Use exp/log functions to rewrite y as
[tex]y = (1+x)^{\frac1x} \implies y = \exp\left(\ln\left(1+x)^{\frac1x}\right)\right)[/tex]
One of the properties of logarithms lets us bring down the exponent, so
[tex]y = \exp\left(\dfrac{\ln(1+x)}x\right)[/tex]
Now take the derivative of both sides with respect to x. By the chain and quotient rules,
[tex]\dfrac{dy}{dx} = \exp\left(\dfrac{\ln(1+x)}x\right) \times \dfrac{\frac x{1+x} - \ln(1+x)}{x^2}[/tex]
Simplify:
[tex]\boxed{\dfrac{dy}{dx} = \frac{x - (1+x)\ln(1+x)}{x^2(1+x)} (1+x)^{\frac1x}}[/tex]
A person who can afford a monthly payment of __________ and signed a mortgage with a monthly payment of __________ was most likely the victim of predatory lending.
A. $900; $1000
B. $900; $800
C. $900; $900
D. $900; $700
Answer:
A . 900-1000
Step-by-step explanation:
Find the distance between the two points in simplest radical form.
(-8,3) and (-2,5)
Here we would be using distance formula to calculate the distance between those two points.
Points are,
(-8,3) (-2,5)★ Distance Formula :
[tex]\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar[/tex]We have :
x1 = -8 x2 = -2 y1 = 3 y2 = -5Substituting the values :
Refer the attachment.Additional Information :Centroid of a triangle :-
[tex]\boxed{ \sf{Centroid \: = \: \dfrac{x_1 \: + \: x_2 \: + \: x_3}{3} }} \: \pink\bigstar[/tex]Midpoint of two points:-
[tex]\boxed{ \sf{M \: = \: \dfrac{x_1 \: + \: x_2 }{2} \: , \: \dfrac{y_1 \: + \: y_2 }{2}}} \: \pink\bigstar[/tex]The sum of squares of lengths of the two sides of a rectangular field is 25m2.Their difference is 1m .what is the length of each side of the field
Answer:
Perimeter of a rectangle = 2×(Length+Breadth)
(i) Length = 16.8 cm
Breadth = 6.2 cm
Perimeter = 2×(Length+Breadth)
= 2×(16.8+6.2) =46 cm
(ii) Length = 2 m 25 cm
=(200+25) cm (1 m = 100 cm )
= 225 cm
Breadth =1 m 50 cm
= (100+50) cm (1 m = 100 cm )
= 150 cm
Perimeter = 2×(Length+Breadth)
= 2×(225+150) =750 cm
(iii) Length = 8 m 5 dm
= (80+5) dm (1 m = 10 dm )
= 85 dm
Breadth = 6 m 8 dm
= (60+8) dm (1 m = 10 dm )
= 68 dm
Perimeter = 2×(Length+Breadth)
= 2×(85+68) =306
Susan has 600 feet of fencing to use in making a yard for her new puppy. The yard she has
planned has a length that is 75 feet less than twice the width. What are the dimensions of the
yard?
Answer:
Length = 175
Width = 125
Step-by-step explanation:
P=2(L+W)
600ft=2(L+W)
300=L+W
300=2W-75ft+W
375=3W
125=W
L=2W-75
L=2(125)-75
L=250-75
L=175
end
A cruise ship is 1480 feet from a light house off a Caribbean Island.
If the angle of elevation from the cruise ship to the top of the light
house is 4º, what is the height of the lighthouse? Round to the
nearest whole foot.
Answer:
104 feet
Step-by-step explanation:
To get the height of the lighthouse, we need to take the sine function of the anglesin4° = 0.07sin4° = h/1480⇒ h/1480 = 0.07⇒ h = 1480 x 0.07⇒ h = 103.6⇒ h = 104 feetAll the clocks below show the time in the aftemoon or evening. Write the times below the clocks using 24 hour time. Time is Time is Times Times
Answer:
1. 15:00
2. 20:10
3. 14:20
4. 14:45
5. 17:45
Step-by-step explanation:
Please help in stuck on this one
Answer:
Step-by-step explanation:
a.
