The area of the resulting surface of this infinite curve is π units.
In this question,
The infinite curve is y = e^−2x, x ≥ 0.
The curve is rotated about x-axis.
Since x ≥ 0, the limits will be 0 to ∞.
Then the area of the resulting surface is,
[tex]A= 2\pi \lim_{b\to \infty} (\int\limits^\infty_0{e^{-2x} } \, dx )[/tex]
Now substitute,
u = -2x
⇒ du = -2dx
⇒ dx = [tex]-\frac{1}{2} du[/tex]
Then,
[tex]\int\limits{-\frac{1}{2}e^{u} } \, du =-\frac{1}{2}\int\limits{e^{u} } \, du[/tex]
Now substitute u and du, we get
⇒ [tex]-\frac{1}{2} \int\limits {e^{-2x} }(-2) \, dx[/tex]
⇒ [tex]-\frac{-2}{2} \int\limits {e^{-2x} } \, dx[/tex]
⇒ [tex](1) \int\limits {e^{-2x} } \, dx[/tex]
⇒ [tex]\int\limits {e^{-2x} } \, dx[/tex]
Thus the area of the resulting surface is
[tex]A= 2\pi \int\limits^\infty_0{e^{-2x} } \, dx[/tex]
⇒ [tex]A= 2\pi [{e^{-2x}(\frac{1}{-2} ) } \,]\limits^\infty_0[/tex]
⇒ [tex]A= \frac{2\pi}{-2} [{e^{-2(\infty)}-e^{-2(0)} } \,]\\[/tex]
⇒ [tex]A= -\pi [0-1} \,]\\[/tex]
⇒ [tex]A= \pi[/tex]
Hence we can conclude that the area of the resulting surface is π units.
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A square has a side that measures 2.75 units. what is the area of a circle with a circumference that equals the perimeter of the square? use 3.14 for π, and round your answer to the nearest hundredth.
The area of a circle with a circumference that equals the perimeter of the square is 9.62 units².
What is circle ?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, it has rotational symmetry around the centre for every angle.the side measurements of the square is 2.75 units.
the perimeter of this square, we must multiply 2.75 by 4 because a square has four equal side measurements.
2.75 × 4 = 11
Let's use the formula for finding radius given the circumference.
[tex]Radius = \frac{circumference}{2\pi }[/tex]
the circumference because our circumference is 11 units.
Radius = [tex]\frac{11}{2pi }[/tex]
put π = 3.14 * 2
radius = 11 / 2 * 3.14
radius = 11/ 6.28 ⇒ 1.75
the area of the circle = [tex]\pi r^{2}[/tex]
area = 3.14 * (1.75)² ⇒9.61325
Lastly, we round this number to the nearest hundredth as it is asked of us in the problem.
9.61325 = 9. 62
Therefore, the area of the circle is 9.62 units².
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Evaluate the expression w2 - v+ 1 for W = -2 and v = -8.
A. -11
B. 5
C. 13
D. -3
Answer:
13
Step-by-step explanation:
w^2 = -2^2 = 4
-v = -1*-8 = 8
Put it together: w^2-v+1 --> 4+8+1 = 13
Evaluate 5(14 – 23) + 8 ÷ 2. (1 point) 26 34 44 56
Answer:
-41
Step-by-step explanation:
5(14-23)+8 ÷ 2
=5(-9)+4
=-45+4
=-41
The solution of the given expression 5(14-23)+8 ÷ 2 is -41.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Example; 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
Simplification usually involves making the expression simple and easy to use later.
WE have given an expression as;
5(14-23)+8 ÷ 2
Solve the bracket then division;
=5(-9) + 4
=-45+4
=-41
Therefore, the solution of the given expression is -41.
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Is it possible for bruce and felicia to have used the same number of tiles? use complete sentences to explain your reasoning.
At any value of x, Bruce would have always used 3 tiles less than Felicia.
What is an expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent norms.Calculate to explain:
Number of tiles Bruce used: 5x + 2Number of tiles Felicia used: 5x + 5On equating the two expressions:5x+2 = 5x+5So, there is no solution.
Any value of x, Bruce would have always used 3 tiles less than Felicia.
Therefore, at any value of x, Bruce would have always used 3 tiles less than Felicia.
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The complete question is given below:
Is it possible for Bruce and Felicia to have used the same number of tiles? Use complete sentences to explain your reasoning.
