The radius of the quadrant whose perimeter is 52cm is 14.56cm.
A quadrant is 1/4th of a circle, consisting of two radii, perpendicular to each other.
So, the perimeter of a quadrant consists of two radii and an arc, which is 1/4th the perimeter of a circle.
Therefore, the perimeter of the quadrant = 2r + (1/4)*(2πr) = 2r + (πr/2).
Now, we are given the perimeter of the quadrant = 52cm and are asked to find its radius.
We suppose the radius to be r cm.
Therefore, we can say that:
52 = 2r + (πr/2).
or, 52 = (4r + πr)/2
or, 52*2 = r(4 + π)
or, r = 104/(4 + π) = 14.56.
Therefore, the radius of the quadrant whose perimeter is 52cm is 14.56cm.
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It is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring. True or False
It is a true statement that it is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring.
What is a cubic equation?A cubic equation is one in which the highest power of the variable present is 3. A quartic equation is one in which the highest power is 4. When we have a cubic or a quartic equation, the usual approach is to reduce the equation to a quadratic equation and solve by factorization.
Thus, it is possible to solve all cubic and quartic equations using an algebraic strategy involving factoring.
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A construction company is building a drainage ditch that is shaped like a "V". The ditch will be 10 feet wide at ground level and 5 feet deep at its lowest point. The depth of the ditch increases at a rate of 1 vertical foot for every 1 horizontal foot out from the lowest point at the center of the ditch .If x is the horizontal distance from the left edge of the ditch, in feet, determine which absolve value function models the ditch's vertical depth below ground level, in feet.
A. f(x) = |x + 5| − 5
B. f(x) = -|x − 5| − 5
C. f(x) = -|x − 5| + 5
D. f(x) = |x − 5| − 5
The absolve value function that models the ditch's vertical depth below ground level, is B. f(x) = -|x − 5| − 5
How to illustrate the function?From the information given, it was stated that the ditch will be 5 feet deep at its lowest point. Also, x is the horizontal distance from the left edge of the ditch.
Now, the absolve value function that models the ditch's vertical depth below ground level will start with a (-) sign since it's below ground level. The appropriate function will be f(x) = = -|x − 5| − 5
In conclusion, the correct option is B.
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Evaluate the expression [tex]\sqrt[5]{3125{e}^{\frac{11 \pi }{2} i}}[/tex], leaving your answer in polar form.
[tex]\sqrt[5]{3125e^{\frac{11\pi}{2}i}}\\=\\\sqrt[5]{3125}\sqrt[5]{e^{\frac{11\pi}{2}}i}\\\\=5e^{\frac{11\pi}{10}i}\\\\\boxed{5\left(\cos \left(\frac{11\pi}{10} \right)+i \sin \left(\frac{11\pi}{10} \right) \right)}[/tex]
Divide 10000 among Irfan and asim in the ratio 2:3
Step-by-step explanation:
ratio of ifran and Asim= I:A
2:3
rule of equation= TOTAL ratio=total amount
=(addition of the two ratios which are 2 and 3=5) and 1000
=5=1000
ratio of ifran(2)=? cross multiplication
=2×1000÷5
=400
=5=1000
ratio of Asim(3)=? cross multiplication
=3×1000÷5
=600
Answer:
Step-by-step explanation:
Irfan and Asim's ratio is 2:3, which means Irfan gets 2 parts while Asim gets 3. There are 5 parts in total, and this equals 10000. Let parts be p. [tex]5p=10000\\\\p=2000[/tex]
This means Irfan gets 2p = 4000 and Asim gets 3p = 6000.
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Can someone help me
The value of (g . f) (0) is -2 and the value of (g . f) (1) is 1.
What is a Function?A function is a law that relates a dependent and an independent variable.
The value of the two functions is given
The value of (g . f) (0)
= g(f(0))
From the table of f(x) at x = 0
= g(1)
From the table of g(x) at x =1
=-2
The value of (g . f) (1)
= g(f(1))
From the table of f(x) at x = 1
= g(0)
From the table of g(x) at x =0
=1
Therefore, the value of (g . f) (0) is -2 and the value of (g . f) (1) is 1.
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A discount store had monthly sales of $86,600 and spent 14% of it on promotions. how much was spent on promotion?
The amount spent on promotion by the store on monthly sales of $86,600, when they are spending 14 percent on promotion is $12,124.
The percent signifies the hundredth part of the whole.
When informed that the promotion is 14 percent of the monthly sales of $86,600.
Therefore, to calculate the total amount spent on promotion, we calculate 14 percent of 86600.
