72 nuts mix the trail 4 ➕ 8
Answer:
Step-by-step explanation:
Which statement accurately describes the relationship between JKL and MNP?
The triangles are not similar
Given data ,
Let the first triangle be ΔJKL
Let the second triangle be ΔMNP
Now , the corresponding sides are
JK / JL ≠ NM / MP
where the corresponding sides of similar triangles are not in the same ratio
And , the common angle to both the triangles is ∠J = ∠M
So , ∠J = ∠M and JK / JL ≠ NM / MP
Hence , the triangles are not similar
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The rear window of Alex's van is shaped like a trapezoid with an upper base
measuring 36 inches, a lower base measuring 48 inches, and a height of 21 inches.
An 18-inch rear window wiper clears a 150° sector of a circle on the rear window, as
shown in the diagram below.
36 in.
21 in.
150 degrees
18 in.
48 in.
a. What is the area, in square inches, of the entire trapezoidal rear window? Show or explain how you got your answer.
b. What fractional part of a complete circle is cleared on the rear window by the 18-inch wiper? Show or explain how you got your answer.
c. What is the area, in square inches, of the part of the rear window that is cleared by the wiper? Show or explain how you got your answer.
d. What percent of the area of the entire rear window is cleared by the wiper? Show or explain how you got your answer.
a) The area of the entire trapezoidal rear window = 882 sq.in.
b) The fractional part of a complete circle is cleared on the rear window by the 18-inch wiper = 5/12
c) The area of the part of the rear window that is cleared by the wiper = 424.12 sq. in.
d) The percent of the area of the entire rear window is cleared by the wiper = 48.09%
We know that the formula for the area of trapezoid,
A = ((a + b) / 2) × h
Here, a = 36 in., b = 48 in. and height of the trapezoid h=21 in
Using above formula, the area of the entire trapezoidal rear window would be,
A = ((36 + 48) / 2) × 21
A = 882 sq.in.
Here, the 18-inch rear window wiper clears a 150° sector of a circle on the rear window.
We know that the measure of entire circle = 360°
So, the fractional part of a complete circle is cleared on the rear window by the 18-inch wiper would be,
150° / 360° = 5/12
Now we need to find the area of the part of the rear window that is cleared by the wiper.
We know that the formula for the area of sector of a circle is:
A = (θ/360) × πr²
Here, the central angle θ = 150° and radius r = 18 in.
A = (θ/360) × πr²
A = (150/360) × π × 18²
A = 424.12 sq. in.
Now we need to find the percent of the area of the entire rear window is cleared by the wiper.
P = [(area of the part of the rear window cleared by the wiper) / (area of the entire trapezoidal rear window)] × 100
P = (424.12 / 882) × 100
P = 48.09%
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Find the area of a triangle whose base (b) is 5 feet and whose height (h) is 2 ft.
(a) 5ft.²
(b) 20ft.²
(c) 100ft.²
(d) 3.5ft.²
Answer:
(a) 5 ft^2
Step-by-step explanation:
The formula for area of a triangle is given by the formula,
A = 1/2bh, where
A is the area in square units,b is the base,and h is the height.Thus, we can plug in 5 for b and 2 for h in the formula to find the area of the triangle in square feet:
A = 1/2(5)(2)
A = (5/2)(2)
A = 10/2
A = 5
Thus, the area of a triangle whose base is 5 ft and whose height is 2 ft is 5 ft^2
can u give me an answer
Answer: 0 , 5
Step-by-step explanation:
Imagine a plane taking off, first it drives to gain speed then flies, thats what you can use for coordinates.
X is the driving and Y is the flight.
The X is at 0, and the Y is at 5.
The following transactions were completed by the company:
The company completed consulting work for a client and immediately collected $5,600 cash.
The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.
The company paid an assistant $1,450 cash as wages for the period.
The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b.
The company paid $720 cash for this period's cleaning services.
In accounting, the accounting equation is a fundamental principle that describes the relationship between a company's assets, liabilities, and equity. This equation is represented as Assets = Liabilities + Equity. Every financial transaction that a company undertakes has an impact on at least two of the components of the accounting equation.
Transaction Analysis:
a. The company completed consulting work for a client and immediately collected $5,600 cash earned.
This transaction increases both cash and revenue. There is no impact on liabilities or equity.
Accounts Affected:
Cash: +$5,600
Revenue: +$5,600
b. The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.