[tex]2^3*2^{-3}=2^0\\b.\\\frac{2^3}{2^5} =2^{-2}\\c.\\2^{-3}*5^{-3}=10^{-3}[/tex]
Which statement correctly explains the difference between a right cylinder and an elliptic cylinder?
A right cylinder has circular bases while an elliptic cylinder has oval bases.
A right cylinder has rectangular bases while an elliptic cylinder has oval bases.
A right cylinder has triangular bases while an elliptic cylinder has oval bases.
A right cylinder has rectangular bases while an elliptic cylinder has circular bases.
If the elements of the cylinder are perpendicular to the planes containing the bases, the cylinder is a right cylinder, otherwise it is called an oblique cylinder. If the bases are disks (regions whose boundary is a circle) the cylinder is called a circular cylinder
CAN SOMEONE PLS ANSWER THIS QUESTION FAST
I WILL MARK BRAINLIEST
Answer:
B 5
Step-by-step explanation:
it is the same ratio as the red
HELP, i need help!!!!!!!!!!!!!!
Answer:
t = 7.46, 0.42
Explanation:
h = 126t - 16t² [ "h" is height, "t" is time ]
when height is 50 feet
126t - 16t² = 50-16t² +126t -50 = 016t² -126t +50 = 0==================
[tex]\sf use \ quadratic \ formula : x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ ax^2 + bx + c = 0[/tex]
==================
[tex]\Longrightarrow \sf t = \dfrac{-126\pm \sqrt{126^2-4\left(-16\right)\left(-50\right)}}{2\left(-16\right)}[/tex]
[tex]\Longrightarrow \sf t = \dfrac{63\pm\sqrt{3169}}{16}[/tex]
[tex]\Longrightarrow \sf t = 7.46, \ 0.42[/tex]
Let's find
h=126t-16t²Put h=50
-16t²+126t=50-16t²+126t-50=0Use quadratic formula
[tex]\\ \rm\Rrightarrow t=\dfrac{-126\pm\sqrt{126²-4(-16)(-50)}}{-32}[/tex]
[tex]\\ \rm\Rrightarrow t=7.5s,0.4s[/tex]
Find the value of cos F rounded to the nearest hundredth, if necessary
Using the trigonometric ratios, the value of cos F in the right angle triangle is 0.28 .
What are right angle triangle?Right angle triangle are triangle that has one of its angles as 90 degrees. The sides and angles can be found using trigonometric ratios.
Therefore,
cos F = adjacent / hypotenuse
adjacent = FE
hypotenuse = 50
50² - 48² = FE²
FE = √2500 - 2304
FE = √196
FE = 14
Therefore,
cos F = 14 / 50
cos F = 0.28
learn more on right triangle here: https://brainly.com/question/6322314
Find the slope of the line passing through the points (7, -3) and (3, -7)
Answer:
The slope of the line is -1
Step-by-step explanation:
You need to use the slope formula
Slope Formula: y2 - y1 / x2 - x1
**The numbers represent subscripts but the subscripts aren't on computers**
Your Coordinate Points:
(7, -3) and (3, -7)
Do -7 - (-3) / 3-7
First, do -7 - (-3)
The negatives cancel to an addition problem.
-7 + 3
Now do -7 + 3. This is a subtraction problem that should be negative.
-7 + 3 = -4
Next, do 3 - 7
That should be 4
-4/4 is what we have right now.
Do -4 divided by 4 which has to contain a negative.
That is simply -1.
The slope of the line is -1
please help, super easy 7th grade math! worth a lot of points
Answer:
57mm
Step-by-step explanation:
Length of missing side= perimeter- known lengths
= 152mm- (30+20+45)mm
= (152 - 95)mm
= 57mm
Given the sequence 1,1,2,3,5,8….,find the 6th term
Answer:
8 is the ans because it is 8
Mrs. Angle has 12 students in her advanced algebra class. On a recent test, the average was 80. When Beth asked for her score, Mrs Angle could not find it, but she did remember adding Beth's score in the average. She also remembered Beth had passed. These are the scores of the other students
65, 65, 70, 70, 80, 85, 90, 90, 90,100.
