The value of cos (a+b) when cos a= 3/5 with 0<a< π/2 and Sin b = - 8/17 with 3π / 2 <b < 2 π, is 0.906.
What is triangle angle sum theorem?According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees. The formula for cos compound angle using angle sum theorem can be given as,
[tex]\cos (a+b)=\cos (a)\cos (b)-\sin (a)\sin (b)[/tex]
The exact value of cos (a+b) has to be find out. It is given that,
[tex]\cos a= \dfrac{3}{5}[/tex]
The value of a is lies between 0<a< π/2. The value of other side of the triangle using the Pythagoras theorem,
[tex]5^2={x^2+3^2}\\x^2=25-9\\x=\sqrt{16}\\x=4[/tex]
Thus, the value of sin a is 4/5 from the trigonometry ratio. the value of sine b is,
[tex]\sin b = -\dfrac{8}{17}[/tex]
The value of b is lies between 3π / 2 <b < 2 π. The value of the other side of the triangle using the Pythagoras theorem,
[tex]17^2={(-8)^2+y^2}\\y^2=289-64\\y=\sqrt{225}\\y=15[/tex]
Thus, the value of cos b is, 15/17. Put the values in above formula,
[tex]\cos (a+b)=\cos (a)\cos (b)-\sin (a)\sin (b)\\\cos (a+b)=\dfrac{3}{5}\times\dfrac{15}{17}-\dfrac{4}{5}\times\dfrac{-8}{17}\\\cos (a+b)=\dfrac{9}{17}+\dfrac{32}{85}\\\cos (a+b)=0.906[/tex]
Thus, the value of cos (a+b) when cos a= 3/5 with 0<a< π/2 and Sin b = - 8/17 with 3π / 2 <b < 2 π, is 0.906.
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Find the area of the figure.
A) 114 cm2
B) 350 cm2
C) 418 cm2
D) 447 cm2
Answer:
418 cm2
Step-by-step explanation:
Divide the figure into a square and a triangle. Find the area of each and add. Make sure you do not combine them, and do one at a time.
s2 = area of square
192 = 361 cm
BH= area of triangle
(6)(19) = 57 cm2
361 + 57 = 418 cm
Answer:
c= 418cm2
Step-by-step explanation:
good bye now human
A rectangle is 4 ft long and 2 ft wide. find its area in square inches.
[tex]\text{Area of rectangle} = \text{length} \times \text{width}\\\\~~~~~~~~~~~~~~~~~~~~~~~=4 ~\text{ft}~\times ~2 ~\text{ft}\\\\~~~~~~~~~~~~~~~~~~~~~~~=8~ \text{ft}^2\\\\~~~~~~~~~~~~~~~~~~~~~~~=1152~\text{in}^2[/tex]
plss help :))))))))))))))))))))))))))))))))))))))))))))))))))0
Step-by-step explanation:
Diameter is 18
So radius will be d/2 which is 9
As the formula of area is
[tex] \pi{\r}^{2} [/tex]
So put the vales
We get s
254
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE
PLEASE HELP PLEASE PLEASE HELP
Answer:
5x10x9 Is the correct answer meaning that the answer is 450
Brainliest would be very appriciated
Step-by-step explanation:
EDIT: my bad i read the question wrong, the answer is D:450
sorry for any confusion ;^;
What I Know Write each as they would appear on a 24-hour digital clock. Morning Afternoon 1. Five minutes pass 8 2. Quarter of 12. 3. Six minutes to 10 4. Twenty minutes past 1 5. Twenty-five minutes to 9 6. Ten minutes to 3 7. Eighteen minutes pass 5 8. Fourteen minutes to 7 9. Half pass 1 10. Twelve minutes past 12
Step-by-step explanation:
1. 8:05
2. 12:45
3. 10:54
4. 1:20
5. 8:35
6. 2:50
7. 5:18
8. 7:44
9. 1:30
10. .12:12
A scale drawing of an American flag is 6 inches tall. The actual flag is 3 feet tall. What is the scale of the drawing?
hallenge
A tank was1/4 of the way filled of water. After 3 L of water was added, it was7/10
full. How many liters of water did it have at first?
