Answers
[tex]\text{Given that,}\\\\[/tex]
[tex]~~~~~~~\cos \theta = \dfrac 89\\\\\\\implies 2\cos^2 \left(\dfrac{\theta}2 \right) -1 = \dfrac 89~~~~~~;\left[1+ \cos 2\theta = 2\cos^2 \theta \right]\\\\\\\implies 2 \cos^2 \left(\dfrac{\theta}2 \right)= \dfrac 89 +1\\\\\\\implies 2 \cos^2 \left(\dfrac{\theta}2 \right)=\dfrac{17}9\\\\\\\implies \cos^2 \left(\dfrac{\theta}2 \right) = \dfrac{17}{18}\\\\\\\implies \cos \left(\dfrac{\theta}2 \right)=\sqrt{\dfrac{17}{18}}~~~~~~~~~~~;\left[\text{Positive value of} ~\cos \left(\dfrac{\theta}2\right) \right][/tex]
[tex]\implies \cos \left(\dfrac{\theta} 2 \right) =\dfrac{\sqrt{17}}{\sqrt{9 \times 2}}\\\\\\\implies \cos \left(\dfrac{\theta} 2 \right)=\dfrac{\sqrt{17}}{3\sqrt 2}\\\\\\\implies \cos \left(\dfrac{\theta} 2 \right)=\dfrac{\sqrt{17} \cdot \sqrt 2}{3\cdot 2}\\\\\\\implies \cos \left(\dfrac{\theta} 2 \right)=\dfrac{\sqrt{34}}{6 }[/tex]
Related Questions
WORTH 80 sorry its zoomed out but is there cluster or outliers where and explain why
Answers
Answer:
15.42, 25.49, 46.19
Step-by-step explanation:
although 32.28, 40.40 could also be considered
Question 1 which of the following is the square of a binomial
a. M^2-2mn+n^2
b. c^2-cd+d^2
c. a^2+b^2
d. 4x^2-9y^2
Question 2
square the binomial (r+s). what is the result?
Answers
Answer:
c just because
Step-by-step explanation:
just because
Joseph researched the ages of some of his favorite professional
football players. He recorded his results in the dot plot below.
Which of the following statements about the distribution are true?
I. There are two peaks at 27 and 28.
II. The distribution is skewed.
III. The distribution does not have an outlier.
IV. The distribution shows a spread of 5.
I only
I, II, and III only
I, III, and IV only
I, II, III, and IV
Answers
The statements that are true about the dot plot are: I, III, and IV only.
What is the Spread of a Data in a Dot Plot?The range, which is the difference between the maximum and minimum value, is a measure of the spread of a data distribution.
In the dot plot given, the spread of the data is: 30 - 25 = 5.
The peak points are at 27 and 28, and the data looks symmetrical in shape with no clear outlier.
Therefore, the statements that are true about the dot plot are: I, III, and IV only.
Learn more about dot plot on:
https://brainly.com/question/25957672
There are 8 hamburger buns in a package. which number of hamburger buns would fill a whole number of packages: 18, 32, 44, 56?
Answers
Answer:
32 and 56?
Step-by-step explanation:
32 and 56 are related to 8.
32=8x4
56=8x7
The number that would fill a whole number of packages of hamburger buns is 32 ad 56.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
18, 32, 44, 56
We need to find which number can be evenly divided by 8 because there are 8 hamburger buns in a package.
Now,
18 is not divisible by 8, because 8 x 2 = 16, and 18 is greater than 16.
32 is divisible by 8 because 8 x 4 = 32.
44 is not divisible by 8, because 8 x 5 = 40, and 44 is greater than 40.
56 is divisible by 8 because 8 x 7 = 56.
Therefore,
32 and 56 would fill a whole number of packages of hamburger buns.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
Given that you have a pentagon. What would be the measure of the sum of the exterior angles?
Answers
Answer:
360°
Step-by-step explanation:
the sum of the exterior angles of any polygon = 360°
James and his family spend a morning picking peaches. They fill several bags. This line plot shows the weight of each bag.
How many more pounds does one of the heaviest bags weigh than one of the lightest bags?
Enter your answer as a fraction in simplest form by filling in the boxes.
