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].
Defined as a set of all points equidistant from a given point.
A)
arc
B)
angle
C)
circle
D)
line segment
Answer:
C
The answer is C and the distant from a given point to a point on the Circle is radius
What is the solution to the equation 3x + 2(x − 9) = 8x + x − 14? (5 points)
Answer:
x= -1
Step-by-step explanation:
Answer:
x = -1
Step-by-step explanation:
3x+2(x-9)=8x+x-14 ;; equation
simplify the equation to the form
3x+2(x-9)=8x+x-14
reorder the terms in parentheses
3x+(+2x-18)=8x+x-14
remove unnecessary parentheses
+3x+2x-18=+8x+x-14
move all terms containing x to the left and all other terms to the right.
+3x+2x-8x-1x=-14+18
simplify left and right side of the equation.
-4x=+4
divide both sides of the equation by -4 to get x.
x=-1
Help please solve by factoring
We know that 6x(-7) is -42 and we also know that 6+(-7) is -1.
So we can write
[tex]x^2+6x-7x-42[/tex]
[tex]x(x+6)-7(x+6)[/tex]
[tex](x-7)(x+6)[/tex]
So our solutions are [tex]x=7,-6[/tex]
5(1-b)=8(b+2) solve for b
Step-by-step explanation:
Hey there!!
Here,
[tex]5(1 - b) = 8(b + 2)[/tex]
[tex] \: \: \: \: \: 5 - 5b = 8b + 16[/tex]
[tex] \: \: \: \: \: \: \: 8b + 5b = 5 - 16[/tex]
[tex] \: \: \: \: \: \: \: 13b = - 11[/tex]
[tex] \: \: \: \: \: \: \: b = \frac{ - 11}{13} [/tex]
Therefore the value of b is -11/13.
Hope it helps...
Step-by-step explanation:
first open up the brackets according to BODMAS to get
5-5b=8b+16
then collect like terms together and make sure to change the sighns eg - becomes +
5-16=8b+5b
you get
-11=13b
then divide both sides with 13 to get b
-11/13=b ( you can leave as a negative decimal according to the question)
A right triangle has one vertex on the graph of y = x^8, x>0, at (x, y), another at the origin, and the third on the positive y-axis at (0, y), as shown in the figure. Express the area A of the triangle as a function of x.
Answer:
Area = [tex]\frac{1}{2}x^{9}[/tex]
Step-by-step explanation:
From the graph attached,
Triangle given is a right triangle.
This triangle ha three vertices (0, y), (x, y) and (0, 0).
Therefore, measure of the base = x units
And measure of the height of the triangle = y units
Area of a triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(x)(y)[/tex]
Since, y = [tex]x^{8}[/tex]
Therefore, Area of the triangle = [tex]\frac{1}{2}(x)(x)^8[/tex]
= [tex]\frac{1}{2}x^{9}[/tex]
Area of the given right triangle is [tex]\frac{1}{2}x^{9}[/tex] units².
can someone help me answer this please
can someone help pls 20 points
A teacher spends $354 on costumes and microphones for six cast members in a play. Each cast member receives a costume that costs $38 and a microphone that costs $c What did the teacher spend on each microphone? The teacher spent $ ___on each microphone. Question 2 Justify your answer.
The teacher spend some amount on buying costumes and microphones for 6 cast members.
GiveN:
Cost of each costume = $38Cost of each microphone = $cTotal money spent = $354Let's frame the equation. Total money is the total amount spent for 6 cast members.
Money spent on costumes = $38 × 6
Money spent on microphone = $c × 6
Equation:
[tex]6 \times 38 + 6 \times c = 354[/tex]
Taking 6 as common,
[tex]6(38 + c) = 354[/tex]
Dividing 6 from both sides,
[tex] \dfrac{6(38 + c)}{6} = \dfrac{354}{6} [/tex]
[tex]38 + c = 59[/tex]
Solving further,
[tex]38 + c - 38 = 59 - 38[/tex]
[tex]c = 21[/tex]
So, the cost of each microphone = $21
The teacher spent this much on each microphone.
#CarryOnLearning
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The teacher spent $21 on each microphone.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
The total amount of teachers have = $354
Cost of costume for all 6 members ;
6 × 38 = $228
Cost of microphone for all 6 members ;
6 × c = 6c
Now,
Cost of microphone + Cost of costume = total amount
6c + 228 = 354
6c = 126
c = 21
Hence "The teacher spent $21 on each microphone".
For more about the equation,
https://brainly.com/question/10413253
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−2π
Is this rational or irrational
It is irrational.
π is an irrational number.
It follows that -2π is also irrational number.
The afternoon temperature in Biscoff Bay was – 2°F. By midnight, a warm front moved in and the temperature rose to 11°F. What was the change in temperature from afternoon to midnight? To solve the problem, Ross subtracted 11–( – 2) and came up with an answer of 13°F. Is Ross correct? Why or why not?
Answer:
Ross is correct. He is right because if you do 11- (-2) the double negatives turn into a positive and the answer is 13.
The answer is "Yes", Ross is right, and the temperature change will be 13 °F.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the mentioned data in the question,
The afternoon temperature in Biscoff Bay = -2 °F
The temperature rose at midnight = 11 °F
Then, the change in temperature will be,
It is changing from -2 °F to 11 °F then,
= 11 - (-2) = 13 °F
To know more about arithmetic operations:
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80iu612345678909876533456
.
