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]
Use calculus to find the volume of the following solid S:
The base of S is the parabolic region {(x,y)|x^2≤y≤1}. Cross-sections perpendicular to the y-axis are squares.
S casts a "shadow" on the x-y plane given by the set
[tex]S' = \left\{(x,y) ~:~ -1 \le x \le 1 \text{ and } x^2 \le y \le 1\right\}[/tex]
Each cross section is a square whose side length is determined by the vertical distance between y = 1 and y = x², which is |1 - x²|. But since -1 ≤ x ≤ 1, this distance simplifies to 1 - x².
The volume of an infinitesimally thin section is then (1 - x²)² ∆x (where ∆x represents its thickness), and so the volume of S is
[tex]\displaystyle \int_{-1}^1 (1-x^2)^2 \, dx = \int_{-1}^1 (1 - 2x^2 + x^4) \, dx[/tex]
The integrand is even, so this integral is equal to twice the integral over [0, 1] :
[tex]\displaystyle \int_{-1}^1 (1-x^2)^2 \, dx = 2 \int_0^1 (1 - 2x^2 + x^4) \, dx = 2 \left(1 - \frac23 + \frac15\right) = \boxed{\frac{16}{15}}[/tex]
Using only 3,4&5 what equals 11
(5×3)-4 = 11
hope it helps...!!!
Answer:
(5*3)-4=11
Step-by-step explanation:
because when you multiply 5*3=15, then subtract 4 from it, it gives you 11. There are no other options becuase 5*4-3=17 and 4*3-5=16 and 5*4+3=23 and 4*3+5=17.
Need help as soon as possible
Answer:
100cm
Step-by-step explanation:
divide the shape into smaller shapes then find the area of each and add them together
Explain how to use basic facts and number patterns to find 5600%7
Answer:
600.
Well, to divide these numbers, we can use certain strategy that fits with out logic. For example, we know that 56 divided by 7 can be done mentally, because it's a simple division that can be immediately solved.
So, 56 divided by 7 is 8, then we add the two zeros to the quotient, because we isolated the first to digit to make the division easier and then we have to add back those zeros.
Therefore the division results in 600.
There are several operations that can be done by using certain strategy, like separating the number in easier parts like we did this time.
solve for a ~
[tex]a {}^{2} - 5a + 6 = 0[/tex]
thankyou ~
Answer:
Hi there!
Given equation :-[tex]\:\mathsf{a^2\:-\:5a\:+\:6\:=\:0}[/tex]
Now=> By splitting the middle term
=> [tex]\:\mathsf{a^2\:-\:2a\:-\:3a\:+\:6\:=\:0}[/tex]
=> [tex]\:\mathsf{a(a\:-\:2)\:-\:3(a\:-\:2)\:=\:0}[/tex]
=> [tex]\:\mathsf{(a\:-\:2)\:-\:(a\:-\:3)\:=\:0}[/tex]
We get ,=> [tex]\:\sf{a\:=\:2\: and\: a\:=\:3}[/tex]
[tex]\:\mathsf{Hope\:this\:helps\:you!\::)}[/tex]
Thank you!
Answer:
[tex]a = 3 \: \: \: and \: \: a = 2[/tex]
Step-by-step explanation:
⬇
[tex]a^{2} - 3a - 2a + 6 = 0[/tex]
⬇
[tex]a \: (a - 3) \: \: (a - 2)[/tex]
⬇
[tex]{}\ a - 3 = 0 \\ a = 2{}[/tex]
Choose all statements that are true.
A 15% of 15 is 1.
B 5% of 50 is 10.
C 10% of 100 is 10.
D 2% of 100 is 5.
E 3% of 200 is 6.
Answer:
C, D, E
Step-by-step explanation:
15 * .15 = 2.25
50 * .05= 2.5
100 * .10= 10
100 * .05= 5
200 * .03= 6
What is the median of the data set? -10, -5, -1, 0, 0, 3, 6, 8
A. 0
B. 0.125
C. 3
D. -1
Answer: A
Answer:
the anwer is a so 0
Step-by-step explanation:
the number that showed up the most is 0 so median is 0
A garden store recently sold 44 seed packets, including 22 squash seed packets. considering this data how many of the next 94 seed packets sold should you expect to be squash seed packets?
