A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle ABC measuring 1 radian and radius AB = 20 feet. What is the length of arc AC, in feet?
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Answer:
The length of the arc AC is;
[tex]AC=20ft[/tex]Explanation:
Given the radius AB as 20ft.
[tex]AB=20\text{ ft}[/tex]And angle ABC measures 1 radian.
Using the Method 1;
Length of Arc AC is;
[tex]AC=\omega r[/tex]Substituting the angle in radian and the radius;
[tex]\begin{gathered} AC=1\times20\text{ ft} \\ AC=20\text{ ft} \end{gathered}[/tex]The length of Arc AC is 20 ft
Method 2;
We will firstly convert the angle from radian to degree.
As shown below;
[tex]\begin{gathered} \theta=1\text{ rad}\times\frac{180}{\pi} \\ \theta=57.3^0 \end{gathered}[/tex]Then we will apply the formula for calculating the length of an arc;
[tex]C=\frac{\theta}{360}\times2\pi r[/tex]Substituting the value of the angle and the radius.
[tex]\begin{gathered} C=\frac{57.3}{360}\times2\pi\times20ft \\ C=\frac{57.3}{360}\times40\pi ft \\ C=20ft \end{gathered}[/tex]Therefore, the length of the arc AC is;
[tex]AC=20ft[/tex]Related Questions
Which is the best estimate for the sum 2/9+10/11? * O A. 0 + 0 = 0 OB. 1/2 + 1/2=1 O C. 1 + 1 = 2 O D. 0 + 1 = 1 Please explain the process of how you at your answer
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this is because 9 is bigger than 2 almost 4 times, so the answer of the division must be close to 0.
now on the other side
[tex]\frac{10}{11}\approx1[/tex]10 is still smaller than 11 but the difference is small causing that the division be aroun 0.9 or 1.
when you add the estimates together you obtain
[tex]\begin{gathered} \frac{2}{9}+\frac{10}{11}=\text{?} \\ 0+1=1 \end{gathered}[/tex]What is the value of x?M (3x - 16) O (x + 6)N (x) A 5B 38 C 22D 42
Answers
From , the properties of triangle;
Angle M + Angle N + Angle O = 180
(3x -16) + (x + 6) + x = 180
3x - 16 + x + 6 + x = 180
5x - 10 = 180
5x = 180 + 10
5x = 190
x = 190/5
...
Simplify the following expressions. Make sure it is simplified completely when selecting your answer. Choose the correct answer below.
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The correct option is option number 2.
the diagram below is a picture of a broken post. determine the height of the post before it was broken.
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step 1
Find the hypotenuse of the right triangle
Applying Pythagorean Theorem
c^2=7^2+24^2
c^2=625
c=25 ft
therefore
the height is equal to
h=25+24=49 ft
answer is 49 ftwith the polynomial provided I need help finding the zeros and putting them onto the graph as well as drawing the line correctly
Answers
Let's multiply out the polynomial first:
[tex]\begin{gathered} f(x)=(x-1)(x+3)^2 \\ f(x)=(x-1)(x^2+6x+9) \\ f(x)=x^3+6x^2+9x-x^2-6x-9 \\ f(x)=x^3+5x^2+3x-9 \end{gathered}[/tex]As we can see clearly that this is a cubic function, the highest degree is "3", which is odd. Hence,
This is an odd function.
Leading Coefficient is the number in front of the highest degree variable, that is x^3. So, there is "1" in front, thus the leading coefficient is positive.
Since we have one factor that is (x-1), it cuts the x-axis at:
x - 1 = 0
x = 1
We have another factor (x+3)^2. Since this is squared, here, the curve will bounce and touch the x-axis at:
(x+3)^2 = 0
x + 3 = 0
x = -3
Thus, the zeros are at x = 1 (cuts) and at x = -3 (bounces).
From basic cubic function (leading coefficient 0) we know as that x goes to infinity, the funtion goes to infinity. As x goes towards negative infinity, the function also approaches negative infinity.
Now, we can draw the curve:
1. Use a calculator to find each angle measure to the nearest degree.a) sin A = 0.4848b) cos Y = 0.7431c) cos X = 0.4226d) tan B = 19.0811
Answers
Given
a) sin A = 0.4848
b) cos Y = 0.7431
c) cos X = 0.4226
d) tan B = 19.0811
To find:
Each angle measure to the nearest degree.