What would the answer be ?
Answer: 7
Step-by-step explanation: there are 4 full circles so that equals 4. 1+1=2, 1/8+7/8=1. 4+2+1=7
See the diagram below.
The 7/8 and 1/8 combine to 8/8 = 1. So we add an extra pie to the original two full pies to get 3 total.
show work. A 2-ft wide circular track for a camera dolly is set up for a movie scene. The two rails of the track form concentric circles. The radius of the inner circle is 59 ft. How much farther does a wheel on the outer rail travel than a wheel on the inner rail of the track in one turn?
Step-by-step explanation:
oh that is again something you can nicely envision :
the inner circle has a radius of 59 ft.
so, because of the 2 ft wide track the outer circle has a radius of 59+2 = 61 ft.
the circumference of a circle is
2×pi×r
the answer to the question is simply the difference bergen the 2 circumference values.
inner circle :
2×pi×59 = 118pi
outer circle :
2×pi×61 = 122pi
the difference is
122pi - 118pi = 4pi = 12.56637061... ft ≈ 12.6 ft
the wheel on the outer track travels about 12.6 ft farther than a wheel on the inner track in one full turn.
Brainliest?! :]
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer:
Slope of parallel line:[tex]-1\frac{3}{5}[/tex]
Slope of perpendicular line: [tex]\frac{5}{8}[/tex]
Step-by-step explanation:
Because parallel lines have equal gradients, but perpendicular lines have gradients which equal to -1 when multiplied.
Hope it helps:)
Answer:
Slope of parallel line:[tex]-1\frac{3}{5}[/tex]
Slope of perpendicular line: [tex]\frac{5}{8}[/tex]
Identify the quotient in the form of a + bi.
1 + 6 divided by
−3 + 2i
The quotient of the expression in form of a + bi is 9/13 - 20/13i
Rationalizing complex expressionsGiven the following expressions
1+6i/-3+2i
Rationalizing the given rational complex number, we will have;
= 1+6i/-3+2i * -3-2i/-3-2i
= (1+6i)(-3-2i)/9+4
= -3-2i-18i-12i²/13
Simplify the result to have:
= -3+12-20i/13
= 9-20i/13
Express in the form a + bi
9/13 - 20/13i
Hence the quotient of the expression in form of a + bi is 9/13 - 20/13i
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The diagram shows a circle with centre
O.
A, B, and C lie on the circumference of
the circle.
X, A and Y lie on a tangent to the circle.
Work out:
(i)
(ii) ABC
С
x
ö
163°
В
B
A69°
The diagram is not drawn accurately.
r
o
O
ACB =
=
.
0
LABCE
0
Answer:
This is my notes
Step-by-step explanation:
The value of angles are,
⇒ ∠ACB = 48°
⇒ ∠CBA = 48°
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
A, B, and C lie on the circumference of the circle.
And, X, A and Y lie on a tangent to the circle.
Now, We get;
⇒ ∠XAC + ∠CAB + ∠BAY = 180°
⇒ 63° + ∠CAB + 69° = 180°
⇒ ∠CAB = 180 - 132
⇒ ∠CAB = 48°
Hence, We get;
⇒ ∠ACB = 48°
⇒ ∠CBA = 48°
Thus, The value of angles are,
⇒ ∠ACB = 48°
⇒ ∠CBA = 48°
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A straight boardwalk is being built over a
circular wetlands area, so that it divides
the area in half. A hiking path goes around
the outside. The boardwalk is 50 m long.
How long is the hiking path that goes
around the wetlands?
Answer:
157 if youre going by 3.14
157.08 if youre going by π
Step-by-step explanation:
you want to find the circumference
circumference is 2πr
the radius id 50/2=25, because radius is half of the diameter (the diameter is the length across a circle
2 * 3.141 * 25 = 157
The length of the path that goes around the outside of the circle stands at 157.08 meters.
What is a circle?A circle stands as a curve traced out by a point moving in a plane so that its distance from a given point exists constant; alternatively, it stands for the shape created by all points in a plane that exists at a set distance from a given point, the center.
