Find all angles, 0≤θ<360, that satisfy the equation below, to the nearest 10th of a degree.
4cos2θ+9=−14cosθ
Answers
Since cosine is negative in the second and 3rd quadrant, the required angles are 120 and 240 degrees
Trigonometry identityTrigonometry identities are expressed as a function of cosine, sine and tangent.
Given the trigonometry expression shown
4cos2θ+9=−14cosθ
Equate to zero
4cos2θ+9 + 14cosθ = 0
According to trig identity
cos2θ = 2cos²θ - 1
Substitute to have:
4(2cos²θ - 1)+9 + 14cosθ = 0
Expand
8cos²θ - 4 + 9 + 14cosθ = 0
8cos²θ+ 14cosθ + 5 = 0
let P = cosθ to have;
8P² + 14P + 5 = 0
Factorize the result
8P² + 10P + 4P + 5 = 0
2P(4P+5)+1(4P+5)=0
(2P+1) = 0 and 4P+5 = 0
2P = -1 and P = -5/4
P = -1/2 and -5/4
Recall that P = cosθ
If P = -1/2
cosθ = -1/2
θ = -60
Since cosine is negative in the second and 3rd quadrant, the required angles are 120 and 240 degrees
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Related Questions
function or not a function?
Answers
Answer:
function
Step-by-step explanation:
no repeated domain means its a function
how do you stop a skunk from smelling?
Answers
Answer:
Hold its nose
Step-by-step explanation:
You can actually de-scent a skunk if it is the powerful defensive odor you are referring to. When you have a skunk de-scented, they are no longer able to spray, and at this point they are now similar to having a pet cat or dog; lovable and highly desire affection and attention from their owners.
a.) Find h(g(x)) if
h(x)= 2x+9
and
g(x) = 4*
Answers
Answer:
h(4)=17
Step-by-step explanation:
h(g(x)), h(x)= 2x+9; g(x)=4
2(4)+9= 8+9=17
In the diagram of right triangle GFE below, altitude FD is drawn. Which of the
following ratios is equivalent to sin E?
answers: GD/DF, GF/GE, DE/FD, FE/GE
Answers
The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. The correct option is B.
What is Sine (Sinθ)?The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,
Sin(θ) = Perpendicular/Hypotenuse
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The hypotenuse is the longest side of the triangle.
In the ΔGEF, the value of Sin(E) is,
Sin(E) = GF/GE
In the ΔDEF, the value of Sin(E) is,
Sin(E) = FD/FE
Hence, the correct option is B.
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A paper is 0.55 mm thick. How high pile of 274 sheets? The paper is 24.5 long and 18.5 cm wide. Calculate volume of the pile of paper.
Answers
The height of the pile is 150.7 mm, and the volume is V = 6,830,477.5 mm³.
How high will be the pile of papers?We know that each paper is 0.55mm thick, then if we pile 274 of these, the height of the pile will be:
H = 0.55mm*274 = 150.7mm
Now we want to get the volume of the pile of paper. Remember that for a rectangular prism of height H, width W, and length L, the volume is:
V = H*W*L
In this case, we have:
H = 150.7mmW = 18.5 cm = 185 mmL = 24.5 cm = 245 mmThen the volume is:
V = (150.7mm)*(185 mm)*(245 mm) = 6,830,477.5 mm³
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Which equation represents h in the triangle? A) h = 6sin37° B) h = 10sin37° C) h = 6 10 sin37° D) h = 10 6 sin37°
Answers
Answer:
A
Step-by-step explanation:
Consider the left triangle within the big triangle.
Identity :
sin θ = opposite side / hypotenuse
=============================================================
Taking the sine value of the angle to find h :
⇒ sin37° = h/6
⇒ h = 6sin37°
Opposite 37 is h
Angle opposite 6 is 90
Sine rule:
h/sin37 = 6/sin90
xsin37
h = 6 x sin37/ sin90
h = 3.6108....
h = 3.6 to 1dp
A) 6xsin37= 3.6108...
