Answers
Answer:
Given equation:
[tex]10^{5x-2}=2^{8x-3}[/tex]
Take natural logs of both sides:
[tex]\implies \ln 10^{5x-2}= \ln 2^{8x-3}[/tex]
[tex]\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax[/tex]
[tex]\implies (5x-2)\ln 10=(8x-3) \ln 2[/tex]
Expand brackets:
[tex]\implies 5x\ln 10 - 2\ln 10=8x \ln 2 -3 \ln 2[/tex]
Collect like terms:
[tex]\implies 5x\ln 10 - 8x \ln 2 =2\ln 10-3 \ln 2[/tex]
Factor left sides:
[tex]\implies x(5\ln 10 - 8 \ln 2) =2\ln 10-3 \ln 2[/tex]
[tex]\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax[/tex]
[tex]\implies x(\ln 10^5 - \ln 2^8) =\ln 10^2- \ln 2^3[/tex]
[tex]\textsf{Apply log Quotient law}: \quad \ln_a\frac{x}{y}=\ln_ax - \ln_ay[/tex]
[tex]\implies x\left(\ln\left(\dfrac{10^5}{2^8}\right)\right) =\ln\left(\dfrac{10^2}{2^3}\right)[/tex]
Simplify:
[tex]\implies x\left(\ln\left(\dfrac{3125}{8}\right)\right) =\ln\left(\dfrac{25}{2}\right)[/tex]
[tex]\implies x=\dfrac{\ln\left(\dfrac{25}{2}\right)}{\ln\left(\dfrac{3125}{8}\right)}[/tex]
[tex]\implies x=0.4232297737...[/tex]
Related Questions
P(-3,4), Q(-1,4), R(-2, 1), S(-4, 1)
180° about vertex R what are the coordinates
Answers
The coordinate s (-4, 1) is lying on the 180 degrees of the vertex R.
What is a coordinate system?
A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
There are four coordinates are given
P(-3,4), Q(-1,4), R(-2, 1), S(-4, 1)
Point S is just lying about 180 degree to the vertex R so the coordinates will be S ( -4,1)
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Jimmy is writing a paper for one of his classes. The paper has to be 3,000 words long, and so far he has written 666 words. If he
only has 6 more days to write his paper and wants to write the same number of words each day, then how many words must he write per day to finish the paper?
A. 425
B. 389
C. 2,334
D. 889
Answers
6 days = 2334 words
1 day = 1 * 2334/6 = 389 words
Therefore the answer is B
Select the correct answer. Consider the given function. 5, x < -2 3, 2 f(x) = 0, 0≤x≤2 -3, 2 Which graph represents the given function?
help!!
Answers
⇒ open circle at (-2, 5) with a line to the left
⇒ closed circle at (-2, 3) with a line segment to an open circle at (0, 3)
⇒ closed circle at (0, 0) with a line segment to an open circle at (2, 0)
⇒ closed circle at (2, -3) with a line to the right
A right rectangular pyramid is shown below. Which of the following shapes cannot result from a cross section?
Answers
Answer:
The cross section is a trapezoid.
Step-by-step explanation:
A company plans to ship 2,000 packages of chocolate. The company randomly selecta
100 packages and finds that five packages have an incorrect weight
Based on this data, how many packages out of 2,000 should be predicted to have an
incorrect weight?
Answers
Answer:
100 packages
Step-by-step explanation:
If 5 packages out of 100 are incorrect , then there's a 1/20 chance that a package has an incorrect weight
Therefore out of 2000
it's
[tex] \frac{1}{20} \times 2000 = 100[/tex]
Hope it helps
Sorry I'm not really good at explaining
How many three digit numbers can you make by arranging the numbers 5, 4, and 9.
Answers
okay,here is about a formula.
n=2x
where x is the numbers.
n=2×3
n=6.
therefore the three digit numbers which can be obtained is 6.
what is 750× 2
what is the square root of 90
Answers
Square root of 90 can be written as 3 multiplied by Square root of 10
A shop has 31 plant pots.
Some are blue, some are yellow and the rest are red.
There are five more blue pots than yellow pots.
There are four times as many blue pots as there are red pots..
Calculate how many pots there are of each colour.
Answers
Answer:
16 blue, 11 yellow, and 4 red
Step-by-step explanation:
Find the amount accumulated after investing m principal P for t and an internet rate compounded annually P=40500 r=3.8% t=20 k=12
Answers
The amount of money accumulated after investing the given amount of money at the given rate and time period is $85389.
What is an interest in banking?Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.
The formula for calculating compound interest is expressed as;
A = P(1 + r/k)^(k*t)
Where A is final amount, P is initial principal balance, r is interest rate, k is number of times interest applied per time period and t is number of time periods elapsed.
Given that;
Initial principal balance P = $40500Interest rate r = 3.8= 3.8/100 = 0.038Time t = 20 yearsNumber of times interest applied per time period = 12 (annually) = 12/12 = 1 Amount accumulated A = ?A = P(1 + r/k)^(k*t)
A = 40500(1 + 0.038/1)¹ˣ²⁰
A = 40500 × (1.038)²⁰
A = 40500 × 2.10837
A = $85389
Therefore, the amount of money accumulated after investing the given amount of money at the given rate and time period is $85389.