Given that the boardwalk divides the circle area into two halves, and exists straight with a length of 50 meters. Thus, the straight Boardwalk exists within the length of the diameter of the circle.
Now, the perimeter of the circle exists the length of the path that goes around the outside.
Thus, the perimeter of the circle stands,
Perimeter = π × Diameter
= π × 50 meters
= 157.07963 meters ≈ 157.08 meters
Thus, the length of the path that goes around the outside of the circle exists 157.08 meters.
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Find the area
(Please)
Give explanation
Answer:
960 cm²
Step-by-step explanation:
Area of trapezoid: (a + b)(h)/2
A = (20 + 40)(32)/2
A = 60(32)/2
A = 1920/2
A = 960 cm²
BRANLIEST please if this helps!can someone please help me solve this? thank you!
Find the circumference:
Circumference = pi x radius x 2 = 138.16 feet
Linear travel = circumference x rotations
linear travel = 138.16 x 20 = 2.763.2 feet.
Round off to 2,763 feet
GIVING BRAINLIEST + STARS
I know A to B is 20m/s but what is C to D?
Answer:
See below ↓↓
Step-by-step explanation:
A to B
Avg. speed = Distance covered / Time takenAvg. speed = 200 m / 10 sAvg. speed = 20 m/sC to D
Avg. speed = Distance covered / Time takenAvg. speed = (500 - 200) m / (60 - 30) sAvg. speed = 300 m / 30 sAvg. speed = 10 m/sIn the figure below, the segments IJ and IK are tangent to the circle centered at O. Given that OJ=8.4 and OI=15.9, find IK.
Answer:
IK = 13.5
Step-by-step explanation:
A^2 + B^2 = C^2
(8.4)^2 + B^2 = (15.9)^2
70.56 + B^2 = 252.81
B^2 = 182.25
B =13.49925... ≈ 13.5 = IK
Want Brainliest? Please help! :(
Find the circumference and the area of a circle with diameter 6 m.
Use the value 3.14 for pi, and do not round your answers. Be sure to include the correct units in your answers.
Answer:
Circumference=18.84 m
Area = 28.26 [tex]m^{2}[/tex]
Step-by-step explanation:
Circumference = 2πr
= 2 x 3.14 x 3 (radius = 6/2 = 3)
= 18.84 m
Area = π[tex]r^{2}[/tex]
= 3.14 x [tex]3^{2}[/tex]
= 28.26 [tex]m^{2}[/tex]
Answer:
Circumference=18.84 m
Area = 28.26
Step-by-step explanation:
Please answer soon!
What is the median number of repairs per vehicle as shown in the box plot below?
Answer:
B, or 4
Step-by-step explanation:
Since the line in the middle of the box plot shows the median it tells us that the median is 4
Answer:
4
Step-by-step explanation:
because it is the middle number
HELP ME!!!! please....
What is the value of b?
Enter your answer in the box.
b =
A right triangle with base labeled as b. The hypotenuse is labeled as 34. The perpendicular is labeled as 16. The angle made between base and perpendicular is marked as a right angle.
Answer:
30
[tex]b = \sqrt{ {c}^{2} - {a}^{ {2} } }[/tex]
[tex]b = \sqrt{ {34}^{2} - {16}^{2} } [/tex]
[tex]b = \sqrt{1156 - 256} [/tex]
[tex]b = \sqrt{900} [/tex]
[tex]b = 30[/tex]
Which answer best describes the shape of this distribution?
(A)uniform
(B)skewed left
(C)bell-shaped
(D)skewed right
Answer:
I'm not 100% sure but it might be b
Step-by-step explanation:
Factor the expression. 16m2 – 24mn + 9n2
(4m – 3n)(4m + 3n)
(4m – 3n)2
(16m – 3n)(m + 3n)
(4m + 3n)2
16m2 – 24mn + 9n2
((16 • (m2)) - 24mn) + 32n2
(24m2 - 24mn) + 32n2
= (4m - 3n)2
Using a 10' long piece of strut as a straightedge, you are trying to determine the outside diameter of a grain storage silo. You and your partner very carefully measure from the ends of the straightedge, squarely, in to the wall of the silo and find that the “H” distance is 14 3/4" at both ends. What is the radius of the silo in inches? Note: The values calculated for this question may be used for additional questions. (Round the answer to the nearest 1/8".)