Therefore, the total amount on promotion = 14% of $86,600 = $ (14/100 * 86,000) = $ (14*866) = $12,124.
Therefore, the amount spent on promotion by the store on monthly sales of $86,600, when they are spending 14 percent on promotion is $12,124.
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Which proportion is not true?
A. 2/3 = 4/6
B. 5/8 = 25/40
C. 9/10 = 81/90
D. 4/7 = 24/28
Answer:
D. 4/7 = 24/28
Step-by-step explanation:
In any proportion, the value of the numerator and denominator does not change if is multiplied by the same value.
We know that 4*6 = 24, so the numerator holds true. However, 7*6 is 42. In the same vein, 7*4 is 28, so the denominator would hold true. However, 4*4 is 16. Thus, the proportion has not been multiplied by the same value.
In order to get 24/28 from 4/7, you would have to multiply by 6/4, which is not the same value.
enter your answer in scientific notation
Answer:
[tex]1.7x10^{4}[/tex]
Step-by-step explanation:
To divide the scientific notation, divide 5.1 to 3 then subtract the exponents of your ten - following the quotient rule.
5.1/3 = 1.7, then 9-5 = 4
final answer is [tex]1.7x10^{4}[/tex]
Adele is 5 years older than Timothy. In 3 years, Timothy will be 2/3 of Adele’s age. What is Adele’s age.
Answer:
12
Step-by-step explanation:
Let a = Adele's current age
Let t = Timothy's current age
Adele is 5 years older than Timothy:
a = t + 5 {equation 1}
In 3 years Timothy will be 2/3 of Adele's age:
(2/3)(a + 3) = t + 3 {equation 2}
Since we are looking for Adele's age, let's rearrange equation 1 to:
t = a - 5
Substitute that into equation 2 and solve for a.
(2/3)(a+3) = a - 5 + 3
(2/3)(a + 3) = a - 2
Multiply through by 3 to clear the fraction
2(a+3) = 3a - 6
2a + 6 = 3a - 6
Add 6 to both sides, subtract 2a from both sides
12 = a
Adele is 12 years old
This means Timothy is 7 years old.
Check equation 2 to verify:
(2/3)(a + 3) = t + 3
(2/3)(12+3) = 7 + 3
(2/3)(15) = 10
10 = 10
Answer is correct
I need help on these 2 questions please ASAP
Step-by-step explanation:
Q9
a) :
First, find the common difference for the sequence. add the first term to the second term
3+3= 6
add second term to the third term
3+6=9
add third term to the fourth term
6+9=15
b) 15 +24= 39
24+39=63
39+63= 102
Q10
a) 2 , 10 , 8
b) find the common difference for the sequence. Subtract the first term from the second term.
10-2= 8
Subtract the second term from the third term
8-10= -2
c) 10
An icicle with a diameter of 15.5 centimeters at the top, tapers down in the shape of a cone with a length of
350 centimeters.
a. Ice has a density of 0.93 grams per cubic centimeter. Find the mass of the icicle to the nearest gram.
b. On a warm day, the icicle begins to melt. In the first hour, its diameter decreases about 0.7 centimeter in the first hour
and its length decreases by 15 centimeters. How many cubic centimeters of ice melt in the first hour?
c. The icicle's dimensions continue to decrease at a constant rate. A bucket with a diameter of 25 centimeters and a
height of 30 centimeters is placed to catch the water as it drips from the melting icicle. Will the bucket overflow after
the icicle has been melting for 5 hours? Explain. HELP PLEASE
Answer:
Step-by-step explanation:
Note: I will leave the answers as fraction and in terms of pi unless the question states rounding conditions to ensure maximum precision.
From the question, we can tell it is a inversed-cone (upside down)
Volume of Cone = [tex]\pi r^{2} \frac{h}{3}[/tex]
a) Given Diameter , d = 15.5cm and Length , h = 350cm,
we first find the radius.
[tex]r = \frac{d}{2} \\=\frac{15.5}{2} \\=7.75cm[/tex]
We will now find the volume of the cone.
Volume of cone [tex]\pi (7.75)^{2} \frac{350}{3} \\= \frac{168175\pi }{24}[/tex]
We know the density of ice is 0.93 grams per [tex]1cm^{3}[/tex]
[tex]1cm^{3} =0.93g\\\frac{168175\pi }{24} cm^{3} =0.93(\frac{168175\pi }{24} )\\= 20473 g[/tex](Nearest Gram)
b) After 1 hour, we know that the new radius = 7.75cm - 0.35cm = 7.4cm
and the new length, h = 350cm - 15cm = 335cm
Now we will find the volume of this newly-shaped cone.
