The center of the circle can be found using a ruler-and-compass construction by drawing two arcs that intersect at the center of the circle. The radius of the circle can also be found using a ruler by measuring the distance from the center of the circle to any point on the circumference of the circle.
To make a ruler-and-compass construction of the center of a given circle, follow these steps:
Draw a line segment through the center of the circle using a ruler. This line segment should intersect the circle at two points.
Using a compass, draw an arc with the center at one of the intersection points and the radius equal to the length of the line segment.
Draw another arc with the center at the other intersection point and the same radius.
The point where the two arcs intersect is the center of the circle.
Use a ruler to draw a line from the center of the circle to any point on the circumference of the circle. This line is the radius of the circle.
The center of the circle can be found using a ruler-and-compass construction by drawing two arcs that intersect at the center of the circle. The radius of the circle can also be found using a ruler by measuring the distance from the center of the circle to any point on the circumference of the circle.
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Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions.x+3y−z=53x−y+2z=34x+2y+(a2−8)z=a+5Fora=there is no solution. Fora=there are infinitely many solutions. Fora=±the system has exactly one solution.
The values of a for which the system has no solutions, exactly one solution, or infinitely many solutions are a = -8, a = 8, and a ≠ ±8, respectively.
The system has no solutions when the coefficients of the variables are the same but the constants are different. In this case, the coefficients of x, y, and z are the same in the first and second equations, but the constants are different (5 and 3). Therefore, there is no solution for a = -8.
The system has infinitely many solutions when the coefficients of the variables and the constants are the same in all equations. In this case, the coefficients of x, y, and z are the same in the first and second equations, and the constants are the same (5 and 5). Therefore, there are infinitely many solutions for a = 8.
The system has exactly one solution when the coefficients of the variables are different in all equations. In this case, the coefficients of x, y, and z are different in the first and second equations, and the constants are different (5 and 3). Therefore, there is exactly one solution for a ≠ ±8.
In conclusion, the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions are a = -8, a = 8, and a ≠ ±8, respectively.
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A helicopter spots two landing pads in opposite directions below the angle of depression to pad A to pad B is 46 and 16 degrees respectively if the straight line distance from the helicopter to pad A is 5 miles , find the distance between the landing pads.
The distance between the landing pads is approximately 12.82 miles.
What is straight line?A straight line is the shortest distance between two points in a two-dimensional space. It is a one-dimensional geometric object that extends infinitely in both directions.
Let's label the distance between the helicopter and Pad A as "x" and the distance between the helicopter and Pad B as "y". Also, let's label the distance between Pad A and Pad B as "d".
We can start by using the tangent function to find the height of the helicopter above Pad A:
tan(46) = h / x
h = x tan(46)
Similarly, we can find the height of the helicopter above Pad B:
tan(16) = h / (x + d)
h = (x + d) tan(16)
Since the helicopter is flying at a constant height, we can equate the two expressions for h and solve for d:
x tan(46) = (x + d) tan(16)
xtan(46) = xtan(16) + dtan(16)
d = x(tan(46) - tan(16)) / tan(16)
Substituting x = 5 miles and the values for the tangent functions, we get:
d = 5 (0.9851 - 0.2760) / 0.2760
d = 5 (0.7091) / 0.2760
d = 12.82 miles
Therefore, the distance between the landing pads is approximately 12.82 miles.
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Fran and Winston have a combined income
of $80 000. One quarter of Winston's income
is the same as one-sixth of Fran's income.
How much does each person earn?
F = Fran's income
W = Winston's income
[tex]F+W=80000\hspace{5em}\stackrel{ \textit{one quarter} }{\cfrac{W}{4}}=\stackrel{ \textit{one sixth} }{\cfrac{F}{6}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{F+W=80000}\implies F=80000-W \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 2nd equation}}{\cfrac{W}{4}=\cfrac{F}{6}}\implies \stackrel{\textit{substituting from above}}{\cfrac{W}{4}=\cfrac{80000-W}{6}}\implies 6W=320000-4W \\\\\\ 10W=320000\implies W=\cfrac{320000}{10}\implies \boxed{W=32000}~\hfill \stackrel{ 80000~~ - ~~32000 }{\boxed{F=48000}}[/tex]
If you have a 65 and you turn in a grade for 40% what would that grade turn into?