B) 10xsin37 =6.018...
C) 6x 10 xsin37 = 36.108...
D) 10 x 6 x sin37 = 36.108...
Thus, answer is A
Hope this helps!
Evaluate function at the given value using the remainder theorem.
f(a)=a^4-2a^3-10a^2-7a at a=-2
Answers
Answer:
6
Step-by-step explanation:
[tex]f(a)=a^4-2a^3 -10a^2 -7a \\\\f(-2) = (-2)^4-2(-2)^3 -10(-2)^2 -7(-2)\\\\~~~~~~~~~=16-2(-8)-10(4)+14\\\\~~~~~~~~~=30+16-40\\\\~~~~~~~~~=46-40\\\\~~~~~~~~~=6[/tex]
HELP ASAP....NO LINKS AND NO JOKES PLEASE
Which point represents one solution of the system of inequalities below
3x+8y<=480
y-x<=20
A. (50,50)
B. (40,40)
C. (20,60)
D. (10,40)
Answers
Explanation:
Given Inequalities:
(i) 3x + 8y ≤ 480
(ii) y - x ≤ 20
For first inequality:
(a) y intercept: (0, 60)
(b) x intercept: (160, 0)
Plot this line with a solid line and shade below.For second inequality:
(a) y intercept: (0, 20)
(b) x intercept: (-20, 0)
Plot this line with a solid line and shade below.The point (40, 40) falls between these two inequalities.
What is the image of (12, -9) after a dilation by a scale factor of 1/3 centered at the origin
Answers
Answer:
(4,-3)
Step-by-step explanation:
The scale factor is 1/3. So, multiply the numbers by 1/3.
12*1/3 is 4.
-9*1/3 is -3.
The new coordinates are (4,-3).
How many one-third cup servings are in 9 cups of strawberries?
Answers
Answer:27?
Step-by-step explanation:
So since there needs to be 3 1/3ds in each cup you just multiply 3x9=27
Help is this a reflection or a rotation??
My exam is on Tuesday and I’m confused
Answers
Answer:
reflection
Step-by-step explanation:
its like a mirror, if it were rotated, they wouldnt line up as the same image. think of this like looking in a mirror! :)
I'm to lazy to do this-
(image below)
plx do this correctly for brainly :D
also 20 points
:)
Answers
The probability that the lunch combo will have an ham sandwich is 3 / 7.
How to find the probability of Ham sandwich?Probability simply means possibility. It describes how likely an event will occur or happen.
Mathematically,
probability = number of favourable outcome to A / total number of possible outcome
Therefore,
probability that a lunch combo will include a ham sandwich = 6 / 14 = 3 / 7
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Martin and Linda live 855 miles apart. At the same time, they start driving toward each other on the same road. Linda’s constant rate is 35 mph. Martin’s is 60 mph. How long will it take them to meet?
Answers
Answer:
Step-by-step explanation:
Givens
Linda 35 mphMartin 60 mphdistance travelled = 855 milesFormula
Linda's speed * t + martin's speed * t = 855
s1 * t + s2 *t = 855
Solution
35*t + 60*t = 855t Combine the left
95t = 855 Divide both sides by 95
95t/95 = 855/95
t = 9
Answer
They will meet in 9 hours.
Answer:
Option (D) is correct, 9 hours.
a+2< -10 enter the correct answer
Answers
Answer:
a<-12
Step-by-step explanation:
What is the radius of a circle if it’s center is (1,2) and one point on the circle is (1,6)?
Answers
because the x values are identical the radius would be found by subtracting the y values.
6-2 = 4
the radius is 4
Find the volume of a sphere with a radius of 2 cm.
to the nearest hundredth.