Number of tiles Bruce used: 5x + 2
Number of tiles Felicia used: 5x + 5
What is the Value of x
Answer:
x = 11
Step-by-step explanation:
A segment parallel to a side of a triangle cuts off proportional segments on the sides.
48/6 = (3x + 7)/5
8 = (3x + 7)/5
3x + 7 = 40
3x = 33
x = 11
Seven is not an example of _____.
an expression
a term
a variable
a constant
Answer:
a variable.
Seven is a number and cannot be a variable.
When rolling two dice what is the probability of rolling a sum of six or two even numbers.
The probability of rolling a sum of six or two even numbers.
is P = 1/3
How to find the probability?
Here we are rolling two dice, and each dice has 6 possible outcomes, then the total number of outcomes is:
6*6 = 36
Now, the outcomes that given a sum of 6 are:
dice 1 dice 2.
1 5
5 1
2 4
4 2
3 3
We have 5 outcomes there.
The outcomes where both numbers are even are:
dice 1 dice 2.
2 2
2 4
4 2
4 4
4 6
6 2
6 4
6 6
We have 8 outcomes here (such that 2 are in the ones we counted before).
Then the total number of outcomes that either add to 6 or have both even numbers are:
5 + 8 - 2 = 12
Then 12 out of 36 outcomes either add to 6 or have both even numbers, this means that the probability is:
P = 12/36 = 1/3
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Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
The five number summary and interquartile range for the data-set is given by:
Minimum: 48Lower quartile: 54.Median: 63.5.Upper quartile: 74Maximum: 80.Interquartile range: 20What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.In this problem, we have that:
The minimum value is the smallest value, of 48.The maximum value is the smallest value, of 80.The data-set has even cardinality, hence the median is the mean of the middle elements, which are 63 and 64, hence the median is of 63.5.The first quartile is the median of the five elements of the first half, hence it is of 54.The third quartile is the median of the five elements of the second half, hence it is of 74.The IQR is the difference between the quartiles, hence 74 - 54 = 20.More can be learned about five number summaries at brainly.com/question/17110151
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Rashon walked 10 miles in 4 hours. if he walked the same distance every hour, how far did he walk in one hour? write your answer in feet if 1 mile equals 5280 feet.
Answer:
Step-by-step explanation:
Miles per hour: [tex]\frac{10miles}{4hrs} = 2.5\frac{miles}{hour}[/tex]
Feet per hour:
[tex]2.5\frac{miles}{hours} (\frac{5280ft}{1mile} )[/tex]
[tex]=13,200\frac{ft\\}{hr}[/tex]
Variables y and x have a proportional relationship wher y=18 when x=2 what is the value of x when y=36
Answer:
4
Step-by-step explanation:
18 + 18 = 36
So you got 36 cuz you times by two so you times the same for x
which is
2 x 2 = 4
Answer:
4
Step-by-step explanation:
We can set up a proportion.
18:2 = 36: x
If we multiply 18 by 2, and multiply 2 by 2, we can get 18:2 = 36:4, so x is equal to 4
Find the volume of the cylinder shown using the formula in the box below. Round your answer to the nearest tenth. Show your work
Answer: 1960.2 cm
Step-by-step explanation:
v = πr^2h
v = π7.4^2(11.4)
= π54.76(11.4)
= 171.9464(11.4)
= 1960.2
The volume of the cylinder rounded to the nearest tenth is 1,960.2 cubic cm
What is the volume of the cylinder?Volume of the cylinder = πr²h
Where,
r = radius = 7.4 cm
h = height = 11.4 cm
π = 3.14
So,
Volume of the cylinder = πr²h
= 3.14 × 7.4² × 11.4
= 3.14 × 54.76 × 11.4
= 1,960.18896
Approximately to the nearest tenth
= 1,960.2 cubic cm
Therefore, 1,960.2 cubic cm is the volume of the cylinder with radius 7.4 cm and height 12.4 cm
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11%
5. The grid shows how many eggs Ms. Benton bought.
eggs she
The shaded boxes represent the number of
used to make the cookies. What percent and fraction
of the eggs bought were not used to make the cookies?
Show your work in the space below. Remember to
check your solution.
Answer:
36
Step-by-step explanation:
don't know but let me check right quick
Please Help!
The total arm and blade of a windshield wiper is 9 in. long and rotates back and forth through an angle of 92 degrees. The shaded region in the figure is the portion of the windshield cleaned by the 7-in. wiper blade. What is the area of the region cleaned?
answer with the last three decimal places
The area of the region cleaned by the 7-in wiper blade with the angle subtended being 92⁰ as described in the task content is; 39.32in².
