(2y + 5) = −2y + 9 Distribute Negative
14 + -1(2y) + (-1)(5) = -2y + 9
14 + −2y + −5 = −2y + 9
(−2y) + (14 + −5) = −2y + 9 Combine the like terms
−2y + 9 = −2y + 9
-2y + 9 + 2y = -2y + 9 + 2y Add 2y to both sides
9 = 9
9 - 9 = 9 - 9 Subtract 9 from both sides
0 = 0
All are solutions.
Hope this helps!
Can anyone please do these questions? This is Unit 1 Geometry basics Homework 5 Angle Relationships.
Answer:
Step-by-step explanation:
11). 6x + 7 = 8x - 17 [Since vertical angles are equal in measure]
8x - 6x = 17 + 7
2x = 24
x = 12
12). (11x - 15) + (5x - 13) = 180°
16x - 28 = 180°
16x = 180 + 28
16x = 208
x = 13
13). Since DB⊥AC,
m∠CBD = 90°
m∠CBE + m∠DBE = 90°
(5x - 42) + (2x - 1) = 90°
7x - 43 = 90
7x = 133
x = 19
14). Since QS bisects angle PQR,
m∠PQS = m∠RQS
10x + 1 = [tex]\frac{82}{2}[/tex]
10x + 1 = 41
10x = 40
x = 4
15). 10x - 61 = 18y + 5 [Vertical angles]
10x - 18y = 61 + 5
10x - 18y = 66
5x - 9y = 33 ------(1)
(18y + 5) + (x + 10) = 180 [linear pair of angles are supplementary]
18y + x + 15 = 180
x + 18y = 165 ------(2)
By adding equation (1)×2 and equation (2)
(10x - 18y) + (x + 18y) = 66 + 165
11x = 231
x = 21
16). (5x - 17) + (3x - 11) = 180 [[linear pair of angles are supplementary]
8x - 28 = 180
8x = 180 + 28
8x = 208
x = 26
(3x - 11)° = 78 - 11
= 67°
67° + 90° + (2y + 5)°= 180° [Sum of angles on a line]
162 + 2y = 180
2y = 180 - 162
2y = 18
y = 9
17). NP bisects ∠MNQ.
Therefore, m∠MNQ = 2(m∠PNQ)
8x + 12 = 2×78
8x + 12 = 156
8x = 156 - 12
8x = 144
x = 18
m∠MNQ = (8x + 12)° = 156°
m∠RNM = m∠ONQ [Vertical angles]
(3y - 9)° = 180° - m∠MNQ
3y - 9 = 180 - 156
3y - 9 = 24
3y = 33
y = 11
Using the knowledge of the angle relationships to create an equation, the value of x and y in the image given are:
11. x = 12
12. x = 13
13. x = 19
14. x = 4
15. x = 21; y = 8
16. x = 26; y = 9
17. x = 18; y = 11
Applying the knowledge of angle relationships, we can solve each given problem by first, creating a an equation from the relationship between angles, then solve for the variables.
11. [tex]6x + 7 $ and $ 8x - 17[/tex] are vertical angles.
Since vertical angles are congruent, therefore:[tex]6x + 7 = 8x - 17[/tex]
Solve for x[tex]6x - 8x = -7 - 17\\\\-2x = -24\\\\x = 12[/tex]
12. [tex]11x - 15 $ and $ 5x - 13[/tex] are linear pair angles.
Since, the sum of linear pair angles equals 180 degrees, therefore:[tex](11x - 15) + (5x - 13) = 180[/tex]
Solve for x[tex]11x - 15 + 5x - 13 = 180\\\\16x - 28 = 180\\\\16x - 28 + 28 = 180 + 28\\\\16x = 208\\\\x = 13[/tex]
13. <DBE and <CBE are complementary angles.