Explanation:
It is given that,
a) sin A = 0.4848
b) cos Y = 0.7431
c) cos X = 0.4226
d) tan B = 19.0811
That implies,
a) sin A = 0.4848.
Then,
[tex]\begin{gathered} A=\sin^{-1}(0.4848) \\ =28.99\degree \\ =30\degree \end{gathered}[/tex]b) cos Y = 0.7431.
Then,
[tex]\begin{gathered} Y=\cos^{-1}(0.7431) \\ =42.0038\degree \\ =42\degree \end{gathered}[/tex]c) cos X = 0.4226.
Then,
[tex]\begin{gathered} X=\cos^{-1}(0.4226) \\ =65.001\degree \\ =65\degree \end{gathered}[/tex]d) tan B = 19.0811.
Then,
[tex]\begin{gathered} B=\tan^{-1}(19.0811) \\ =86.99\degree \\ =87\degree \end{gathered}[/tex]Hence, the measure of each angle is,
a) A = 30°.
b) Y = 42°.
c) X = 65°.
d) B=87°.
Triangle ABC is shown. Select all the triangles that are scale drawings of triangle ABC.
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Athe the triangles are similar to triangle ABC.
Draw parallel to . You can draw any length and place it anywhere on the coordinate plane, but not on top of .Find and record the ratio, n, of the length of to the length of . Then, multiply the length of by n and record the resulting length.
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In a diagram,
Then,
[tex]\frac{DE}{BC}=n[/tex]For example, suppose that n=2; thus,
[tex]DE=2BC[/tex][tex]\Rightarrow2\cdot CA[/tex]We can form a new triangle DEF whose side EF is parallel to CA; therefore,
[tex]\Rightarrow EF=2CA[/tex]Ryan's motorcycle is now worth $2500. Ithas depreciated 12% each year since itwas purchased. If he bought it four yearsago, what did it cost brand new? Roundto the nearest dollar
Answers
Given a principal of P and a depreciation rate of r %,
after n years the new amount A is given by
[tex]A=P(1-r^{})^n[/tex]In this case,
[tex]A=\text{ \$2500 r = 12\% n = 4years}[/tex]Then, we have
[tex]\begin{gathered} 2500=P(1-0.12^4) \\ \text{ Which implies that } \\ P=\frac{2500}{(1-0.12)^4}=\frac{2500}{0.88^4}=\frac{2500}{0.5997}=\text{ \$4169} \end{gathered}[/tex]Hence the cost brand new is $4169
Mr adams shares out 24 pencils between niamh and jack in the ratio 3:5
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The number of pencils taken by Niamh is 9 and by jack is 15.
\What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Given that Mr Adams shares out 24 pencils between Niamh and Jack in a ratio of 3:5.
Let the common factor between the sharing be x. Form an equation and solve.
Niamh's share = 3x
Jack's share = 5x
3x+ 5x = 24
8x = 24
x = 3
Niamh's share = 3x = 3 x 3 = 9 Pencils
Jack's share = 5x = 5 x 3 = 15 Pencils
Therefore, the number of pencils taken by Niamh is 9 and by jack is 15.
The complete question is given below.
Mr Adams shares out 24 pencils between Niamh and jack in a ratio 3:5. Find the number of pencils taken by Niamh and Jack.
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#3 iFind the volume of the sphere. Round your answer to the nearest hundredth.4 ftThe volume is aboutcubic feet.
Answers
Given: A sphere with a radius of 4 ft.
Required: To determine the volume of the sphere.
Explanation: The volume of a sphere is given by the formula-
[tex]V=\frac{4}{3}\pi r^3[/tex]Substituting the value of the radius, r=4 into the formula as-
[tex]V=\frac{4}{3}\times3.14\times4^3[/tex]Further solving-
[tex]\begin{gathered} V=267.946\text{ ft}^3 \\ \approx267.95\text{ ft}^3 \end{gathered}[/tex]Final Answer: The volume is about 267.95 cubic feet.
If W (-10,4),X(-3,-1)and Y (-5,11) classify angle WXY by its sides
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So,
Let me graph the three points here below:
To classify this triangle by its sides, the first thing we need to do is to find the measure of each segment. For this, we could use the formula for the distance between two points for each one.
Let's start with segment WX.