What is the area cleaned by the 7-in wiper blade?According to the task content, it follows that the wiper blade is 7-in long and subtends an angle of 92°.
Consequently, the area swept by the blade in discuss can be determined by the Area of sector formula and hence, is;
Area = (92/360) × (22/7) × 7².
Area = 39.32 in².
Ultimately, it follows from the solving steps above that the area of the region cleaned by the 7-in wiper blade with the angle subtended being, 92⁰ is; Area = 39.32 in².
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Find the maclaurin series for f(x) using the definition of a maclaurin series. [assume that f has a power series expansion. do not show that rn(x) → 0. ] f(x) = e−6x
The equation of [tex]f(x) = e^{-6x}[/tex] by maclaurin series is [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex].
The maclaurin series for f(x) is defined by the following formula:
[tex]f(x) = \sum_{i=0}^{\infty} \frac{f^{(i)} (0)}{i!} .x^{i}[/tex]--------------(1)
Where [tex]f^{i}[/tex] is the i - th derivative of the function
If f(x) = [tex]e^{-6x}[/tex], then the formula of the i - th derivative of the function is:
[tex]f^{i} =(-6)^{i} .e^{-6x}[/tex]----------------------(2)
Then,
[tex]f^{i}(0) = (-6)^{i}[/tex]
Lastly, the equation of the trascendental function by Maclaurin series is: [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6)^{i}.x^{i} }{i!} \\f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex]---------------(3)
Hence,
The equation of [tex]f(x) = e^{-6x}[/tex] by maclaurin series is [tex]f(x)=\sum_{i=0}^{\infty} \frac{(-6.x)^{i} }{i!}[/tex].
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Which of the following equations is the translation 2 units down of the graph of y = |x |?
a.) y = | x - 2|
b.) y = | x + 2|
c.) y = | x | + 2
d.) y = | x | - 2
Answer:
d
Step-by-step explanation:
up and down is outside of the x stuff so its c or d
and c is moving it up
d is moving it down
Answer:
d) y = | x | - 2
Step-by-step explanation:
In order to translate a graph downward 2 units ,we subtract 2 from the original function.
therefore,
If the Original function is y = |x|
Then the Function of the translated graph is y = | x | - 2
Change from rectangular to spherical coordinates. (let ≥ 0, 0 ≤ ≤ 2, and 0 ≤ ≤. ) (a) (5, 5 3 , 10 3 )
The spherical coordinate that is converted from the given rectangular coordinate is (12.62, 46.67°, 35.3°).
Here, the given rectangular coordinate is (5, 5.3, 10.3).
Therefore, the value of 'x' is 5, the value of 'y' is 5.3 and the value of 'z' is 10.3.
We can convert the rectangular coordinate (x, y, z) into spherical coordinate (ρ, θ, Φ) by the below mentioned method.
We know, ρ² = (x²+y²+z²)
Therefore, ρ
= √(x²+y²+z²)
= √[(5)²+(5.3)²+(10.3)²]
= √(25+28.09+106.09)
= √(159.18)
= 12.62
Again, tan θ = (y/x)
Therefore, θ = tan⁻¹(y/x) = tan⁻¹(5.3/5) = tan⁻¹(1.06) = 46.67°
Similarly, cos Φ = (z/ρ)
Therefore, Φ = cos⁻¹(z/ρ) = cos⁻¹(10.3/12.62) = cos⁻¹(0.816) = 35.3°
Here, the spherical coordinate is (ρ, θ, Φ).
Therefore, the required spherical coordinate for the given rectangular coordinate is (12.62, 46.67°, 35.3°).
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I don't understand this question
Answer:
7 people are going in the minivan.
Step-by-step explanation:
Since Chris AND the other 18 people are going, add 1 to 18 (19).
There are 3 cars, which have 4 each. We can use multiplication to determine that there are a total of 3 x 4 people in the cars, which is equivalent to 12.
Since the remaining party people are going in the minivan, we will subtract 12 from 19 to get 7.
Therefore, 7 people are going in the minivan.
Hope this helps!
Solve the system of equations by graphing.
2x^2 + 8y^2 = 50
x^2 + y^2 = 13
The solutions for the given system are (3,2), (3,-2), (-3,2) and (-3,-2).
