the radial form is, 6 times the eight root of x to the fifth power.
What is radical form?Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.
here, given that,
6x^5/8
now,
the radial form is,
6 times the eight root of x to the fifth power.
Hence, the radical form is, 6 times the eight root of x to the fifth power.
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Let $\overline{TU}$ and $\overline{VW}$ be chords of a circle, which intersect at $S$, as shown. If $ST
The value of the SW is 12 units.
What is a chord in a circle?
The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle. It should be noted that the diameter is the longest chord of a circle that passes through the center of the circle.
Since we want to find SW to get SV, we can change SW to x.
We already know the other lengths:
ST = 3
SU = 18
SW=x
SV=x-3
So, 3(18)=x(x-3).
From here, we see that when expanded, this becomes 54 = x² - 3x.
Solving the quadratic, we see that SW is 12, therefore SV is 9.
Hence, the value of the SW is 12 units.
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complete question: Let TU and VW be chords of a circle, which intersect at S, as shown. If ST = 3, TU = 15, and VW = 3, then find SW.
In what ratio is the line joining 1/3 and 2 1 divided by the line 3x Y 9?
Line formed by joining the given points ( 1,3) and ( 2,1) divided in the ratio by the given equation of the line 3x + y = 9 is equal to 3 :2.
As given in the question,
Equation of the given line : 3x + y = 9 __(1)
Standard equation line formed by joining the two points :
( x₁ , y₁ ) = ( 1,3)
(x₂ , y₂) = ( 2,1 )
( y - y₁) / (y₂ -y₁ ) = ( x -x₁)/(x₂ - x₁ )
⇒(y - 3)/(1 - 3) = ( x -1)/(2 -1)
⇒(y -3)/-2 = (x -1)/1
⇒-2x +2 = y - 3
⇒ y + 2x = 5 __(2)
Subtract (2) from (1) we get,
3x + y = 9
2x + y = 5
x = 4
⇒y = -3
Point of intersection is ( 4, -3)
Distance between ( 4, -3) and ( 1,3) is:
= √ ( 4 -1)² + ( -3 -3 )²
= √9 + 36
= √45
= 3√5
Distance between ( 4, -3) and ( 2 ,1) is:
= √ ( 4 -2)² + ( -3 -1 )²
= √4 + 16
= √20
= 2√5
Required ratio to divide a line by given points is :
= 3√5 / 2√5
= 3/2
Therefore, the equation of the line 3x + y =9 divides the line formed by joining the given points in the ratio is 3:2.
The above question is incomplete, the complete question is:
In what ratio is the line joining the points (1,3) and (2,1 ) divided by the line 3x+y=9?
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Select all the correct answers.
Which three pairs of side lengths are possible measurements for the triangle?
45
B
45
с
AB= 6, AC=6√/2
BC=7√2, AC = 14
AB= 11, AC = 22
BC=8, AC = 8√3
AB= 15, BC = 15
AB= 16, AC=16
Submit
Answer:
AB = 6, BC = 6
AB = 4, AC = 4√2
BC = 2√2, AC = 4
(if im not wrong)
calculate the iterated integral. 3 0 1 4xy x2 + y2 dy dx 0
-(24/5)x(1/2) is the final result of the integral, tells us that the integral of 4xy(x^2 + y^2) upon the specified rectangular domain is explained as:
The given integral is in the form of an iterated integral, which is known as we need to integrate with respect to x first, and then integrate the resulting expression with respect to y.
The integral with respect to x is:
∫(4xy)(x^2 + y^2)dx from x=3 to x=0
This can be evaluated as shown below:
(2/5)(4xy)(x^3 + 3xy^2) evaluated at x=0 and x=3
= (2/5)(4xy)(0^3 + 30^2y^2) - (2/5)(4xy)(3^3 + 33^2y^2)
= 0 - (2/5)(4xy)(27 + 27y^2)
= -(24/5)xy(1 + y^2)
The integral with respect to y is:
∫( -(24/5)xy(1 + y^2)) dy from y=0 to y=1
This can be evaluated as shown below:
-(24/5)x(1/2)y^2(1+y^2) evaluated at y=0 and y=1
= -(24/5)x(1/2)1^2(1+1^2) - -(24/5)x(1/2)0^2(1+0^2)
= -(24/5)x(1/2)
hence the final result of the iterated integral is:
-(24/5)x(1/2)
therefore it is the final result of the integral, indicating that the integral of 4xy(x^2 + y^2) over the specified rectangular domain is -(24/5)x(1/2).
