The derivative of h(x) is h'(x) = 3ln(x).
Using the first part of the fundamental theorem of calculus, we can find the derivative of the function h(x) by evaluating its integrand at x and taking the derivative of the resulting expression with respect to x.
So, we have:
h(x) = ∫ 3ln(t) dt (from 1 to x)
Taking the derivative of both sides with respect to x, we get:
h'(x) = d/dx [∫ 3ln(t) dt]
By the first part of the fundamental theorem of calculus, we know that:
d/dx [∫ a(x) dx] = a(x)
So, we can apply this rule to our integral:
h'(x) = 3ln(x)
Therefore, the derivative of h(x) is h'(x) = 3ln(x).
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To find the derivative of h(x) = ∫ 3ln(t) dt, we first need to use the chain rule to differentiate the function inside the integral :d/dx (ln(t)) = 1/t We'll be using Part 1 of the Fundamental Theorem of Calculus to find the derivative of the given function.
Given function: h(x) = ∫[1 to x] 3ln(t) dt
According to Part 1 of the Fundamental Theorem of Calculus, if we have a function h(x) defined as:
h(x) = ∫[a to x] f(t) dt
Then the derivative of h(x) with respect to x, or h'(x), is given by:
h'(x) = f(x)
Now, let's find the derivative h'(x) of our given function:
h'(x) = 3ln(x)
So, the derivative h'(x) of the function h(x) is 3ln(x).
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A ring-shaped region is shown below. Its inner radius is 8m, and its outer radius is 11m. 8m 11m Find the area of the shaded region. Use 3.14 for π. Do not round your answer.
Answer:
329.91 cm^2
Step-by-step explanation:
A ring-shaped region is shown below. Its inner radius is 8m, and its outer radius is 11m. 8m 11m Find the area of the shaded region. Use 3.14 for π. Do not round your answer.
Your answer
Given data
inner radius= 8cm
area= πr^2
area= 3.142*8^2
area= 3.142*16
area= 50.272 cm^2
outer radius= 11cm
area= πr^2
area= 3.142*11^2
area= 3.142*121
area= 380.182 cm^2
Hence the area of the shaded part is
=380.182-50.272
=329.91 cm^2
Solve the following equation for p. Select all possible solutions. | p/2-1 |= 0.5
0.5
4
2
3
1
5
Answer:
4
Step-by-step explanation:
What is the difference between -2^4 and (-2)^4
I know the answer but how do you explain it?
Answer:
no difference
When you multiply negative numbers together an even number of times, they change from negative to positive.
Step-by-step explanation:
please help me find the slope and y intercept! i’m the worst at math, i’d really appreciate it <333 (click on photo)
Answer:
3.) y-int = 0
4.) y-int = -1
5.) slope = 2
y-int = 4
6.) slope = -1
y-int = -6
7.) slope = 5
y-int = 8
8.) slope = 7
y-int = 1/2
Step-by-step explanation:
basically, you want to get each of your functions in terms of (y = mx + b)
for each of these:
m will be your slope
b will be your y-intercept
what is the answer to 2 - (-5)
Answer:
7
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
learn the table of how these symbols work.
in this case its two minuses which make plus so 2+5=7
I need help ASAP pleaseeeeee
Answer: area of smaller is 18 and larger is 45 so the answer is 27
Step-by-step explanation:
What is the slope-intercept equation of the line below?
Answer:
D. y = 2x -3
Step-by-step explanation:
The equation of a line in slope-intercept form is
y = mx + b
We need to find m, the slope, and b, the y-intercept.
We can find those two numbers from the graph.
We look in the graph and see that the y-intercept, b, is -3.
Now we have y = mx - 3.
Now we look for the slope. Start at (0, -2). We need to go vertically and horizontally to the next point that is easy to read. We see that point (1, -1) is on a grid intersection making it easy to read, so we will use that point.
Go up 2 units. That is a rise of positive 2. Now go right 1 unit. That is a run of positive 1.
slope = rise/run = 2/1 = 2
m = 2, so now we have
y = 2x - 3
Answer: D. y = 2x -3
Un cable de 42 pies se corta en 3 tramos. Si cada tramo tiene 2 pies de longitud más que el anterior; calcular la longitud del tramo mayor.