What is a Quadratic Function?
The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
The solution of these equations represents the points at which the parabolas intersect.
2x²+8y²=50 (1)
x² + y²= 13 (2)
Multiplying the equation 2 by -2, you have:
2x²+8y²=50 (1)
-2x² -2 y²= -26(2)
Sum both equations, you have: 6y²= 24. Now, you can find y.
6y²= 24
y²=4
y=±2
If y=2, from equation 2, you have
x² + y²= 13
x² + 2²= 13
x² + 4= 13
x² =13-4
x² =9
x=±3
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In circle D, which is a secant?
EF
DC
Line segment A B
Line G H
The secant of circle D is the 'line GH'. Where the line segment EF is the diameter of the circle, line segment DC is the radius, and the ray AB is the tangent of the given circle.
What is the secant of the circle?The line that passes through the circle and touches the circle at two points is said to be a secant line of the circle.
Which is the secant line in the given circle D?The given circle D has a center at D.
The radius of the circle is given by the line segment CD
The diameter (or) the longest chord of the circle is given by the line segment EF
The ray AB passes touches the circle at point B, which is called the tangent of the circle.
Where the line GH passes through the circle and touches at two points. So, this line GH is said to be the secant of the circle.
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Disclaimer: The given question is incomplete(needs a diagram). Here is the required diagram attached.
Question: In circle D, which is a secant?
a) EF
b) DC
c) Line segment AB
d) Line GH
Answer:
ray ab
Step-by-step explanation:
A simple random sample is guaranteed to reflect exactly the population from which it was drawn.
a. true
b. false
Answer:
B
Step-by-step explanation:
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
x ≤ -2
Step-by-step explanation:
3(x + 2) ≤ 5(-2 - x)
Distribute on both sides.
3x + 6 ≤ -10 - 5x
Add 5x to both sides.
8x + 6 ≤ -10
Subtract 6 from both sides.
8x ≤ -16
Divide both sides by 8.
x ≤ -2
Answer:
[tex]\textsf{D. }x\leq-2[/tex]
Step-by-step explanation:
Given inequality: [tex]3(x+2)\leq5(-2-x)[/tex]
Step 1: Distribute [tex]3[/tex] and [tex]5[/tex] through the parentheses.
[tex]\implies 3(x)+3(2)\leq5(-2)+5(-x)[/tex]
[tex]\implies 3x+6\leq-10-5x[/tex]
Step 2: Subtract [tex]6[/tex] from both sides.
[tex]\implies 3x+6-6\leq-10-6-5x[/tex]
[tex]\implies 3x\leq-16-5x[/tex]
Step 3: Add [tex]5x[/tex] to both sides.
[tex]\implies 3x+5x\leq-16-5x+5x[/tex]
[tex]\implies 8x\leq-16[/tex]
Step 4: Divide both sides by [tex]8[/tex].
[tex]\implies \dfrac{8x}{8}\leq\dfrac{-16}{8}[/tex]
[tex]\implies x\leq-2[/tex]
Find the radius of convergence, then determine the interval of convergence
By the ratio test, the series converges for
[tex]\displaystyle \lim_{k\to\infty} \left|\frac{(x+2)^{k+1}}{\sqrt{k+1}} \cdots \frac{\sqrt k}{(x+2)^k}\right| = |x+2| \lim_{k\to\infty} \sqrt{\frac k{k+1}} = |x+2| < 1[/tex]
so that the radius of convergence is 1, and the interval of convergence is
|x + 2| < 1 ⇒ -1 < x + 2 < 1 ⇒ -3 < x < -1
The radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series. This can be obtained by using ratio test.
Find the radius of convergence R and the interval of convergence:Ratio test is the test that is used to find the convergence of the given power series.
First aₙ is noted and then aₙ₊₁ is noted.
For ∑ aₙ, aₙ and aₙ₊₁ is noted.
