Answer:
[tex]\displaystyle \sin(\theta)= \frac{\sqrt{17}}{17}[/tex]
[tex]\displaystyle \cos(\theta)= \frac{4 \sqrt {17} }{ 17 }[/tex]
Step-by-step explanation:
We want to find sin(θ) and cos(θ) given that tan(θ) = 1/4 and sin(θ) > 0.
First, since tan(θ) and sin(θ) are both positive, cos(θ) must be positive as well.
Recall that tangent is the ratio of the opposite side to the adjacent side.
Therefore, the hypotenuse is:
[tex]h=\sqrt{4^2+1^2}=\sqrt{16+1}=\sqrt{17}[/tex]
So, with respect to θ, the opposite side is 1, the adjacent is 4, and the hypotenuse is √17.
Then it follows that:
[tex]\displaystyle \sin(\theta)=\frac{1}{\sqrt{17}} = \frac{\sqrt{17}}{17}[/tex]
And that:
[tex]\displaystyle \cos(\theta)= \frac{4}{\sqrt{17}} = \frac{4 \sqrt {17} }{ 17 }[/tex]
Find the value of x.
35
21
Х
X=
= [?]
Help
Step-by-step explanation:
Using Pythagoras theorem
x=✓(35²-21²)=✓784=28 units
do this for brainliest! :)
Answer:
Question 13 is 27/2 (decimal form, 13.5, Mixed fraction 13 1/2)
Question 14 = 4
Step-by-step explanation:
hope this helped you:)
what function equation is represented by the graph
f(x) = 4^x+5
f(x) = 3^x+4
f(x) = 3^x+5
f(x) = 4^x+4
Answer:
B
Step-by-step explanation:
We know that when x=0 y=5
B and D are the only ones that meet this criteria
we know that when x=2 y= 13 or so
D no longer works
it has to be B
Which of the binomials below is a factor of this trinomial?
3y2 + 18x+ 24
F(t)=212-6t
what is the value of t when F (t) = 140?
Answer: -628
Step-by-step explanation:
F(140) = 212 - 6(140)
F(140) = 212 - 840
F(140) = -628
Solve for x and y. Please help, I will mark as brainliest and give many points
Answer:
x=13 y=25
Step-by-step explanation:
Answer:
x = 30°, y = 45°, w = 14√2, v = 7√2Step-by-step explanation:
ΔABC has AB = 2BC, hypotenuse is twice the leg
⇒ x = 30°ΔBCD is isosceles right triangle
⇒ y = 45°ΔMPN is isosceles right triangle (∠M = 45°)
⇒ w = MN = √2PN = 14√2ΔMKP is isosceles right triangle (∠M = 45°)
v= KP = MK = 1/2MN = 1/2(14√2) = 7√2r+4 at r=13 help me
The value of the expression is 17.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
r + 4
When r = 13
r + 4
= 13 + 4
= 17
Thus,
The value is 17.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ5
Find the length of side x
Answer:
≈3.464
Step-by-step explanation:
1. the required 'x' belongs to the hypotenuse of the given triangle. It means, the formula of its length is:
x=4*cos30°=4*sin60°, note sin60°=cos30°=√3/2≈0.866.
2. according to the formula above the required length 'x' is:
x=4*0.866=3.464 (or 2√3)
I owe $8500 on my credit card. The card has a promotional interest rate of 0% for 24 months. To repay the debt, I'm going to pay a fixed amount toward the balance every month. After 12 months, my remaining debt will be $6460. Which of the following equations correctly relates the remaining debt (D) to the number of months (t) I've been making payments? (Select all that apply.)
Question 4 options:
D=6460+170t
D=170t−6460
170t+D=8500
D=−170t+8500
D+6460=8500t
Answer:
170t+D=8500
D=170t−6460
Step-by-step explanation:
Mathematical models are used to explain real life situations.
We can see from the question that the total debt is $8500 while there is interest rate of 0% for 24 months. We are also told that after 12 months, the remaining debt was $6460.
Now, the equations that correctly model the situation are;
170t+D=8500D=170t−6460Learn more about mathematical models:https://brainly.com/question/731147
What factor is missing? 24 + 12= ____(8+4)
Answer:
3
Step-by-step explanation:
24 + 12 = ___(8+4)
36 = ___(12)
36/12 = 3
Solve for the value of n.
Answer:
3n-4= 44
3n=40
no u can solve
Answer:
17°
Step-by-step explanation:
3n - 5° + 90° + 44° = 180° { being linear pair }
3n + 129° = 180°
3n = 180° - 129°
3n = 51°
n = 51° / 3
n = 17°
Hope it will help :)
List the factors in the expression 4r + 5s +8.