Please someone help I really need help
Answer: 26
Step-by-step explanation:
65x40%
calculate 65x0.4
Please give me brainliest
cylinder has a height of 16 centimeters and a radius of 4 centimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
By answering the above question, we may state that As a result, the cylinder cylinder's volume is around 804.23 cubic centimetres.
what is cylinder?The cylinder, which is frequently a three-dimensional solid, is one of the most fundamental curved geometric shapes. In simple geometry, it is known as a prism with a circle as its basis. The term "cylinder" is also used to refer to an infinitely curved surface in a number of modern domains of geometry and topology. A "cylinder" is a three-dimensional object made up of curved surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure with two bases that are both identical circles connected at its height, which is defined by the separation of the bases from the centre. Cans of iced drinks and the wicks from toilet paper are examples of cylinders.
The following is the formula for a cylinder's volume:
[tex]V = \pi r^2h[/tex]
where the volume is V, the radius is r, and the height is h.
Inputting the values provided yields:
[tex]V = \pi * 4^2 * 16 = 804.24[/tex]
To the closest hundredth, we round to:
V ≈ 804.24 ≈ 804.23 (rounded to two decimal places) (rounded to two decimal places)
As a result, the cylinder's volume is around 804.23 cubic centimetres.
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What is the vertex of 2(n+9)(n-6)
Answer:
(-1.5, -112.5)
Step-by-step explanation:
f(n) = 2(n + 9)(n - 6) = 0
n = -9, n = 6
½(6 - (-9)) = ½(15) = 7.5
-9 + 7.5 = -1.5
f(-1.5) = 2(-1.5 + 9)(-1.5 - 6)
= 2(7.5)(-7.5)
= -(15 × 7.5)
= -(75 + 37.5)
= - 112.5
can someone show me how to do this
Answer: (0, 2)
Step-by-step explanation:
The solution of a system of equations is where the lines intersect at.
We will use substitution to solve the system.
Equations:
y = 1/2x + 2
y = -1/5x + 2
Set both equations to equal each other:
1/2x + 2 = -1/5x + 2
Simplify:
7/10x = 0
x = 0
Plug 0 back in:
y = 1/2(0) + 2
y = 0 + 2
y = 2
The solution is (0, 2)
(This can also be seen by looking at the graph)
Hope this helps!
What is another way to express 63+35
Answer: 35+63
The only way to label the expression without changing our numbers is 35+63. We still get the sum of 98 and the same numbers are being used, they are just in a different order.
I hope this helped and Good Luck <3!!!
Name the property illustrated.
√2+√8 is a real number
The property illustrated is
O the closure property of addition.
O the commutative property of addition.
O the associative property of addition.
O the identity property of addition.
O the inverse property of addition,
O the distributive property of multiplication over addition
O the closure property of multiplication.
O the commutative property of multiplication.
O the associative property of multiplication
O the identity property of multiplication.
O the inverse property of multiplication.
The property illustrated in "√2+√8 is a real number" is the closure property of addition,
The property illustrated in the given statement is the closure property of addition, which states that the sum of two real numbers is also a real number.
The closure property of addition states that the sum of any two real numbers is also a real number. In the given statement, √2 and √8 are both real numbers, and therefore their sum √2+√8 is also a real number.
This property applies to all real numbers, and it is an important property of the number system. which states that the sum of two real numbers is also a real number.
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13 If tan(x) = 13/8 (in Quadrant-1), find 8 cos(2x) = (Please enter answer accurate to 4 decimal places.)
The value of 8 cos(2x) accurate to 4 decimal places is -3.6009.
We can start by drawing a right triangle in Quadrant 1 with an angle x, where the opposite side is 13 and the adjacent side is 8.
Using the Pythagorean theorem, we can find the hypotenuse of the triangle:
[tex]c^2 = a^2 + b^2\\ c^2 = 13^2 + 8^2\\ c^2 = 169 + 64\\ c^2 = 233\\ c = \sqrt{(233)}[/tex]
Now we can use trigonometric identities to find cos(2x):
[tex]cos(2x) = cos^2(x) - sin^2(x)[/tex]
We can find sin(x) using the triangle we drew earlier:
sin(x) = opposite / hypotenuse
sin(x) = 13 / [tex]\sqrt{(233)}[/tex]
And we can find cos(x) using the triangle as well:
cos(x) = adjacent / hypotenuse
cos(x) = 8 / [tex]\sqrt{(233)}[/tex]
Plugging these values into the identity for cos(2x):
[tex]cos(2x) = cos^2(x) - sin^2(x)\\cos(2x) = (8 / \sqrt{(233))^2} - (13 /\sqrt{(233))^2} \\cos(2x) = (64 / 233) - (169 / 233)\\cos(2x) = -105 / 233[/tex]
Finally, we can find 8 cos(2x):
8 cos(2x) = 8 * (-105 / 233)
8 cos(2x) = -3.6009 (rounded to 4 decimal places)
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what is 2x + y = 2 in y=mx+b form?