What is Beth's score?
Answer:
75Step-by-step explanation:
Let the Beth's score is x.
The average is 80.
Solve the following equation:
average = sum / number(65*2 + 70*2 + 80 + 85 + 90*3 + 100 + x)/11 = 80805 + x = 80*11x = 880 - 805x = 75Beth's score was 75
help me out guys thank u
Answer:
[tex] \sf \: a5 = 769[/tex]
At noon, there are 700 juniors and 1,100 seniors at a college fair. After 12:00 p.m., 20 juniors arrive every 15 minutes and 45 seniors leave every 15 minutes. What is the ratio of juniors to seniors at 2:00pm in fraction form
Answer:
find the common factor in the given algebraic expressions 4 (x-y) , 6(y-x)
please help me out, simple
Answer:
Answer is 45⁰
Step-by-step explanation:
The angle ATB IS 45⁰
what is the unit rate of 36 ounces of 5.79
A unit ounce is 0.16
If 36 ounces worth 5.79, 1 ounce will be
= 5.79 / 36
= 0.1608
NEED HELP ASAP!!!
On a coordinate plane, sketch the graphs. y=|x| , y=|x+3| , and y=|x-2|
Answer:
Step 1. Plot x-intercept
Step 2. Plot y-intercept
Step 3. Connect dots
y = |x|
x-intercept = (0,0)
y-intecept = (0,0)
y = |x + 3|
x-intercept = (-3,0)
y-intecept = (0,3)
y = |x - 2|
x-intercept = (2,0)
y-intecept = (0,2)
BRAINLIEST please if this helped!9. Find the value of x. Round your answer to the nearest tenth.
sin Xº = 4/15
Answer: 15.5 degree
Step-by-step explanation:
Write the exponential function y = 22(1.35)' in the form y = aekt.
(a) Once you have rewritten the formula, give k accurate to at least four decimal places.
k%3D
help (numbers)
If t is measured in years, indicate whether the exponential function is growing or decaying and find the annual and
continuous growth/decay rates. The rates you determine should be positive in the case of growth or decay (by choosing
decay the negative rate is implied).
(b) The annual? rate is
% per year (round to the nearest 0.01%).
Answer:
y = 22·e^(0.3001t), growingannual rate: 35%continuous rate: 30.01%Step-by-step explanation:
When an exponential function is in the form ...
y = ab^t
the factor 'b' is called the growth factor. When t is in years, it is related to the annual growth rate (r) by ...
b = 1 +r
In the alternate form, this can be written ...
y = a·e^(kt)
Comparing the forms, we see that ...
b = e^k ⇒ k = ln(b)
__
(a)y = 22·1.35^t
k = ln(1.35) ≈ 0.3001
y = 22·e^(0.3001t)
The growth factor is greater than 1, so the function is growing.
__
(b)The annual growth rate is ...
r = 1.35 -1 = 0.35 = 35.00%
__
(c)The continuous growth rate is ...
k = 0.3001 = 30.01%
15 over r - 1 when r= 5
Find the equation of the line through (-5,9) that is parallel to y=-2x+2
Answer:
Step-by-step explanation:
y - 9 = -2(x + 5)
y - 9 = -2x - 10
y = -2x - 1
Which of the following are not polynomials?
Answer:
D
I really wish is right!!!
is 5/74 rational or irrational?
Answer:
Rational
Step-by-step explanation:
5.74 is the same as 5.74 over 1. In other words, 5.74 can be written with a numerator and denominator, like this:
5.74 = 5.74/1
5.74 x 100/ 1 x 100
You can multiply the numerator and denominator of any fraction by the same number and keep the value of the fraction the same. Here we will multiply the numerator and denominator by 100 to get rid of the decimal point.
5.74 × 100/ 1 × 100
When we calculate the numerator and the denominator above, we get this fraction:
574/100
The fraction above is the same as 5.74. Furthermore, the numerator and the denominator of the fraction above are integers. Therefore, we can conclude that the answer to "Is 5.74 a rational number?" is yes.
Lainey is sliding down a water slide that is 423 feet long at a rate of 47 feet per second. How long will it take Lainey to travel from the top to the bottom of the slide?
Answer:
It will take Lainey 9 seconds to travel from top to bottom
Further explanation:
The formula of speed will be used to calculate the time to reach from top to bottom of the slide.
Given
\begin{gathered}Distance=d=423\ feet\\Speed=s=47\ feet\ per\ second\end{gathered}
Distance=d=423 feet
Speed=s=47 feet per second
The formula for speed is:
s=\frac{d}{t}s=
t
d
Putting the values of distance and speed in the formula:
\begin{gathered}47=\frac{423}{t}\\t=\frac{423}{47}\\t=9\ seconds\end{gathered}
47=
t
423
t=
47
423
t=9 seconds
It will take Lainey 9 seconds to travel from top to bottom
Keywords: Speed, distance
Learn more about speed
Please Help!!!!!!!! In a recent year,24.7% of all registered doctors were female. If there were 43,200 female registered doctors that year, what was the total number of registered doctors?
Round your answer to the nearest whole number.
This is one single number just a bit under 175 thousand. Delete the comma if needed.
========================================================
Work Shown:
x = number of total doctors
24.7% of x = number of female doctors
0.247x = 43200
x = 43200/(0.247)
x = 174,898.785425101 approximately
x = 174,899 when rounding to the nearest whole number
[80 POINTS] An engineer is designing a new drill bit as shown in the diagram. To finalize the design, the engineer needs to know the volume of the drill bit.
What is the volume of the drill bit?
Answer:
2,106 pi mm3
Step-by-step explanation:
Volume of the drill bit is equals to [tex]2,106\pi mm^{3}[/tex].
What is volume?" Volume is defined as the total space occupied by a three dimensional object enclosed in it. It is measured in cubic unit."
Formula used
Volume of the cone = [tex]\frac{1}{3} \pi r^{2}h[/tex]
Volume of the cylinder =[tex]\pi r^{2}h[/tex]
r = radius of the cone / cylinder
h = height of the cone / cylinder
According to the question,
Given,
Radius of the cylinder = 9 mm
Radius of the cone = 9 mm
Height of the cone = 24 mm
Height of the cylinder = 18 mm
Substitute the values in the formula to obtained the required volume,
Volume of the cone [tex]= \frac{1}{3} \pi (9^{2})(24)[/tex]
[tex]= \pi (81)(8)\\=648\pi mm^{3}[/tex]
Volume of the cylinder [tex]= \pi (9^{2} )(18)[/tex]
[tex]=1458\pi mm^{3}[/tex]
Required Volume of the drill pit
= Volume of the cone + Volume of the cylinder
[tex]= (648\pi + 1458\pi )mm^{3} \\= 2106\pi mm^{3}[/tex]
Hence, Option(B) is the correct answer.
Learn more about volume here
https://brainly.com/question/1578538
#SPJ2
Dante is saving money to buy a game. So far he has saved $24, which is two-thirds of the total cost of the game. How much does the game cost?
Answer:
The game costs 36$ dollars.
Step-by-step explanation:
2/3 of 36 is 24 :p
The total cost of the game Dante wants to buy is 26 dollars.
What is a fraction?A fraction describes some parts of a certain quantity. Fractions are of two types one is a proper fraction and another is an improper fraction. In a proper fraction, the numerator is smaller than the denominator and n improper fraction numerator is greater than the denominator.
Assuming The total cost of the game is x dollars.
Given that 24 dollars is (2/3)rd of the total cost of the game.
So we can write 24 is (2/3)rd of the total cost of the game.
∴ 24 = (2/3)×x.
24 = (2/3)x.
x = 24×(3/2).
x = 12×3.
x = 36 dollars.
learn more about fractions here :
https://brainly.com/question/10354322
#SPJ2