Answers
The length of arc AB is 3π given that radius of the circle is 27 units and the angle made by the arc AB at the center of the circle is 20°. This can be obtained using the formula to find arc length.
Find the length of the arc AB:Formula used for finding arc length:
If the angle made by the arc at the center of the circle is in degrees, the formula to find the length of the arc is,⇒ L = 2 π r (θ/360°)
where r is the radius of the circle and θ is the angle made by the arc at the center of the circle.
If the angle made by the arc at the center of the circle is in radians, the formula to find the length of the arc is,⇒ L = r × θ
where r is the radius of the circle and θ is the angle made by the arc at the center of the circle.
Here in the question it is given that,
r = 27 units
θ = 20°
Since the angle made by the arc at the center of the circle is in degrees, the formula to find the length of the arc is,
⇒ L = 2 π r (θ/360°)
L = 2 π (27) (20°/360°)
L = π (27) (20°/180°)
⇒ L = 3 π
Hence the length of arc AB is 3 π given that radius of the circle is 27 units and the angle made by the arc AB at the center of the circle is 20°.
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Related Questions
Estimate the product of 0. 235 and 13. 467 to the nearest hundredth.
Answers
Answer:
3.16
Step-by-step explanation:
An estimate is usually made to 1 or 2 significant digits. Here, we want an estimate accurate to hundredths, which will be 3 significant digits.
EstimateWe can round the numbers to some reasonable values, then look at the effect of the rounding error.
0.235 × 13.467 = (0.25 -0.015) × (13.5 -0.033)
= 0.25(13.5) -0.25(0.033) -0.015(13.5) +0.015(0.033)
= 3.375 -0.00825 -0.2025 + (something small)
≈ 3.375 -0.008 -0.203 = 3.375 -0.211 = 3.164
0.235 × 13.467 ≈ 3.16
Mental mathNote that the values we have can make use of mental math methods.
0.25 = 1/4 = (1/2)(1/2)
0.015 = 0.01(1 +1/2)
That is, dividing numbers by 2 mentally is usually not terribly difficult. (Here, it is made more difficult by the odd digits involved.)
0.25 × 13.5 = (1/2)(13.5/2) = 1/2(6.75) = 3.375
0.015 × 13.5 = 0.135 +0.135/2 = 0.135 +0.0675 = 0.2025
or, recognizing that 1.35 = 1.5 -.15, ...
0.015 × 13.5 = (0.01)(1.5) × (10)(1.5-.15) = 1.5²×(.1 -.01) = .225 -.0225
__
Additional comment
A calculator gives the actual product as 3.164745, so our estimate is accurate to hundredths.
Find the surface area of the cylinder and round to the nearest tenth. (Use the π button on your calculator)
Answers
The surface area of the cylinder with the given height and radius is 835.2 square inches
How to determine the surface area?The given parameters are
Height, h = 12 inches; this is represented by the distance between the curved surfaces of the cylinderRadius, r = 7 inches; this is represented by the distance between the center of the circle to its circumferenceThe surface area is then calculated using the following formula
A = 2πr² + 2πrh
Substitute the given values in the above equation
So, we have:
A = 2 * 3.14 * 7^2 + 2 * 3.14 * 7 * 12
Evaluate the exponents
A = 2 * 3.14 * 49 + 2 * 3.14 * 7 * 12
Evaluate the products
A = 307.72 + 527.52
Evaluate the sum
A = 835.2
Hence, the surface area of the cylinder with the given height and radius is 835.2 square inches
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Use the diagram to complete the following tasks.
Given: S' is the midpoint of QT.
Finish the following statement: AQRSA_
Identify the congruent Zs.
Justify your answer.
R
S
Answers
This exercise is about a proof in Euclidian geometry. See the explanation below.
What is Euclidian Geometry?The study of solid and flat objects using the axioms and theorems developed by the Greek mathematician Euclid is known as Euclidean geometry (c. 300 bce).
What is the statement that completes the above proof?Given that S is the midpoint of [tex]\overline{QT}[/tex]:
Hence QS = TS ......................1
It is right to indicate that
PQ = TV ........................2
And ∠RSQ is vertically opposite to ∠TSV
Hence
∠RSQ = ∠TSV.........................3
Given 1, 2, and 3,
Δ QRS ≅ ΔVTS
Therefore,
Δ QRS ≅ ΔVTS
and ∠ RSQ can be termed to be congruent to ∠TSV.