Answer:
y=2-2x
so y=2x+2--£8;£++£
Answer: y=−2x + 2
Step-by-step explanation:
Subtract 2x from both sides of the equation.
y= 2 − 2x
Reorder 2 and −2x.
y= −2x + 2
At a temple to Sekhmet, there is a circular
reed bed to be planted with 4 different types
of reed, one in each of the four sections, as
shown here. The radius is 360cm and there
are two strings crossing at right angles of
lengths 560cm and 640cm.
Find out how far from the centre of the circle
the crossing point is
Therefore, the distance from the center of the circle to the crossing point of the two strings is 40sqrt(2) cm, or approximately 56.57 cm to two decimal places.
How far from the centre of the circle the crossing point is?The Pythagorean theorem can be used to calculate the distance between the circle's centre and where the two strings cross. Let A and B represent the spots where the threads converge, with O serving as the circle's centre. Next, we have:
OA2 plus OB2 equals AB2.
The circle's radius being equal to half the separation between the two strings, we get:
The equation OA = OB = sqrt((560/2)2 + (640/2)2) (156800)
And because the circle's diameter is twice its radius, we get the following equation: AB = 2 * radius = 2 * 360 = 720.
Now that we have the values, we can calculate:
2 * (156800) = AB2 => 2 * (156800) = 7202 => 313600 = 518400 - 2 * OA2 => OA2 = 102400 / 2 => OA = sqrt(51200) => OA = 40sqrt (2)
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4(5x+3y) need help or get f
After factoring out, 4(5x+3y) simplifies to 20x + 12y.
What is simplification?The act of replacing a complex mathematical expression with a simpler equivalent is known as simplification (usually shorter).
An equivalent fraction is one in which the numerator and denominator are both divisible by the same non-zero number. If a fraction's numerator and denominator are both divisible by a number greater than 1, the fraction can be reduced to an equivalent fraction by reducing both its numerator and its denominator.
To simplify 4(5x+3y), we can use the distributive property of multiplication over addition:
4(5x + 3y) = 4(5x) + 4(3y)
Simplifying the multiplication:
4(5x + 3y) = 20x + 12y
Therefore, 4(5x+3y) simplifies to 20x + 12y.
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14 Data collected in mall recorded the shoe color worn by 30 customers. Based on this information, if
there are 360 customers in this mall, how many customers would you expect to have a black shoe?
Black
Brown
Number of
Customers
13
17
156 customers are expected to wear a black shoe.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes
As per the given data:
Customers with black shoes = 13 out of 30
Customers with brown shoes = 17 out of 30
Total customers in the mall = 360
Probability that a customer wears black shoes:
P(B) = 13/30 = 0.433
Number of customers out of 360 expected to wear black shoes:
= P(B) × 360
= 0.433 × 360
= 156 customers.
Hence, 156 customers are expected to wear a black shoe.
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Write an exponential function (y=ab^x) whose graph passes through the points (2,16) and (5,128)
Answer:
Well question is not clear rewrite
At a fair last weekend, Zach sold homemade jewelry. If he sold the jewelry for R dollars and it cost him C dollars to make the jewelry, the formula P = R - C describes his profit P in dollars. If his profit was $49.32 and he sold the jewelry for $81.18, how much did it cost him to make the jewelry?
Answer:
We can use the given formula to solve for the cost C:
P = R - C
We know that P = $49.32 and R = $81.18, so we can substitute these values into the formula:
$49.32 = $81.18 - C
Next, we can solve for C by isolating it on one side of the equation:
C = $81.18 - $49.32
C = $31.86
Therefore, it cost Zach $31.86 to make the jewelry he sold at the fair.
Help Please!!
Let n = 773,186,2de be a base-ten numeral with d and e its last
two digits. Give all of the choices of the two-digit numbers de for
which n is divisible by 12.
The last "Expert" that ans
In order for a number to be divisible by 12, it must be divisible by both 3 and 4.
To be divisible by 3, the sum of the digits must be divisible by 3.
7 + 7 + 3 + 1 + 8 + 6 + 2 + d + e = 34 + d + e
Since 34 is not divisible by 3, we need d + e to be a multiple of 3 in order for the sum to be divisible by 3.