This transaction does not impact any account initially. Revenue will increase when payment is received.
Accounts Affected:
Accounts Receivable: +$4,100
Revenue: +$0
c. The company paid an assistant $1,450 cash as wages for the period.
This transaction decreases cash and increases expenses. There is no impact on liabilities or equity.
Accounts Affected:
Cash: -$1,450
Expenses: +$1,450
d. The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b.
This transaction increases cash and decreases accounts receivable. There is no impact on liabilities or equity.
Accounts Affected:
Cash: +$2,050
Accounts Receivable: -$2,050
e. The company paid $720 cash for this period's cleaning services.
This transaction decreases cash and increases expenses. There is no impact on liabilities or equity.
Accounts Affected:
Cash: -$720
Expenses: +$720
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Complete Question
The following transactions were completed by the company
a. The company completed consulting work for a client and immediately collected $5,600 cash earned.
b. The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.
c. The company paid an assistant $1,450 cash as wages for the period.
d. The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b
e. The company paid $720 cash for this period's cleaning services Required: Enter the impact of each transaction on individual items of the accounting equation. (Enter decreases to account balances with a minus sign.)
Find the area of the shape
The area of the given figure with rectangle and triangle is 27.5 square centimeters.
The given figure has a rectangle and two triangles.
The area of the rectangle is length times width
Length = 5 cm
Width = 4 cm
Area of rectangle = 5×4
=20 square centimeters
Area of triangle =1/2 base ×height
=1/2×2.5×3
=3.75 square centimeters
As there are two triangles, 2(3.75)=7.5 square centimeters
Total area = 20+7.5
=27.5 square centimeters
Hence, the area of the given figure with rectangle and triangle is 27.5 square centimeters.
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The grid shown below is in the shapr of a rectangle. What is the area innsquare units, of the shaded part of the rectangle? It have 48
Based on the information provided, it seems that you have a rectangular grid with a shaded area, and the grid contains option D. 48 square units.
To calculate the area of the shaded part, we would need to know the dimensions of the rectangle as well as the specific location and size of the shaded region within it.
If you can provide more details about the dimensions of the rectangular grid and the shaded region, I would be happy to help you calculate the area of the shaded part. Once we have that information, we can apply the formula for calculating the area of a rectangle,
which is Area = length × width. The result will give us the area of the shaded part in square units.
The area in square units, of the shaded part of the rectangle It has 48. Therefore the correct option D
The Question was Incomplete, Find the full content below :
The grid shown below is in the shape of a rectangle. What is the area, in square units, of the shaded part of the rectangle? a 14 b 24 c 28 d 48
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a triangle is shown below, find the m
The value of angle L is 61°
What is exterior angle theorem?Exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
If angle A and B are interior angles and angle C is the exterior angle, what this theorem is saying is that;
A+B = C
Similarly,
angle L and angle E are the interior angles and 113 is the exterior angle, therefore;
113 = L + 52
L = 113 -52
L = 61°
Therefore angle L is 61°
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
The coordinates of vertex D in the parallelogram are (-7, -10).
We have,
To find the coordinates of vertex D of the parallelogram, we need to use the properties of a parallelogram.
One of these properties states that opposite sides of a parallelogram are parallel and have equal lengths.
Given that A = (8, 2), B = (6, -4), and C = (-5, -4), we can find the coordinates of D as follows:
Find the vector representing one of the sides of the parallelogram.
We can use the vector AB.
Vector AB = (x-coordinate of B - x-coordinate of A, y-coordinate of B - y-coordinate of A)
= (6 - 8, -4 - 2)
= (-2, -6)
Add this vector to point C to find the coordinates of D.
Coordinates of D = (x-coordinate of C + x-coordinate of AB, y-coordinate of C + y-coordinate of AB)
= (-5 - 2, -4 - 6)
= (-7, -10)
Therefore,
The coordinates of vertex D are (-7, -10).
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Solve each equation by completing the square. Round to the nearest
necessary.
2x² - 2x +7=5
-2x^2 + 10x =14
4x^2 + 6x = 12
All the expressions after completing the square each equation are,
⇒ (x - 1/2)² = 5/4
⇒ (x - 5/2)² + 3/4 = 0
⇒ (2x + 3/2)² = 57/4
Given that;
Expressions are,
⇒ 2x² - 2x + 7 = 5
⇒ -2x² + 10x = 14
⇒ 4x² + 6x = 12
Now, We can completing the square each equation as;
⇒ 2x² - 2x + 7 = 5
⇒ x² - x + 7/2 = 5/2
⇒ x² - x + 1/4 - 1/4 + 7/2 = 5/2
⇒ (x - 1/2)² = 1 + 1/4
⇒ (x - 1/2)² = 5/4
⇒ -2x² + 10x = 14
⇒ - x² + 5x = 7
⇒ x² - 5x = - 7
⇒ x² - 5x + 25/4 - 25/4 = - 7
⇒ (x - 5/2)² = - 7 + 25/4
⇒ (x - 5/2)² = - 3/4
⇒ (x - 5/2)² + 3/4 = 0
⇒ 4x² + 6x = 12
⇒ (2x)² + 2×2x×3/2 + 9/4 -9/4 = 12
⇒ (2x + 3/2)² = 12 + 9/4
⇒ (2x + 3/2)² = 57/4
Thus, All the expressions after completing the square each equation are,
⇒ (x - 1/2)² = 5/4
⇒ (x - 5/2)² + 3/4 = 0
⇒ (2x + 3/2)² = 57/4
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A ferris wheel has a radius of 10 inches and is 2 inches off the ground. It makes a complete revolution every 10 seconds.
If a rider is directly horizontal to the center of the wheel and moving downward, find an equation that gives his height above the ground as a function of time .
Answer:
y = -10·sin(πt/5) +12
Step-by-step explanation:
You want the equation of the height of a rider of a Ferris wheel that has a radius of 10 and is 2 off the ground, with a period of 10 seconds, moving downward, starting from even with the center.
EquationThe general form of the equation will be ...
y = A·sin(2πt/T) + B
where A is a scale factor that is based on the radius and initial direction, and B is the height of the center of the wheel above the ground.
HeightWe assume that 2 [units] off the ground means the low point of the travel is at that height. Then the middle of the wheel is those 2 [units] plus the radius of the wheel:
B = 2 + 10 = 12
Scale factorThe scale factor A will be the radius of the wheel, made negative because the initial direction is downward from the initial height. That is, ...
A = 10
PeriodThe period (T) is given as 10 seconds.
Height functionPutting these parameters together gives ...
y = -10·sin(2πt/10) +12
y = -10·sin(πt/5) +12
__
Additional comment
We wonder if this wheel is really only 20 inches (20 in) in diameter, as that dimension seems suitable only for a model. We suspect it is probably 20 meters (20 m) in diameter.
Sometimes "m" is confused with "in" when it is written in Roman font and reproduced with poor resolution.
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Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
Does the table show a probability distribution? Select all that apply.
Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
The standard deviation of the random variable x is 1.1145
Since the Probability distribution of a random variable is the collection of value and its probability pair for values of that considered random variable.
The probability of a value of x is never neg.
The sum of the probabilities is always 1.
The sum of all values of P(X = x) equals 1, which is, considering n values
There are no negative values of P(X = x).
Since we are given the probability distribution as below, we will go and calculate the mean and standard deviation using the formula:
E(X)= ∑xP(X=x)
Standard deviation = √Variance(x)
Var(x) = E(x²) - [E(x)]²
X 0 1 2 3 4 5
p(x=x) 0.032 0.152 0.316 0.316 0.152 0.032
First we have to find E(x)
E(x) = (0x0.032) + (1x0.152) + (2x0.316) + (3x0.316) + (0.152) + (5x0.032)
The mean E(x) = 2.5
To find variance, we use Var(x) = E(x²) - [E(x)]²
But we have to calculate E(x²) first, since we already have found E(x)
So,
E(x²) = (0²x0.032) + (1²x0.152) + (2²x0.316) + (3²x0.316) + (4²x0.152) + (5²x0.032)
therefore, E(x²) = 7.492
Now we have all the values we can find the variance:
Var(x) = E(x²) - [E(x)]²
=7.492 - [2.5]²
= 1.242
With variance now we can find the standard deviation;
S.D = √Var(x)
= √1.242
= 1.1145
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task1 part b evaluate
The solution of expression ∫ (0 to 10) (x + 1) dx is,
⇒ 60
We have to given that,
Expression to solve,
⇒ ∫ (0 to 10) (x + 1) dx
Now, We can simplify as,
⇒ ∫ (0 to 10) (x + 1) dx
⇒ ∫ (0 to 10) (x) dx + ∫ (0 to 10) dx
⇒ (x² / 2)₀¹⁰ + ((x)¹⁰₀
⇒ 1/2 (10² - 0) + (10 - 0)
⇒ 1/2 × 100 + 10
⇒ 50 + 10
⇒ 60
Therefore, The solution of expression ∫ (0 to 10) (x + 1) dx is,
⇒ 60
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I have been doing this for 4 hours and still can’t figure these out
The equation of the line is y = x/7 - 1/7
What is equation of a line?The equation of a straight line is y=mx+c . Where m is the gradient or slope and c is the height at which the line crosses the y -axis, also known as the y -intercept.