What does it mean for an angel to be congruent?It is to be noted that the measure of an angle is the same for congruent angles. An ordinary pentagon, for instance, has five sides and five angles, each of which is 108 degrees.
The angles of a regular polygon will always be congruent, regardless of its size or scale.
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At 3:00 PM a man 138 cm tall casts a shadow 149 cm long. At the same time, a tall building nearby casts a shadow 163 m long. How tall is the building?
Answers
The building is 151 meters tall
How to determine the height of the building?From the question, we have the following parameters about the building and the man
Man's height = 138 cm
Man's shadow = 149 cm
Building's shadow = 163 m
Based on the above parameters, we have the following equivalent ratio:
Ratio = Height : Shadow
So, we have:
Man's height : Man's shadow = Building's height : Building's shadow
Substitute the known values in the above equation
138 cm : 149 cm = Building's height : 163 m
Remove the units
138 : 149 = Building's height : 163
Express as fraction
138 /149 = Building's height/163
Multiply both sides by 163
Building's height = 163 * 138 /149
Evaluate the product
Building's height = 151 m
Hence, the building is 151 meters tall
So, the complete parameters are:
Man's height = 138 cm
Man's shadow = 149 cm
Building's shadow = 163 m
Building's height = 151 m
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find the area of the shaded shape pls quickly
Answers
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
Area of shaded region is equal to :
Area of rectangle - Area of two triangles ~
1. Area of rectangle :
[tex]\qquad \sf \dashrightarrow \: length \times width[/tex]
[tex]\qquad \sf \dashrightarrow \: 20 \times 15[/tex]
[tex]\qquad \sf \dashrightarrow \: 300 \: \: cm {}^{2} [/tex]
2. Area of first triangle :
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{2} \times (base) \times (height)[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{2} \times (20 - 18) \times (15)[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{2} \times (2) \times (15)[/tex]
[tex]\qquad \sf \dashrightarrow \: 15 \: \: cm {}^{2} [/tex]
3. Area of second triangle :
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{2} \times (base) \times (height)[/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{2} \times (6) \times(20)[/tex]
[tex]\qquad \sf \dashrightarrow \: 3 \times 20[/tex]
[tex]\qquad \sf \dashrightarrow \: 60 \: \: cm {}^{2} [/tex]
Area of shaded region is :
[tex]\qquad \sf \dashrightarrow \: 300 - (15 + 60)[/tex]
[tex]\qquad \sf \dashrightarrow \: 300 - 75[/tex]
[tex]\qquad \sf \dashrightarrow \: 225 \: \: cm {}^{2} [/tex]
If the vertex of a parabola is at the point (-2, 5), then the equation for the axis of symmetry for the parabola is x = -2. True or false?
Answers
Answer:
true
Step-by-step explanation:
thats really it i believe its true
Find the value of Theta in these diagrams (a and b)
Answers
a. θ = 36. 9°
b. θ = 114. 2°
How to determine the value of theta
a. We use the cosine identity
cos θ = adjacent/hypotenuse
Adjacent = 4cm
Hypotenuse = 5cm
cos θ = 4/ 5
cos θ = 0. 8
Now, we have the inverse of the cosine value
θ = cos^-1 (0. 8)
θ = 36. 9°
b. We use the tangent identity
tan a = opposite / adjacent
tan a = 3. 8/1. 7
tan a = 2. 23
a = tan^-1 ( 2. 23)
a = 65. 8
We have;
a + θ = 180 °; angles on a straight line
θ = 180 - 65. 9
θ = 114. 2°
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. [Multiples / Factors / Primes] *
What is the highest
common factor (HCF)
of 24 and 45?
Answers
Help!!! Brainliest to 1 or 2 answer!!
Answers
Answer:
35-17=3y
Step-by-step explanation:
3y+17=35
-17 -17
3y=35-17
Find a so that line CD will have the given slope: C(3, -3), D(-3,a); m= -4/3
Answers
Work Shown:
m = (y2 - y1)/(x2 - x1)
-4/3 = (a - (-3))/(-3 - 3)
-4/3 = (a+3)/(-6)
-4*(-6) = 3(a+3)
24 = 3a+9
3a+9 = 24
3a = 24-9
3a = 15
a = 15/3
a = 5
Given the function defined in the table below, find the average rate of change,
in simplest form, of the function over the interval 12 ≤ ≤ 36.