Answer:
dividimos los 42 dejando 12 para cada 1 sobran 6 pies para el primero le aumentamos 4 al segundo 2 y el ultimo se quedaria asi y asi tendria 2 pies de longitud mas que el anterios y el mas largo tendria 16 pies el mediano 14 y el mas pequeño 12
Estimate 0.95% of 700
Answer:
6.65
Step-by-step explanation:
0.95% of 700
= 0.0095*700
= 6.65
The value of 0.95% of the number 700 is 6.65.
The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the number 700 is 0.95%. The number will be calculated as below,
Number = 0.95% of 700
Number = 700 x 0.95/100
Number = 6.65
Therefore, the value of 0.95% of the number 700 is 6.65.
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how to do Pythagorean Theorem
Answer:
pythagorean theorem is a^2 +b^2=c^2
Step-by-step explanation:
basically the two shorter sides added together squared is equal to the longest side squared. if trying to find the length of the longest sidee you just have to do the square root of a^2+b^2
A 15-ft by 15-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 304 ft^2, how wide is the walkway?
Answer:
4 ft = width of walkway
Step-by-step explanation:
It helps if you can draw a figure.
Let x = width of walkway
Length of pool + walkway = (2x + 15)
Width of pool + walkway = (2x + 15)
area of pool and walkway together = (2x + 15)(2x + 15) = [tex]4x^{2} = 60x + 225[/tex]
Area of the pool = 15(15) = 225
Now,
The area of the walkway = area of pool and walkway together - area of pool
304 = 4[tex]x^{2}[/tex] + 60x + 225 - 225
304 = [tex]4x^{2}[/tex] + 60x
4[tex]x^{2}[/tex] + 60x - 304 = 0
4([tex]x^{2}[/tex] +15x - 76) = 0
4(x - 4)(x + 19) = 0
x = 4 x = -19
-19 must be discarded because a length cannot be negative
Therefore x = 4 ft = width of walkway
Jessica and her friends have gone to dinner. When they finished eating their bill came to $82. Jessica decided that she wanted to give a 19% tip
Answer:
97.58
Step-by-step explanation:
Answer: D $15
Step-by-step explanation:
Can someone help me.
Answer:
A.5,683.0000
B. 1,289,293.0000
C.3,567,920.0000
Step-by-step explanation:
anyone knows the answer?
Answer:
20 miles
Step-by-step explanation:
x = break even miles
$10 + x($1.50 = x($2.00)
10 + 1.5x = 2x
0.5x=10
x = 20 miles
A chemical solution contains 4% alcohol. If there is 24 ml of alcohol, what is the volume of the solution?
Answer: 600 ml
Step-by-step explanation:
Let the volume of the solution be represented by x.
Therefore, we can form an equation based on the information given which will be:
= 4% × x = 24.
4/100 × x = 24.
0.04 × x = 24
0.04x = 24
x = 24/0.04
x = 600
The volume of the solution is 600ml
write an equation in slope intercept form for the line that travels through (1,-2) and (6,8)
Answer:
y=2/1x
Step-by-step explanation:
Subtract (6,8) by (1, -2)
8--2/6-1=10/5
Simply
10/5=2
Plug in
y=2x
Henry drove 567 miles in 9 hours. At the same rate, how long would it take him to drive 315 miles?
Answer:
in one hour = 567÷9
= 63
hence, to drive 315 miles he would need = 315×63 hours
divide yourself my dear friend.
Was it helpful?
comment down
If there is any kind of suspicious mistake
then sorry
Answer:
5 hours.
Step-by-step explanation:
567/9 = 63mph
315/63 = 5
Use the graph of the polynomial function to find the factored form of the
related polynomial. Assume it has no constant factor.
5
A. (x + 1)(x - 7)
B. (x + 1)(x + 7)
C. (x - 1)(x - 7)
D. (x - 1)(x + 7)
Answer:
The answer is
(x-1) (x-9)
The factored form of the related polynomial function is [tex](x-1)(x+7).[/tex]
What is polynomial function ?Polynomial function is a function that involves non-negative integer powers or positive integer exponents of a variable in an equation like the quadratic equation, cubic equation.
We have,
In the graph given in question, we can see that [tex]x-[/tex]intercepts the axis twice.
And graphs behave differently at various [tex]x-[/tex]intercepts. Sometimes the graph will cross over the [tex]x-[/tex]axis at an intercept and other times the graph will touch the [tex]x-[/tex]axis and bounce off.
Now, in graph;
The [tex]x-[/tex]intercept at [tex]x=1[/tex], i.e. the solution of the [tex]x-1=0[/tex] and passes through the axis.
Now,
The [tex]x-[/tex]intercept at [tex]x=7[/tex] is the solution of [tex]x-7=0[/tex] and again passes through the axis.
So, from the above statements we can say that the factored form of the related polynomial is [tex](x-1)(x+7).[/tex]
Hence, we can say that the factored form of the related polynomial function is [tex](x-1)(x+7).[/tex]
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The length of a bed would be about
Answer:
2 yards.
Step-by-step explanation:
We know that a length of a bed is DEFINITELY not 2 miles, and it isn't 2 inches either, because they're both too big and too small. However, 2 feet is also pretty small, too, because 2 feet is about the size of a crib. So what's left is 2 yards, so a bed is about 2 yards.
Answer:
2 yards
Step-by-step explanation:
The question is asking what the length of a bed would be.
To answer this question, it's basically common sense, how long is a bed usually, it would be about 5 to 10 feet, big enough to fit a human with no uncomfortability.
So with this info, we can scratch D and B. As for A and C, let's convert them into feet.
1 yard equals 3 feet, meaning two yards would be 6 feet.
1 mile is 5280 feet, this is obviously wrong.
A is our answer.
10 - 20 - 20 - 20 -20 2- + 1000
Answer:
928
Step-by-step explanation:
Answer: It would be 1252
133=7(1+2x) solve
Answer ASAP please
Answer:
x=9
Step-by-step explanation:
Step-by-step explanation:
133=7+14x
133-7=14x
14x=133-4
14x=129
14x=129
14 14
x=129
14
Tommy buys a football for $20 plus 8% tax John buys a helmet for $25 plus 8% tax what is the difference in the amount Tommy and John paid including tax
Answer:
$5.40
Step-by-step explanation:
First, figure out the cost of the items with tax; for Tommy we have 20*0.08 = 1.6, add that 1.6 to the 20 and his purchase is $21.6, for John we have 25*0.08 = 2, add 2 to his 25 and his purchase is $27. To find the difference we subtract 27-21.6 = 5.4 or $5.40
please answer as fast as u can
Hey dude, I'm not completely sure but I think the answer's 30°.
the perimeter if a square is 60 feet, then find the length of the diagonal. if necessary, round to the nearest tenth.
a). 21.2
b). 15
c). 450
d). 30
Answer:
a). 21.2
Step-by-step explanation:
square has 4 sides
one side = 60÷4 = 15
Use pythogoras theorem to find the hypotenuse thus the diagonal of the square.
x = √(15² + 15²)
x = √(225 + 225)
x = √450
x = 21.21 (2 dp)
Running at 5 miles an hour how long will it take you to go 12 miles
Answer:
2 hours and 24 minutes.
Grace and her brother Sid want to raise money to go to band camp. Their parents have agreed to help them up to $400 by paying them $25 when one of them mows the lawn and $10 for each hour that one of them babysits their younger brother. They will have to do a combination of both chores in order to earn the money.
Select the equation that represents the number of lawns they can mow, m, and hours they can babysit, b, to earn $400.
Step-by-step explanation:
25m + 10b = 400
not enough info to solve for m or b. but that's the equation you would use.
What is the value of x?
Answer:
25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
c = x
x^2 = a^2 + b^2
x^2 = 24^2 + 7^2
x^2 = 576 + 49
x^2 = 625
x = 25
perfect adjective word chain
Answer:
Tall, light, test, treat.
I think this ans may help you
choices
3/4
3/5
5/4
4/5
Answer:
4/5
Step-by-step explanation:
sine is opposite over hypotenuse,
so it's 40/50=4/5
Solve for x
x^2 - 7x + 10 = 0
Answer:
Step-by-step explanation:
x²-7x+10=0
(x-2)(x-5)=0
x=2 or x=5
Answer:
Step-by-step explanation:
x2−7x+10=0
Step 1: Factor left side of equation.
(x−2)(x−5)=0
Step 2: Set factors equal to 0.
x−2=0 or x−5=0
x=2 or x=5
(You can confirm this by plugging in the numbers yourself)