Answers
Answer:
3/4
Step-by-step explanation: i took test. pls give brainliest.
solve for the measure of angle JKL in the diagram below? Show your work and explain the steps you used to solve
Answers
Question: calculate the measure of angle JKL, i.e. mJKM+mMKL
Answer:
78°
Step-by-step explanation:
angle JKM is a tangent-chord intersection angle and equals half of the intercepted arc KM of 76°. Thus
mJKM = 76/2 = 38°
angle MKL is an inscribed angle and equals half of the intercepted arc ML of 80°, Thus
mMKL = 80/2 = 40°.
Therefore angle JKL = 38°+40° = 78°.
Find the value of x. If necessary, round your answer to the nearest tenth. The figures are not drawn to scale.
AB = 12, BC = 9, and CD = 8
Answers
Step-by-step explanation:
By the secant-secant theorem, (AC)(BC)=(DC)(x+DC)
Substituting in the given values, (21)(9)=(8)(8+x)
So, 189=64+8x, meaning x = 15.625, or about 15.63.
A gift box in the shape of a
rectangular prism has a base area
of 56 square inches and a height of
4 inches. What is the volume of the
box in cubic inches?
F) 224
G) 448
H) 896
J) 12,544
Answers
So the volume is F (224 inches)
Sasha's family traveled 2/7 of the distance to her aunt’s house on Saturday. They traveled 4/5 of the remaining distance on Sunday. What fraction of the total distance to her aunt’s house was traveled on Sunday?
Answers
The fraction of the total distance Sasha traveled to her aunts house is 6/7
Step-by-step explanation:
Find the area of the trapezoid.
8 cm
6 cm
13 cm
A. 78 cm2
B. 48 cm2
C. 63 cm
D. 104
Answers
Answer:
c; 63 square cm
Step-by-step explanation:
the area of a trapezoid can be described by the equation a = (1/2)(h)(b1 + b2)
this means the height times base 1 and base 2 added together divided by 2
(1/2)(6)(8 + 13) is the equation
this can become 3(21)
which is ultimitaly 63
Answer:
it's gonna be 63cm^2
Step-by-step explanation:
First, were gonna find the area of the rectangular portion, which is 8x6, which is 48cm^2
Next, well do the triangle part. So, we have to subtract 13-8 to get the width of the triangle.
Next, we have to find the area for the triangle. The formula is length x width / 2.
So, we have to multiply 6x5 to get 30.
Then, well divide it by 2, which will give us 15cm^2
Finally, we add the areas of rectangle and the triangle together. 15 + 48 is 63.
Bada-bing, bada-boom, we got 63cm^2 as our answer :)
Milan is drawing a triangle. One side has a length of 9 cm, and another side has a length of 6 units. What could be the length of the third side?
3 cm
7 cm
15 cm
18 cm
Answers
Answer: 7 cm
Step-by-step explanation:
Pls help pls pls ple
Answers
Answer:
10.5 ft
Step-by-step explanation:
This problem is using scaling.
Basically:
2.5(RV) = WZ
Meaning our scale factor is 2.5.
Multiply 4.2 * 2.5
Your answer is 10.5 ft.
to get a free meal tom at his fav resturant, tom needs to spend $50 or more at the resturant. he has already spent 30.25$ how much more does tom need to spend to get his free meal
Answers
how much more Tom needs to spend to get the free meal.
solution:subtract the amount he has spent from the amount he needs to spend to find how much more he needs to spend.
$50 - $30.25
= $19.75
Tom needs to spend $19.75 to get his free meal.
What is the area of a square that had side length of x-6?
Answers
area square= side²
= (x-6)²
= x²-12x+36
Answer:
36
Formula:
Side² = Area
Step-by-Step Explanation
-6 x -6 = 36
C
250
4.9 cm
80°
A
3.8 cm
D
B
ABC is a triangle.
D is a point on AB.
Work out the area of triangle BCD.
Give your answer correct to 3 significant figures.