0
12
36
48
60
37
34
31
28
25
22
Answers
The average rate of change of [tex]f(x)[/tex] on [tex]12\le x\le36[/tex] is the difference quotient
[tex]\dfrac{f(36) - f(12)}{36 - 12} = \dfrac{28 - 34}{24} = \boxed{-\dfrac14}[/tex]
x - 2y = 3
5x + 3y = 2
The lines whose equations are shown intersect at which point?
Answers
The point of intersection of the two lines is at (1,-1)
System of equationThe given system of expression is shown below
x - 2y = 3
5x + 3y = 2
The solution to the system of equation is the point of intersection
From equation 1
x = 3 + 2y
Substitute into 2
5(3+2y) + 3y = 2
15 +10y + 3y = 2
13y = -13
y = -1
Substitute y = -1 into 3
x = 3 + 2y
x = 3+(-2)
x = 1
Hence the point of intersection of the two lines is at (1,-1)
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Deion misses 4% of the free throws he attempts in a seaon. how many total free throws did he attempt if he missed 17
Answers
He has thrown 425 free throws if he missed 17
How to determine the total number of free throws?The given parameters are:
Proportion of free throw missed, p = 4%
Number of free throw missed, n = 17
Let the total number of throws be N.
So we have
n = p * N
Substitute the known values in the above equation
17 = 4% * N
Divide both sides by 4%
N = 425
Hence, he has thrown 425 free throws if he missed 17
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For a right triangle ABC, you are told that cos A = x and sin A = y. Which option below gives an expression that is
equivalent to tan A?
OX
Answers
Equivalent to tan A =[tex]\frac{y}{x}[/tex]
What is meant by the right triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The sum of the other two angles is 90 degrees. The perpendicular and the triangle's base are the sides that make up the right angle. The third side is the longest of the three sides, known as the hypotenuse.A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe the sides of right triangles, we utilize specific terminology.A right triangle is a triangle in which one of the angles is at a right angle or two of the sides are perpendicular, or more formally, an orthogonal triangle, formerly known as a rectangled triangle.Equivalent to tan A:
A right triangle ABC so that m∠C = 90°
The lengths are:
Side a is opposite ∠A,
Side b is opposite ∠B,
Side c (the hypotenuse) is opposite ∠C
Because cos A = x, therefore
[tex]x =\frac{b}{c}[/tex] => [tex]b = cx[/tex] (1)
Because sin A = y, therefore
[tex]y =\frac{a}{c}[/tex] => [tex]a = cy[/tex] (2)
By definition,
tan A = a/b
[tex]=\frac{cy}{cx}[/tex]
[tex]=\frac{y}{x}[/tex]
Equivalent to tan A =[tex]\frac{y}{x}[/tex]
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Darren’s car has a rectangular gas tank whose dimensions are 4 meters by 3 meter by 3 meters. If Darren was only able to drive for 45 hours with a full tank, what is the rate of gas consumption of his car?
Answers
Step-by-step explanation:
that is a huge gas tank. that car is practically a tank.
the volume of the gas tank is
4×3×3 = 36 m³
I assume you use liters for liquid mass.
remember
1 meter (m) = 100 centimeter (cm)
10 cm = 1/10 m = 1 decimeter (dm)
1 liter = 10×10×10 cm³ = 1000cm³ = 1 dm³
1 m³ = 10×10×10 dm³ = 1000 dm³ = 1000 liters
so, his gas tank contained 36,000 liters.
he used the 36,000 liters in 45 hours.
his corresponding rate of gas consumption was
36,000 liters / 45 hours = 800 liters / hour
The data in the table can be entered into a calculator to determine a linear equation of best fit where x represents the number of years with a company and y represents an employee’s salary in dollars.
Answers
Based on the data given, the conclusion that can be drawn from the correlation coefficient associated with the linear equation is C. There's a weak negative correlation between the variables.
How to illustrate the information?From the information given, it can be seen that the value of y is increasing with the increase in the value of x.
This implies that the correlation is positive. Also, the change in the values of y with x are scattered a lot.
Therefore, the conclusion that can be drawn from the correlation coefficient associated with the linear equation is that there's a weak negative correlation between the variables
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Evaluate the expression using a calculator:
Answers
The value of the expression is 0.0265. Using exponents and power rules, the required value is calculated.