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I need help solving this math for Algebra: The problem is in the picture, THANKS!
Answer:
Step-by-step explanation:
The first step to determine the implied domain of the function is to identify any restrictions on the variables x and y. In this case, the function 2y + x^(1/3) = 3x + x^2 does not have any restrictions on x and y, therefore the domain is all real numbers.
We can express this as an interval notation:
(-∞, ∞)
This means that the function is defined for any real value of x and y, which means the domain of the function is all real numbers.
Find two monomials whose product equals -20a^4b², and whose sum is a monomial with a coefficient of 1.
Answer:
-4a²b
5a²b
Step-by-step explanation:
A monomial is a polynomial that has one term only but can have multiple variables.
Given monomial:
[tex]-20a^4b^2[/tex]
The coefficient of the given monomial is -20.
Therefore, we need to find two numbers that multiply to -20 and sum to 1.
Factors of -20:
-1 and 20-2 and 10-4 and 5-5 and 4-10 and 2-20 and 1Therefore, the two numbers that multiply to -20 and sum to 1 are:
-4 and 5Rewrite -20 as the product of -4 and 5:
[tex]\implies -4 \cdot 5 \cdot a^4b^2[/tex]
Rewrite the exponents as sums of equal numbers:
[tex]\implies -4 \cdot 5 \cdot a^{2+2} \cdot b^{1+1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c[/tex]
[tex]\implies -4 \cdot 5 \cdot a^2 \cdot a^2\cdot b^{1}\cdot b^{1}[/tex]
Rearrange as the product of two monomials with the same variables:
[tex]\implies -4a^2 b^{1}\cdot 5 a^2 b^{1}[/tex]
[tex]\implies -4a^2 b\cdot 5 a^2 b[/tex]
Therefore, the two monomials whose product equals -20a⁴b², and whose sum is a monomial with a coefficient of 1 are:
-4a²b5a²bCheck the sum of the two found monomials:
[tex]\begin{aligned}\implies -4a^2b+5a^2b&=(-4+5)a^2b\\&=(1)a^2b\\&=a^2b\end{aligned}[/tex]
Thus proving that the sum of the monomials has a coefficient of 1.
Alonso brings $21 to the market to buy eggs and avocados. he gets eggs that cost $2.50. then, he notices that
the store only sells avocados in bags of 3 for $5. he wants to buy as many avocados as he can with his
remaining money.
let b represent the number of bags of avocados that alonso buys.
1) which inequality describes this scenario?
choose 1 answer:
2.50 + 5b < 21
b
2.50 +5b > 21
2.50 + 3b < 21
2.50 + 3b > 21
j
Answer:
£2.50+5b>21
Step-by-step explanation:
this is because a bag is b and they cost £5 so therefore it's 5b then they have to be under 21 pounds so you use the less than symbol.
Find the sum of the series
1 - 2/3 + 4/9 - 8/27+16/81 - 32/243 + ....
The sum of the series:
1 - 2/3 + 4/9 - 8/27+16/81 - 32/243 + .... = 2/3
All geometric sequences have a starting term a and a common ratio r.
The common ratio r is the number that the terms of the sequence are multiplied to find the next term, hence the name "ratio". All terms in the sequence are the same, hence the name "common".
The common ratios here are the numbers multiplied by 2/3 to get −4/9
and the numbers multiplied by−4/9 to get 8/27.
2/3⋅ 2/3 = [tex]\frac{2*2}{3*3 }[/tex] = 4/9 .
2/3 × (-2/3) = -4/9
The infinite sum of the geometric series can only be found in a specific case: r lies between −1 and 1.
When r is between these values, adding the series will converge - close on both sides - to a certain number.
Otherwise the sum diverges - further apart - i.e. there is no specific value that the series approaches. is in This means that an infinite series can be computed as the number to which the series converges.
This calculation is done using the formula
S∞ = a₁ − r.
a, the first term of the sequence is 2/3.
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what is the reciprocal of 5
Answer:
= 1/5
Step-by-step explanation:
The reciprocal number results from dividing the number 1 by the origial number, by example:
Original number: a
reciprocal number: 1/a
In this case:
original number: 5
reciprocal number: 1/5
The price of a gallon of unleaded gas has risen to $2.90 today. Yesterday's price was $2.83 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer:
2.4%
Step-by-step explanation:
The product of 45 and -2 is
Answer:
(-90)
Step-by-step explanation:
45*-2 = (-90)
Help help help help help help
Graph the image of the given triangle, rotated 270° about the origin.
A graph of the image of the given triangle, rotated 270° about the origin is shown in the image attached below.
What is a rotation?In Mathematics, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
In Geometry, rotating a point 270° about the origin would produce a point that has the coordinates (y, -x).
By applying a rotation of 270° about the origin to the given triangle, the location of P" is given by:
(x, y) → (y, -x)
Ordered pair A (3, 2) → Ordered pair A' (2 -(3)) = (2, -3).
Ordered pair B (-2, -6) → Ordered pair B' (-6, -(-2)) = (-6, 2).
Ordered pair C (10, -8) → Ordered pair C' (-8, -(10) = (-8, -10).
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18. Match the linear function with the point that makes the statement true.
▾ 1. Henry has 8 dozen cookies and bakes 48
cookies an hour.
a. (4,2.9)
b. (1,144)
c. (5,50)
a
a ▾
▼ 2. Julian drives home from work and averages
2
mile per minute. He has to travel 4.5
miles.
a
T
▾ 3. Using a laptop on battery power causes the
battery to decrease 10% an hour.
Answer: ▾ 1. Henry has 8 dozen cookies and bakes 48
cookies an hour.
a. (4,2.9)
Step-by-step explanation:
The statement is describing a linear relationship between the number of hours and the number of cookies produced. This can be represented by a linear equation of the form y = mx + b, where x is the number of hours and y is the number of cookies.
The point (4, 2.9) represents the number of cookies produced after 4 hours, which is 2.9 dozen (8 dozen * 0.36) which is 48 cookies.
▼ 2. Julian drives home from work and averages
2
mile per minute. He has to travel 4.5
miles.
b. (1,144)
Explanation:
The statement is describing a linear relationship between the time in minutes and the distance traveled.
The point (1,144) represents the distance traveled after 1 minute, which is 144 miles, which is 4.5260 miles.
▾ 3. Using a laptop on battery power causes the
battery to decrease 10% an hour.
c. (5,50)
Explanation:
The statement is describing a linear relationship between the number of hours and the percentage of battery power remaining.
The point (5,50) represents the percentage of battery power remaining after 5 hours, which is 50% of the original battery power.
So based on the given information, I matched the linear functions with the points that makes the statement true as
▾ 1. Henry has 8 dozen cookies and bakes 48
cookies an hour.
a. (4,2.9)
▼ 2. Julian drives home from work and averages
2
mile per minute. He has to travel 4.5
miles.
b. (1,144)
▾ 3. Using a laptop on battery power causes the
battery to decrease 10% an hour.
c. (5,50)
Please note that these answers are based on the information provided in the problem statement and may not be the only possible answers.
What are the coordinates of the point on the directed line segment from
(
−
8
,
−
6
)
(−8,−6) to
(
4
,
6
)
(4,6) that partitions the segment into a ratio of 1 to 3
The e coordinates of the point on the directed line segment are (-5, -3).
What is cartesian plane?The cartesian plane is a two-dimensional coordinate plane that is formed when two parallel lines meet. The X-axis is the horizontal line, and the Y-axis is the vertical line. On the Cartesian plane, the coordinate point (x, y) indicates that the point is on the right of the origin if the sign of x is positive; otherwise, the point is on the left of the origin.
Given coordinates (-8, -6) and (4, 6) make a line segment,
and point in the line divide in ratio 1:3
the equation point is,
(x, y) = [tex][(\frac{mx_2 + nx_1}{m + n} ), (\frac{my_2 + ny_1}{m + n} )][/tex]
m = 1, n= 3
x₁ = -8, x₂ = 4, y₁ = -6, y₂ = 6
solving for x,
x = [tex](\frac{mx_2 + nx_1}{m + n} )[/tex]
x = [1(4) + 3(-8)]/4
x = -20/4
x = -5
solving for y,
y = [tex](\frac{my_2 + ny_1}{m + n} )[/tex]
y = [1(6) + 3(-6)]/4
y = -12/4
y = -3
(x, y) = (-5, -3)
Hence the coordinates are (-5, -3).
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You are designing a 5 kilometer course for a local charity run. your assistants provide you with the following measures in yards. you need to convert the distances to kilometers, and then tell your assistants how much further they need to extend the finish line to complete the course.
course streets distance
main street to 6th ave. 781 yards
6th ave. to pleasant road 1,250 yards
pleasant road to city park 275 yards
route through city park 2,337 yards
city park to main street 725 yards
You are designing a 5 kilometer course for charity run. The design now has been covers 4,908.5 meters, hence, you need to add more 91.5 meters on the course.
The conversion from yard to meter is:
1 yard = 0.9144 meters
The course streets and the distances after converted into meters are:
main street to 6th ave. 781 yards = 714.15 meters
6th ave. to pleasant road 1,250 yards = 1143 meters.
pleasant road to city park 275 yards = 251.46 meters
route through city park 2,337 yards = 2,136.95 meters
city park to main street 725 yards = 662.94 meters
Total course = 714.15 + 1143 + 251.46 + 2,136.95 + 662.94
Total course = 4,908.5 meters
The design is 5 km = 5000 meters. Therefore, you still need to add:
5000 - 4,908.5 = 91.5 meters more course.
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how to solve 3x-2y=14 and 5x+6y=42 using substitution
Answer:
(6, 2 )
Step-by-step explanation:
3x - 2y = 14 → (1)
5x + 6y = 42 → (2)
multiply (1) through by - 1
- 3x + 2y = - 14 ( add 3x to both sides )
2y = 3x - 14
substitute 2y = 3x - 14 into (2)
5x + 3(2y) = 42
5x + 3(3x - 14) = 42
5x + 9x - 42 = 42
14x - 42 = 42 ( add 42 to both sides )
14x = 84 ( divide both sides by 14 )
x = 6
substitute x = 6 into either of the 2 equations and solve for y
substituting into (2)
5(6) + 6y = 42
30 + 6y = 42 ( subtract 30 from both sides )
6y = 12 ( divide both sides by 6 )
y = 2
solution is (6, 2 )
write an expression with a value of 12. it should contain four numbers and two different operations.
The expression with a value of 12 and containing four numbers and two different operations are 2 × 2 + 4 + 4 = 12.
To write an expression with a value = 12 it should contain four numbers and two different operations, we can use the following method:
Firstly, multiplying :
2 × 2 = 4 -----1
secondly, adding:
4 + 4 = 8 -----2
finally, adding 1 and 2 we get,
4 + 8 = 12
Therefore, the expression with a value of 12 containing four numbers and two different operations is 2 × 2 + 4 + 4 = 12.
Another example is 35 ÷ 5 + 10 ÷ 2 = 12.#
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Why is absolute value used?
The absolute value is used to represent the magnitude of a number, regardless of its sign.
The absolute value is commonly used in mathematical equations, particularly in situations where the sign of a number does not carry any significance or when a distance or a difference is being measured.
For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5. This is useful when working with negative numbers in calculations, as the absolute value allows them to be treated as positive numbers. Additionally, it is used to define the distance between two points on a number line.
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construct a probability distribution for the number of boys if a couple has 2 kids. find the expected number of boys and the standard deviation. is it unusual to have 0 boys? (hint: list out the 4 possibilities.)
No, it is not unusual to have 0 boys. Each of the four possibilities (0 boys, 1 boy, 2 boys, 0 girls) has a probability of 1/4, so it is equally likely to have 0 boys as any other outcome.