A 10.67 cm³
B 16.75 cm³
C 33.52 cm³
D 8.37 cm³
ATTEMPTS
Answers
Answer:
C 33.52 cm³
Step-by-step explanation:
Here, we have Radius(r)=2(Given)
Volume = 4/3 πr³
= 4/3 · 22/7 · 2³
= 33.5238
Round to the nearest tenth:
C 33.52 cm³
A circle is centered at $O$ and has an area of $48 \pi.$ Let $Q$ and $R$ be points on the circle, and let $P$ be the circumcenter of triangle $QRO.$ If $P$ is contained in triangle $QRO,$ and triangle $PQR$ is equilateral, then find the area of triangle $PQR.$ Will give brainlyist!
Answers
The area of the Triangle PQR which is in the circle, is given as 784.25. See the computation below.
What is a circle?Mathematically speaking, a circle is a 2-dimensional shape whose boundaries are round and are equidistant from a fixed center.
What is calculation of the answer given above?The area of ΔPQR is given as ((√3)/4) x QR²
= (√3)/4) x (6√2 - 2√6)²
= 0.43301270189 x (8.48528137424 x 4.89897948557)²
= 0.43301270189 x 1728
Area of ΔPQR = 784.25
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Write seventy-eight and nine hundredths as a decimal number.
Submit
Answers
Answer: 78.09
Step-by-step explanation:
Seventy-eight is the whole number, so it goes to the left of the decimal point 78.09
Nine-hundredths is decimal, it goes two places to the right of the decimal point because it's hundredths 78.09
Ahmed and Babar share 240g of sweets in the ration 7:3. Calculate the amount Ahmed receives
Answers
The amount received by Ahmed is 168 gm.
What is Ratio?
The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.
Here, let the amount received by Ahmed be 7x
and amount received by Babar be 3x
Total amount of sweets = 240 gm
Now, according to question,
7x + 3x = 240
10x = 240
x = 240/10
x = 24
Thus, the amount received by Ahmed is 7 X 24 = 168 gm and amount received by Babar = 3 X 24 = 72 gm.
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A school is constructing a rectangular play
area against an exterior wall of the school
building. It uses 120 feet of fencing material to
enclose three sides of the play area.
Write an equation to represent &, the length of
the play area in feet, as
function of w. the width in teet.
Write an equation to represent A, the area in
square feet, as a function of w.
the width in feet.
WILL GIVE BRAINLIEST TO WHOEVER ANSWERS
Answers
Answer:
120 = L+2W
LW =area.
to maximize area with given fencing that would make Width = 30 feet and length = 60
A= LW = (120-2W)W = 120W -2W^2
A' = 120-4W =0
W = 30
L=120-2(30) = 60 feet
W by L is 30 by 60 feet for max area
Determine each sum or difference.
A) -3.6+(-21.9) b) -43.91-(-9.44)
Answers
please help I’ll give brainliest
Answers
The function D(t) defines a traveler's distance from
home, in miles, as a function of time, in hours.
D(t) =
300t + 125,
875,
75t + 612.5,
0 ≤t <2.5
2.5 ≤t≤ 3.5
3.5
Mark this and return
Which times and distances are represented by the
function? Select three options. 4
The starting distance, at 0 hours, is 300 miles.
At 2 hours, the traveler is 725 miles from home.
At 2.5 hours, the traveler is still moving farther from
home.
At 3 hours, the distance is constant, at 875 miles.
The total distance from home after 6 hours is 1,062.5
miles.
Answers
Three selected options are as follows:
At 2 hours, the traveler is 725 miles from home.At 3 hours, the distance is constant, at 875 miles.The total distance from home after 6 hours is 1,062.5 miles.What is Distance ?Distance is a numerical measurement of how far apart objects or points are. In Physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.
Here, put the values in option substitute in given equation D(t)
Option 1: At t = 0 hour,
D (0) = 300 X 0 + 125 = 125 ≠ 300 Option Incorrect
Option 2 : At t = 2 hours,
D(2) = 300 X 2 + 125 = 725 Option Correct.