What are the exponent and power rules?The important exponent and power rules are:
a⁻ⁿ = 1/aⁿ; negative exponent(ab)ⁿ = aⁿ × bⁿ; power of a product ruleaⁿ × aˣ = aⁿ⁺ˣ; multiplication ruleaⁿ/aˣ = aⁿ⁻ˣ; division rule[tex]a^{\frac{x}{y} } = \sqrt[y]{a^x}[/tex]; fractional exponentCalculation:The given expression is [tex]126^{-3/4}[/tex]
Using calculator: [tex]126^{-3/4}[/tex] = 0.0265
Applying the exponent rule for evaluating the given expression:
[tex]126^{-3/4}[/tex]
Applying the negative power rule;
I.e., a⁻ⁿ = 1/aⁿ
⇒ [tex]126^{-3/4}=\frac{1}{126^{3/4}}[/tex]
Applying fractional exponent rule;
I.e., [tex]a^{\frac{x}{y} } = \sqrt[y]{a^x}[/tex]
⇒ [tex]\frac{1}{126^{3/4}}=\frac{1}{\sqrt[4]{126^3} }[/tex]
⇒ 1/[tex]\sqrt[4]{2000376}[/tex]
⇒ 1/37.6077
⇒ 0.0265
Therefore, the value of the given expression is 0.0265.
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What is the multiplicity of f(x) = -2x3(x + 2)2?
Answers
To check whether the given quadratic polynomial is reducible or irreducible, we need to calculate the discriminant
Calculate the discriminant for the equation, −2x
2
−2x−1=0
D=b
2
−4ac=(−2)
2
−4(−2)(−1)=−4<0
Quadratic equation is irreducible if D<0
∴ The quadratic polynomial is irreducible.
Correct option is C
I need to find what AE is
Answers
Answer:
18
Step-by-step explanation:
The arrows on lines AB and CD indicate that these 2 shapes are similar and these 2 lines are corresponding so :
Linear scale factor :
12 ÷ 10 = 1.2 or 6/5
Let's use the fraction form
Using the linear scale factor we can make an equation to solve for x :
2x+4 = 6/5(x+8)
Expand the brackets :
2x+4 = 6/5x + 9.6
Subtract 4 from both sides :
2x = 6/5x + 5.6
Subtract 6/5x from both sides :
4/5x = 5.6
Divide both sides by 4/5 :
x = 7
Now substitute this value into the expression for the length of AE :
AE = 2(7) + 4
AE = 14 + 4
AE = 18
Hope this helped and have a good day
Answer:
116 units
Step-by-step explanation:
AE + ED = 180 because they make a straight angle and a straight angle is 180 degrees or half of a circle 360/2.
AE = 2x + 4 and ED = x +8 added together they equal 180
2x + 4 + x + 8 = 180 Combine the like terms
3x + 12 = 180 Subtract 12 from both sides of the equation
3x = 168 Divide both sides by 3
x = 56
Now that we know that x is 56 we can plug that in for AE to find its length
2x + 4
2(56) + 4
112 + 4
116
5x + 1 over 2 y2
What is the value of the expression above when x = 3 and y = 2?
Answers
(5*3 + 1) / 2*2^2
(15+1) / 2*4
16/8
2
PLS HELP>>>>solving functions
Answers
Answer:
The first option:
[tex]x^2-5x+9[/tex]
Step-by-step explanation:
Trust me I am right.
If you need work please ask!
Have a nice day!
Stuck on this problem. Help is needed please!
Answers
Step-by-step explanation:
A.
the height, the 17cm leg and half of the baseline (16/2 = 8cm) create a right-angled triangle.
so, Pythagoras applies.
c² = a² + b²
c being the Hypotenuse (side opposite of the 90° angle).
so, we get
17² = height² + 8²
289 = height² + 64
225 = height²
height = sqrt(225) = 15cm
B.
the answer to this is the surface area of the whole box.
it has 5 sides :
bottom : 20×16 rectangle = 320 cm²
left and right : 20×17 rectangles = 340×2 = 680 cm²
front and back : 16×15/2 triangles = 120×2 = 240 cm²
in total that is
320 + 680 + 240 = 1,240 cm² of cardboard
3. A square garden plot has an area of 24 ft^2. Find the length of each side in simplest radical form. Calculate the length of each side to the nearest tenth of a foot
Answers
The length of each side of the square garden plot in simplest radical form and to the nearest tenth of a foot is 2√6 and 4.9 ft
Area of a squareArea of square = Length ²
Area of the square garden plot = 24 ft²Area of square = Length ²
24 = length ²
find the square root of both sides√24 = √length²
√24 = length
length = 4.898979485566356196394568149411782783
Approximately,
length = 4.9 ft
In radical form
length = √24
= 2√6
Therefore, the length of each side of the square garden plot in simplest radical form and to the nearest tenth of a foot is 2√6 and 4.9 ft
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1) A 20-foot ladder is placed against a building. If the top of the ladder will lean against the building 4sqrt(7) - f feet high, how far away from the base of the building is the bottom of the ladder located? Include a sketch that shows all known information and clearly shows what you need to findShow all work and give the exact answer
Answers
Answer:
12√2.
