What function do you know from calculus is such that its first derivative is itself?The above function is a solution of which of the following differential equations?a. y = ey.b. y = 1.c. y = y.d. y = y2.e. y = 2y.What function do you know from calculus is such that its first derivative is a constant multiple k of itself? The above function is a solution of which of the following differential equations?a. y = ky.b. y = yk.c. y = eky.d. y = k.e. y = y + k.
Answer:
a. y= e raise to power y
c. y = e^ky
Step-by-step explanation:
The first derivative is obtained by making the exponent the coefficient and decreasing the exponent by 1 . In simple form the first derivative of
x³ would be 2x³-² or 2x².
But when we take the first derivative of y= e raise to power y
we get y= e raise to power y. This is because the derivative of e raise to power is equal to e raise to power y.
On simplification
y= e^y
Applying ln to both sides
lny= ln (e^y)
lny= 1
Now we can apply chain rule to solve ln of y
lny = 1
1/y y~= 1
y`= y
therefore
derivative of e^y = e^y
The chain rule states that when we have a function having one variable and one exponent then we first take the derivative w.r.t to the exponent and then with respect to the function.
Similarly when we take the first derivative of y= e raise to power ky
we get y=k multiplied with e raise to power ky. This is because the derivative of e raise to a constant and power is equal to constant multiplied with e raise to power y.
On simplification
y= k e^ky
Applying ln to both sides
lny=k ln (e^y)
lny=ln k
Now we can apply chain rule to solve ln of y ( ln of constant would give a constant)
lny = ln k
1/y y~= k
y`=k y
therefore
derivative of e^ky = ke^ky
How do the surface areas of similar prisms compare when dimensions are doubled?
O A The surface area of the larger prism is 2 times the surface area of the smaller prism.
OB. The surface area of the larger prism is 4 times the surface area of the smaller prism.
OC. The surface area of the larger prism is 8 times the surface area of the smaller prism.
Answer:
The surface area of the larger prism is 4 times the surface area of the smaller one.
(which agrees with answer B in your list)
Step-by-step explanation:
Notice that the lateral surface area of prisms always consists of parallelograms, whose areas are given by the product base times height. = B x H
Therefore if the dimensions of the prism double, then the base and height of the parallelograms will double as well, making such individual ares of the lateral faces go from:
B x H to --> 2 B x 2 H = 4 (B x H)
that is 4 times the original lateral face's area.
with the faces for the top and bottom bases of the prism, something similar happens, so we conclude that the surface area of the larger prism is 4 times the surface area of the smaller one.
Answer:
c
Step-by-step explanation:
edge 2021
-6mn + 5mn - 3x2 - 4x2
Help
Answer:
Step-by-step explanation:
3x^2 - 4x^2 - 6mn + 5mn
-x^2 - mn
Combine like terms: A. 7a + 7b - 13a - 11b B. -5a - 12a + 2b - 3b Explain
how does "money breeds money" apply to simple interest
Answer:
The saying money breeds money means that with money, you have the possibility to create more money. Simple interest is the idea that you have something, and you obtain a percentage of that every designated time period. That being said, simple interest = money breeds money
Suppose we are estimating a population proportion by its sample equivalent.