Volume of cone = [tex]\pi (7.4)^{2} \frac{335}{3} \\= \frac{91723\pi }{15} cm^{3}[/tex]
Volume of cone being melted = New Volume - Original volume
= [tex]\frac{168175\pi }{24} -\frac{91723\pi }{15} \\= \frac{35697\pi }{40} cm^{3}[/tex]
c) Lets take the bucket as a round cylinder.
Given radius of bucket, r = 12.5cm (Half of Diameter) and h , height = 30cm.
Volume of cylinder = [tex]\pi r^{2} h\\=\pi (12.5)^{2} (30)\\=\frac{9375\pi }{2} cm^{3}[/tex]
To overflow the bucket, the volume of ice melted must be more than the bucket volume.
Volume of ice melted after 5 hours = [tex]5(\frac{35697\pi }{40} )\\=\frac{35697\pi }{8} cm^{3}[/tex]
See, from here of course you are unable to tell whether the bucket will overflow as all are in fractions, but fret not, we can just find the difference.
Volume of bucket - Volume of ice melted after 5 hours
= [tex]\frac{9375\pi }{2} -\frac{35697\pi }{8 } \\=\frac{1803\pi }{8}cm^{3}[/tex]
from we can see the bucket can still hold more melted ice even after 5 hours therefore it will not overflow.
Rodrick is visiting the local museum exhibit and has a maximum of $30 dollars to spend. The entry ticket cost $7. He can spend g dollars. Write an inequality that can find g and the amount of money Rodrick can spend at the gift shop.
Entry ticket = $7
Gift shop money = $g
Maximum to spend = $30
Inequality => 7+g ≤ 30
Hope it helps!
Perform the indicated operation and write the answer in the form a + bi.
(3 +81) (4-3i)
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: 36 + 23 i[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: (3 + 8i)(4 - 3i)[/tex]
[tex]\qquad \tt \rightarrow \: (3 \sdot 4)+ (3 \sdot - 3i) + (8i \sdot4) + (8i \sdot - 3i)[/tex]
[tex]\qquad \tt \rightarrow \: 12 - 9i + 32i - (24 {i}^{2} )[/tex]
[tex]\qquad \tt \rightarrow \: 12 + 23i -( 24 \sdot - 1)[/tex]
[tex]\qquad \tt \rightarrow \: 12 + 23i + 24[/tex]
[tex]\qquad \tt \rightarrow \: 36 + 23i[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
[tex]\Large\maltese\underline{\textsf{A. What is Asked \space}}[/tex]
Perform the indicated operation and write the answer with the form a+bi.
2 numbers given, one of which is complex
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!\space\space}}[/tex]
Multiply these two numbers, just like you always multiply binomials.
[tex]\bf{(3+8i)(4-3i)}[/tex] | multiply
[tex]\bf{3\times4+3\times(-3i)+8i\times4+8i\times(-3i)}[/tex] | simplify
[tex]\bf{12-9i+32i-24i^2}[/tex] | this can be simplified A LOT
[tex]\bf{12+23i-24i^2}[/tex] | as strange as it may seem, this can be simplified even more, because isn't i^2 the same as -1?
[tex]\bf{12+23i-24\times(-1)}=12+23i+24}[/tex] | add 12 and 24
[tex]\bf{36+23i}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=36+23i}[/tex]. The answer is written in the form a+bi, as requested.
[tex]\boxed{\bf{aesthetic\not101}}[/tex]
Check all of the functions that are odd. f(x)=x3-x2 f(x)=x5-3x3 2x f(x) = 4x 9 f (x) = startfraction 1 over x endfraction
The odd functions are f(x)=x⁵-3x³+2x and f(x)=1÷x.
Given functions are f(x)=x³-x², f(x)=x⁵-3x³+2x, f(x)=4x+9 and f(x)=1÷x.
A function is said to be odd function if and only if: f(-x) = -f(x)
For every value of x in its domain.
1. f(x)=x³-x²
Substituting -x in this, we get
f(-x)=(-x)³-(-x)²
f(-x)=-x³-x²
From above we see that
f(-x)≠-f(x)
So, this function is not odd.
2. f(x)=x⁵-3x³+2x
Substituting -x in this, we get
f(-x)=(-x)⁵-3(-x)³+2(-x)
f(-x)=-x⁵+3x³-2x
f(-x)=-(x⁵-3x³+2x)
From above we see that
f(-x)=-f(x)
So, this function is odd
3. f(x)=4x+9
Substituting -x in this, we get
f(-x)=4(-x)+9
f(-x)=-4x+9
From above we see that
f(-x)≠-f(x)
So, this function is not odd.