The radius of the silo is the distance from its center to the outside wall
The radius of the silo is 7 3/8" or 7 3/8 inches
How to determine the radius?From the question, we have the following parameters:
Length of strut = 10'Outside diameter of silo = 14 3/4"The radius is then calculated as:
Radius = 0.5 * Diameter
This gives
Radius = 0.5 * 14 3/4"
Evaluate the product
Radius = 7 3/8"
Hence, the radius of the silo is 7 3/8" or 7 3/8 inches
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The following figure shows a cube. Which expression represents the surface area of the cube?
Answer:
6 ⋅ 16
This is the sum of the areas of the 6 square faces.
The surface area of the cube in the figure given is 96 squared units
What is surface area of a cube?The surface area of a cube is calculated by finding the total area of all six faces. Since all sides of a cube are equal in length, you can use the formula:
Surface area of a cube = 6 × (side length)²
In other words, you square the length of one side of the cube and then multiply it by 6 to get the total surface area.
Let's say the side length of the cube is "s," then the formula becomes:
Surface area of a cube = 6 × s²
In the question given, we can calculate the surface area of this cube as;
Surface area = 6 * s²
s = 4
Surface area = 6 * 4²
Surface area = 6 * 16 = 96 unit²
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100 POINTS AND BRAINLIEST. I need help ASAP.
Screenshots Below.
Consider the table of values for functions f(x) and g(x).
x f(x) g(x)
−2 14 4
−1 12 1
0 1 0
1 2 1
2 4 4
3 8 9
4 16 16
Which statements are most likely true based on the given values?
Select each correct answer.
f(x) is a polynomial function.
f(x) is an exponential function.
g(x) is a polynomial function.
g(x) is an exponential function.
The output values of g(x) will remain greater than those of f(x) as the input values continue to increase.
The output values of f(x) will surpass those of g(x) as the input values continue to increase.
Answer:
Step-by-step explanation:
First what we must do is rewrite the table to find a solution:
0.25^x −0.75x+1
64 3.25
16 2.5
4 1.75
1 1
0.25 0.25
0.0625 −0.5
0.015625 −1.25
We see where the values of the function are the same:
x = 0 (1)
x = 1 (0.25)
answer:
x = 0
x = 1
Answers:
f( x ) is an exponential function.g( x ) is a polynomial function.The output values of f( x ) will surpass those of g( x ) as the input values continue to increase.How do you simply a ratio? I have no clue how to do that.
I am confused can somebody help me
F ( - 5 ) =
Answer:
-5f
Step-by-step explanation:
Answer:
f(- 5) = 57
Step-by-step explanation:
substitute x = - 5 into f(x) , that is
f(- 5) = 3(- 5)² + 3(- 5) - 3
= 3(25) - 15 - 3
= 75 - 18
= 57
A student wants to interview students about their favorite sport. The students asks 50 people who play a sport for the school. Is this an example of a random sample or a biased sample?
A
Random sample
B
Biased sample
Answer:
Random
Step-by-step explanation:
A community college is planning to expand its library. Forty students were asked
how many times they visited the library during the previous semester. Their
responses are given below. Construct a frequency distribution, letting each class
have a width of 1.
2 4 5 68
24568
3 4 5 7 8
3 5 5 7 9
4 55 79
COLLE
02
1
22222
1
1 2
n
98666
10
10
U
E
D
C
1
L
5
Number of Visits
0
1.
(0,0)
Here is the constructed frequency distribution table:
Number of visits Number of students
0 - 1 5
2 - 3 9
4 - 5 11
6 - 7 5
8 - 9 8
10 - 11 2
What is a frequency distrubution?A frequency table is used to arrange a large amount of data using their frequency. The class width is the difference between the upper boundary and the lower boundary.
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