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At a store, Eva bought two shirts and five hats for $154.00. Nicole bought
three same shirts and four same hats for $168.00. What is the price of each
shirt? _____
Answers
2s+5h=154
3s+4h=168
3s+4h=168
-3s -3s
4h=168-3s
\4 /4
h= 42-0.75s
2s+(42-0.75s)=154
1.25s+42=154
-42 -42
1.25s=112
/1.25 /1.25
s=$89.6
100 points for this question I beg
Answers
Answer:
22°Step-by-step explanation:
Refer to picture
Added angles a and b as interior angles of same triangle with angle x to make solving simple.
Angle a is same as 42° since both angles intercept same arc AB.
a = 42°Angle b is supplementary with 64° angle as linear pair
b = 180° - 64° = 116°Some of the interior angles of a triangle is 180
x + 42° + 116° = 180°x + 158° = 180°x = 180° - 158°x = 22°Starting time: Elapsed time: 50 minute Ending time: 9:05 A.M.
[tex]help[/tex]
Answers
Answer:
8:15 am.
Step-by-step explanation:
So the starting time will be 50 minites before 9:05 am.
That will be 9:05 - 50
= 9:00 - 45
= 8:15 am.
A Ferris wheel has a diameter of 60 m, with a minimum height of 9 m above the
ground. It takes 20 seconds for the Ferris wheel to complete one rotation. If a rider
boards a car when it is at its lowest point
O: What is the minimum height of the rider?
A: Minimum height of the rider is __ meters.
No Links Or I’ll Report You
Answers
By knowing geometrical dimensions, the minimum height of the rider in the Ferris wheel, modeled by a sinusoidal function, is equal to a height of 9 meters.
How to analyze a Ferris wheel
The model of the height of a Ferris wheel is represented by a sinusoidal model, which is presented below:
h = A + B · sin ωt (1)
Where:
A - Midpoint height, in meters. B - Amplitude, in metersω - Angular frequency, in radians per second.t - Time, in secondsSinusoidal functions are bounded functions, the minimum height of the Ferris wheel represents the lower bound of the function and the maximum height is the upper bound. Therefore, the minimum height of the rider is:
[tex]h_{min} = 39\,m - 30 \,m[/tex]
[tex]h_{min} = 9\,m[/tex]
By knowing geometrical dimensions, the minimum height of the rider in the Ferris wheel, modeled by a sinusoidal function, is equal to a height of 9 meters.
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Simplify radical expression
√10z^5 - z^2 √10z
Answers
Answer:
√10z^3(z - 1)(z + 1).
Step-by-step explanation:
The GCF is √10z* z^2
= √10z^3
So factoring we get
√10z^3(z^2 - 1) The expression in brackets is difference of 2 squares so:
= √10z^3(z - 1)(z + 1)
a classmate states that if the radius of a circle is doubled, then its area is doubled. do you agree or disagree? if you disagree, how much larger do you think the area will be?
Answers
Answer:
yes
the area of a circle is πr^2
A=πr^2
which means the area of a circle is dependent on the size of the radius of the circle.
Take for instance, the radius is 3cm and π= 3.142
A = 3.142×(3^2)
A = 28.278cm^2
Another example, if the radius of the circle is increased to 4cm, what will be the area.
A = 3.142×(4^2)
A = 50.272cm^2
Edna raises money for charity and donates $123 per week. How much does Edna donate to charity each year? Note: There are
52 weeks in a year.
A. $6,426
B. $6,406
C. $6,396
D. $6,356
Answers
What is the square root of 9
Answers
Verification:
= 3 * 3
=> 9
help please What is the simplest form of the expression representing this product?
x+10/x2+7x-18 * 3x2-12x+12/3x+30
Answers
Answer:
x-2
x+9
Step-by-step explanation:
Answer:
[tex]\frac{x-2}{x+9}[/tex]
Step-by-step explanation:
Factorizing Fraction 1
[tex]\frac{x+10}{x^{2}+7x-18 }[/tex][tex]\frac{x+10}{(x+9)(x-2)}[/tex]Factorizing Fraction 2
[tex]\frac{3x^{2} -12x+12}{3x+30}[/tex][tex]\frac{x^{2} -4x+4}{x+10}[/tex][tex]\frac{(x-2)^{2} }{x+10}[/tex]Now, multiply the fractions :
[tex]\frac{x+10}{(x+9)(x-2)}[/tex] × [tex]\frac{(x-2)^{2} }{x+10}[/tex][tex]\frac{x-2}{x+9}[/tex]Rewrite without parentheses and simplify.
(2-5y)²
Answers
Answer:
Your answer is in the Picture.
Step-by-step explanation:
Visit cymath is you want to factor polynomial or simply for you.
