Answer:
[tex]\displaystyle{\theta=\dfrac{5\pi}{4}\, , \, \dfrac{9\pi}{4}}[/tex]
Step-by-step explanation:
Given the equation [tex]\displaystyle{2\cos \theta = 2\sin \theta}[/tex]. We have to divide both sides by 2 which gives us [tex]\displaystyle{\cos \theta = \sin \theta}[/tex]. Then divide both sides by [tex]\displaystyle \cos \theta[/tex] which gives us [tex]\displaystyle{1=\dfrac{\sin \theta}{\cos \theta}}[/tex].
We know that:
[tex]\displaystyle{\dfrac{\sin \theta}{\cos \theta} = \tan \theta}[/tex]
So we can rewrite the equation as [tex]\displaystyle{1=\tan \theta}[/tex].
We know that [tex]\displaystyle{\tan \theta = 1}[/tex] when [tex]\displaystyle{\theta = \dfrac{\pi}{4}+\pi k}[/tex] for [tex]\displaystyle{k \in I}[/tex] (k is any integer). However, the equation is given with the interval [tex]\displaystyle{\pi \leq \theta \leq 3\pi}[/tex]. Therefore, we have to substitute k-values that satisfy the interval.
It appears that only k = 1, 2 which gives us [tex]\displaystyle{\theta_1 = \dfrac{\pi}{4}+\pi}[/tex] and [tex]\displaystyle{\theta_2 = \dfrac{\pi}{4}+2\pi}[/tex]can be used since both satisfies both values and interval.
Simplifying both solutions:
[tex]\displaystyle{\theta_1 = \dfrac{\pi}{4}+\dfrac{4\pi}{4} \, , \, \theta_2=\dfrac{\pi}{4}+\dfrac{8\pi}{4}}\\\\\displaystyle{\theta=\dfrac{5\pi}{4}\, , \, \dfrac{9\pi}{4}}[/tex]
Find the derivative of
y= 1/(3x^3)
Answer:
[tex]\displaystyle y' = \frac{-1}{x^4}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \frac{1}{3x^3}[/tex]
Step 2: Differentiate
Rewrite: [tex]\displaystyle y = \frac{x^{-3}}{3}[/tex]Derivative Property [Multiplied Constant]: [tex]\displaystyle y' = \frac{1}{3} \frac{d}{dx}[x^{-3}][/tex]Basic Power Rule: [tex]\displaystyle y' = \frac{1}{3}(-3x^{-4})[/tex]Simplify: [tex]\displaystyle y' = \frac{-1}{x^4}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
PLEASE HELP!!
Also the last option is
4 units left and 3 units down
Answer:
B
Step-by-step explanation:
I'm so stuck I was taught this 5 months ago I don't remember this lol.
Answer:
C. 24 12/20
Step-by-step explanation:
4 3/4 × 6 4/5
24 3/4 × 4/5
24 12/20
The population of bacteria doubles every 6 hours. By how much will it grow in three days. Write the equation
Answer:
Step-by-step explanation:
let x be the population
so we have ,
2x= 6h
?= 3 days or 3×24h
by cross multiplication we have
2x× 72h= 6h×?
?= 2x×72/6 = 24x
So, in three days the bacteria will b 24 times current population.
Can someone please help me with math.
Please answer both of you can
Is 8 a solution to the equation 3(x-6)=3x/4?
Explain your answer
with the radius of 2 Find the volume of the sphere. Round your answer to the nearest tenth. Use 3.14 for it. The volume of the sphere is about in?
Answer:
Solution given:
radius[r]=2in
π=3.14
we have
volume of sphere=[tex] \frac{4}{3} \pi {r}^{3} [/tex]=[tex] \frac{4}{3} ×3.14× {2}^{3} [/tex]=33.5in³is your answer.
Let's see
V=4/3πr³V=4/3π(2)³V=4/3π(8)V=32π/333.5in³PLZS HELP NEED BY TODAY!!