Answers
Answer:
[tex]10.4\: \sf cm^2\:(3\:sf)[/tex]
Step-by-step explanation:
[tex]\Large\boxed{\sf Formulae}[/tex]
Sine Rule
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Cosine rule
[tex]c^2=a^2+b^2-2ab\cos C[/tex]
Area of a triangle
[tex]\textsf{Area of a triangle}=\dfrac12ab\sin C[/tex]
where:
C is the anglec is the side opposite the anglea and b are the sides adjacent the angle[tex]\Large\boxed{\sf Calculation}[/tex]
To find the area of ΔBCD, find:
length of CDangle CDBlength of BDThen use the sine rule for area of a triangle
Calculate length CD using cosine rule:
[tex]\implies CD^2=4.9^2+3.8^2-2(4.9)(3.8)\cos 80^{\circ}[/tex]
[tex]\implies CD^2=31.98334186...[/tex]
[tex]\implies CD=5.655381673...\:\sf cm[/tex]
Calculate ∠ADC using sine rule:
[tex]\implies \dfrac{\sin 80}{CD}=\dfrac{\sin ADC}{4.9}[/tex]
[tex]\implies ADC=\sin^{-1}\left(\dfrac{4.9 \sin 80}{CD}\right)=58.568949^{\circ}[/tex]
Therefore, ∠CDB = 180° - 58.568949° = 121.431051°
Use sine rule to calculate DB:
[tex]\implies \dfrac{DB}{\sin 25}=\dfrac{CD}{\sin CBD}[/tex]
[tex]\implies DB=\dfrac{5.655381673\sin25}{\sin 33.568949}=4.322471258..\: \sf cm[/tex]
[tex]\Large\boxed{\sf Solution}[/tex]
Use the sine rule for area of a triangle to find area of ΔBCD:
[tex]\implies A=\dfrac12(CD)(DB)\sin CDB[/tex]
[tex]\implies A=\dfrac12(5.655381673)(4.322471258)\sin (121.431051)[/tex]
[tex]\implies A=10.4\: \sf cm^2\:(3\:sf)[/tex]
Cedar Point amusement park has some of the tallest roller coasters in the United States. The Mantis is 165 feet shorter than the Millennium Force.
Write and solve an equation that can be used to find the height x of the Mantis.
Answers
15. A plane took off and rose at an angle of 8º with the horizontal ground. As the plane flies over a water tower, it has covered a distance from the take off point of 2000 feet. How far apart are the take off point and the water tower?
Answers
I wrote it all down so you can understand it better
The required distance between the take-off point and the water tower is 1980.1 feet.
Given that,
A plane took off and rose at an angle of 8º with the horizontal ground. As the plane flies over a water tower, it has covered a distance from the take-off point of 2000 feet.
To determine how far apart are the take-off point and the water tower.
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.
Here,
Now,
The distance flying over inclination is 2000 feet at an angle of 8° with horizontal.
Now,
Required horizontal distance = 2000 * cos 8°
= 1980.1 feet.
Thus, the required distance between the take-off point and the water tower is 1980.1 feet.
Learn more about trigonometry equations here:
brainly.com/question/22624805
#SPJ2
1. Josie lives at the coordinates (8,-4). Ruby lives at (-4, 2). When
Josie rides her bike to Ruby's house, she stops by the ice cream shopthat is 2/3 of the way from her house to Ruby's. What is the location of the shop?
Answers
in a cyclic quadrilateral ABRS, if AR=BS, prove that AS=RB and AB is parallel to SR
Answers
arc. BRS-arc. SR=arcade-arc. SR(removing SR in both side)
arc. AS=arc. BR
AS=BR(arc. AS=arc. BR)
AB//SR(same reason)
What is the approximate area of Laura’s yard?
Answers
To find the area of an irregular shape (in general)
⇒ is best to split it into different regular shapes
⇒ (in this case), let's split into a half-circle and a square
Area of the half-circle:
⇒ half the area of a circle ([tex]\pi r^2[/tex])
⇒ Area of half-circle = [tex]\frac{1}{2}\pi r^2[/tex]
r: length of radius ⇒ half of length of the diameter ⇒ 8.5m[tex]\pi[/tex] = 3.14Area of Half Circle = [tex]\frac{1}{2}\pi (8.5)^2 = 113.5m^2[/tex]
Area of square
⇒ length * width
⇒ Area of Square = 17 * 17 = 289[tex]m^2[/tex]
Total Area = 113.5 + 289 = 402.5 ≈ 402[tex]m^2[/tex]
Hope that helps!
b. Tyler's playlist has 36 songs. Noah's playlist has one quarter as many songs as
Tyler's playlist. How many songs are on Noah's playlist?
w = 4 times 36
w = 36 divided by 4
4w = 36
w/4 = 36
Answers
Answer:
9 songs
Step-by-step explanation:
¼ of 36
¼ × 36 = 9
Write 9/10 as an equivalent fraction with a denominator of 100 then write the fraction as a decimal
Answers
Answer:
Since the denominator has to be 100 and 9/10, 0.90, and 90% are all equal the you would just need to make the 9 into a 90. Therefore, yout answer will be 90/100.
