The area of the sector is 75.43 centimeters if the radius is 6 centimeters and the central angle 4pi/3 radians.
What is a circle?It is defined as the combination of points that and every point has an equal distance from a fixed point (called the center of a circle).
We have the radius of the circle r = 6 centimeters
Central angle = 4π/3 = 240°
We know the area of the sector :
[tex]\rm =\dfrac{\theta}{360\°}\pi r^2[/tex]
[tex]\rm =\dfrac{240\°}{360\°}\pi (6)^2[/tex]
= 0.667×3.1415×36
= 75.43 square centimeters
Thus, the area of the sector is 75.43 centimeters if the radius is 6 centimeters and the central angle 4pi/3 radians.
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The product of two consecutive positive integer is 306. We need to find the Integers.
Hope you guys are help me.
Answer:
Let the given set of integers be n and (n+1)
n(n+1)=306
n to the power square +n−306=0
(n+17)(n−16)=0
Therefore, n=16 and integers are 16 and 17.
Answer:
17, 18
Explanation:
Let the integers be y, y + 1
=======================
y * (y + 1) = 306 (products of them)y² + y = 306 (multiply)y² + y - 306 = 0y² + 18y - 17y -306 = 0 (factorize)y(y+18) -17(y+18) = 0 (take out common variables)(y-17)(y+18) = 0 (collect into groups)y = 17, -18 y = 17 (as required positive integer)Next integer:
y + 117 + 118A store has clearance items that have been marked down by 45%. They are having a sale, advertising an additional 40% off clearance items. What percent of the original price do you end up paying?
Answer:
33%
Step-by-step explanation:
x = original price now take 45% off <=====means you pay 55% of original
.55 x is the new price now take 40% MORE off (leaving 60%)
.55x * .6 = .33 x
What is the difference between the 8th square number and the 4th square number?
Answer:
240
Step-by-step explanation:
The 8th square number is 2^8 = 256.
The 4th square number is 2^4 = 16.
Their difference is 256 - 16 = 240.
7x-9=803 solve for x and x only
Answer:
116
Step-by-step explanation:
7x-9=803
(add 9 to both sides)
7x=812
(divide by 7)
x=116
Can someone help with trigonometry? 12 points
Answer:
A° = 44.42°
Step-by-step explanation:
Soh Coh Toa
Soh: sin(theta) = Opp/Hyp
Coh: cos(theta) = Adj/Hyp
Toa: tan(theta) = Opp/Adj
We are using Coh: cos(theta) = Adj/Hyp because we need to find Angle A and that 5 is Adjacent and 7 is the Hypotenuse.
cos(A°) = 5/7
A° = cos^-1 (5/7)
A° ≈ 44.4153086
A° = 44.42°
Complete the equation
2/8= _ divided by _
Answer:
2 divided by 8
Step-by-step explanation:
2/8
/ means division sign
Select the correct answer. What is the range of the function shown on the graph?
Answer:
B
Step-by-step explanation:
The lower limit of the range of the function is -6, as it does the y-value does not decrease below that amountThe upper limit is not shown, hence we can assume it to be infinity (∞)Range
Lower limit < y < Upper limit-6 < y < ∞The best option is B
What is the area of the
figure shown?
in?
3 in.
10 in.
5 in.
10 in.
Intro
Done
Answer:
65in^2
Step-by-step explanation:
5*10+(1/2)*3*10=65
A dog is chained to a pole. If the dog can run within an area of 380 ft.², how long is the chain?
ty if you could help :)
Answer:
The chain is around 11 feet in length.
Step-by-step explanation:
Area of a circle = π × r²
380 ft² = π × r²
121 ft² = r²
11 ft = r
I NEED THAT ANSWER ASAP
Answer:
y=-4x-7
Step-by-step explanation:
remember the equation y=mx+b, where the slope is the m along with the x because it is an ever changing variable, and b is being the y intercept, that basically gives the answer.
Drake and Evan are teammates on a high school swim team drake swim 312. 63 m during practice evan swim exactly 1/3 times farther than drake exactly how far did Evan swim?
Answer:
416.84 m
Step-by-step explanation:
First Step:
Multiple 312.63 by 1/3
312.63*1/3=104.21
Second Step:
Add 312.63 to 104.21
312.63+104.21=416.84
[tex]✤ \: \underline{ \underline{ \frak{Understanding~the~question : - }}} \\ \\ [/tex]
In this question, we have been provided that Evan swims 1/3 times farther than Drake, thus, the total distance covered by Evan will be equal to the sum of 312.63 m and the 1/3rd of 312.63 m. Thus, at first we will calculate the one third of the distance and then add them up to get our final answer.