Since the some of complementary angles equals 90 degrees, therefore,[tex]m \angle DBE + m \angle CBE = 90[/tex]
Substitute[tex](2x - 1) + (5x - 42) = 90[/tex]
Solve for x[tex]2x - 1 + 5x - 42 = 90\\\\7x - 43 = 90\\\\7x = 90 + 43\\\\7x = 133\\\\x = 19[/tex]
14. Since QS bisects <PQR, therefore,
m<PQS = 1/2(PQR)
Substitute[tex]10x + 1 = \frac{1}{2} (82)[/tex]
Solve for x[tex]10x + 1 = 41\\\\10x = 41 - 1\\\\10x = 40\\\\x = 4[/tex]
15. [tex](x + 10) $ and $ (10x - 16)[/tex] are linear pair angles.
Since the sum of linear pair angles equals 180 degrees, therefore,[tex](x + 10) + (10x - 16) = 180\\[/tex]
Solve for x[tex]x + 10 + 10x - 61 = 180\\\\11x - 51 = 180\\\\11x = 180 + 51\\\\11x = 231\\\\x = 21[/tex]
Find y:Since [tex](10x - 61) $ and $ (10y + 5)[/tex] are vertical angles, they are congruent. Therefore,
[tex](10x - 61) = (10y + 5)[/tex]
Plug in the value of x and solve for y[tex]10(21) - 61 = 18y + 5\\\\149 = 18y + 5\\\\149 - 5 = 10y\\\\144 = 18y\\\\8 = y\\\\\mathbf{y = 8}[/tex]
16. Since [tex](5x - 17) $ and $ (3x - 11)[/tex] are linear pair, their sum equals 180 degrees. Therefore,
[tex](5x - 17) + (3x - 11) = 180[/tex]
Solve for x[tex]5x - 17 + 3x - 11 = 180\\\\8x - 28 = 180\\\\8x = 180 + 28\\\\8x = 208\\\\x = 26[/tex]
Find y:[tex](2y + 5) + 90 + (3x - 11) = 180[/tex] (angles on a straight line = 180 degrees)
Plug in the value of x and solve for y[tex]2y + 5 + 90 + 3(26) - 11 = 180\\\\2y + 5 + 90 + 78 - 11 = 180\\\\2y + 162 = 180\\\\2y = 180 - 162\\\\2y =18\\\\y = 9[/tex]
17. Since NP bisects <MNQ, therefore,
[tex]m \angle PNQ = \frac{1}{2}(m \angle MNQ)[/tex]
Substitute[tex]78 = \frac{1}{2}(8x + 12)[/tex]
Solve for x[tex]78 \times 2 = 8x + 12\\\\156 = 8x + 12\\\\156 - 12 = 8x \\\\144 = 8x\\\\18 = x\\\\x = 18[/tex]
[tex]m \angle RNM + m \angle MNQ = 180^{\circ}[/tex] (linear pair)
Substitute[tex](3y - 9) + (8x + 12) = 180[/tex]
Plug in the value of x and solve for y[tex]3y - 9 + 8(18) + 12 = 180\\\\3y - 9 + 144 + 12 = 180\\\\3y + 147 = 180\\\\3y = 180 - 147\\\\3y = 33\\\\y = 11[/tex]
Therefore, using the knowledge of the angle relationships to create an equation, the value of x and y in the image given are:
11. x = 12
12. x = 13
13. x = 19
14. x = 4
15. x = 21; y = 8
16. x = 26; y = 9
17. x = 18; y = 11
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What kind of transformation is illustrated in this figure?
O translation
.
O reflection
dilation
Orotation
Answer:
translation
Step-by-step explanation:
shape, size, measurement all stayed the same. they just moved locations :)
The next two numbers in the series 1 , 4 , 9 , 16 , 25 ,....................are
Answer:
36, 49
explanation:
The pattern in this series is going by perfect squares:
(1)² = 1(2)²= 4(3)² = 9(4)² =16(5)² = 25From this, we can tell the next 2 numbers in the series will be:
(6)²=36(7)²=49Is the equation x9 – 5x3 + 6 = 0 quadratic in form? Explain why or why not.