[tex]\begin{gathered} WX=\sqrt[]{(4-(-1))^2+(-10-(-3))^2} \\ WX=\sqrt[]{(5^2)+(-7)^2} \\ WX=\sqrt[]{25+49} \\ WX=\sqrt[]{74} \end{gathered}[/tex]Now, continue with XY:
[tex]\begin{gathered} XY=\sqrt[]{(11-(-1))^2+(-5-(-3))^2} \\ XY=\sqrt[]{12^2+(-2)^2} \\ XY=\sqrt[]{148} \end{gathered}[/tex]And finally, WY:
[tex]\begin{gathered} WY=\sqrt[]{(11-4)^2+(-5-(-10))^2} \\ WY=\sqrt[]{7^2+5^2} \\ WY=\sqrt[]{74} \end{gathered}[/tex]As you can see, sides WY and WX are equal. So, the triangle has two equal sides and one different.
For this reason, the triangle is an isosceles triangle.
Find the product (-10) (-2)
Answers
Remember that in a multiplication between two negative numbers the result always will be positive
(-10)(-2)=20
The result is 20
Answer:
20
Step-by-step explanation:
the product just means to multiply, so you do:
-10 x -2 = 20
Which linear equation describes the line passing through point (10, 3) and has a y-intercept at (0, -1)?10y = -3x +y = -x +y=2- 1= 5*-y=31-x-13*-52
Answers
Answer: y = 2x/5 - 1
Explanation:
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
The given points are (0, -1) and (10, 3). thus,
x1 = 0, y1 = - 1
x2 = 10, y2 = 3
m = (3 - - 1)/(10 - 0) = (3 + 1)/10 = 4/10 = 2/5
By substituting m = 2/5 and c = - 1 into the slope intercept equation, the equation of the line is
y = 2x/5 - 1
Please explain how Pascals triangle works?
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Pascals triangle or Pascal's triangle is a special triangle that is named after Blaise Pascal, in this triangle, we start with 1 at the top, then 1s at both sides of the triangle until the end. The middle numbers are so filled that each number is the sum of the two numbers just above it.
Generally, we can use Pascals' triangle to find the coefficients of binomial expansion
For example, we want to expand
[tex](x\text{ + y\rparen}^2[/tex]Using Pascal's triangle, we can get the coefficients of the expansion:
[tex](x\text{ + y\rparen}^2\text{ = 1x}^2\text{ + 2xy + 1y}^2[/tex]Hong Tang's gross weekly salary is $615. His weekly federal withholding is $55. The Social Security tax is 6.2 percent of the first $90,000. The Medicare tax is 1.45 percent of gross pay. The state tax is 1.5 percent of gross pay. Each week he pays $22.40 for medical insurance. How much is deducted from Tang's weekly wages for state tax and Medicare tax combined?
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We have that the Medicare tax is 1.45% of gross pay, and the state tax is 1.5%. Then, if Hong Tang's gross weekly salary is $615, then::
[tex]\begin{gathered} (615)(0.0145)=8.92 \\ (615)(0.015)=9.22 \\ \Rightarrow8.92+9.22=18.14 \end{gathered}[/tex]therefore, from state tax and Medicare tax combined, Hong Tang gets deducted $18.14
Solve each system by substitution.y - 4x = 3 2x - 3y = 211. Rewrite the first equation in terms of . y=2. Substitute the value of into the second equation. 2x - 3 = 213. Solve for X .4. Substitute the value of in one of the original equations. Solve for y .5. Write your answer as an ordered pair (x,y) .Solution: ( , )
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We have to solve this system by substitution.
This method let us define a varaible in function of the other (or others, if they are more than two) and then replace it in the other equations by this relation.
The system is:
[tex]\begin{gathered} y-4x=3 \\ 2x-3y=21 \end{gathered}[/tex]1. From the first equation, we can easily define y in function as x:
[tex]\begin{gathered} y-4x=3 \\ y=4x+3 \end{gathered}[/tex]2. Now, we substitute y in the second equation:
[tex]\begin{gathered} 2x-3y=21 \\ 2x-3(4x+3)=21 \end{gathered}[/tex]3. We got an equation that is expressed only in function of x, so we can solve it as:
[tex]\begin{gathered} 2x-3(4x+3)=21 \\ 2x-3\cdot4x-3\cdot3=21 \\ 2x-12x-9=21 \\ -10x=21+9 \\ -10x=30 \\ x=\frac{30}{-10} \\ x=-3 \end{gathered}[/tex]4. If we replace x in the equation for y, we get:
[tex]\begin{gathered} y=4x+3 \\ y=4(-3)+3 \\ y=-12+3 \\ y=-9 \end{gathered}[/tex]5. Then, we can write the answer a s a pair (x,y) = (-3,-9)
What's the perimeter of rectangle DEFG, shown?