The equation of a line can be expressed as;
y-y1 = m(x -x1)
where m is the slope
The slope = 1/7
x1 = 8 and y1 = 1
Therefore;
y -1 = 1/7( x -8)
7(y-1) = x-8
7y -7 = x-8
collecting like terms
7y = x - 8+7
7y = x -1
y = x/7 -1/7
The intercept is -1/7 and the slope is 1/7
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Hello! Find Domain and range, thank you :-)
the graph of a quadratic function has a y intercept at (0,3) and its vertex at (4,8 1/3) what are its x intercepts in order from least to greatest
can you also explain the steps?
The x-intercepts, in order from least to greatest, are (2.46, 0) and (5.54, 0).
Use the vertex form of a quadratic function, which is [tex]y = a(x-h)^2 + k,[/tex] where (h, k) is the vertex and "a" is the coefficient of the[tex]x^2[/tex]term. Since the vertex is at (4, 8 1/3), the quadratic function's equation is y = a(x-[tex]4)^2 + 8 1/3.[/tex]
Use the y-intercept to find the value of "a".
The y-intercept is (0,3), so when x=0, y=3.
Plugging these values into the equation above, we get: [tex]3 = a(0-4)^2 + 8 1/3[/tex].
Simplifying, we get 3 = 16a + 25/3, or 9/3 = 16a. Therefore, a = 9/48 or a = 3/16.
To obtain the complete equation, enter the value of "a" into the vertex form equation: [tex]y = (3/16)(x-4)^2 + 8 1/3.[/tex]
To find the x-intercepts, set y = 0 and solve for x.
The equation becomes: [tex]0 = (3/16)(x-4)^2 + 8 1/3[/tex].
Subtracting 8 1/3 from both sides, we get: [tex]-8 1/3 = (3/16)(x-4)^2[/tex]. Multiplying both sides by -1, we get: [tex]8 1/3 = (3/16)(x-4)^2.[/tex]
Take the square root of both sides to isolate[tex]x-4: \sqrt{(8 1/3) } = \sqrt{((3/16)(x-4)^2)}[/tex] Simplifying,
we get: [tex]\sqrt{(25/3)} = (3/4)(x-4).[/tex]
Solving for x, we get two solutions: [tex]x = 4 + 4\sqrt{(3)/3 } or x = 4 - 4\sqrt{(3)/3 }[/tex]
Sort the answers in order of best to worst. The x-intercepts are (2.46, 0) and (5.54, 0) because the first answer is around 5.54 and the second solution is roughly 2.46.
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Make selections to complete the proof.
Given: ∠WXZ≅∠YXZ, ∠XZW≅∠XZY, WX⎯⎯⎯⎯⎯⎯≅YX⎯⎯⎯⎯⎯, WZ⎯⎯⎯⎯⎯⎯≅YZ⎯⎯⎯⎯⎯
Prove: ∆WXZ≅∆YXZ
The required angles are,
∠BAC = 73 degree
∠BCA = 17 degree
∠DCF = 17 degree
∠CDF = 80 degree
∠CFD = 95 degree
Since we can see that,
In triangle ABC
The angle B is right angled
Since we know that,
Sum of interior angles of triangle = 180 degree
Therefore, in triangle ABC
⇒ (9x -8 ) + (2x-1) + 90 = 180
⇒ 11x = 99
⇒ x = 9
Thus,
Angle BAC = 9x - 8
= 9x9 - 8
= 73 degree
Angle BCA = 2x - 1
= 2x9 - 1
= 17 degree
Now in triangle, CDF,
Angle C is alternate angle for both the triangles,
Therefore,
Interior angle C of triangle CDF = angle DCF = 17 degree
Angle CDF = 9y - 1
= 9x9 - 1
= 80 degree
Angle CFD = 11y + 4
= 11x9 - 4
= 95 degree
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Susie paid 2/5 of the price of her movie ticket. Her parents paid the remaining portion of the movie ticket price. What decimal is equivalent to the fraction of the price of the movie ticket Susie paid?