The probability distribution for the number of boys if a couple has 2 kids is as follows:
P(0 boys) = 1/4,
P(1 boy) = 2/4,
P(2 boys) = 1/4.
The expected number of boys is the weighted sum of the number of boys (0, 1, and 2) multiplied by the respective probability of each:
[tex]E(# boys) = 0*1/4 + 1*2/4 + 2*1/4 = 1 boy.[/tex]
The standard deviation is calculated using the formula:
[tex]SD = sqrt(P(0 boys)*(0-1)^2 + P(1 boy)*(1-1)^2 + P(2 boys)*(2-1)^2) = sqrt(1/4*1 + 2/4*0 + 1/4*1) = sqrt(1/4) = 0.5.[/tex]
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Form a polynomial whose real zeros and degree are given.
Zeros : -3, 0, 9
degree: 3
A polynomial with the given zeros can be written as:
P(x) = x^3 - 6x^2 - 27x
How to write the given polynomial?If we have a polynomial of degree N with the given N zeros:
{x₁, x₂, ..., xₙ}
Then we can write that polynomial as:
P(x) = (x - x₁)*(x - x₂)*...*(x - xₙ)
In this case we know that the degree is 3, and the zeros are:
{-3, 0, 9}
Then we can write that polynomial as:
P(x) = (x + 3)*(x - 0)*(x - 9)
Expanding that we will get:
P(x) = (x^2 + 3x)*(x - 9)
P(x) = x^3 + 3x^2 - 9x^2 - 27x
P(x) = x^3 - 6x^2 - 27x
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find the minimum time that the train takes to travel between two consecutive stations that are 52.5 miles apart.
Therefore , the solution of the given problem of speed comes out to be
30.22 minutes taken to cover the distance.
Describe speed.Speed at a distance is a measure of how swiftly something is moving. A moving object's speed determines how far it travels in a given amount of time. Speed is determined by the formula: speed = distance x time. Meters every second (m/s), kilometers / hour (km/h), and kilometres per second (mph) are the most often used units for measuring speed (mph).
Here,
Similar to part b, but with the knowledge of the cruise distance and the necessity to solve for time, maximum cruising time is achieved.
1) Accelerating: 13.2 seconds, d = 871.2 feet.
2) Deceleration: 13.2 seconds, d = 871.2 feet.
3) When cruising: d = 45 miles - 871.2 feet - 871.2 feet = 237600 feet - 1742.4 feet = 235857.6 feet
t = 235857.6/132 = 1786.8s
Total: 1786.8 + 13.2 + 13.2 = 1813.2 seconds, or 30.22 minutes.
Therefore , the solution of the given problem of speed comes out to be
30.22 minutes taken to cover the distance.
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Find the perimeter of the figure below. Notice that one side length is not given.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
7 yd
8 yd
9 yd
13 yd
16 yd
0
The perimeter of the figure is 58 feet if the missing side length is 10 feet.
How to find the perimeter of a composite shape?Perimeter is defined as the length of the circumference or outline of the geometry. This means that is the sum of the all the external side lengths of an image or figure.
From the two-dimensional geometry in the attached image, we see the dimensions as;
The missing side length = 15 - 5 = 10 ft
Therefore, we will add all the external lengths to get the perimeter as;
Perimeter of the figure = 5 + 7 + 10 + 10 + 15 + 11
= 58 feet
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19. smartphones redux consider our group of 8 people from exercise 17. a) how many smartphones do you expect in the group? b) with what standard deviation? c) if we keep picking people until we find a smartphone, how long do you expect it will take until we find one?
It is difficult to estimate the exact number of smartphones in the group and the standard deviation, as this depends on what type of smartphones each person has. It could take between 1 and 8 people to find a smartphone, depending on the number of smartphones already in the group.