4. f(x)=1÷x
Substituting -x in this, we get
f(-x)=1÷(-x)
f(-x)=-(1÷x)
From above we see that
f(-x)=-f(x)
So, this function is odd.
Hence, the function f(x)=f(x)=x³-x² is not odd, f(x)=x⁵-3x³+2x is odd, f(x)=4x+9 is not odd and f(x)=1÷x is odd.
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Answer:
B.) f(x)=x5-3x3+2x is odd
D.) f (x) = 1/ x is odd
Step-by-step explanation:
just did it on edg
find the size of the angles marked with letters in each diagram
Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0
How to determine the equations?The given parameters are:
Length = y
Width = y - 5
Area = 750
The area of a rectangle is:
Area = Length * Width
So, we have:
y * (y - 5) = 750
Expand
y^2 - 5y = 750
Rewrite as:
y^2 - 5y - 750 = 0
Factorize
(y + 25)(y – 30) = 0
Hence, the equations that can be used are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0
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Complete question
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room?
If an object moves along the y-axis (marked in feet) so that it’s position at time X (in seconds) is given by f(x) = 108x -12x^2 , find the following:
The velocity equation is:
[tex]v(x) = 108 - 24x[/tex]
Such that:
[tex]v(0) = 108 ft/s\\v(2) = 60ft/s\\[/tex]
And the velocity is zero for x = 4.5
How to find the velocity equation?
We know that the position equation is:
[tex]f(x) = 108*x - 12*x^2[/tex]
To get the velocity, we need to differentiate with respect to x, so we get:
[tex]v(x) = \frac{df(x)}{dx} = 108 - 2*12*x = 108 - 24*x[/tex]
Now we want to get the velocity for x = 0 and x = 2, we will get:
[tex]v(0) = 108 - 24*0 = 108\\\\v(2) = 108 - 24*2 = 60[/tex]
Then, when x = 0, the velocity is 108 ft/s, when x = 2 the velocity is 60 ft/2.
Finally, we need to solve:
[tex]v(x) = 108 - 24*x = 0\\\\x = 108/24 = 4.5[/tex]
The velocity is zero when x = 4.5
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A cash card has a starting value of $25. If the card is not used within the first year of its purchase, the value on the card begins to decrease by $2.50 per month.
Using linear function concepts, we have that from the information given:
The relationship is linear.The independent variable is the number of months.The dependent variable is the value of the card.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.x is the independent variable.y is the dependent variable.From the information given, the y-intercept is of 25 and the slope is of $2.50, hence the value after t months is given by:
V(t) = 25 - 2.5t.
Thus:
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Which of the following is NOT a factor of b3 +6b²?
63
062
Ob
(b + 6)
Answer:
b³
Step-by-step explanation:
The lowest common multiple of the expression is b². This because, taking out a factor of b, b ( b² + 6b ), taking out a factor of b², b² ( b + 6 ),
taking out a factor of ( b + 6 ), ( b + 6 ) b². As a result b² is only the option which is not a factor.
I want to fence in a square vegetable patch. The fencing for the east and west sides cost $7 per foot, and the fencing for the north and south sides cost $4 per foot. Find the total cost (I'm dollars) of the fencing as a function of the length (in feet) of a side x.
The total cost of the fencing is a function of the length of a side x (feet) is 10x + 14y.
How to find the perimeter?The perimeter is made by adding the south, north, east, and west side.
Given that
The cost of fencing for the east and west sides is $7 per foot, and the cost of fencing for the north and south sides is only $5 per foot.
We have to find total cost of the fencing is a function of the length of a side x (feet).
The east and west fencing cost is $7/ft but the south and north fencing cost is $5/ft.
x = north and south fencing
y = the east and west sides, then you can get this equation.
Total cost= (south +north) × 5 + (east+ west) × 7
Total cost =(x + x) × 5 + (y+ y) × 7
Total cost = 5(2x) + 7(2y)
Total cost = 10x + 14y
Hence, the total cost of the fencing is a function of the length of a side x (feet) is 10x + 14y.
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Here is a list of numbers:
8.1, 1, 4.4, 0.4, 9, 5.5,
5.1, 5.7, 1.2
State the median.
Give your answer as a decimal.
Ozzie Foster deposits $2,000 at the end of each year (ordinary annuity) into an Individual Retirement Account at Bishop Bank. The account pays 7% compounded annually. a) How much will be in the account in 25 years? b) If Ozzie had deposited the $2,000 at the beginning of each year (annuity due), how much would be in the account in 25 years?