Answer:
weird
Step-by-step explanation:
What is the solution to the equation -6x + 9 – 4x = 14? I need some more help
Answer:
x= - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
- 6x + 9 - 4x = 14, that is
- 10x + 9 = 14 ( subtract 9 from both sides )
- 10x = 5 ( divide both sides by - 10 )
x = [tex]\frac{5}{-10}[/tex] = - [tex]\frac{1}{2}[/tex]
give the slope of the line (if it exists) and the y intercept (if it exists) and graph the line 5y=3. what is the slope?
Answer:
0
Step-by-step explanation:
help me please! don’t right nonsense! i have 15 minutes left!
Answer:
let M(-3,-4) be (x1, Y1)
T(5,0) be (x2,y2)
m:n = 2 : 3
using section formula
Q(x,y) = {mx2 + nx1/(m+n), my2 + ny1/(m+n)}
{ ( 10 -9)/5, (0 -12)/5}
(1/5, -12/5)
This could be answer if internally
How do you solve this equation?
13 – 3r =-26
Answer:
r = 13
Step-by-step explanation:
-3r=-26-13
-3r=-39 divide by 3
r=13
Step-by-step explanation:
13 - 3r = -26
13 − 3r −13 = −26 − 13
−3r=−39
divide by 3
r = 13
what number is 10 times less than 20?
Answer:
180
Mathematically, 10 times less than 20 would be: Take 20, subtract (10 x 20). Answer: -180.
Willie makes $0.12 off of every shirt he sells. He sold 179 shirts this week, how much did he make in total?
Answer:
$21.48
Step-by-step explanation:
0.12*179=21.48
Mr. Chong celebrated his seventy fifth birthday in 1998. In what year was he born?
Answer:
1924
Step-by-step explanation:
1998
- 75
--------
1924 so he was born in 1924
Find the measure of
Jamal drew the function below. Which explains whether or not his function is linear?
His function is linear because it graphs out a straight line. If you were to pick any two points on that line, and find the slope, you should find that the slope is the same no matter which two points you picked.
Answer:
linear
Step-by-step explanation:
there's a constant rate of change/constant slope and the function is a straight line
What is the inverse of the following function? y = 12x −6
Answer:
f ^−1(x)=x/12+1/2
Step-by-step explanation:
How do you solve 2 1/3 + 5y = 4
Answer:
Not sure but that's my answer
What is the prime factorization of 96? 8 · 12 2 · 2 · 2 · 2 · 3 25 · 3 25 · 32
Answer:
2^5 *3
Step-by-step explanation:
You can solve this multiple ways but should get 2^5*3
Answer:
[tex]2^5*3[/tex]
Step-by-step explanation:
[tex]96\\\\=2*48\\\\=2*2*24\\\\=2*2*2*12\\\\=2*2*2*2*6\\\\=2*2*2*2*2*3\\\\=2^{5}*3[/tex]
1. Minti can do a piece of work in 12 days. Minti and Rinki together can finish the work in 8 days.
Find: (a) the number of days in which Rinki alone can finish the work.
(b) the work left if Rinki alone works on it for 4 days.
Answer:
Minti - 12 days
Minti & Rinki - 8 days
Use Formula 3
time= (12 * 8) / (12 -8)
time = 96 / 4
time for Rinki alone = 24 Days
*****************************************************
Rinki alone for 4 days will leave 20 days of work to be done.
Step-by-step explanation:
Each year, the science club puts on a science show for the students in the elementary school. Luis is planning demonstrations to show properties of metals. For one property, he decides to use a ball of pizza dough and a rolling pin.
Which property of metals is Luis most likely going to demonstrate using these materials
luster
opacity
conductivity
malleability
Answer:
D. Malleability because he is most likely going to show how you can easily roll pizza dough
Step-by-step explanation:
Answer:
malleability or D
Step-by-step explanation:
HELP ME PLEASE I NEED THIS and tell me how to solve for it
Answer:
616.6 square cm
Step-by-step explanation:
Area of a regular octagon
[tex] = 2 {a}^{2} (1 + \sqrt{2} ) \\ = 2 \times {12}^{2} (1 + 1.414) \\ = 2 \times 144 \times 2.141 \\ = 288 \times 2.141 \\ = 616.608 \\ = 616.6 \: {cm}^{2} [/tex]
3/5(1 + p) = 21/20
find the solution to p
Answer:
3/4
Step-by-step explanation:
3/5(1+p)-21/20
3/5+3/5p=21/20
3/5p=21/20-3/5
3/5p=21/20-12/20
3/5p=9/20
p=9/20÷3/5
p=9/20*5/3
p=45/60
p=3/4
Give another name for line g
Answer:
line b
Step-by-step explanation:
what is 2 (x+2) + 3x =2 (x+1) + 1
Step-by-step explanation:
2x+4 +3x = 2x +2 +1
4+x= 2x+3
4-3=2x-x
1=x
x=1
Enter the decimal 1.18 as an improper fraction in simplest form.
Answer:
59/50
Step-by-step explanation:
118/100 divided by 2/2
=59/50