Answer:
20°
Step-by-step explanation:
ok so if 40 degrees is on one side its also on the side parallel from it
a straight line = 180 degrees
so 180 - 40 = 140
so 7x =140
we now divide 7 on both sides and get x=20 because the 7 cancels out
180 -40 =140
7x = 140
7x/7 =140/7
x=20
Hope I helped?
pls help figure out part c, part e, and part f
Yalll listen i was at a party with friends in the ghetto and the ice crean truck came and they had the hot cheetos with cheese and chill poured on it ....it was bussin bussin
Answer:
wowo cool
Step-by-step explanation:
Answer:
sounds cheeesyyy
Step-by-step explanation:
Can someone please help me?
Answer:
scalene
Step-by-step explanation:
Find a unit vector in the direction of the given vector.
v = 9i − 6j
Given:
The given vector is:
[tex]v=9i-6j[/tex]
To find:
The unit vector in the direction of the given vector.
Solution:
If a vector is [tex]v=ai+bj[/tex], then the unit vector in the direction of the this vector is
[tex]\hat v=\dfrac{v}{|v|}[/tex]
Where, [tex]|v|=\sqrt{a^2+b^2[/tex]
We have,
[tex]v=9i-6j[/tex]
Here, [tex]a=9[/tex] and [tex]b=-6[/tex]. So,
[tex]|v|=\sqrt{9^2+(-6)^2}[/tex]
[tex]|v|=\sqrt{81+36}[/tex]
[tex]|v|=\sqrt{117}[/tex]
[tex]|v|=3\sqrt{13}[/tex]
Now, the unit vector in the direction of the given vector is:
[tex]\hat v=\dfrac{9i-6j}{3\sqrt{13}}[/tex]
[tex]\hat v=\dfrac{9i}{3\sqrt{13}}-\dfrac{6j}{3\sqrt{13}}[/tex]
[tex]\hat v=\dfrac{3}{\sqrt{13}}i-\dfrac{2}{\sqrt{13}}j[/tex]
Therefore, the required unit vector is [tex]\hat v=\dfrac{3}{\sqrt{13}}i-\dfrac{2}{\sqrt{13}}j[/tex].
3 drinks and 2 hot dog costs 7.70 and 2 drinks and one hot dog is 4.55 system of equation on drink and one hot dog to the nearest cents
Answer:
Drink = 1.4
Hot dog = 1.75
x + y = 3.15
Step-by-step explanation:
Let drink = x ; hot dog = y
3x + 2y = 7.70 - - (1)
2x + y = 4.55 - - - (2)
From (2)
y = 4.55 - 2x - - - (3)
Put y = 4.55 - 2x in (1)
3x + 2(4.55 - 2x) = 7.70
3x + 9.1 - 4x = 7.70
-x = 7.7 - 9.1
-x = - 1.4
x = 1.4
Put x = 1.4 in (3)
y = 4.55 - 2(1.4)
y = 4.55 - 2.8
y = 1.75
Drink = 1.4
Hot dog = 1.75
x + y = 3.15
Simplify 15.6 divided by negative 3..
Answer:
-5.2
Step-by-step explanation:
15.6 ÷ (-3) = -5.2
What is the difference in a SSS Postulate (side-side-side) and SAS Postulate (Side-angle-side)? How do i know which one its going to be? Thanks!!!
Pls help ASAP I DONT have time
Answer:
B: y = 3x + 6
Help plsssssss:)))))))
Answer:
x = -14
Steps:
Rewrite the equation as -8 = 6+x
Then move all terms not containing x to the right side of the equation.
x = -8-6
Afterwords subtrack.
x = -14.
hope this helps :)
22
Consider the expression below.
3x - (2y + 2)
Evaluate the expression when x = 0.02, y = 0.1, and z = 0.3.