The ordinary annuity and annuity due as required in the task content are; $126,498.08 and $135, 431.43 respectively.
What is the annuity due?a) The amount which would be in the account in 25 years can be evaluated by means of the annuity factor obtained from the table under column 7% and row 25 years and hence, the value in 25 years would be; $2,000 × 63.24904
= $126,498.08.
b) For the annuity due case; the future value is;
= (1+0.07) × $2000((1+0.07)^(25) - 1)/0.07
= (1.07) × $2000(5.43-1)/0.07
= $135, 431.43.
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The graph shows the translation, g(x), of the function f(x). What integer represents the horizontal translation of f(x) to g(x)?
The integer that represents the horizontal translation of f(x) to g(x) is 4
How to determine the integer?The attached graph represents the missing piece in the question
From the graph, we can see that:
The function g(x) is 4 units to the left of the function f(x)
This means that:
g(x) = f(x + 4)
Hence, the integer that represents the horizontal translation of f(x) to g(x) is 4
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Draw the solution set for each of the following inequalities
Answer:
Step-by-step explanation:
A line is parallel to y = 5x + 3 and
intersects the point (3, 9).
What is the equation of this
parallel line?
y = 5x + [?]
Answer:
y = 5x - 6
Step-by-step explanation:
1. In a linear equation, it is represented by y = mx + b
2. A line parallel to another has the same slope (m) but a different y-intercept (b)
3. So we know that it is y = 5x as the first half. However, we need to find the new y-intercept.
4. Let's plug in the point we know into the equation, and see what amount we are missing (the y-intercept)
5. y = 5(3)
6. y = 15, however, we know that y = 9. That's a difference of -6.
This shows us that the y-intercept is -6 making the full equation:
y = 5x - 6
We can check by putting the point back into the equation:
y = 5(3) - 6
y = 15 - 6
y = 9
This correlates with the original point, we have solved the equation.
Assume that each of the n trials is independent and that p is the probability of success on a given trial. Use the binomial probability formula to find P(x).
n=15, x=2, p=5
P(x)=
Using the binomial distribution, it is found that P(X = 2) = 0.0032.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
n = 15, x = 2, p = 0.5.
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{15,2}.(0.5)^{2}.(0.5)^{13} = 0.0032[/tex]
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Which best describes the relationship between the lines?
2x – y = −1
4x – 2y = 6
same line
perpendicular
neither
parallel
same line preparations
Answer:
Parallel
Step-by-step explanation:
So the best way to compare two lines is to convert it into slope-intercept form which is given in the form of: y=mx+b where m is the slope, and b is the y-intercept, in this form it's really easy to see if they're the same line, parallel, or perpendicular.
Original Equation:
2x - y = -1
Subtract 2x from both sides
-y = -2x - 1
Divide both sides by -1
y = 2x + 1
Original Equation:
4x - 2y = 6
Subtract 4x from both sides
-2y = -4x + 6
Divide both sides by -2
y = 2x - 3
As you can see both equations have a slope of 2, but different y-intercepts, so they're not the same line, but they'll also never intersect, because they increase by the same amount, thus they are parallel
A bag contains four batteries
Answer:
If this is the question about sample space, a possible answer is 24 and 64 ways in sample space.
Step-by-step explanation:
Hopefully, this is helpful :)
Four dragons (red, yellow, green, and blue) are getting ready to perform. The red dragon and the yellow dragon do not want to go on stage first. In how many different ways can the dragons go on stage?
Using the arrangements formula, it is found that there are 12 ways for the dragons to go on stage.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, we have that:
For the first dragon, either the green or the blue dragon, hence two outcomes.For the remaining dragons, there are 3! possible ways.Hence the number of ways by which they can go on stage is:
N = 2 x 3! = 12.
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Answer:
Using the arrangements formula, it is found that there are 12 ways for the dragons to go on stage.
What is the arrangements formula?
The number of possible arrangements of n elements is given by the factorial of n, that is:
A_n = n!A
n
=n!
In this problem, we have that:
For the first dragon, either the green or the blue dragon, hence two outcomes.
For the remaining dragons, there are 3! possible ways.
Hence the number of ways by which they can go on stage is:
N = 2 x 3! = 12.
A class was given 9(whole number) 1/2 litres of juice to share equally. If there are 36 pupils in the class, how many millilitres of juice will each student get?
Answer:
263 8/9 millilitres
Step-by-step explanation:
9.5 litres = 9500 millilitres
9500/36 = 263 8/9