Possible values for d + e are 3, 6, and 9.
To be divisible by 4, the last two digits of the number must be divisible by 4.
Therefore, we need de to be a multiple of 4.
Possible values for de are 12, 16, 32, 36, 52, 56, 72, 76, and 92.
Out of these, only 12, 36, 52, and 76 have a sum of digits that is a multiple of 3.
So the possible values for de are 12, 36, 52, and 76.
Therefore, the choices of the two-digit numbers de for which n is divisible by 12 are 12, 36, 52, and 76.
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Math part 3 question 2
[tex] \: [/tex]
[tex] \sf \: g( x ) = x - 8[/tex][tex] \: [/tex]
To find:-[tex] \sf \: ( fg ) (4) = ?[/tex][tex] \: [/tex]
Solution:-[tex] \sf \: f( x )*g( x ) = (3x²)*( x - 8)[/tex][tex] \: [/tex]
put the value of x = 4
[tex] \: [/tex]
[tex] \sf \: f( 4 )*g( 4 ) = 3(4)²*( 4 - 8 ) \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3×16*(-4) \\ \sf \: \: \: \: \: \: \: \: \: \: \: = 48*( -4 ) \\ \: \: \: \: \underline{ \sf \red{ \: = -192 \: }}[/tex]
[tex] \: [/tex]
hope it helps! :)
Find the value of x and y
.Write your answer in
simplest form.
X
45°
X =
y =
6
y
Answer:
34
Step-by-step explanation:
3dds
What is the area of the triangle when the height is 10 and the base is 12 and the line is 13
Answer:
60
Step-by-step explanation:
Answer:
The area of the triangle is 60 unit²
Step-by-step explanation:
We know that the area of a triangle is :
[tex]A= \frac{1}{2}(Base \times Height)[/tex]
Since Base = 12 unit and Height = 10 unit
So
[tex]A= \frac{1}{2}(12\times 10)=60\\[/tex]
Hence the area of this triangle is = 60 unit²
Exam 1S22: Problem 5 Previous Problem Problem List Next Problem (8 points) Solve the following inequality. Write the answer in interval notation. x(x-7) x2 - 5x – 50 SO - Answer: Preview My Answers
In interval notation, the solution of the inequality is (25, ∞).
To solve the inequality x(x-7) < x^2 - 5x - 50, we can rearrange the terms and factor the quadratic expression:
x^2 - 7x < x^2 - 5x - 50
-2x < -50
x > 25
In interval notation, the solution is (25, ∞).
So, the answer is (25, ∞).
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Write an equivalent expression to m-(8-3m) without parentheses
m - (8 - 3m)
m - 8 + 3m
m + 3m - 8
4m - 8
Answer:
Step-by-step explanation:
m-(8-3m)
m-8 + 3m
=m+3m-8
=4m-8
What is 10x the value of the 7/10 in 637. 739
As per the given digit value, 10 times the value of the 7 in 637.739 is 7.
To understand this problem, we need to understand the concept of place value. In our base-10 number system, each digit in a number has a specific value based on its position, or place, in the number. The rightmost digit represents the ones place, the next digit to the left represents the tens place, the next represents the hundreds place, and so on.
In the number 637.739, the digit in the tenths place is 7. This means that the 7 represents 7 tenths, or 0.7. We can see this by writing the number in expanded form:
6 hundreds + 3 tens + 7 tenths + 7 hundredths + 3 thousandths + 9 ten-thousandths
So, if we want to find 10 times the value of the digit in the tenths place (which is 7), we need to multiply 0.7 by 10:
0.7 x 10 = 7
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Find the missing variable and indicated
angle measure.
X =
G
50°
K
H
28°
(15x-3)°
m2KHL =
J
O
The value of x is 7
What is angle on a straight line?The total sum of angles on a straight line is 180°. This means by adding all angles on a line ,it must give 180°.For example , if four angles, A, B , C ,D are align on a straight line, the sum of these angles, A+B+C +D = 180°
Therefore ;
50+28+15x-3 = 180
78-3 +15x = 180
75 +15x = 180
collect like terms
15x = 180-75
15x = 105
divide both sides by 15
x = 105/15
x = 7
therefore the value of the missing variable (x) is 7
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20. Find a \( 2 \times 2 \) matrix \( A \) for which \[ \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right] A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right] \text {. } \]
The matrix \( A \) that satisfies the given equation is \[ A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]. \]
To find a \( 2 \times 2 \) matrix \( A \) such that \[ \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right] A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right] \text {. } \], we can solve for A by multiplying both sides of the equation by the inverse of the left matrix. The inverse of \[ \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right] \] is \[ \left[\begin{array}{ll} -3 & 2 \\ 5 & -2 \end{array}\right]. \] Multiplying both sides of the equation by this inverse gives \[ \left[\begin{array}{ll} -3 & 2 \\ 5 & -2 \end{array}\right] \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right]A= \left[\begin{array}{ll} -3 & 2 \\ 5 & -2 \end{array}\right] \left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right], \] which simplifies to \[ A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]. \] Thus, the matrix \( A \) that satisfies the given equation is \[ A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]. \]
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The radius of this circle corresponds to the radius of the circle whose answer is x2 + y2 = 9, where the circle's centre is on the x-axis.