PLZ HELP MEEEEE!!!!!
Solve the system of equations below.
3x +8= 2
7x + 3y = 1
Answer:
I love alegbra anyways
The ans is in the picture with the steps how i got it
(Hope it helps can i plz have brainlist :D hehe)
Step-by-step explanation:
A sign says that the price marked on all music equipment is 30℅ off the original price. you buy an electric guitar for the sale price of $315. How much money did you save
In the triangle below, the measure of angle A = 52°. Find the measure of angle C.
Answer:
128°
Step-by-step explanation:
180-52=128
Question 7
Write the integer that is equivalent to |10|
Answer:
10
Step-by-step explanation:
Looking out for me balcony the angle of elevation to the top of the next building is approximately 22° in the English depression to the bottom of the building approximately 29° if the building is 200 feet away how tall is the building?
I will give brainliest to whoever solves it right. hint its not 80.7 feet
Answer:
Step-by-step explanation:
[tex]\tan22=h_1/200,\ \tan29=h_2/200
h_2+h_1=200(\tan29+\tan22)
H\approx 191.667ft
H\approx 191’ 8”
The points (28,36) and (29, 31) fall on a particular line. What is its equation in slope-intercept form?
Answer:
y=-5x+176
Step-by-step explanation:
Write an algebraic equation showing that the two points equal each other and then evaluate it.
A coordinate plane.
Which statements are true? Check all that apply.
The line that goes through the points (3,7) and (–2,7) is a horizontal line.
The equation x = –8 is a vertical line that goes through the point (–8,3).
The line that goes through the points (0,5) and (0,–7) is a vertical line.
The points on a horizontal line have the same x-coordinate.
Answer:
A , B, and C
Step-by-step explanation:
i just did it
100 point question. I attached a screenshot of the problem.
Answer:
9
Step-by-step explanation:
Find all solutions of the equation in the interval [0, 2π). 2cosθ+ 1= 0
Hello!
[tex]\large\boxed{\frac{2\pi}{3} \text{ and } \frac{4\pi}{3}}[/tex]
2cosФ + 1 = 0
Begin by isolating for cosФ. Subtract both sides by -1:
2cosФ = -1
Divide both sides by 2:
cosФ = -1/2
Using the unit circle, we know that from [0, 2π), values that have a cosine of -1/2 are 2π/3 and 4π/3.
Therefore, the solutions of this equation are:
Ф = 2π/3 and 4π/3
Sophie has 5 pieces of string that are each 5 feet long. Cooper has 4 pieces of string that are each
3 feet long. Estimate how much more string Sophie has than Cooper has. Enter your answer in the bo
Answer:
Sophie has 12 feet more
Step-by-step explanation:
find a curve that passes through the point (1,-2 ) and has an arc length on the interval 2 6 given by 1 144 x^-6
Answer:
[tex]f(x) = \frac{6}{x^2} -8[/tex] or [tex]f(x) = -\frac{6}{x^2} + 4[/tex]
Step-by-step explanation:
Given
[tex](x,y) = (1,-2)[/tex] --- Point
[tex]\int\limits^6_2 {(1 + 144x^{-6})} \, dx[/tex]
The arc length of a function on interval [a,b]: [tex]\int\limits^b_a {(1 + f'(x^2))} \, dx[/tex]
By comparison:
[tex]f'(x)^2 = 144x^{-6}[/tex]
[tex]f'(x)^2 = \frac{144}{x^6}[/tex]
Take square root of both sides
[tex]f'(x) =\± \sqrt{\frac{144}{x^6}}[/tex]
[tex]f'(x) = \±\frac{12}{x^3}[/tex]
Split:
[tex]f'(x) = \frac{12}{x^3}[/tex] or [tex]f'(x) = -\frac{12}{x^3}[/tex]
To solve fo f(x), we make use of:
[tex]f(x) = \int {f'(x) } \, dx[/tex]
For: [tex]f'(x) = \frac{12}{x^3}[/tex]
[tex]f(x) = \int {\frac{12}{x^3} } \, dx[/tex]
Integrate:
[tex]f(x) = \frac{12}{2x^2} + c[/tex]
[tex]f(x) = \frac{6}{x^2} + c[/tex]
We understand that it passes through [tex](x,y) = (1,-2)[/tex].