17 points!!
Thanks to the other user
To find the decimal equivalent of 2/5, you can divide the numerator (2) by the denominator (5):
2 ÷ 5 = 0.4
Therefore, the decimal equivalent to 2/5 is 0.4.
(Mines) Simple Equation2/5 which is know as 2 ÷ 5 is 0.4TipWhenever you see a fraction like 2/5 just divide and it will turn into decimal.
i need some help on this please
Using the intersecting chord theorem, we can calculate the value of x as: 12
How to solve the Intersecting chord theorem?The intersecting chord theorem states that If two chords intersect in a circle , then the products of the measures of the segments of the chords are equal.
Applying the intersecting chord theorem to the two chords of the circle, we can say that:
3x = (9 * 4)
3x = 36
x = 36/3
x = 12
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What is the slope of this line?
A line passing through the points (negative 4, negative 3) & (0, 1).
© 2017 StrongMind. Created using GeoGebra.
Enter your answer as a number, like this: 42
Or, if the slope is undefined, enter a lowercase letter "u," like this: u
Answer:
[tex]m = \frac{1 - ( - 3)}{0 - ( - 4)} = \frac{4}{4} = 1[/tex]
50 Points! Multiple choice geometry question. Photo attached. Thank you!
In a rectangle, the value of x is,
⇒ x = 5
We have to given that;
ABCD is a rectangle.
And, AC = 5x + 2
BD = x + 22
Since, We know that;
Diagonal of a rectangle are equal in length.
Hence, We get;
AC = BD
(5x + 2) = (x + 22)
5x - x = 22 - 2
4x = 20
x = 20/4
x = 5
Thus, the value of x is,
⇒ x = 5
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find the numerical value of the log expression
Answer:
Step-by-step explanation:
The numerical value of the given log expression is -73.
From definitions of logarithms, we know that :
[tex]log(a*b) = log(a) + log(b)\\log(a / b) = log(a) - log(b)[/tex]
[tex]log(a^n) = n*log(a)[/tex]
Therefore,
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = \frac{4}{3}*log(b) - 8*log(a) - 5*log(c)[/tex]
substituting the given values
[tex]log(a) = 10\\log(b) = 9\\log(c) = 1\\[/tex]
we get the value of the given expression
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = \frac{4}{3}*9 - 8*10 - 5*1[/tex]
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = 12 - 80 - 5[/tex]
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = -73[/tex]
Therefore the numerical value of the given log expression is -73.
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The graph shows the distribution of the amount of chicken (in ounces) that adults eat in one sitting. The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
A graph titled Chicken Consumption has amount (ounces) on the x-axis, going from 3.2 to 12.8 in increments of 1.2. The highest point of the curve is at 8.
What percentage of adults eat between 5.6 and 8 ounces of chicken in one sitting?
2.5%
34%
47.5%
95%
Using concepts of the normal and of the uniform distribution, it is found that the correct option is:
The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
In an uniform distribution, all outcomes are equally as likely, thus they have the same height.
In the normal distribution,
The outcomes with the highest likelihood are those closest to the mean, thus they have the highest height.
This means that the mean of this distribution is 8.
The standard deviation cannot be a negative value,
So in this problem, it is 1.2,
Which means that the correct option is:
The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
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make t the subject of the formula k=2(t+3)/t-3
t = (6 + 3k)/(k - 2) is the formula for t in the equation k=2(t+3)/t-3.
The given equation is k=2(t+3)/t-3.
We need to isolate t on one side of the equation.
Let's start by cross-multiplying:
k(t - 3) = 2(t + 3)
Expanding the brackets:
kt - 3k = 2t + 6
Now, let's gather all the terms with t on one side and all the constant
terms on the other side:
kt - 2t = 6 + 3k
Factoring out t on the left side:
t(k - 2) = 6 + 3k
Finally, we can solve for t by dividing both sides of the equation by (k - 2):
t = (6 + 3k)/(k - 2)
Therefore, t is the subject of the formula, and it is given by t = (6 + 3k)/(k - 2).
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Given m ∥ n, find the value of x.
The value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3
What are angles formed by a pair of parallel lines cut by a transversal line?When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.
(2x - 13) + 123 = 180° {supplementary angles}
2x - 13 + 123 = 180°
2x + 110 = 180
2x = 180 - 110 {collect like terms}
2x = 70
x = 70/2 {divide through by 2}
x = 35
Therefore, the value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3
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Systolic blood pressure readings are normally distributed with a mean of 121 and a standard deviation of 15. (A reading above 140 is considered to be high blood pressure). Find the percentage of people with blood pressure below 133.
The percentage of people with blood pressure below 133 is 78.81%.
First, we need to calculate the Z-score for the value 133 using the formula:
Z = (X - μ) / σ
where X is the value (133), μ is the mean (121), and σ is the standard deviation (15).
Z = (133 - 121) / 15
Z = 12 / 15
Z = 0.8
Next, we can use a standard normal distribution table or a calculator to find the area under the curve to the left of the Z-score 0.8.
Looking up the Z-score of 0.8 in the standard normal distribution table, we find that the area to the left of 0.8 is 0.7881.
Therefore, the percentage of people with blood pressure below 133 is 78.81%.
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The equation of line, L is given by r=3i+3j-k+t 2i-j+3k Find an Cartesian equation for the plane pi which contains L and the origin.
The equation of the plane pi is: -6x-7y-9z=0.
To find the equation of the plane that contains the given line L and the origin as well, we first need to find two vectors that lie on the plane. One vector can be the direction vector of the line L, which is (2i - j + 3k). Now to find the second vector, we can take the vector from the origin to any point on the line L, and this vector will lie on the plane.
Let us now take t=0, and find the point on the line L:
r = 3i + 3j - k + 0(2i - j + 3k)
= 3i + 3j - k
So, the vector from the origin to this point is simply (3i + 3j - k). We can just take (3i + 3j - k) as our second vector.
Now, we can find the normal vector of the plane by taking the cross-product of two vectors that we just found, we get:
n = (2i - j + 3k) * (3i + 3j - k)
= -6i - 7j - 9k
Therefore, the equation of the plane pi is: -6x-7y-9z=0.
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Use ≈ 3.14 and round your answer
to the nearest hundredth.
10 ft
6 ft
square feet
The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.
We know that,
In geometry, a cylinder is one of the basic 3d shapes with two parallel circular bases at a distance. A curving surface connects the two circular bases at a predetermined distance from the centre. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases. One real-world example of a cylinder is an LPG gas-cylinder.
The surface area of this cylinder is defined as the product of the radius of the base and the height of the cylinder.
The surface area of this cylinder = (2π x r)h
We have given a radius of the base is 8 cm and the height of the cylinder is 10 cm.
The surface area of this cylinder = (2π x r)h
= (2π x 8)10
= (50.24)10
= 502.4
Thus, The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.
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The complete question is attached below:
Convert the polar representation of this complex number into its standard form. A 4-451 B. -43-4/ C. -8√5 +8/ D. 4-4√3 i
The complex number in standard form is written as:
Z = 1.99 + i*0.201, so the correct option is a
How to write the complex number in standard form?Remember that a complex number can be written in standard form as:
Z = a + b*i
And in polar form the notation is (R, θ):
[tex]Z = R*e^{i*\theta} = R*cos(\theta) + i*R*sin(\theta)[/tex]
Here we have the complex number:
Z = 2(cos(11pi/6) + i*sin(11pi/6))?
So here we just need to solve these expressions, we will get:
Z = 2*(0.995 + i*0.100)
Z = 1.99 + i*0.201
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Complete question:
"Convert the polar representation of this complex number into its standard form: z = 2(cos 11pi/6+ i sin 11pi/6)? "
Help with number 8 please
The simplification of the expression, ∛8x⁴y⁸ / 125 is [tex]\frac{2\sqrt[3]{x^{4}y^{8} } }{5}[/tex].
How to solve an exponential expression?The exponential expression can be solved as follows:
Therefore, let's simplify the expression.
To simplify the expression we have to deal with the exponential by applying it laws and also the cube root.
∛8x⁴y⁸ / 125
let's solve them individually,
125 = 5³ = 5 × 5 × 5
8 = 2³ = 2 × 2 × 2
Therefore,
∛8x⁴y⁸ / 125 = [tex]\frac{2\sqrt[3]{x^{4}y^{8} } }{5}[/tex]
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