NEED HELP ASAP HELPING A FRIEND
Answer:
Step-by-step explanation:
So it 22
Answer: 0.007
Step-by-step explanation:
I need this done, please
Plz helpp I’m bad at math
Answer:
40
Step-by-step explanation:
because a straight line is 180 degrees so 140 plus 40 equals 180
Answer:
40
Step-by-step explanation:
straight line is 180 degrees
180=140+x
140+40=180
Each side of a circumscribed equilateral triangle is 16 meters. find the radius if the circle
This is for now I need help pls !!!!!!!
Which of the following statements are true?
A) 3 lbs of sugar is sugar is required to make 60 muffins.
B) 120 lbs of sugar is required to make 6 muffins.
C) 0 lbs of sugars required to make 0 muffins.
D) The maximum number of muffins that can be made is 220
Answer:
C
Step-by-step explanation:
Because 0 lbs of sugar is required to make 0 muffins
I hope this is right
A 30 pack of Flaming Hot Cheetos cost $10.82 at
Costco. A 50 pack of Flaming Hot Cheetos cost
$17.25.
a) Which is the better buy? (You are trying to
compare the cost of a 30 pack and 50 pack of
chips. This is not possible without finding
the unit rate.)
b) What is the difference between the unit
prices? (You need to use the information
from part a to answer this question.)
Answer:
50 pack
[tex]\$0.01[/tex]
Step-by-step explanation:
Number of packs at Costco = 30
Cost of 30 packs at Costco = $10.82
Number of packs at the other place = 50
Cost of 50 packs = $17.25
Cost of one pack when 30 packs are bought
[tex]\dfrac{10.82}{30}=\$0.36[/tex]
Cost of one pack when 50 packs are bought
[tex]\dfrac{17.25}{50}=\$0.35[/tex]
It is better to buy the 50 pack.
Difference in the unit prices = [tex]0.36-0.35=\$0.01[/tex].
Which expression represents the perimeter of the figure below? *
2x + 4 y
w + 2x + 4y
w + x + y
2w + 2x + 4y
Step-by-step explanation:
Perimeter of figure =
[tex]w + x + x + y + y + y + y \\ = 1 \times w + 2 \times x + 4 \times y \\ = w + 2x + 4y[/tex]
G varies directly as the square of j and inversely as m. If g=0.05 when j = 0.4 and m=1.6, what is g when j =6 and m=4
Answer: The value of G = 4.5
Step-by-step explanation:
As per given,
[tex]G\propto \dfrac{j^2}{m}[/tex]
When we replace proportional sign with an equal to sign, we get
[tex]G=k\dfrac{j^2}{m}[/tex], where k = constant
If G=0.05 when j = 0.4 and m=1.6, then
[tex]0.05=k\dfrac{0.4^2}{1.6}\\\\ 0.05=k(0.1)\\\\ k=0.5[/tex]
Now,
[tex]G=0.5\dfrac{j^2}{m}\\\\\Rightarrow\ G=0.5\dfrac{6^2}{4}\\\\\Rightarrow\ G=4.5[/tex]
hence, when j =6 and m=4, the value of G = 4.5
A surveyor holds a laser range finder 3 feet above the ground and determines that the range finder is 92 feet from a building and 106 feet from the top of the building. What is the height h of the building? Round your answer to the nearest tenth.
Answer:
55.64
Step-by-step explanation:
The range finder is 92 feet from the building and 106 feet from the top of the building i.e. hypotheses
We will use the Pythagorean theorem:
x^2 = 106^2 - 92^2
= 11,236 - 8,464
= 2,772
= √2,772
x = 52.64978632
The height of the building:
h = x + 3
= 52.64978632 + 3
= 55.64978632
or
≈ 55.64 feet
Step-by-step explanation:
the answer to the nearest is 55.64
John has 516.071 more points than Sam. Sam has 4092.1 points. How many points does John have? (Do not round.) *
Answer:
John has 4608.171 points
Step-by-step explanation:
4092.1 + 516.071 = 4608.171
Hope this helps
Have a nice day :)
53+2444= ??????? HELP I D K THE ANSWER
Answer:
2497
Step-by-step explanation:
Answer:
2497
Step-by-step explanation:
53 + 2444
= 0053 + 2444
= 2497