Volume of cylinders, spheres, and cones word problems
A graduated cylinder is filled with 367 cm3 of liquid. The liquid is poured into a different cylinder that has a
radius of 3 cm.
What will the height of the liquid be in the new cylinder?
cm
Answers
Volume of fluid
=
V
=
36
π
cm
3
Radius of new cylinder
=
r
=
3
cm
To start the solution, solve for the height
h
in the formula for the volume of a cylinder:
V
=
π
r
2
h
π
r
2
h
π
r
2
=
V
π
r
2
h
=
V
π
r
2
V =π
r
2
h
π
r
2
h
π
r
2
=
V
π
r
2
h =
V
π
r
2
Substituting the values of the volume and the radius, the height of the fluid is:
h
=
V
π
r
2
=
36
π
cm
3
(
3
cm
)
2
=
(
4
)
(
9
)
π
cm
3
(
9
)
cm
2
=
4
π
cm
=
12.5663706144
≈
12.6
cm
h =
V
π
r
2
=
36
π
cm
3
(
3
cm
)
2
=
(
4
)
(
9
)
π
cm
3
(
9
)
cm
2
=4π cm =12.5663706144≈12.6 cm
Thus, the fluid reaches up to
12.6
cm
12.6
cm
in the new cylinder.
I NEED HELP!!!!!!!!!!!!!!!!
Answers
Step-by-step explanation:
just think back to the standard circle of radius = 1.
there the trigonometric functions are all represented as sides of right-angled triangles, where the radius is the baseline.
just like the triangle we are seeing here.
the only difference : the baseline (radius) is 17 and not 1.
and that is fine. everything is as in the standard circle, but multiplied by the radius (which is also true for the standard circle, but multiplying by 1 does not change anything, right ?).
a)
angle A is or focus. so, just imagine the triangle turned counterclockwise by 90° (so that AC is horizontal and CB is vertical).
do you see it now ?
sin is the vertical leg, cos the horizontal leg. and the leg lengths here are the standard functions multiplied by the radius.
so,
17 × sin A = 8
sin A = 8/17 = 0.470588235... ≈ 0.47
b)
17 × cos A = 15
cos A = 15/17 = 0.882352941... ≈ 0.88
c)
now B is our focus. imagine the triangle being mirrored at point B, so that B is left, and AC is right. your see it now ?
tan B = sin B / cos B
sin B = 15/17 = 0.882352941... ≈ 0.88
cos B = 8/17 = 0.470588235... ≈ 0.47
tan B = 15/17 / 8/17 = 15/8 = 1.875 ≈ 1.88
d)
cos B = 8/17 = 0.470588235... ≈ 0.47
How many vertices, edges, and faces are in the polyhedron below? List them.
Answers
Based on observation, in this polyhedron, there are a total of six vertices, nine edges, and five faces.
What are vertices?In geometry, this refers to the point where two line meet. In this case, the vertices are A, B, C, D, E, F for a total of six vertices.
What are the edges?This term refers to line segments, for example the line between B and C is an edge. Based on this, there are nine edges in this shape.
What are faces?This refers to flat surfaces; in this, case the total of flat surfaces are five.
Learn more about geometry in: https://brainly.com/question/16836055
Andy made 7 baskets during a basketball game each basket was worth 2 or 3 points how many different numbers could represent the total points scored by jordan
Answers
Answer:
2+3+2+3+2+3+2=17 because each was worth 2 or 3
What is the value of b:
-8-b=-6
1) b=-2
2) b=2
Answers
Answer:
b = -2
Step-by-step explanation:
Add 8 to both sides: -8 - b + 8 = -6 + 8
-b = 2
Divide both sides by -1: -b/-1 = 2/-1
b = -2
What is the slope of a line that goes through the points (3, 7) and (8, 11)
Question 4 options:
117
54
−83
45
Answers
Answer:
[tex]\sf \dfrac{4}{5}[/tex]
Step-by-step explanation:
(3,7) ⇒ x₁ = 3 & y₁ = 7
(8 ,11) ⇒ x₂ = 8 & y₂= 11
Slope
[tex]\boxed{Slope = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}[/tex]
[tex]\sf =\dfrac{11 -7}{8 -3}\\\\\\ = \dfrac{4}{5}[/tex]
explain why the other expressions do not have like terms A. 14m + mn B. 2y + 2x + 4 C. -3/4m + 8m + m D. 4 - 3p E. 5.75t + 7.75t - t F. 8xy - 6xy