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The perimeter is the sum of the length of all the sides.
A pail of ice cream contains 5 quarts. Convert the volume to pints.
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ANSWER
[tex]10pints[/tex]EXPLANATION
Given That the pail of ice cream contains 5 quarts
Recall 1 quarts gives 2 pints
Hence, 5 quarts will give;
[tex]5\times2=10[/tex]Hey I got the the idea! But it looks like the answer doesn’t have the other number? Which kinda makes me think it if we even did this lol!
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The area of a right triangle can be calculated as half the product of each leg length.
So, if the legs measure 4 cm and 3 cm, we have:
[tex]\begin{gathered} A=\frac{4\cdot3}{2} \\ A=2\cdot3 \\ A=6\text{ cm}^2 \end{gathered}[/tex]Therefore the triangle area is 6 cm².
15. What is missing in the problem, 48 is ____ % of 120? A. base B. percentage C. rateD. time
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The following equation-definition will be consider to solve the problem:
[tex]Base*Rate=Part[/tex]Where the base in this case is 120.
The rate is the porcentage, which is the missing part in the problem.
And 48 is the part. Hence, the solution is:
The solution is C. rate
Kiara sets up a passcode on her tablet, which allows only four digit codes. She has heard that it’s more secure if a digit is repeated in the passcode. A spy sneaks at Kiara’s tablet and sees her fingerprints on the screen over three numbers. what is the probability the spy is able to unlock the tablet on his first try? express your answer as a fraction.
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Let:
A = Unlock the table on the first try
a = Number of Possible right digits
N = Total number of possible digits
the probability the spy is able to unlock the tablet on his first try is:
[tex]\begin{gathered} P(A)=\frac{a}{N} \\ P(A)=\frac{1}{10} \end{gathered}[/tex]The table shows the number of gallons of paint Mrs. Brown used to paint the of rooms in her house. Find the slope of the line
Answers
Answer:
The slope is [tex]\frac{3}{2}[/tex] or [tex]1.5[/tex]
Step-by-step explanation:
The slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
Now, in this case, when you get tables, you could choose two coordinates.
So, for instance, you chose the coordinates: (2,3) and (6,9)
Since we have the two coordinates, we now could solve for the slope.
-
Substituting and finding the slope:
1) [tex]m =\frac{9-3}{6-2} \\[/tex]
2) [tex]m = \frac{6}{4} = \frac{3}{2}[/tex]
3) [tex]m = \frac{3}{2}[/tex] or [tex]1.5[/tex]
what is the mean and the mode of the dot plot
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The mean of the data plot is approximately 12.2
Explanation:The data is: 6, 8, 8, 10, 11, 12, 12, 15, 15, 15, 16, 18
The mean of the given dot plot is:
[tex]\begin{gathered} \frac{6+2(8)+10+11+2(12)+3(15)+16+18}{12} \\ \\ =\frac{146}{12}=12.2 \end{gathered}[/tex]If AB has length 10 and BC has length 19, findlength of AC:measure of angle B in degrees:measure of angle C in degrees:Answer should be in degrees and not radians.
Answers
Given a right angle triangle ABC
As shown in the figure:
The hypotenuse = BC = 19
One of the legs = AB = 10
We will use the Pythagorean theorem to find the other leg:
[tex]\begin{gathered} AB^2+AC^2=BC^2 \\ 10^2+AC^2=19^2 \\ AC^2=19^2-10^2 \\ AC^2=361-100=261 \\ AC=\sqrt[]{261}=16.16 \end{gathered}[/tex]Now, we will find the measure of the angle B:
[tex]\begin{gathered} \cos B=\frac{adjacent}{hypotenuse}=\frac{10}{19} \\ B=\cos ^{-1}\frac{10}{19}\approx58.24 \end{gathered}[/tex]The sum of the angles of the triangle = 180
so, the measure of angle C will be =
[tex]\begin{gathered} 180-(\angle A+\angle B) \\ =180-(90+58.24) \\ =180-148.24 \\ =31.76 \end{gathered}[/tex]So, as a conclusion to the answer:
[tex]\begin{gathered} AC=16.16 \\ \angle B=58.24 \\ \angle C=31.76 \end{gathered}[/tex]I need so help with my math
Answers
We have to change the oz to lb. So we get that
[tex]\begin{gathered} 5oz=0.3125lb \\ 10oz=0.625lb \end{gathered}[/tex]so the problem goes as
[tex]9.3125-6.625=2.6875lb[/tex]and that is
[tex]2lb11oz[/tex]
1. A segment has a left end named P (0,14) and a midpoint named F (-1,-2). Find the
coordinates of x and y of the other end of the segment.