Option 3: At t = 2.5 hours,
D(2.5) = 875 Option Incorrect
Option 4: At t = 3 hours,
D(3) = 875 Option Correct
Option 5: At t = 6 hours,
D(6) = 75 X 6 + 612.5 = 450 + 612.5
= 1062.5 miles Option Correct
Thus, Option two, four and five are correct.
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if x=0 and y<0, where is the plot (x,y) located
Answers
Mark me the Brainliest!
Answer:
The point will be plotted on Y axis
If 14 is 35% of a value, what is that value?
Pls help
Answers
Answer:
40
Step-by-step explanation:
14 = 35% of x
35% = 0.35
So lets make an equation and solve for x:
14 = 0.35x
x = 14÷0.35
x = 40
To check our answer let's put it back into the question :
35% of 40 = 14
10% = 4 , 30% = 12 , 5% = 2
35% = 12+2 = 14 ✅
Hope this helped and have a good day
What is the area of the sector shown in the diagram below?
14 cm
OA. 34.2 cm²
OB. 30.8 cm²
OC. 136.8 cm²
D. 4.9 cm²
Answers
The area of the sector shown in the diagram below is A = 136.8 cm²
Area of a sectorThe formula for calculating the area of a sector is expressed as:
A = r²Ф/2
Given the following
radius = 14cm
Ф = π/6
Substitute
A = (14)²π/12
A = 196(3.14)/2
A = 136.8 cm²
Hence the area of the sector shown in the diagram below is A = 136.8 cm²
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Dale has $1,000 to invest. He has a goal to have $2,600 in this investment in 8 years. At what annual rate compounded continuously will Dale reach his goal?
Answers
Answer:
11.94 %
Step-by-step explanation:
Compound interest formula FV = PV e^(it) i = decimal interest per year
t = time FV = future value
2600 = 1000e^(i * 8)
solve for i = 11.94 %
Given that
a:c=1:6
b:c= 2:5
Find the ratio a:b:c
Give your answer in its simplest form
and
Answers
The ratio of a : b : c in its simplest form is 5 : 12 : 30 respectively
How to solve ratio?a : c = 1 : 6b : c = 2 : 5So,
a / b = 1/6
b/c = 2/5
lowest common multiple of c in both ratio1/6 + 2/5
=(5 + 12) /30
a : b and b : c
= 5/30 and 12/30
Therefore,
a : b : c = 5 : 12 : 30
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Part B
Now that you know the missing side length, is triangle BCD a right triangle? Give you
reason.
Answers
The length of the other leg of the right triangle will be 13.86 cm.
The complete question is given below.
The triangle BCD is a right triangle. The length of the hypotenuse is 19 centimeters. The length of one of the legs is 13 centimeters.
What is the length of the other leg?
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
Let the unknown sides be x. Then we have,
19² = 13² + x²
361 = 169 + x²
x² = 361 – 169
x² = 192
x = 13.856 ≈ 13.86 cm
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Consider a flow network in which vertices, as well as edges, have capacities. That is, the total positive flow entering any given vertex is subject to a capacity constraint
Answers
Maintain the same constraints on edge capacity, skew symmetry, and flow conservation in the ordinary maximum-flow problem on a flow network of comparable size.
What is flow network?A flow network is a directed graph with each edge having a capacity and each edge receiving a flow, according to graph theory. The amount of flow on an edge must not exceed the edge's capacity.
Let's suppose the network flow is given by;
G = (V, E)
With edge capacity:
c: E → R
And vertex capacity:
d: V → R
Maintain the same constraints on edge capacity, skew symmetry, and flow conservation.
Consider the new stipulation: for each:
v ∈V
So,
[tex]\rm \sum_{u \in v } \{ f(u,v)|f(u,v) > 0 \} \leq d(v)[/tex]
Thus, if maintain the same constraints on edge capacity, skew symmetry, and flow conservation the ordinary maximum-flow problem on a flow network of comparable size.
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