(a) We have a sample of n = 10 units and we find the proportion is p = .4. If the true proportion is p= .3 find PC Ô-p|>.2)
(b) Consider the same problem as in part (a) but now, our sample size is n = 400. Find P( P-p> .001)
Answer:
(a) 0.16759
(b) 0.9649
Step-by-step explanation:
Given that:
n = 10 , p = 0.3 and [tex]\hat p = 0.4[/tex]
[tex]P(|\hat p - p| > 0.2 ) = 1 - P ( |\hat p -p| \leq 0.2)[/tex]
= [tex]1 - P(-0.2 \leq \hat p-p \leq 0.2)[/tex]
= [tex]1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{\dfrac{pq}{n}}} \leq \dfrac{\hat p -p}{\sqrt{\dfrac{pq}{n}}} \leq \dfrac{0.2}{\sqrt{\dfrac{pq}{n}}} \end {pmatrix}[/tex]
[tex]=1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{\dfrac{(0.3)(1-0.3)}{10}}} \leq Z \leq \dfrac{0.2}{\sqrt{\dfrac{(0.3)(1-0.3)}{10}}} \end {pmatrix}[/tex]
[tex]=1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{\dfrac{(0.3)(0.7)}{10}}} \leq Z \leq \dfrac{0.2}{\sqrt{\dfrac{(0.3)(0.7)}{10}}} \end {pmatrix}[/tex]
[tex]=1 - P \begin {pmatrix} \dfrac{-0.2}{\sqrt{0.021}} \leq Z \leq \dfrac{0.2}{\sqrt{0.021}} \end {pmatrix}[/tex]
[tex]=1 - P \begin {pmatrix} -1.380 \leq Z \leq 1.380 \end {pmatrix}[/tex]
= 1 - P( Z ≤ 1.380) - P(-1.380)
= 1 - ( 0.91620 - 0.08379 )
= 1 - 0.83241
= 0.16759
b) when n = 400; p =0.3 , q = 1 - p = 1 - 0.3 = 0.7
[tex]P( |\hat p - p | > 0.001) = 1- P ( |\hat p - p | < 0.001 )[/tex]
[tex]= 1- P ( -0.001 < \hat p - p < 0.001 )[/tex]
[tex]= 1- P ( \dfrac{-0.001}{\sqrt{\dfrac{pq}{n}}} < \dfrac{ \hat p - p}{\dfrac{pq}{n}} < \dfrac{0.001}{\sqrt{\dfrac{pq}{n}}} )[/tex]
[tex]= 1- P ( \dfrac{-0.001}{\sqrt{\dfrac{0.3\times 0.7}{400}}} < Z < \dfrac{0.001}{\sqrt{\dfrac{0.3 \times 0.7}{400}}} )[/tex]
[tex]= 1- P ( \dfrac{-0.001}{\sqrt{5.25 \times 10^{-4}}} < Z < \dfrac{0.001}{\sqrt{5.25 \times 10^{-4}}} )[/tex]
[tex]= 1- P ( -0.0436< Z < 0.0436)[/tex]
= 1 - P ( Z < 0.0436) - P ( -0.0436)
= 1 - (0.5176 - 0.4825)
= 1 - 0.0351
= 0.9649
1200-5(3x+30)=600 show the steps to solve this problem
Answer:
x=+30
Step-by-step explanation:
1200-5(3x+30)=600
We move all terms to the left:
1200-5(3x+30)-(600)=0
We add all the numbers together, and all the variables
-5(3x+30)+600=0
We multiply parentheses
-15x-150+600=0
We add all the numbers together, and all the variables
-15x+450=0
We move all terms containing x to the left, all other terms to the right
-15x=-450
x=-450/-15
x=+30
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 30}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{1200 - 5(3x + 30) = 600}[/tex]
Distribute 5 through the parentheses
[tex] \dashrightarrow{ \sf{1200 - 15x - 150 = 600}}[/tex]
Subtract the numbers: 150 from 1200
[tex] \dashrightarrow{ \sf{ - 15x + 1050 = 600}}[/tex]
Move 1050 to right hand side and change it's sign
[tex] \dashrightarrow{ \sf{ - 15x = 600 - 1050}}[/tex]
Subtract 1050 from 600
[tex] \dashrightarrow{ \sf{ - 15x = 450}}[/tex]
Divide both sides of the equation by -15
[tex] \dashrightarrow{ \sf{ \frac{ - 15x}{ - 15} = \frac{ - 450}{ - 15} }}[/tex]
Calculate
[tex] \dashrightarrow{ \sf{x = 30}}[/tex]
Hope I helped!
Best regards! :D
Question 1 (1 point)
What is the slope of the line that passes through the points
(8,-15) and (-12,25)?
A No answer provided
a 2
6.-2
c15
D-1/2
Answer:
B) -2
Step-by-step explanation:
[tex]\frac{25-(-15)}{-12-8} =\frac{40}{-20} =-2[/tex]
x=
[tex] {3}^{y} [/tex]
[tex]y = {3}^{5} [/tex]
express in terms of X and or y
what is the average of the following numbers 66.9,5.6,70.1
Answer:
47.53
Step-by-step explanation:
First you add all of the numbers together.
66.9+5.6+70.1=142.6
Then you divide the sum of numbers by how many number there are.
142.6/3=47.53
I think I know it but just needing help if I get it wrong. Help me please !!
Answer:
8n=55
Step-by-step explanation:
The product(multiplication) of 8 AND a number(meaning the multiplication of 8 and a number which is said to be n) is(equal to) 55.
I hope I explained it well enough. lol
Answer:
B - the second answer .... 8n =55
Step-by-step explanation:
What is the product of (-0.9)×(-2.4)
Answer:
the answer is 2.16
Step-by-step explanation:
just use a calculator and it will tell you the answer
How do you do letter d? I keep getting the wrong answer
Answer:
18
Step-by-step explanation:
The integral is the area between f(x) and the x-axis. Remember that area below the x-axis is negative.
The area between x=0 and x=6 is a trapezoid.
The area between x=6 and x=9 is a rectangle.
The area between x=9 and x=15 is a triangle.
The area between x=15 and x=21 is a triangle.
The area between x=21 and x=27 is a trapezoid.
A = ½ (3+9) (6) + (3)(9) + ½ (6)(9) + ½ (6)(-9) + ½ (-9+-6) (6)
A = 36 + 27 + 27 − 27 − 45
A = 18
Simplify the following expression.
5 (2x - 3) + 4(x + 1)
Answer:
Step-by-step explanation:
10x - 15 + 4x + 4
14x - 11
The length of a toucan is about two thirds the length of a macaw. Toucans are about 24 in. long. What is the length of macaw
Answer:
12, 12 and 12 so 36
Step-by-step explanation:
Use the properties of exponents to simplify the expression: 2(x13)65⋅y23
If the distance marked on centimeter scale is from 2.5 to 4.5,
then the line segment is how many cm long?
Answer:
2.0cm longStep-by-step explanation:
If the distance marked on a centimeter scale is from 2.5 to 4.5, then the final destination is 4.5cm and the initial point = 2.5.
Distance between the two points will give us the length of the line segment.
Distance between the two points = final point - initial point
Distance between the two points = 4.5 - 2.5
Distance between the two points = 2.0 cm
Hence the line segment is 2.0cm long
solve the given triangles by finding the missing angle and other side lengths.
Answer:
32 degrees is the missing angle
Step-by-step explanation:
I subtracted 40 and 112 from 180.
Answer:
40+112+x=180
x=180-152
=28 degree.
At noon, the temperature in Ebonsville, Texas was 29℉. By midnight, the temperature had fallen to −10℉. What was the change in temperature over the 12-hour period?
Answer:
i believe it's 39
Step-by-step explanation:
29 -39 = -10
What is equivalent to 6/25. A.0.20 B.0.22 C. 0.24 D. None
Answer:
C. .024
Step-by-step explanation:
You multiply 25 by 4 to get 100 and then you multiply 6 by 4 to get twenty four. After that you divide both numbers by one hundred and you get C
-1
The distance AB
rounded to the
nearest tenth = [?]
Help Resources
-2
-1
0
Skip
B
Hint: Use the distance formula:
d = (x2 – X1)2 + (y2 - yı)?
Enter
Answer:
AB = 4.5
Step-by-step explanation:
Distance between A(-1, 2) and B(1, -2):
[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] A(-1, 2) = (x_1, y_1) [/tex]
[tex] B(1, -2) = (x_2, y_2) [/tex]
[tex] AB = \sqrt{(1 - (-1))^2 + (-2 - 2)^2} [/tex]
[tex] AB = \sqrt{(2)^2 + (-4)^2} [/tex]
[tex] AB = \sqrt{4 + 16} = \sqrt{20} [/tex]
[tex] AB = 4.5 [/tex] (nearest tenth)
Adam built a tree house with a rectangular base. The length of the base is 7 inches more than its width.
Ifw represents the width of the tree house, which inequality could be used to determine what lengths would make the area of the base
of the tree house greater than 293 square Inches?
W + 7 > 293
202 + 286 > 2,051
w2 + 7w > 293
12 + 293 > 293
Submit
w²+7w>293 is the inequality which we use to determine what lengths would make the area of the base of the tree house greater than 293 square Inches
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that Adam built a tree house with a rectangular base.
The length of the base is 7 inches more than its width.
Length=W+7
W is the width
The area of the base of the tree house greater than 293
We need to find the inequality to represent the area of the base of tree
Area of rectangle=Length×width
293=(w+7)w
293=w²+7w
As area is greater we have
w²+7w>293
Hence, w²+7w>293 is the inequality which we use to determine what lengths would make the area of the base of the tree house greater than 293 square Inches
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Divide $70 in the ratio 1:2:4
Answer:
Here Ratio=1:2:4
total money =$70
Step-by-step explanation:
let the ratio number be 1x,2x and4x
Now,
1x+2x+4x =$70
or, 7x. =$70
or, x. =$70÷7=$10
again,
1x=1×$10=$10,
2x=2×$10=$20 and
4x=4×$10=$40
<1 and <2 are —-
Adjacent angles
Supplementary angles
Right angles
Vertical angles
Write a rule to describe each transformation.
11. P (3,4), Q (3,5), R (4,5), S (5,0)
to
P’ (0,3), Q’ (0,4), R’ (1,4), S’ (2,-1) 12.
F (-4,1), E (-4,3), D (-1,3) to
F’ (1,4), E’ (3,4), D’ (3,1)
B (-3, -5), C (-2,-2), D (-1,-2) to
B’ (3,-5), C’ (2,-2), D’ (1,-2)
Choose the function to match the graph.
Answer:
your pics a little blurry but if i am reading it right
the first one
f(x)=log x+5
Write the following words as an algebraic expression. The sum of the quotient of a number x and 5 and the product of 6 and a number y
Answer:
[tex]\frac{x}{5} + 6y[/tex]
Step-by-step explanation:
graph the unequal x ≤ - 5
Answer:
Step-by-step explanation:
Simplify the expression using
order of operations
12 (10-5) - 40 + (4+1)
ans is 25
Step-by-step explanation:
12(10-5)-40+(4+1)
=12 of 5 - 40 + 5
= 60 - 40 +5
=60 +5 - 40
=65-40
=25
Answer:
-25
Step-by-step explanation:
We start off by using PEMDAS. 10-5 then 4+1.
12(5)-40+5
we multiply, then add and subtract giving us -25
the perimeter of the isosceles triangle with base length y-2 and legs of length y
Answer:
3y-2
Step-by-step explanation:
y+y+y-2
3y-2
The perimeter of the isosceles triangle with base length y - 2 and length of legs y is 3y - 2. legs.
Here,
Base length of triangle is y - 2.
Length of legs of triangle is y.
What is Perimeter of triangle?
Perimeter of triangle is sum of all three sides of a triangle.
Now,
Base length of triangle is y - 2.
Length of legs of triangle is y.
Perimeter = y - 2 + y + y
= 3y - 2
Hence, The perimeter of the isosceles triangle with base length y - 2 and legs of length y is 3y - 2.
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