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( -2,-18 ) is the coordinate of the other endpoint of the segment.
What are the coordinates of the endpoint?
The midpoint formula is expressed as;
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
Given the data in the question;
Endpoint P (0,14)
x₁ = 0y₁ = 14Midpoint F (-1,-2)
x = -1y = -2Endpoint 2
x₂ = ?y₂ = ?To determine the other endpoint, plug the given points into the midpoint formula above and solve for x₂ and y₂.
(x,y) = ( (x₁+x₂)/2, (y₁+y₂)/2 )
(-1,-2) = ( (0 + x₂ )/2, ( 14 +y₂ )/2 )
(-1,-2) = ( (0 + x₂ )/2, ( 14 +y₂ )/2 )
First we solve for x₂.
-1 = (0 + x₂ )/2
-1 × 2 = 0 + x₂
-2 = x₂
x₂ = -2
Next, solve for y₂.
-2 = ( 14 + y₂ )/2
-2 × 2 = ( 14 + y₂ )
-4 = 14 + y₂
y₂ = -4 - 14
y₂ = -18
Therefore, the coordinates of the endpoint are ( -2,-18 ).
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Mr. Emmer gave a test in his Chemistry class. The scores were normally distributed with a mean of 82 and a standard deviation of 4. A student is randomly chosen. What is the probability that the student scores a 70 or below?
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The probability that a randomly chosen student scores 70 or below is 0.0013
Firstly, we want to calculate the z-score
We have this as;
[tex]\begin{gathered} z-\text{score = }\frac{x-\mu}{\sigma} \\ \text{where x = 70} \\ \mu\text{ = mean = 82} \\ \sigma\text{ = standard deviation = 4} \\ z-\text{score = }\frac{70-82}{4}\text{ = -3} \end{gathered}[/tex]Using this z-score, we proceed to calculate the probability as follows;
[tex]P\text{ (X }\leq-3)[/tex]We use the standard normal distribution table for this
As we can see, this z-score value falls within 3 standard deviation from the mean
According to the empirical rule, the probability value here is 0.0013
You hang two strands of decorative lights.
a strand of red and blue decorative lights a strand of yellow and green decorative lights
Strand 1: changes color every 16 seconds Strand 2: changes color every 28 seconds
Both strands just changed color. After how many seconds will the strands change color at the same time again?
The strands will change color at the same time again after
seconds.
Answers
Both the decorative light strands will change change the colors at the same time again after 448 seconds
In the above question, it is given that,
Two strands of decorative lights, red and blue is one strand and green and yellow is another are hanged
Strand one changes colors in = 16 seconds
Strand two changes colors in = 28 seconds
We need to find, after how many seconds will the strands change color at the same time again
To find this, we will take the LCM(Lowest Common Multiple) of both strands time
Factors of 16 = 2 x 2 x 2 x 2
Factors of 28 = 2 x 2 x 7
LCM( 16 and 28) = 2 x 2 x 2 x 2 x 2 x 2 x 7 = 448
Therefore, It can be concluded that, both the decorative light strands will change change the colors at the same time again after 448 seconds
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F=9/5C + 32 solve for C
Answers
To solve for C let us do these steps
1. Put the term of C on one side and the other terms on the other side
Subtract 32 from both sides to move the term 32 to the other side
[tex]\begin{gathered} F-32=\frac{9}{5}C+32-32 \\ F-32=\frac{9}{5}C \end{gathered}[/tex]2. Make the coefficient of C = 1
Divide both sides by 9/5
[tex]\begin{gathered} \frac{F-32}{\frac{9}{5}}=\frac{\frac{9}{5}C}{\frac{9}{5}} \\ \frac{5}{9}(F-32)=C \\ C=\frac{5}{9}(F-32) \end{gathered}[/tex]You can Multiply the bracket (F- 32) by 5/9
[tex]C=\frac{5}{9}F-\frac{160}{9}[/tex]