[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|[/tex] = β
If β < 1, then the series convergesIf β > 1, then the series divergesIf β = 1, then the series inconclusiveHere [tex]a_{k}[/tex] = [tex]\frac{(x+2)^{k}}{\sqrt{k} }[/tex] and [tex]a_{k+1}[/tex] = [tex]\frac{(x+2)^{k+1}}{\sqrt{k+1} }[/tex]
Now limit is taken,
[tex]\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|[/tex] = [tex]\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }/\frac{(x+2)^{k} }{\sqrt{k} }|[/tex]
= [tex]\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }\frac{\sqrt{k} }{(x+2)^{k}}|[/tex]
= [tex]\lim_{n \to \infty} |{(x+2) } }{\sqrt{\frac{k}{k+1} } }}|[/tex]
= [tex]|{x+2 }|\lim_{n \to \infty}}{\sqrt{\frac{k}{k+1} } }}[/tex]
= [tex]|{x+2 }|[/tex] < 1
- 1 < [tex]{x+2 }[/tex] < 1
- 1 - 2 < x < 1 - 2
- 3 < x < - 1
We get that,
interval of convergence = (-3, -1)
radius of convergence R = 1
Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.
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1/?
Which number produces a rational number when Multiplied 1/5
Answer:
-2/3
Step-by-step explanation:
A rational number is a number that can be expressed as a fraction so when you add 2 fractions it’s a rational number
Show do i solve for the missing answers
Calculate angles in a triangle
HELP
Answer:
angle a = [tex]\boxed{154}^{\circ}[/tex]
Step-by-step explanation:
The angles in a triangle add up to 180°.
∴ ∠a + 13° + 13° = 180°
⇒ ∠a + 26° = 180°
⇒ ∠a = 180° - 26°
⇒ ∠a = 154°
Answer:
Angle a equals= 154°
Step-by-step explanation:
you have two angles which add up to 26°
remember that triangle always adds up to 180°
so you calculate 180-26 and you get 154
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.
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Consider this equation.
How many valid solutions does the equation have?
=
Answer:
1
Step-by-step explanation:
(10x + 25) / (3x + 12) = (5x) / (x + 4)
5(2x + 5) / 3(x + 4) = 5(x) / (x +4)
(2x + 5) / 3 = x
2x + 5 = 3x
x = 5
Check.
(10*5+ 25) / (3*5 + 12) = (5*5) / (5 + 4)
75/27 = 25/9
25/9 = 25/9
What is the slope of the linear equation that has the values shown in the table? Show your work
Slope can be found from two points using the equation [tex]\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex].
Take any two points to substitute in. In this example, I'll use the first two points, (-4, 15), and (-2, 9). Put these into the equation and you'll get
[tex]\frac{(9-15)}{(-2-(-4))}[/tex]. Simplify further to get [tex]\frac{-6}{2}[/tex]. Divide this and you'll get the slope, -3!
hope this helps!
Find the Diameter of the Circle with the following equation. Round to the nearest tenth.
(x - 2)2 + (y + 6)2 = 20
Answer:
11.8 units
Step-by-step explanation:
The circle equation is given as:
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2Where
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2r
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we have
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sides
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 2
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 22r = 11.8
The circle equation is given as:(x - 2)^2 + (y + 6)^2 = 35A circle equation is represented as:(x - a)^2 + (y - b)^2 = r^2WhereDiameter = 2rBy comparing both equations, we haver^2 = 35Take the square root of both sidesr = 5.9Multiply by 22r = 11.8Hence, the diameter of the circle is 11.8 units
Answer: 8,9.
Step-by-step explanation:
[tex](x-2)^2+(y+6)^2=20\\Circle \ equation\\\boxed {(x-a)^2+(y-b)^2=r^2}\\r^2=20\\r*r=\sqrt{20}*\sqrt{20}\\ r=\sqrt{20}\\ r=\sqrt{4*5}\\ r=2\sqrt{5} \\ D=2r\\D=2*2\sqrt{5}\\ D=4\sqrt{5}\\ D\approx8,9.[/tex]
What is the answer to the question: 9 to the second power times 13
Answer:
1053
Step-by-step explanation:
Rewrite 2x = 128 as a logarithmic equation.
Ologx128=2
O log2x = 128
O log₂128 = x
Olog128x = 2
The logarithmic equation is:
log₂128 = x
So the correct option is the third one
How to rewrite this as a logarithmic equation?
Here we have the expression.
2ˣ = 128
Now, if we apply the natural logarithm to both sides, we can get:
ln(2ˣ) = ln(128)
Because of the property of natural logarithms, we can write the left side as:
ln(2ˣ) = x*ln(2) = ln(128)
Now, if we isolate x, we get:
x = ln(128)/ln(2)
And remember that:
ln(k)/ln(n) = logₙ(k)
Then we can rewrite the logarithmic equation as:
x = log₂(128)
Which is the third option.
If you want to learn more about logarithmic equations, you can read:
https://brainly.com/question/236421
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