The number of smartphones in the group of 8 people is difficult to estimate, as it depends on the type of smartphone each person has. For example, if there are 2 people with iPhones, 3 people with Android phones, and 3 people with Windows phones, then there would be 8 smartphones in the group. However, if there is only one person with an iPhone and the other 7 have different types of phones, then there would be only 4 smartphones in the group. The standard deviation of the number of smartphones in the group would depend on how many different types of smartphones are present and the total number of smartphones in the group. The amount of time it would take to find a smartphone would depend on the number of smartphones already in the group. If there are already 4 or more smartphones, then it would take only 1 person to find a smartphone. If there are only 3 smartphones, then it could take up to 8 people before one of them has a smartphone.
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These squares are the same size. Each square is divided into equal parts. According to these models, why are 23 and 812 equivalent fractions ?
The squares represent a visual representation of equivalent fractions. Each square is divided into a certain number of equal parts, and the number of parts that are shaded in represents the numerator of the fraction. The total number of parts the square is divided into represents the denominator of the fraction.
In the first square, it is divided into 23 equal parts and 8 of them are shaded in. Therefore, the fraction represented by that square is 8/23.
In the second square, it is divided into 812 equal parts and 23 of them are shaded in. Therefore, the fraction represented by that square is 23/812. Since both squares are divided into the same number of equal parts, the fractions 8/23 and 23/812 represent the same quantity, just in different forms. Therefore, they are equivalent fractions.
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How many solutions does the pair of equations y 0 and y =- 5 have?
The pair of equations y = 0 and y = -5 has no solutions.
The pair of equations y = 0 and y = -5 can be written as:
y = 0
y = -5
Since both equations have the same value of y, 0 and -5, the equations are not equal and therefore there is no solution.
The pair of equations y = 0 and y = -5 have no solutions. This is because the equations have the same value of y, 0 and -5, which means that the equations are not equal. Therefore, there is no solution to this pair of equations. To determine if the pair of equations has a solution, you must check to see if the equations are equal. If the equations are not equal, then there is no solution. In this case, the equations are not equal, and thus there is no solution.
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Calculate the length of edge AD in the triangle-based pyramid below.
Give your answer to 2 d.p.
Check the picture below.
[tex]\tan(37^o )=\cfrac{\stackrel{opposite}{49}}{\underset{adjacent}{DB}}\implies DB=\cfrac{49}{\tan(37^o )} \\\\\\ \sin(56^o )=\cfrac{\stackrel{opposite}{DB}}{\underset{hypotenuse}{AD}}\implies AD=\cfrac{DB}{\sin(56^o )} \\\\\\ AD=\cfrac{ ~~ \frac{49}{\tan(37^o )} ~~ }{\sin(56^o )}\implies AD=\cfrac{49}{\tan(37^o ) \sin(56^o )}\implies AD\approx 78.43[/tex]
Make sure your calculator is in Degree mode.
Show your work for the equation gives the exact answer do not approximate :)
Answer:
[tex]log_{3}11[/tex]
Step-by-step explanation:
[tex]3^x=11[/tex]
[tex]x=log_{3}11[/tex]
Hope this helps :)
Please let me know if this is correct or not
Have a great day!
Answer:
x=2.18265833 x=ln(11)/ln(3)
Step-by-step explanation:
Move all terms not containing x to the right side of the equation. Subtract 7 from both sides.
3x= 11
Take the natural logarithm of both sides of the equation to remove the variable from the exponent. ln(3x)=ln(11)
Expand ln (3x) by moving x outside the logarithm.x ln(3)=ln(11)
Divide each term in xln(3)=ln(11) by ln(3) and simplify.
Simplify the left side.
Cancel the common factor of ln(3).
Can someone please help in number 7? I need to show work.
Answer: 2.5
Step-by-step explanation:
Thanks if you can solve this
The required time for Cormac to catch Leif is, 2.85 minute
What is the relation between time, distance & speed ?The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.
Distance = Time × Speed
Given that,
Cormac runs at a speed = 105 m/minute
Leif runs at a speed = 65 m/minute
Leif is 100 m away from the Cormac,
So, total distance covered by Leif = 100 + Distance covered After Cormac started
Distance covered After Cormac started = 65t
Distance covered by Cormac = 100t
To catch Leif,
100t = 65t + 100
35t = 100
t = 2.85 minute
Hence, the required time is 2.85 minute
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