⠀
[tex]✤ \: \underline{ \underline{ \frak{Given:-}}} \\ \\ [/tex]
There are two teammates in a high school teamDrake swims 312.63 m Evan swims 1/3 times farther than Drake⠀
[tex]✤ \: \underline{ \underline{ \frak{To~Find :-}}} \\ \\ [/tex]
The distance travelled ( swim ) by Evan⠀
[tex]✤ \: \underline{ \underline{ \frak{Solution :-}}} \\ \\ [/tex]
Calculating the one - third,
[tex] \sf \longrightarrow \dfrac{1}{3} \: of \: 312.63 \: m \\ \\ \\ \sf \longrightarrow \dfrac{1}{3} \times 312.63 \: m \\ \\ \\ \sf \longrightarrow \dfrac{1}{ \cancel3} \times \cancel{312.63} \: m \: \\ \\ \\ \sf \longrightarrow 1 \times 104.21 \: m \: \: \\ \\ \\ \sf \longrightarrow 104.21 \: m \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
Thus,
⠀
[tex] \sf \longrightarrow Distance~covered~by~Evan =312.63 \: m + 104.21 \: m \\ \\ \\ \sf \longrightarrow Distance~covered~by~Evan =416.84 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
Thus, the distance covered by Evan is 416.84 m.
⠀
[tex]\underline{\rule{227pt}{2pt}} \\ \\ [/tex]
Complete the point-slope equation of the line through (3,6) and (5,-8)
Answer:
y = - 7x + 17
Step-by-step explanation:
Given, (3,6) and (5,-8)
Equation of a straight line is y = mx + c
Here, y = -8, x = 5 and m = ?
m = [tex]\frac{Change in Y}{Change in X}[/tex]
m = [tex]\frac{-8 - 6}{5 - 3}[/tex]
m = - 7
Substituting x, y and m in y = mx + c we get,
- 8 = - 7(5) + c
c = 35 - 8
c = 17
The equation is y = - 7x + 17 (Answer).
Which of the following do not represent a function of x?
F
G
H
J
Answer:
f,j
Step-by-step explanation:
Which graph represents f(x)=4sin(2πx)?
The function f(x)=4sin(2πx) is a sinusoidal function
The graph of the function f(x)=4sin(2πx) is graph (c)
How to determine the graph of the function f(x)=4sin(2πx)?The parent function of a sine function is
f(x) = sin(x)
The function f(x)=4sin(2πx) implies that the parent function f(x) = sin(x) has been horizontally and vertically stretched
So, the graph of the function f(x)=4sin(2πx) would have a higher amplitude and shorter period than its parent function
Hence, the graph of the function f(x)=4sin(2πx) is graph (c)
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If n is an even integer, which of the following is not necessarily even?
A.2n
B.n/2
C.3n
D. n^2
E.n^2/2
Answer:
B
Step-by-step explanation:
imagine if n=2 so B equal to 1
7) Mofor invests $3,101 in a savings account
with a fixed annual interest rate
compounded 2 times per year. After 6
years, the balance reaches $3. 932. 82.
What is the interest rate of the account?
Answer:
4%
Step-by-step explanation:
[tex]A = P(1+r/n)^{nt}[/tex]
A = final amount
P = initial amount
r = interest rate per time period
n = number of times compounded per time period
t = number of time period
A = 3932.82
r = what we want to find
n = 2
t = 6
[tex]A = P(1+r/n)^{nt}\\3932.82 = 3101(1+r/2)^{12}[/tex]
divide both sides by 3101 to isolate the exponent and its parts
[tex]3932.82/3101 = (1+r/2)^{12}[/tex]
put both sides to the power of (1/12) to help isolate the variable
[tex](3932.82/3101)^{1/12}= (1+r/2)[/tex]
subtract 1 from both sides to isolate the variable and its coefficient
[tex](3932.82/3101)^{1/12}-1= (r/2)[/tex]
multiply both sides by 2 to get r
[tex]((3932.82/3101)^{1/12}-1) * 2= r[/tex]
r ≈ 0.04 = 4%
P(, b)
s(a)
70)
T
16
Is the figure shown in the xy-coordinate plane a parallelogram? Why or why not? Use the
given coordinates to justify your answer. Yes it is because all four sides are parallel to each other.
Part A:
1. What is the slope of side OP?
2. What is the slope of side TS?
3. Are side OP and side TS parallel/perpendicular/neither? Parallel
Part B
1. What is the slope of side OT?
2. What is the slope of side PS?
3. Are side OT and side PS parallel/perpendicular/neither? Parallel
Part C
1. What is the length of side OP?
2. What is the length of side TS?
3. Are side OP and TS congruent or not congruent? They are congruent
Part D
1. What is the length of side PS?
2. What is the length of side OT?
3. Are side PS and side TS congruent or not congruent? They are not congruent
Part B
1. What is the midpoint of diagonal PT?
2. What is the midpoint of diagonal OS?
3. Do the two diagonals PT and OS bisect each other? Yes
Answer:
lmk when you got the answer
The heights of 100 people in an office building were recorded and the results were normally
distributed. Which histogram shows a normal distribution that could represent this data?