what is circle ?In mathematics, a circle is a geometric figure made up of all the points in a sphere that are equally spaced from the circle's centre. The radius of the circle is the distance measured from any location on the circle to its centre. The width of a circle is the distance across the circle that passes through its centre, and the circumference of a circle is the distance around the circle. The equations of circles in the coordinate plane can be used to characterise them. The equation for a circle with centre (h,k) and radius r has the following conventional form:
(x - h)² + (y - k) (y - k)² = r² where (x,y) are any location on the circle's coordinates.
given
We can begin by completing the cube to rewrite the equation in standard form:
x2 - 2x + y2 = 8
(x - 1)2 + y2 = 9
We can see from this standard shape that the circle's centre is (1, 0), which is located on the x-axis. This circular has a radius of √9 units, or 3 units. Thus, the following assertions are true:
The circular has a radius of three units.
The x-axis is where the circle's middle is located.
The radius of this circle corresponds to the radius of the circle whose answer is x2 + y2 = 9, where the circle's centre is on the x-axis.
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Find the area of the circle which has a diameter 22 cm
Answer:
Exact form: 121π
Decimal form: 380.1327111...
Step-by-step explanation:
The area of the circle is given by the formula A = πr², where A is the area of the circle and r is the radius.
Given the diameter of 22cm, we know that the radius is 11cm, as the radius is half the diameter.
We can then put this into the formula to find the area of the circle:
A = πr²
A = π * 11²
A = 121π
Note that the answer here is given in terms of π so it can be expressed in its exact form, as 121π is an irrational number roughly equivalent to 380.1327111... The answer you need to provide will depend on whether the question asks for the exact form, or to a certain number of decimal places / significant figures. If it the latter, you can round off the decimal answer as appropriate.
Subtract.x2+3xy−4y26x−3y−x2+xy−2y25x+3yx2+3xy−4y26x−3y−x2+xy−2y25x+3y=(Simplify your answer. Type your answer in factored form.)
The factored form is 2y(x - y) - 11x.
What is factored form?Factored form of a polynomial is when the polynomial is written as a product of its factors. Each factor is either a polynomial or a number. Factored form is useful for identifying the zeros of a polynomial and for solving polynomial equations.
To simplify the given expression, we need to combine like terms and factor if possible.
First, let's combine the like terms:
x^2 + 3xy - 4y^2 - 6x + 3y - x^2 - xy + 2y^2 - 5x - 3y
= 2xy - 2y^2 - 11x
Next, let's see if we can factor the expression:
2xy - 2y^2 - 11x
= 2y(x - y) - 11x
Since we cannot factor any further, the simplified expression in factored form is:
2y(x - y) - 11x
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A right circular cylinder has the dimensions shown below.
r = 5 cm
h = 9 cm
Find the exact surface area of the cylinder.
Include correct units.
Show all your work.
Answer:
The surface area of a right circular cylinder consists of three parts: the top and bottom circular faces, and the curved lateral surface.
The area of each circular face is given by the formula A = πr^2, where r is the radius. Therefore, the total area of the two circular faces is:
2A = 2πr^2
The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height. Therefore, the lateral surface area of the cylinder is:
A = 2πrh
Substituting the given values, we get:
A = 2π(5 cm)(9 cm)
Simplifying, we get:
A = 90π cm^2
Adding the areas of the circular faces and the lateral surface, we get the total surface area:
Total surface area = 2A + A = 3A
Substituting the value of A, we get:
Total surface area = 3(90π cm^2) = 270π cm^2
Therefore, the exact surface area of the cylinder is 270π square centimeters.
Bobby has 4 shoes and sells 5 shoes. How many shoes does Bobby have left?
Answer:
Step-by-step explanation:
4-5 would be less than 1 so it would be -1