Step-by-step explanation:
You can do this by the Pythagoras theorem:
20^2 = x^2 + (4sqrt7)^2 where x is the distance required.
x^2 = 20^2 - (4sqrt7)^2
= 400 - 112
= 288
x = √288
= √144 *√2
= 12√2.
expand and simplify -2(x + 4x^2) + 3(x^2 + 2x)
Answers
......................
Write the following expression using exponents -3x7x7x7x7x7x7
Answers
Solution -:
[tex] \bold{ \underline{ \underline{Given}}}[/tex]
-3x7x7x7x7x7x7
[tex]\bold{\underline {\underline{lets \: begin}}}[/tex]
We have,,
[tex] -3 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \\ = - 3¹ \times {7}^{6} [/tex]
exponent and shortcut to express a multiplication of number by itself several times explain us how many time we should multiply the number by itself this process of using exponent is called raising to a power where the exponent is the power.Law of exponent -: a ⁰ = 1 a ^ m × a ^ n (a^m)^na^m × b^ mAs like example→ 2⁴
here 2 is base and 4 is power , index or exponent. and 2⁴ is known as Exponential form.
there are 6 girls and 8 boys in Mr. Stevenson's class the ratio of girls to boys in the class can be expressed as the simplified ratio ?/4 what is the missing number ?
Answers
Answer: 3
Step-by-step explanation:
The missing number in the simplified ratio ?/4 is 3.
Here, we have to find the missing number in the simplified ratio ?/4, we need to determine the ratio of girls to boys in Mr. Stevenson's class.
Given that there are 6 girls and 8 boys in the class, the ratio of girls to boys can be expressed as:
Number of girls : Number of boys = 6 : 8
To simplify the ratio, we can divide both the number of girls and the number of boys by their greatest common divisor (GCD).
In this case, the GCD of 6 and 8 is 2.
Dividing both 6 and 8 by 2, we get:
Number of girls : Number of boys = 6/2 : 8/2 = 3 : 4
So, the simplified ratio of girls to boys is 3/4.
Therefore, the missing number in the simplified ratio ?/4 is 3.
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If BD = 16 yd and the area of rhombus ABCD is 72 yd^2, what is AC?
Answers
Formula for finding area of rhombus: [tex]\frac{d1 * d2}{2}[/tex]
d₁ = 16 yd
Area = 72 yd²
Rhombus Area =>
[tex]\frac{16 * d2}{2} = 72[/tex]
16*d₂ = 144
d₂ = 9
AC = 9 yd
Hope it helps!
Divide. Write the quotient in lowest terms.
4 2/3 / 7
Answers
The quotient in lowest term exists 2/3.
What is an improper fraction?An improper fraction exists as a fraction whose numerator exists equivalent to, larger than, or of equivalent or higher degree than the denominator.
Given the quotient: [tex]$4\frac{2}{3} \div 7[/tex]
Write [tex]$\frac{2}{3}[/tex] in improper fraction
[tex]$4\frac{2}{3}= \frac{14}{3}[/tex]
Dividing throughout by 7 on both sides of the equation, we get
[tex]$4\frac{2}{3} \div 7 = \frac{14}{3}\div 7[/tex]
Change the division sign to multiplication by taking the reciprocal of 7
[tex]$\frac{14}{3}\div 7 = \frac{14}{3} \times \frac{1}{7}[/tex]
Simplifying the above equation, we get
[tex]$\frac{14}{3}\div 7 = \frac{2}{3}[/tex]
Therefore, the quotient in lowest term exists 2/3.
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Solve -6x + 3 ≥ 21.
OA. x2 3
OB. x≤-3
OC. x≥-3
OD. x≤3
Answers
Answer:
B
Step-by-step explanation:
- 6x + 3 ≥ 21 ( subtract 3 from both sides )
- 6x ≥ 18
divide both sides by - 6, reversing the symbol as a result of dividing by a negative quantity.
x ≤ - 3