The expected squash seed packets is its mean or average value
You should expect 47 squash seed packets in the next 94 seed packets
How to determine the expected squash seed packets?The given parameters are:
Sample size (n) = 44 seed packetsSquash seed (x) = 22 seed packetsPopulation (N) = 94 seed packetsThe expected squash seed packets is calculated as:
E(x) = x/n * N
This gives
E(x) = 22/44 * 94
Evaluate the product
E(x) = 47
Hence, you should expect 47 squash seed packets in the next 94 seed packets
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Finish the polynomial by adding one number to make it a perfect square
x^2+18x+
Answer:
81
Step-by-step explanation:
[tex] {x}^{2} + 18x + {(( \frac{1}{2})(18)) }^{2} [/tex]
[tex] {x}^{2} + 18x + {9}^{2} [/tex]
[tex] {x}^{2} + 18x + 81[/tex]
[tex] {(x + 9)}^{2} [/tex]
a. Use the appropriate formula to find the value of the annuity
b. Find the interest
Rate
Periodic Deposit
$6000 at the end of each year
15.5% compounded annually
Time
10 years
The value of the $6000 annuity given annual compounding is $124,836.12.
What is the value of the annuity?
The value of the annuity can be determining using this formula: amount deposited x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
n = number of years r = interest rate$6000 x [(1.155^10) - 1/0.155] = $124,836.12
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Find the indicated side for each triangle below:
Problem 5
Apply the Law of Sines
s/sin(S) = r/sin(R)
s/sin(78) = 10/sin(48)
s = sin(78)*10/sin(48)
s = 13.162274
Answer: 13.162274 approximately=============================================================
Problem 6
Use the Law of Sines here as well.
x/sin(X) = y/sin(Y)
x/sin(53) = 6/sin(22)
x = sin(53)*6/sin(22)
x = 12.791588
Answer: 12.791588 approximatelyAnswer:
Sine Rule
[tex]\sf \dfrac{a}{sinA}=\dfrac{b}{sinB}=\dfrac{c}{sinB}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Question 5
[tex]\sf \implies \dfrac{s}{sin(78)}=\dfrac{10}{sin(48)}[/tex]
[tex]\sf \implies s=\dfrac{10sin(78)}{sin(48)}[/tex]
[tex]\sf \implies s=13.16227426[/tex]
s = 13.2 (nearest tenth)
Question 6
[tex]\sf \implies \dfrac{x}{sin(53)}=\dfrac{6}{sin(22)}[/tex]
[tex]\sf \implies x=\dfrac{6sin(53)}{sin(22)}[/tex]
[tex]\sf \implies x=12.79158761[/tex]
x = 12.8 (nearest tenth)
300,000+5,000+80+8· 1/100 +9· 1/10,000
Answer:
305,080.0809
Step-by-step explanation:
3 x 100,000 : digit 3 is in the hundred thousands place
5 x 1000 : digit 5 is in the thousands place
8 x 10 : digit 8 is in the tens place
8 x 1/100 : digit 8 is in the hundredths place which means it is the second number after the decimal
9 x 1/10,000 : digit 9 is in the ten thousandths place which means it is the fourth number after the decimal
we get the following number:
305080.0809
X/5= 7
X/2= 6.5
Find x
Answer:
1. Answer is 35
2. Answer is 13
Step-by-step explanation:
All you have to do is multiply 5 on both sides for number 1 and multiply by 2 on both sides for number 2.
I need help finding the direction please. 100 points!
=======================================================
Explanation:
Take note that the x and y coordinate of this vector are the same.
This leads to a 45-45-90 reference triangle. If the vector was in the first quadrant (the northeast), then the answer would be 45 degrees.
However, we need to add on 180 so we get to the third quadrant instead where x and y are both negative. This gets us to 180+45 = 225 degrees
---------------
If you wanted to use a calculator, then you would compute the value of [tex]\tan^{-1}(b/a)[/tex] where <a,b> is the vector in question.
Since a = b in this case, we have b/a = 1 and the arctangent of this is 45 degrees. The adjustment of adding on 180 still applies like from before.
What is the equation of the line that passes through the point (3,7) and has a slope of 2/3
Answer:
[tex]Y=\frac{2}{3} x +5[/tex]
Hope This Helped! :) Please Mark Brainliest!
PLEASE HELP 100 POINTS AND BRAINLY
Answer:
Step-by-step explanation:
Answer:
(2 , 2) is the solution
Step-by-step explanation:
7x - 4y = 6
-6x + 7y = 2
49x - 28y = 42
-24x + 28y = 8
25x = 50
therefore
x = 2
7x - 4y = 6
7×2 - 4y = 6
14 - 4y = 6
14 - 6 = 4y
8 = 4y
8 ÷ 4 = 4y ÷ 4
2 = y
therefore
x = 2
y = 2
hope this will helpful to you....
What is the measurement of angle P? MPO O A.) 36° O B.) 64° O C.) 116° O D.) 244°
Answer:
Well, there is no picture so theres no way to know what it could be. All I can do is guess.
B
Question is on the screenshot.
help me help me help me
Answer:
read step by step
Step-by-step explanation:
6 is +4.
19, 23, 27, 31
7 is all perfect square numbers
25, 36, 49, 64
8 is x2.
32, 64, 128, 256
9 is each number multiplied by the next. ex: 1x2=2, 2x3+6, 3x4=12
so the next few would be 30, 42, 56, 72
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PLS AND TY IT IS DUE SOON :))
Answer:
b = 0.62
Step-by-step explanation:
Hello!
We can look at the y-values of the function to find our multiplier. A multiplier will determine if the graph decays or grows in an exponential function, and by how much.
When x is 0, we can see the y-value is around 3, but as x approaches 1, the y-value comes to around 2.
We can find the multiplier by dividing the current term by the previous term.
2 ÷ 32/30.6666...This number is closest to 0.62, so the approximation is 0.62.
2/3
0.6666..
Approximation is 0.62 (b)
Hope this helped! Stay healthy!♡
Emily walked 5 2/6 miles in the morning and another 3 3/5 miles in the afternoon What was the total distance she walked?
Answer:
The correct answer would be 8 14/15 miles.
Step-by-step explanation:
You have to get the fractions 5 2/6 and 3 3/5 to a common denominator (30) getting you the fractions 10/30 and 18/30. 10/30+18/30 is 28/30 which can simplify to 14/15. 5+3 = 8 getting you the answer of 8 14/15
Order the integers from greatest to
least: 4, -3, 0, 8, -5.
A 5, 3, 0, 4,8
B 3.-5, 0. 4.8
8, 4.0, 3, 5
D 0, -3, 4, 5,8
Answer:
8, 4, 0, -3, -5
(greatest to least order)
-Answer: C-
Step-by-step explanation:
8 is positive so its greatest
-5 is negative but it is farthest away from 0 so it is least
A right triangle has a hypotenuse with a length 12 and a leg with
length 5. How long is the triangle's other leg?
Answer:
13
Step-by-step explanation:
pythagorean theorum
a^2+b^2=c^2
12^2+5^2=c^2
144+25=c^2
c^2=169
c=13
The length of the triangle's other leg is approximately 10.908.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
We can use the Pythagorean theorem to solve for the length of the other leg of the right triangle.
The Pythagorean theorem states that for any right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides (the legs).
That is, for a right triangle with legs a and b and hypotenuse c:
c² = a² + b²
In this case,
We know that the hypotenuse has a length of 12 and one of the legs has a length of 5.
Let's denote the length of the other leg as "x".
So we can set up the equation:
12² = 5² + x²
Simplifying, we get:
144 = 25 + x^2
Subtracting 25 from both sides, we get:
119 = x²
Taking the square root of both sides, we get:
x ≈ 10.908
Therefore,
The length of the triangle's other leg is approximately 10.908.
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Using proportions to solve for missing sides.
RST~YSZ, find YZ.
Answer:
YZ = 28
Step-by-step explanation:
A proportion involving the known and unknown sides is ...
TR/ST = ZY/SZ
__
This proportion uses SZ, which is not shown on the diagram. The length of SZ can be found from ...
SZ +ZT = ST . . . . . . . segment sum theorem
SZ + 5 = 40 . . . . with given values
SZ = 35 . . . . . subtract 5
__
So, the proportion with values filled in is ...
(3x -7)/40 = (2x +2)/35
7(3x -7) = 8(2x +2) . . . . . . . multiply by 280
21x -49 = 16x +16 . . . . . . . eliminate parentheses
5x = 65 . . . . . . . . . . add 49 -16x
x = 13 . . . . . . . . divide by 5
YZ = 2x +2 = 2(13) +2
YZ = 28
_____
Additional comment
RT = 3x -7 = 3(13) -7 = 32
sheri caught twice as many fireflies as robert. jessica caught 10 more flies than robert all together they caught 150 flies. how many flies did jessica catch?
Answer:
45 fireflies
Step-by-step explanation:
Because,
Sheri caught 70 and Robert caught 35.
150-35-70= 35
35+10 is equal to 45.
Following the rules given is the right answer
Due in a MINUTE!!! Need help!
Answer:
GH = 15
Step-by-step explanation:
In a trapezoid, the length of the median is one-half the sum of the lengths of the bases. Therefore:
[tex]9x - 3 = \frac{1}{2} (19 + 5x + 1)[/tex]
[tex]18x - 6 = 5x + 20[/tex]
[tex]13x = 26[/tex]
[tex]x = 2[/tex]
[tex]9(2) - 3 = 18 - 3 = 15[/tex]
Consider the rhombus ABCD with the side length AB of 14 cm and the measure of the angle B of 120 °. Through the vertex A goes a certain secant that intersects the extensions of the sides BC and CD in E, respectively F.
Calculate:
[tex] \frac{1}{ce} + \frac{1}{cf} [/tex]
Answer:
1/14
Step-by-step explanation:
In the given geometry, we have similar triangles:
ΔCEF ~ ΔBEA ~ ΔDAF
This lets us write the relations for corresponding sides ...
CF/CE = DF/DA
where DF = CF -CD
We can rearrange this relation to give the value we're looking for as follows.
__
Making the substutition for DF, and multiplying by CE, we have ...
CF = CE(CF -CD)/DA
Both DA and CD are sides of the rhombus, so are both 14 cm in length. Multiplying by DA and making the number substitution, we have ...
DA·CF = CE·CF -CE·CD
14·CF = CE·CF -14·CE . . . . substitute 14 for DA and CD
14(CF +CE) = CE·CF . . . . . add 14·CE
(CF +CE)/(CE·CF) = 1/14 . . . . divide by 14·CE·CF
1/CE +1/CF = 1/14 . . . . . . . . . simplify
Vera has challenged Alexey to a round of Marker Mixup. Marker Mixup is a game where there is a bag of 5 red markers numbered 1 through 5, and another bag with 5 green markers numbered 6 through 10
Alexey will grab 1 marker from each bag, and if the 2 markers add up to more than 12 he will win If the sum is exactly 12, he will break even, and If the sum is less than 12, he will lose $6
What is Alexey's expected value of playing Marker Mixup?
Answer:
Step-by-step explanation:
The total possble combinations = 5 * 5 = 25 ways.
The number of ways to get exactly 12
= 2,10 3,9 4,8 5,7 = 4 ways.
The ways to get > 12
= 3,10 4,9 4,10 5,8 5,9 5,10 = 6 ways.
So the number of ways to get < 12 = 25 - 4 - 6 = 15 ways.
Expected value
= 4(0) + 6(x) + 15(-6)
I have written x as you have not said how much he gets if he wins.
Answer:
−$2.40
Step-by-step explanation:
correct on khan
I know that the answer is 27 and that 3 + x = 7 but where do you get 4?
Answer:
27
step by step explanation
if you are calculating for the area of the figure, divide the shape into two figures and you will get two rectangles
for shape 1
length=3 width=5
for shape2
length 7-3=4
width=3
area of shape1. =3×5=15
area of shape2. =4×3=12
area of the shape= 12+15 = 27
This recipe makes 10 flapjacks.
How much of each ingredient is needed to make 35 flapjacks by following this recipe?
Recipe: Makes 10 flapjacks
140 g margarine
120 g sugar
100 ml syrup
240 g oats
50 g raisins
Answer:
Multiply each measure of ingredients by 3.5
Step-by-step explanation:
This recipe makes 10 flapjacks. We want to be able to make 35 flapjacks.
Divide 35 by 10 to find the ratio of these 2 numbers.
35 / 10 = 3.5
Now we can multiply the measures by this number to find out how much of each ingredient we need.
140 * 3.5 = 490
120 * 3.5 = 420
100 * 3.5 = 350
240 * 3.5 = 840
50 * 3.5 = 175
Answer:
Recipe: Makes 35 flapjacks
490 g Margarine
420 g sugar
350 ml syrup
840 g oats
200 g raisins