Answer:
NOO
Step-by-step explanation:
In order for an equation to be quadratic, the highest degree that is needed is two. The highest exponent provided is 3 therefore no it is not a quadratic function
Felipe earns $9 per hour for helping his grandmother with her yard work. Write and solve a multiplication equation to find how many hours he must help his grandmother I’m order to earn $54
Answer:
Felipe work for 6 hours to earn $54
Step-by-step explanation:
I guess I was help full for u
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Help needed ASAP will give BRAINLIEST
Answer:
177.2 i think
Step-by-step explanation:
PLEASE HELP I WILL MARK YOU BRAINLIEST
Answer:
X= 62 Y=620
Step-by-step explanation:
Y is right because its ten times more than x and x is right because you take the three side and you multiply each one by 2 then you add then all together and you get 62.
Can i be made brainliest i need it
plz help if you can..
n = 2
My picture shows my work :)
Which would NOT be found in the set of rational numbers? A. 5 B. 1/2 C. -12.5 D. 1.61803398874989484820
Answer:
D
Step-by-step explanation:
This is because rational numbers don't continue as a decimal infinitely
A. Without computing each sum, find which is greater, O or E, AND by how much.
O = 1 + 3 + 5 + 7 + ... + 101
E = 2 + 4 + 6 + 8 + ... + 102
and need to explain it
Answer:
Www
Step-by-step explanation:
11. Susan was given the following number to convert to scientific notation: 12,050,000
Her answer was 1.25 x 107, but it was marked wrong on her paper. Why?
Answer:
eliminated, the bedtime increases by one minute. ... Description: This activity requires students to tell time to the half-hour (e.g. 4:00, 5:30, 11:30).
Step-by-step explanation:
This table displays the height of water as a pool is being filled. A 2-column table with 4 rows. Column 1 is labeled Time (minutes) with entries 10, 11, 12, 13. Column 2 is labeled height (inches) with entries 3.75, 4.1, 4.45, 4.8. Arrows are drawn from each row to the next. Use the table to interpret the rate of change.
What is the change for each consecutive input?
What is the change for each consecutive output?
What is the rate of change for the relationship?
Answer:1. 0.35. 0.35
Step-by-step explanation:
I did the question on edgenuity
The change for each consecutive time given is: 1
The change of each consecutive height given is: 0.35
The rate of change for the relationship between time and height is: 0.35
The table that displays the height of water when a pool is being filled against time is shown in the image attached. (See attachment).
Recall:
Rate of change can be calculated as: change in output / change in input
Change in output = difference between consecutive outputs
Change in input = difference between consecutive inputs
In the question given,
Time is input
Height is output
Thus:
Change for each consecutive input (time):
13 - 12 = 12 - 11 = 11 - 10 = 1Therefore, the change of each consecutive input (time) is: 1
Change for each consecutive output (height):
4.8 - 4.45 = 4.45 - 4.1 = 4.1 - 3.75 = 0.35Therefore, the change of each consecutive output(height) is: 0.35
Rate of change of the relationship between time and height:
Rate of change = change in height / change in time
Rate of change = 0.35/1 = 0.35
In summary:
The change for each consecutive time given is: 1
The change of each consecutive height given is: 0.35
The rate of change for the relationship between time and height is: 0.35
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Find the value of the remaining variable in the formula. Use 3.14 as an approximation for a (pi).
P=2L+2W (perimeter of a rectangle); L = 4, W= 2
P =
Enter your answer in the answer box.
Answer:
P = 12
Step-by-step explanation:
Given formula for the perimeter 'P' of a rectangle is,
P = 2L + 2W
If the values of L and W are,
L = 4 and W = 2
Perimeter of the rectangle = 2(L + W)
= 2(4 + 2)
= 2 × 6
= 12 units
Therefore, value of remaining variable 'Perimeter' = 12 units
(There is no use of 'pi' in calculating the perimeter of a rectangle).
Point D best represents which of the following numbers?
tot
14
14.5
15
15.5
16
Answer:
yea your correct and 16.5
Step-by-step explanation:
Answer:
???
Step-by-step explanation:
???
What is the value of (4)(-7)(-2)?
Answer:
=(4)(-7)(-2)
=-28*(-2)
=+56 is the answer
Step-by-step explanation:
hope it help ^_^
Raleigh went to a gaming arcade for his birthday. His parents gave him $55 to spend. He purchased $14.25 in
food and drinks, and put the rest of the money on a gaming card to spend at the arcade. Each game cost
$1.25.
How Many games can Raleigh play in the arcade?
Answer:
23 games
Step-by-step explanation:
40.75 divide by 1.25 comes out 23.28
Answer:
g<32.6
Step-by-step explanation:
1.25g+14.25<55
1.25g+14.25-14.25<55-14.25
1.25g<40.75
1.25g/1.25<40.75/1.25
g<32.6
What is the third multiple of 167?
PLEASE HELP!!!Choose the name of the angle notated by the arc(SHOW WORK) A.MPO B.NPO C.LPM D.PLO
B. NPO
Explanation:Because P is the middle letter in the arc.
Answer: B. NPO
Step-by-step explanation: the angle has to be in middle
In a year group of 108 students, 60 liked football,
53 liked tennis and 10 liked neither. Calculate
the number of students who liked football but not tennis.
Answer:
you know what to do that is the soup for the next couple of weeks and see how much is a ps4 controller or an official at the lot of the boy's
s: 12b - 3 = 106 + 9
What is the same value as the expression 7/5+2 1/4+1.6
When ax3 +x2 -2x +b is divided by x+1, the remainder is 10. When it is divided by x-3, the remainder is -46. What is the value of a and b?
Step-by-step explanation:
Given
X+ 2 = 0
X = -2
on putting in polynomial
-8a +2b= 0
- 8a = 2b
b = -4a
Now
when divided by x - 1 give remainder -15
so
x - 1 = -15
x = -14
on putting in polynomial
-2744a + 198 + 14b - 4 = -14
-2744a + 56a = - 208
-2688a = -208
a = 168/13
Now
b = 672/13
-
=\80
2.4
()
14 15
0
L: 2
4
А) . 1
( - ) 90
| —
Answer:
....
Step-by-step explanation:
a patio has an area of 120 square feet. the length of the patio is 12 feet. what is its width
w = 10 feet
Step-by-step explanation:Area formula
A = l×w
120ft² = 12ft×w
w = 120ft²/12ft
w = 10 feet
If g(x-1) = (2-g(x))/8 and g(1) = 3, find the value of g(2).
Answer:
-22
Step-by-step explanation:
g(2-1)=g(1)=(2-g(2))/8=3
2-g(2)=24
-g(2)=22
g(2)=-22
Evaluate the expression when a=3.
a^2+12
[tex]3^{2} + 12 = 9 + 12 = 21[/tex]
The answer is 21.
Answer:
The correct answer is 21.
Step-by-step explanation:
To solve this problem, we simply substitute 3 for a in the expression.
Given the expression,
a^2 + 12
we should replace "a" with 3, as denoted by the problem, giving us:
(3)^2 + 12
Now, we simplify using the order of operations. PEMDAS tells us that we should simplify what is in the parentheses first because it has an exponent.
9 + 12
Now, we can just add the two remaining terms together, giving us:
21
Therefore, the answer is 21.
Hope this helps!
Which of the following is NOT a subset of the rational numbers
Integers
Whole Numbers
Perfect square integers
Irrational numbers
What property is (6+2)+4=4+(6+2)
Answer: commutative property of addition
Step-by-step explanation:
(a+b)+c=a+(b+c) -- Commutative property of addition
Commutative property of addition is when the numbers are added, the sum are the same, regardless of the order of numbers.
Thus, (6+2)+4=4+(6+2) is commutative property of addition.Hope this helps!! :)
Please let me know if you need further explanation with properties of addition.