So, we have:
[tex]-2 = \frac{6}{1^2} + c[/tex]
[tex]-2 = \frac{6}{1} + c[/tex]
[tex]-2 = 6 + c[/tex]
Make c the subject
[tex]c = -2-6[/tex]
[tex]c = -8[/tex]
[tex]f(x) = \frac{6}{x^2} + c[/tex] becomes
[tex]f(x) = \frac{6}{x^2} -8[/tex]
For: [tex]f'(x) = -\frac{12}{x^3}[/tex]
[tex]f(x) = \int {-\frac{12}{x^3} } \, dx[/tex]
Integrate:
[tex]f(x) = -\frac{12}{2x^2} + c[/tex]
[tex]f(x) = -\frac{6}{x^2} + c[/tex]
We understand that it passes through [tex](x,y) = (1,-2)[/tex].
So, we have:
[tex]-2 = -\frac{6}{1^2} + c[/tex]
[tex]-2 = -\frac{6}{1} + c[/tex]
[tex]-2 = -6 + c[/tex]
Make c the subject
[tex]c = -2+6[/tex]
[tex]c = 4[/tex]
[tex]f(x) = -\frac{6}{x^2} + c[/tex] becomes
[tex]f(x) = -\frac{6}{x^2} + 4[/tex]
You can use the formula for finding the arc length on specified interval on x axis.
The curves whose arc length on the given interval is described are
[tex]f(x) = 6x^{-2} -8[/tex]
and
[tex]f(x) = -6x^{-2} + 4[/tex]
What is the length of the arc of a function f(x) from x = a to x = b?If the function is differentiable in the given interval, then we have:
[tex]s = \int_a^b\sqrt{(1 + (f'(x))^2)}\:dx[/tex]
where s denotes the length of the arc of the given function from x = a to x = b
Using the above formula, as we're already given the arc length, thus,
[tex]\int_a^b\sqrt{(1 + (f'(x))^2)}\:dx = \int_2^6\sqrt{(1 +144x^{-6})}\:dx[/tex]
This gives us
[tex]f'(x) = \pm \sqrt{144x^{-6}} = \pm 12x^{-3}[/tex]
Integrating both sides with respect to x, we get:
[tex]f(x) = \pm \int 12x^{-3}\\\\f(x) = \pm 6x^{-2} + c[/tex]
where c is constant of integration.
Since the curve passes through (1,-2), thus, putting f(x) = -2, x = 1, we get:
[tex]f(x) = \pm 6x^{-2} + c\\-2 = \pm 6 + c\\c = -2 \mp 6 = -8, or ,4[/tex]
c = -8 when we have [tex]f(x) = 6x^{-2} + c[/tex]
c = + 4 when we have [tex]f(x) = -6x^{-2} + c[/tex]
The curves whose arc length on the given interval is described are
[tex]f(x) = 6x^{-2} -8[/tex]
and
[tex]f(x) = -6x^{-2} + 4[/tex]
Learn more about length of the arc of a curve here:
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Sections 10.1-10.3 Review
A bag contains 1 green, 4 red and 5 yellow balls. Two balls are selected at
random. Find the probability if there is no replacement of P(1 red and 2 yellow).
Answer:
20/45
6/45
Step-by-step explanation:
A bag contains 1 green, 4 red, and 5 yellow balls. Two balls are selected at random. Find P( 1 red and 1 yellow) and P(2 red).
--------------------
# of red/yellow pairs: 4*5 = 20
# of random pairs: 10C2 = 45
P(1red & 1yellow) = 20/45
# of red pairs: 4C2 = 6
# of random pairs = 45
P(2 red) = 6/45
Factorise x2 + x - 30
Answer:
If your polynomial is x^2+x-30, then your answer is (−5)(+6)
If x is a positive integer, which of the following must be an even integer that is twice the value of an odd integer.
A. 2x
B. 2x + 1
C. 2x + 2
D. 4x + 1
E. 4x + 2
cos=0.985 rounded to nearest tenth
HELP ME PLSSSSSS Kaitlyn is covering all faces of a tissue box cover shaped like a rectangular prism. The cover has dimensions of 9” x 5” x 3.75”. What is the total area in square inches that she will need to cover?
Answer:
168.75
Step-by-step explanation:
......
Answer:
168.75
Step-by-step explanation:
Grayson is going to invest $710 and leave it in an account for 17 years. Assuming the
interest is compounded continuously, what interest rate, to the nearest hundredth of
a percent, would be required in order for Grayson to end up
with $920?
Answer:
1.52%
Step-by-step explanation:
Convert the mixed number into a improper fraction 5 1/3
Answer:
16/3
Step-by-step explanation: