Answer:
The answer is "[tex]\int e^{ax}\ dx=\frac{e^{ax}}{a}+c[/tex]".
Step-by-step explanation:
Please find the complete question in the attached file.
[tex]\int^{m}_{a}\ f(x)\ dx=\frac{1}{2}\\\\f(x)=ke^{-kx}, \ [0, \infty]\\\\[/tex]
let m is the median
[tex]so,\\\\ \int^{m}_{a}\ f(x)\ dx=\frac{1}{2}\\\\\to \int^m_0 k\cdot e^{-kx}=\frac{1}{2}\\\\\to [\frac{k\cdot e^{-kx}}{-k}]^m_0=\frac{1}{2}\\\\\to [- e^{-kx}]^m_0=\frac{1}{2}\\\\\to - e^{-km} +1=\frac{1}{2}\\\\\to e^{-km} =\frac{1}{2}\\\\\to e^{km} =2\\\\\to \ln(e^{km}) =\ln 2\\\\\to km= \ln \ 2\\\\\to m=\frac{\ln \ 2}{k}\\\\ \text{the answer is: } \\\\ \to \int e^{ax}\ dx=\frac{e^{ax}}{a}+c[/tex]
Write the equation of the line that contains the points (-2,5) and (6,9).
Answer: y=2/4x+6
I think it´s right sorry if it is´nt
In a class test.containing 15 questions 4 marks are given for every correct answer and -2 marks are given for every wrong answer james attempt all the question but only 9 of his answers correct .What is his total score
Answer:
48
Step-by-step explanation:
(9*4) + (6*2)
36 + 12
= 48
Step-by-step explanation:
no:questions=15
correct questions =9
marks for correct answers =9×4=36
incorrect answers=6
marks for incorrect answers =(-2)×6=(-12)
full marks =36 - (-12)
=36 + 12
=48
Given that triangle GHJ = triangle XYZ What is m
The value of the square root of 42
[tex]\sqrt{42} =6.480740698/\sqrt{42}[/tex]
Answer:
6.4807 Step-by-step explanation:
The square root of 42 is 6.4807.
Explain why a + 2b = 110 in the triangle shown
Answer:
Step-by-step explanation:
According to the Triangle Angle-Sum Theorem, all the angles of a triangle have to add up to equal 180 degrees. For us, in our triangle:
a + 2b + 70 = 180 so
a + 2b = 180 -70 and
a + 2b = 110. That's why.
What is the value of y ?
Answer:
67
Step-by-step explanation:
Answer.
67°
Step-by-step explanation:
the two lines are parallel so,
angle on line XY 67° is alternate angle on BD so, angle will be opposite angle y.
therefore, angle y= 67°
i got help from an awesome app called Gauthmath you can check it out on play store and app store. in my opinion avery good app with tutors and concept videos.
11) Write the explicit formula
for the sequence below and
use it to find the 47th term:
-3, 5, 13, 21,...
Answer:
365
Step-by-step explanation:
tn = t1 + (n - 1)(d)
t(47) = -3 + (47 - 1)(8)
t(47) = -3 + (46)(8)
t(47) = -3 + 368
t(47) = 365
Solve for x in these two similar triangles
Someone help please!!!
Answer:
10%
Step-by-step explanation:
if the total hours of sports being played is 50 hours, and the time playing soccer is 5 hours, you just divide 5 by 50 (technically will be .1, but to make it a percent you multiply by 100)
You roll two 6-sided dice.
What is the probability that you would roll an even number on the first dice and a number greater than 4 on the second?
Given a right triangle ABC with altitude BD drawn to hypotenuse AC. If AC = 24 and DC = 6, what is the length of BC?
Answer:
BC = 12Step-by-step explanation:
BD is the altitude, it breaks ΔABC into two similar triangles:
ΔABD ~ ΔBCDThe ratios of corresponding sides:
AD/BD = BD/DC ⇒ BD² = AD*DC ⇒ BD² = (24 - 6)*6 ⇒ BD² = 108On the other hand:
BC² = BD² + DC² ⇒ BC² = 108 + 6² = 144 BC = √144BC = 12is f(x)=–3?
–7
–4
4
5
Answer:
4 is the answer...........
_4 is the best answer of this question
Simplify (sin^2 0+cos^2 0) (sin 0+cos 0)
Can someone help? I don’t understand.
Answer:
C) [tex]sin\theta+cos\theta[/tex]
Step-by-step explanation:
[tex](sin^2\theta+cos^2\theta)(sin\theta+cos\theta)[/tex]
[tex]sin\theta+cos\theta[/tex]
Recall the Pythagorean Trigonometric Identity where [tex]sin^2\theta+cos^2\theta=1[/tex], so [tex]1(sin\theta+cos\theta)=sin\theta+cos\theta[/tex]
Answer:
C
Step-by-step explanation:
To start this problem off, we should know an important trig rule:
[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]
From here, it is simple:
[tex](\sin^2(\theta)+\cos^2(\theta))(\sin(\theta)+\cos(\theta))=\\1(\sin(\theta)+\cos(\theta))=\\\sin(\theta)+\cos(\theta)[/tex]
C
I hope this helps! Let me know if you have any questions :)
Is this statement true or false?
A down payment is paid before you begin monthly payments.
true
false
Answer:
True
Step-by-step explanation:
A down payment is mostly for deposit reasons with insurance. It also let's the landlord know you will be moving in soon. They will use that money for repairs when you move out. You have a chance of getting it pack if they find no damages :D
78.4 divided by 0.56
An aeroplane flies 1860 miles in 4 hours. What is its average speed?
Answer:
The average speed is 465 mph
Step-by-step explanation:
1860/4 = 465
Answer:
The average speed is 465 mph
Step-by-step explanation:
Average speed = distance/time
1860 miles / 4 hours = 465 mph
Cuantos nanómetros soporta el cuerpo
Step-by-step explanation:
1 mn diameter self assembled
nature inspired structure
plzx solve it with steps....
how many terms of the A P -6,11/2,-5......are needed to give the sum -25??
plzx give me all the steps....!!
I think the second number is supposed to be negative, -11/2 = -5.5, because otherwise the sequence is not arithmetic.
The n-th term of the sequence, starting with n = 1, is then
-6 + 0.5 (n - 1) = 0.5n - 6.5
and we want to find the number N such that
[tex]\displaystyle\sum_{n=1}^N(0.5n-6.5)=-25[/tex]
We have
[tex]\displaystyle\sum_{n=1}^N(0.5n-6.5) = 0.5\sum_{n=1}^Nn-6.5\sum_{n=1}^N1\\ = 0.5\times\frac{N(N+1)}2 - 6.5N \\= 0.25N^2-6.25N = -25[/tex]
Solve for N :
0.25 N ² - 6.25N + 25 = 0
N ² - 25N + 100 = 0
(N - 20) (N - 5) = 0
N = 20 or N = 5
what is the name of the shape made by the equation below?
r=2+2 sin(theta)
Answer:
cardioid
Step-by-step explanation:
r=2+2 sin(theta)
This is of the form
r =a+b theta
This is a limacon
When a = b, it is called a cardioid.
Evaluate
tan 332°30'
Cos 229°47'
and sec(-38°22')
HELPPP
Geometric stuff and please explain
Perimeter = Sum of the sides measures
Perimeter = | AB | + | AT | + | BT |
Perimeter = ( x + 3 ) + ( 4x ) + ( 2x + 2 )
40 = x + 4x + 2x + 3 + 2
Colect like terms
40 = ( 1 + 4 + 2 )x + ( 3 + 2 )
40 = 7x + 5
Subtract both sides - 5
40 - 5 = 7x + 5 - 5
35 = 7x
Switch sides
7x = 35
Divide both sides by 7
7x ÷ 7 = 35 ÷ 7
x = 5
_____________________________
AB = x + 3 = 5 + 3 ======》 AB = 8
AT = 4x = 4 × 5 =========》 AT = 20
BT = 2x + 2 = 2(5) + 2 ===》 BT = 12
According to the law of inequality in a triangle, the sum of any two random sides must be greater than the size of the other side which means :
AB + AT > BT
&
AB + BT > AT
&
AT + BT > AB
If the sides is true in the above inequalities, then those sides are able to form a triangle ;
But if even one of the above inequalities is violated, those sides will not be able to form a triangle.
8 + 20 > 12 ( Check )
8 + 12 > 20 ( Nope this inequlity violated )
Thus the measures of the sides can not represent the measures of the sides of a triangle .
And we're done ...
I suck at math but what's greater 0.67 or 0.6
Answer:
0.67!
Step-by-step explanation:
0.6 is just 0.60 which is less than 0.67
Please help me!! Perimeter: about ______ ft squared
Area: about ________ ft squared
Answer:
55.1 ft ; 236.7 ft^2
Step-by-step explanation:
radius = 7.5 ft
Perimeter of the semicircles = 2 * radius * pi = 2 * 7.5 * pi = 47,12389 ft
Perimeter of the rectangle = 4 * 2 = 8 ft
Total perimeter = 55,12389 ft
Area of the semicircles = radius^2 * pi = 7.5^2 * pi = 176,714587 ft^2
Area of the rectangle = 4 * 15 = 60 ft^2
Total area = 236,714587 ft^2
The Jones family wants to enclose their circular garden with a fence. To the 1 point
nearest meter, what is the minimum length of fencing they need to buy?
Note that radius of garden is 62.5m. User as 3.14.
Answer:
Step-by-step explanation:
We have to find the circumference.
Length of the fence = 2πr
= 2* 3.14 * 62.5
= 392.5
= 393 m
Hi guys pls answer this it’s easy tbh
Answer:
this is the accurate answer of your questions
Which 3 expressions are equivalent to the
expression : 3x-12-2(x+12)
Answer:
second option , third option and last option
Step-by-step explanation:
3x - 12 - 2(x + 12)
=3x - 12 -2x - 24
=x - 36
in this given figure find the value of x
QUESTION:- find the value of x
ANSWER:-[tex]180 - 6x + 180 - 5x + 180 - 4x = 180 \\ 360 + 180 - 15x = 180[/tex]
[tex]360 - 15x = 180 - 180 \\ 360 = 15x \\ 24 \degree = x[/tex]
Answer:
x = 24
Step-by-step explanation:
The exterior angles of the triangle sum to 360° , that is
5x + 4x + 6x = 360
15x = 360 ( divide both sides by 15 )
x = 24
Plzzz help me with thiss
Answer:
Step-by-step explanation:
rather than doing all of the sums, you should just learn the formula (for the pattern)
it is n(highest + lowest) where n is number of numbers
2
for example 2+3+4+5+6 = 20
5(6+2) = 20
2
~~~~~~~~~~~~~~~~~~~~
1+2+3+4+5+6+7+8 = 36
8(9) = 72/2= 36
2
Which statements are true of the function represented
by this graph?
Which graph?
___________
4 1/3 - 2 1/2 divided by 1 2/3
Answer:
Exact Form: [tex]\frac{17}{6}[/tex]
Decimal Form: 2.83
Mixed Number Form: [tex]2 and 5/6[/tex]
Step-by-step explanation:
Answer:
[tex]1\frac{1}{10}[/tex]
Step-by-step explanation:
[tex]4\frac{1}{3}-2\frac{1}{2}[/tex]
[tex]4\frac{2}{6} -2\frac{3}{6}=1\frac{5}{6}[/tex]
[tex]1\frac{5}{6} =\frac{11}{6}[/tex]
[tex]1\frac{2}{3}=\frac{5}{3}[/tex]
[tex]\frac{11}{6}[/tex] ÷ [tex]\frac{5}{3} =[/tex]
[tex]\frac{11}{6} *\frac{3}{5}=[/tex]
[tex]\frac{11}{2}*\frac{1}{5} =[/tex]
[tex]=\frac{11}{10}[/tex]
[tex]=1\frac{1}{10}[/tex]
Hope this is helpful