Answer:
d
Step-by-step explanation:
SOMEONE PLES HELP ME !!!
1. even or odd
2. Positive or negative
Step-by-step explanation:
The degree fix, is 4 and the leading coefficient of is 3 There are values. distinct real zeros and 3. relative maximum 2 [analyze]
10% of the 50 coffee mugs at Adam's Pancake House are dirty. How many dirty coffee mugs are there at the pancake house?
Answer:
5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
0.10*50=5
Ashley's ladder is 1.85 meters high. what is the height in centimeters, of Ashley's ladder
Answer:
185cm
Step-by-step explanation:
Answer:
185 cm
Fun Fact : my name is Ashley
Please help!! Will mark brainlyest.
it's for my friend............................................
Answer:
Ok get ready to get taken down by either Sarah, Katie, or Eric lol
Step-by-step explanation:
Please help this is due in 10 minutes!!!
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
[tex] \textbf{Let's calculate the volume of hemisphere} [/tex]
[tex] \textbf{Given :} [/tex]
[tex] \textsf{radius = 11 inches} [/tex][tex] \textbf{Volume of a hemisphere is :} [/tex]
[tex] \sf{v=\dfrac{2}{3}\pi r³} [/tex][tex] \sf{v=\dfrac{2}{3}\cdot 3.14 \cdot 11³} [/tex][tex] \sf{v=\dfrac{2}{3}\cdot 3.14\cdot 1331} [/tex][tex] \sf{v=\dfrac{8358.68}{3}} [/tex][tex] \sf{v\approx 2786.2 in³} [/tex]2 . Using the slope-intercept form of a line, find the equation of the line with slope and y-intercept-2. Then graph the line on the grid provided and explain how you determined your graph
Answer:
see below
Step-by-step explanation:
slope intercept form slope = -2 y axis intercept = -2
y = -2x - 2 to graph this pick two values of x say -3 and + 2
plug these values into the equation to find the corresponding y values, plot the points and then draw a line connecting them
please help me this is timed!!
which point represents the unit rate?
a
b
c
d
Answer:
C, because it is one unit across
filler filler filler
The owner of a flower shop sells 18 roses for $90. What is the cost in dollars per rose?
Answer:
5 $ per rose
Step-by-step explanation:
it is 5 $ as
if we do 90 / 18 we get 5
or 5 × 18 is also equal to 90
therefore it is 5$ per rose
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What slope would make the lines
perpendicular?
y = 1/2x-1
y = [?]x - 1
Answer:
y = [-2]x - 1
Step-by-step explanation:
y = [-2]x - 1 will make the lines perpendicular.
Because the product of slopes of perpendicular lines is -1
-> 1/2*(-2) = -1
Hope it helps you in your learning process.
what is (3x + 4)(5x − 2)
Answer:
15x² + 14x - 8
Step-by-step explanation:
Apply the distributive property by multiplying each term in (5x - 2) by each term in (3x + 4).
5x(3x) + (-2)(3x) + 5x(4) + (-2)(4)
= 15x² - 6x + 20x - 8
Combine like terms:
15x² + 14x - 8
(3x + 4)(5x − 2) is the factored form of 15x² + 14x - 8.
hope this helps!
Use the drop down-menus to complete the sentences. when parallel light rays exit a concave lens, they . when parallel light rays exit a convex lens, they .
Answer:
When parallel light rays exit a concave lens, they
✔ diverge
.
When parallel light rays exit a convex lens, they
✔ converge
.
Step-by-step explanation:
The requried, parallel light rays diverge when passing through a concave lens, and converge when passing through a convex lens.
What is reformation?Refraction is the bending of light as it passes from one medium to another medium of different optical densities, such as from air to water or from air to a glass lens.
When parallel light rays exit a concave lens, they diverge as the concave lens is thinner at the center and thicker at the edges. This shape causes the light rays to bend away from the optical axis and spread apart from each other, resulting in a virtual image that is smaller than the object.
On the other hand, when parallel light rays exit a convex lens, they converge towards a focal point as the lens is thicker at the center and thinner at the edges. This shape causes the light rays to bend towards the optical axis and meet at a focal point, resulting in a real image that is inverted and can be larger or smaller than the object depending on the distance of the object from the lens.
Therefore, the behavior of parallel light rays upon exiting concave and convex lenses is quite different due to their distinct shapes and curvatures, resulting in opposite effects on the direction of light rays and the formation of images.
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