PLEASE ANSWER
Given JAM and segment PB such that PB JM, what is the missing justification in the proof that JP/PA = MB/BA
Answers
Answer:
B. AA similarity postulate
Gabrielle angles her pool cue against the edge of her pool table, as shown below. What is the measure of angle a and angle b
Answers
The relationship between angle A and angle B is supplementary angles.
∠A = 2(5) + 40 = 50 degrees
∠B = 5 + 125 = 130 degrees
What are supplementary angles?Supplementary angles are angles that sum up to 180 degrees. The sum of the two angles for a supplementary angles is 180 degrees .
Therefore, the relationship between angle A and angle B is supplementary angles.
Therefore,
∠A + ∠B = 180 degrees
∠A = 2x + 40
∠B = x + 125
2x + 40 + x + 125 = 180
2x + x + 40 + 125 = 180
3x + 165 = 180
3x = 180 - 165
3x = 15
x = 15 / 3
x = 5
Therefore,
∠A = 2(5) + 40 = 50 degrees
∠B = 5 + 125 = 130 degrees
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Two buildings are 96 ft apart . The first building is 164ft tall. The second building is 92ft tall. If a string is stretched between the top of the two buildings so that it forms a straight line from the top of one to the top of the other, how long would the string be
Answers
Answer:
120ft
Step-by-step explanation:
Which expression is equivalent to 6^4 • 6^3?
(6•6•6•6)+(6•6•6)
(6+6+6+6)•(6+6+6)
(6•6•6•6)•(6•6•6)
(6•6•6•6•6)•(6•6•6•6)
Answers
Answer: C)
Step-by-step explanation:
25 points please help
Answers
Answer:
See below ~
Step-by-step explanation:
The functions which have a range ≥ -1 :
y = |x - 1| + 2y = |x + 2| - 1The first function (according to the attachment) is not part of this because on applying any value for x, it will be either less than or equal to -1.
If an astronaut has a mass of 90 kg, and visits Jupiter which has a gravitational field of 25.3 N/kg, how much will he weigh there?
A. 115.3N
B. 64.7 N
C. 3.55 N
D. 2,277 N
Answers
Answer: 2277 Newtons
Step-by-step explanation:
I will show you how to do this the Physics way, so first we must write down our given values.
gravitational field = gravity = 25.3 N/kg
Mass of the astronaut = 90kg
Fun fact: know that if you convert the Newtons to a different unit, Newtons = kg (m/s^2) so we can say that instead of N/kg, we can write it as m/s^2 because if we divide kg(m/s^2) with kg, you’ll end with m/s^2
If you’re in physics, we always work with m/s^2 for every acceleration that exists. So we basically have 25.3 m/s^2 for gravity.
To find the weight, we can use the F=ma formula but rewritten as Weight = mass * gravity
Weight = (90kg)(25.3 m/s^2) = Option D = 2277 Newtons
5. Find the equation of the line that is perpendicular to the given line and passes through the given point. y = 5x-1; (-1, 1)
Answers
Answer:
y = -0.2x+ 0.8
Step-by-step explanation:
If a line is perpendicular to another line then the slope of the line = the negative reciprocal of the other line
Here Line AB has the equation y = 5x - 1. Here slope = 5
This comes from the fact that if a line has the equation y= mx + c then the slope = m and the y intercept = c
If XY is the line perpendicular to AB then its slope = -1/5. Let the y intercept of XY be c
Then equation of line XY is: y = (-1/5)x + c = -0.2x + c (1)
Since it passes through (-1, 1) ie through x = -1, y=1, substitution these values into the above equation (1), we get
1 = (-0.2)(-1) + c or
1 = 0.2 + c or
c = 0.8
Need help for this please
Answers
first, the perimeter of the rectangles is 30*2 = 60 (the 7 is not a part of the overall perimeter so we do not need to add it)
the "perimeter" (circumference) of the 2 semi circles = (22/7)*7 = 22by using the formula C = pi*d (2 semi circles of the same diamter = 1 circle)
now just add the 2 answers
22 + 60
= 82 yards
can anyone help me with this? 10th grade geometry
Answers
Answer:
In romania I was doing this in the 6th grade
Step-by-step explanation:
5.
A B and D C are parallel lines.
"slope" means inclination. and as you can imagine, parallel lines must have the same inclination, or they would not be parallel.
so, the slope of D C must be also 2/7.
4.
same thing as with 5.
both lines are parallel and must therefore have the same slope.
so, the slope of D C is also 3/4. and the first answer is correct.
Question 11(Multiple Choice Worth 5 points)
(03.06A LC)
Which statement is true for the equation 2x - 2x - 7 = -7?
It has infinitely many solutions.
It has two solutions.
It has one solution.
It has no solution.
Answers
Answer:
A) It has infinitely many solutionsStep-by-step explanation:
Given equation
2x - 2x - 7 = - 7Variables cancel and the equation simplifies as
- 7 = - 70 = 0Since we got both sides equal, it doesn't change with any value of x.
It means the equation has infinitely many solutions.
It has infinite solution
type in the correct solutions to match each graph.
Answers
Answer:
congruent and parallel those are two of them i dont know the other 2 sorry
Step-by-step explanation: