Answer with Step-by-step explanation:
We are given that
[tex]f(x)=4x[/tex]
Interval=[2,5]
[tex]h=\frac{b-a}{n}=\frac{5-2}{n}=\frac{3}{n}[/tex]
[tex]x_i=i\frac{3}{n}[/tex]
Where i=1,2,3,... n
[tex]f(x_i)=4i\times \frac{3}{n}=\frac{12i}{n}[/tex]
Riemann sum=[tex]\lim_{n\rightarrow \infty}\sum_{i=1}^{n}f(x_i)\cdot h=\lim_{n\rightarrow \infty}\sum_{i=1}^{n}(\frac{12i}{n}\times \frac{3}{n}[/tex]
Riemann sum=[tex]\lim_{n\rightarrow \infty}\frac{36}{n^2}\sum_{i=1}^{n}i[/tex]
Riemann sum=[tex]\lim_{n\rightarrow \infty}\frac{36}{n^2}\times \frac{n(n+1)}{2}[/tex]
By using
[tex]\sum n=\frac{n(n+1)}{2}[/tex]
Riemann sum=[tex]\lim_{n\rightarrow \infty}\frac{18n(n+1)}{n^2}=\lim_{n\rightarrow \infty}18(1+\frac{1}{n})[/tex]
Apply the limit
Area under the curve=[tex]18[/tex] square units
The Riemann sum formula for [tex]\(f(x) = 4x\)[/tex] over [2, 5] using right-hand endpoints and n subintervals is [tex]\(R_n = \sum_{k=1}^{n} 4\left(2 + k \cdot \frac{3}{n}\right) \cdot \frac{3}{n}\)[/tex]. The area is obtained by taking the limit as n approaches infinity.
The Riemann sum for a function f(x) over the interval [a, b] using right-hand endpoints and dividing the interval into n subintervals is given by:
[tex]\[ R_n = \sum_{k=1}^{n} f(c_k) \Delta x \][/tex]
where [tex]\( c_k \)[/tex] is the right-hand endpoint of the [tex]\( k \)[/tex]-th subinterval, [tex]\( \Delta x \)[/tex] is the width of each subinterval, and [tex]\( n \)[/tex] is the number of subintervals.
For the function f(x) = 4x over the interval [2, 5], the width of each subinterval [tex]\( \Delta x \)[/tex] is given by:
[tex]\[ \Delta x = \frac{b - a}{n} \][/tex]
In this case, [tex]\( a = 2 \), \( b = 5 \), and \( f(x) = 4x \)[/tex]. Therefore:
Now, the right-hand endpoint [tex]\( c_k \)[/tex] for each subinterval is given by:
[tex]\[ c_k = a + k \Delta x \][/tex]
Substitute the values:
[tex]\[ c_k = 2 + k \cdot \frac{3}{n} \][/tex]
[tex]\[ \Delta x = \frac{5 - 2}{n} = \frac{3}{n} \][/tex]
Now, substitute these expressions into the Riemann sum formula:
[tex]\[ R_n = \sum_{k=1}^{n} f(c_k) \Delta x \][/tex]
[tex]\[ R_n = \sum_{k=1}^{n} 4(2 + k \cdot \frac{3}{n}) \cdot \frac{3}{n} \][/tex]
Simplify this expression. To find the area under the curve, take the limit as n approaches infinity:
[tex]\[ \lim_{n \to \infty} R_n \][/tex]
This limit will give you the area under the curve f(x) = 4x over the interval [2, 5].
A right triangle has a height of 20 centimeters and a base of 10 centimeters. What is the area of the triangle?
Answer:
100 cm^2
Step-by-step explanation:
The formula for triangle area is L x W / 2.
20 x 10 = 200
200 / 2 = 100
Answer:
100
Step-by-step explanation:
the area is given by half base times height and we are already given the base and the height so take a half times 10 times 20 .
what’s the answer is ?
Answer:
A. Tina + 2 = Tony
Step-by-step explanation:
You're only adding 2 since Tina's brother is 2 years older than her.
Answer:
A: Tina +2 = Tony
Step-by-step explanation:
Since TINA is 2 years OLDER than TONY. You need to add 2 to Tina's age to get Tonys'
If 5 coins are tossed together, then find the probability of getting more tails than
heads.
Answer
5
Step-by-step explanation:
Answer: It is a 50% chance to get more tails than heads
Step-by-step explanation:
Which irrational number can be added to Pi to get a sum that is rational?
StartFraction 1 Over pi EndFraction
Negative StartFraction 1 Over pi EndFraction
Negative pi
Pi
Answer:
C negitive pi
Step-by-step explanation:
Have a great day!
The irrational number can be added to Pi to get a sum that is rational is negative pi.
We have given that StartFraction 1 Over pi EndFraction
Negative StartFraction 1 Over pi EndFraction
Negative pi
Pi
We have to determine the irrational number that can be added to Pi to get a sum that is rational.
What is the irrational number?
The irrational numbers are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers.
Therefore the irrational number can be added to Pi to get a sum that is rational is negative pi.
To learn more about the irrational numbers visit:
https://brainly.com/question/1776973
#SPJ2
A researcher teaches rats to recognize a specific object that by giving them their favorite treat when they touched the object. To measure their ability to recognize the specific object a week later, she records the number of times the rat touches the specific object compared to a different object. It was hypothesized that the rats would touch the specific object more than the different object to demonstrate what they learned about the specific object. If the researcher tested this hypothesis at a .05 level of significance and computes a test statistic of t = 2.842 in a sample of 28 rats, what is the degree of freedom for the test?
Answer:
The degree of freedom for the test is 27.
Step-by-step explanation:
The experiment performed by the researcher is to determine the number of time the rat touches the specific object compared to a different object.
The parameter under study is the mean number of times the rat touches the specific object.
The hypothesis for the test is defined as:
H₀: The mean number of times the rat touches the specific object is not more than that for a different object, i.e. μ ≤ μ₀.
Hₐ: The mean number of times the rat touches the specific object is more than that for a different object, i.e. μ > μ₀.
A t-test for single mean is performed.
The information provided is:
α = 0.05
t = 2.842
n = 28
The degrees of freedom for a single mean t-test is:
df = (n - 1)
= 28 - 1
= 27
Thus, the degree of freedom for the test is 27.
On a coordinate plane, 2 lines are shown. The first solid straight line has an equation of y greater-than-or-equal-to negative one-fifth x + 1, has a negative slope, and goes through (negative 5, 2) and (0, 1). Everything above the line is shaded. The second dashed solid line has equation y less-than 2 x + 1, has a positive slope, and goes through (negative 2, negative 3) and (0, 1). Everything to the right of the line is shaded. Which ordered pairs make both inequalities true? Check all that apply. (–2, 2) (0, 0) (1,1) (1, 3) (2, 2)
Answer:
The answers are (1,1) and (2,2) or C and E
Step-by-step explanation:
Just did it on edge 2021
The ordered pairs are (1,1) and (2, 2).
What are ordered pairs?In arithmetic, an ordered pair is a pair of gadgets. The order in which the items appear in the pair is good-sized: the ordered pair is different from the ordered pair except for a = b. Ordered pairs also are known as 2-tuples, or sequences of period 2.
What are ordered pairs examples?An ordered pair is a pair of numbers in a specific order. for instance, (1, 2) and (- 4, 12) are ordered pairs. The order of the two numbers is crucial: (1, 2) isn't equal to (2, 1) -- (1, 2)≠(2, 1)
Learn more about ordered pairs here https://brainly.com/question/1528681
#SPJ2
k + 22 = 29
Solve the equation.
Look at the attached picture⤴
Hope it will help u...
Answer:
k=7
Step-by-step explanation:
To solve, we need to isolate the variable: k
k +22 =29
Subtract 22 from both sides to "reverse" the addition
k+22=29
-22 -22
k=7
Prompt
Describe a simulation used to determine a game of darts.
Answer:
anonymous simulation
Answer:
Anonymous simulation would be used to determine a game of darts.
Step-by-step explanation:
got this correct on EDGE2021
The diagram shows a square with a perimeter of 40 cm
Answer:
10cm
Step-by-step explanation:
If you are asking what is the length of each side?
The answer is simple first divide the total perimeter by the number of sides.(ONLY FOR A SQUARE) then you get your length.
I'm having trouble with solving logs...can anyone please explain how to solve these two?
#19
[tex]a) 3-3log30\\\\b) \frac{1}{3} log_{6} (8w^6)[/tex]
Answer:
A.) [tex]3-3\log _{10}\left(30\right)[/tex] or -1.43136... (Decimal Form)
B.) [tex]\log _6\left(2\right)+2\log _6\left(w\right)[/tex]
Explanation: I inserted image to explain how to solve the second one, but for the first one you can't go any further except writing it in standard form or changing it into a decimal.
Your welcome :3
Please help me with these square root problems, Part 1. Please show and check the work.
[tex]1. \sqrt{2x-5} - \sqrt{x+6} =0\\\\2. \sqrt{2x-5} + \sqrt{x+6}=0\\ \\3. \sqrt{x-5} - \sqrt{x+6}= 2\\ \\4. \sqrt{2x-5} -\sqrt{x+6}=2[/tex]
Answer:
x = 11
Step-by-step explanation:
sqrt (2x - 5) = sqrt (x + 6)
Square both sides
2x - 5 = x + 6
x = 11
Verify:
sqrt[2(11) - 5] = sqrt(11 + 6)
sqrt(17) = sqrt(17)
Answer:
x = 11
Step-by-step explanation:
√2x-5 - √x+6 = 0
√2x-5 = √x+6
(√2x-5)² = (√x+6)²
2x - 5 = x + 6
2x - x = 6 + 5
x = 11
What is the anwser to the problem 9×7
Answer:
63
Step-by-step explanation:
please mark branliest answer
Answer:
63
Step-by-step explanation:
If 1 = 2x + 6 and 2 = -x + 24, find 1 and 2.
Given:
∠1 = 2x+6 ans ∠2= -x+24
To find the values of ∠1 and ∠2.
Formula:
The values of the vertical angles are always equal.
Here,
∠1 and ∠2 are vertical angles.
So, by this condition,
∠1=∠2
or,[tex]2x+6 = -x+24[/tex]
or, [tex]2x+x = 24-6[/tex] [ Taking all the variables in one side and all the constant in other side]
or, [tex]3x = 18\\[/tex]
or, [tex]x = \frac{18}{3}[/tex]
or, [tex]x = 6[/tex]
So,
∠1 = [tex]2(6)+6 = 18^\circ[/tex]
∠2 =[tex]-6+24 = 18^\circ[/tex]
Hence,
The values of ∠1 and ∠2 are 18°.
Daniel created an intersection with his race track. One of the angles at the intersection is 55°. What are the three other angle measurements formed by the intersection?
Answer:
55, 125 and 125
Step-by-step explanation:
In this question, we are asked to find the other 3 angles in an intersection.
Please check attachment for what the diagram of the intersection might look like.
The intersection consists simply of 4 angles meeting at a point with the 2 angles on each side vertically opposite to the angles on the other side.
since one of the angles is 55, and we are having a straight line, the other angle would be 180-55 = 125.[ sum of angles on a straight line is 180]
These two angles are vertically opposite, this means that the other three angles are 55,125 and 125.
In ΔDEF, the measure of ∠F=90°, the measure of ∠E=79°, and EF = 23 feet. Find the length of DE to the nearest tenth of a foot.
Answer:
120.4ft
Step-by-step explanation:
Find the diagram in the attachment.
The triangle shown is a right angled triangle with the side DE as the hypotenuse, EF is adjacent side while DF is the opposite side.
To get DE, we will use the SOH CAH TOA trigonometry identity
Using CAH which is defined as:
Cos(theta) = Adjacent/Hypotenuse
Cos 79°= 23/Hypotenuse
Hypotenuse = 23/cos79°
Hypotenuse = 23/0.191
Hypotenuse = 120.4feet
DE = 120.4feet (to nearest tenth)
Answer:
Step-by-step explanation:
The triangle DEF is right angle triangle
The missing F
F=90 E=79 = 11
E=79 EF= 23
Find the Length of DE to the nearest tenth of a foot
Wendy already owns 3 necklaces, and addictions necklaces are priced at One for a dollar how much money does when do you need to spend on your necklace is in order to own a total of 12 necklaces
Answer: $9
Step-by-step explanation: If Wendy wants to own a total of 12 necklaces, that means Wendy wants to buy 9 more necklaces, since she already owns 3. We know that each necklace is a dollar.
So if Wendy buys 9 necklaces for a dollar each, then the total price will be $9 for Wendy to own a total of 12 necklaces.
( 9 x 1 = 9)
Wendy has 3 necklaces, and she needs a total of 12. So 12 - 3 is 9. She'll need to buy 9 more necklaces.
If each necklace cost $1, that means for 9 necklaces she will spend $9.
1 × 9 = 9
That means $9 has to be spent, in order to own 12 necklaces.
Alexa is pushing a construction barrel up a ramp 4 feet long into the back of a truck. She is using a force of 120 pounds in a horizontal direction and the ramp is 45 degrees from the horizontal. How much work is Alexa doing?
Answer:
Alexa did about 339.41 foot-pound of work in moving the barrel up the ramp.
Step-by-step explanation:
Work done is defined as the dot product of Force and displacement i.e.
W = F.d
Expanding the dot product, we get:
W = Fd cos(Ф)
Here,
W is the amount of work done, F is the Force applied, d is the displacement and Ф is the angle made by Force F with the horizontal. If we observe the given statement we can clearly see that:
Force applied = F = 120 pounds
Displacement = d = 4 feet
Angle of F with horizontal = Ф = 45 degrees
Substituting the values in the formula we get:
W = 120 x 4 x cos(45)
W = 339.41 foot-pound
This means, Alexa did about 339.41 foot-pound of work in moving the barrel up the ramp.
Final answer:
Alexa is doing approximately 339.33 pounds-feet of work to push the construction barrel up a 4-foot ramp at a 45-degree angle, calculated using the cosine of the angle to find the component of the force parallel to the direction of motion.
Explanation:
To calculate the work done by Alexa, we need to consider the component of the force she exerts that is parallel to the direction of motion up the ramp. Since the force exerted is in the horizontal direction and the ramp is at a 45-degree angle to the horizontal, we use the cosine of the angle to find this component. The formula for work is:
Work = Force × Distance × cos(θ)
Where the force is 120 pounds, the distance is 4 feet, and θ (theta) is the angle of the ramp, which is 45 degrees.
The component of the force parallel to the ramp is 120 pounds × cos(45°) = 120 pounds × 0.7071 (since the cosine of 45 degrees is √2/2, which approximately equals 0.7071).
The work performed by Alexa is:
Work = 120 pounds × 0.7071 × 4 feet × = 339.325 pounds-feet
Alexa is doing approximately 339.33 pounds-feet of work to push the construction barrel up the ramp.
Enter the equation of the circle with C(5, -13) and radius r = 36.
Answer:
(x+3)²+y²=36
Step-by-step explanation:
The equation of a circle is
( x − h ) ² + ( y − k ) ² = r ² , where ( h , k ) is the center and r is the radius.
If the center is at ( − 3 , 0 ) and the endpoint of the radius is at ( 3 , 0 )
, then the length of the radius is the distance between the two points, which is 3 − ( − 3 ) = 6 .
We can substitute
(
−
3
,
0
)
for
(
h
,
k
)
, and
6
for
r
.
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
(
x
−
(
−
3
)
)
2
+
(
y
−
0
)
2
=
6
2
(
x
+
3
)
2
+
y
2
=
36
Determine which of the following statements must be true. PLEASE HELP !!
Answer:
HA < CH because MHA is a right triangle and CAH is an acute triangle which means that it is smaller
Step-by-step explanation:
Answer:
HM > CH
Step-by-step explanation:
In ∆ HAM,
m<HAM=90°
and, in ∆ CHK
m<HKC= 73°
angle HAM > angle HKC
Therefore, side opposite to angle HAM > side opposite to angle HKC
or, HM > CHthe answer choices are
median & mode ?
mean
mode
median
Answer:
median
Step-by-step explanation:
Answer:
A) Median and Mode
Step-by-step explanation:
Step 1: Write all of the numbers in numeric order
3, 4, 5, 5, 7, 9, 19
Step 2: Find the number you are looking for (5).
3, 4, 5, 5, 7, 9
Step 3: Eliminate answer choices.
Median and mode? Yes.
Mean ( Adding all the numbers and dividing it by however many numbers there are )? No.
Mode ( a number that appears most frequently )? Yes, but the answer is A.
Median ( When you put them in order the number in the middle)? Yes, but the answer is A.)
What is the equation of a line that is parallel to y=0.6x + 3 and passes through the point (-3,-5)
Answer:
y=0.6x-3.2
Step-by-step explanation:
Factor the expression.
k2 + 20k + 100
Answer:
( k + 10 ) ( k + 10 )
Step-by-step explanation:
k² + 20k + 100
( k + 10 ) ( k + 10 )
( k + 10 )²
k = -10
Can I get brainliest.
Please. Help me answer this question.
if there are 10 girls and 15 boys, what is the ratio of boys to girls
Answer:
15:10 or 3:2
Step-by-step explanation:
Answer:
3:2
Step-by-step explanation:
15:10
=3:2
What is the value of z in 1/4 raised to the 3z-1 = 16 raised to the z+2 times 64 raised to the z-2
Answer:
3/8
Step-by-step explanation:
In terms of powers of 4, we have ...
(4^-1)^(3z -1) = (4^2)^(z+2)×(4^3)^(z-2)
Taking logarithms base 4*, we have ...
-(3z -1) = 2(z +2) +3(z -2)
-3z +1 = 5z -2 . . . . simplify
3 = 8z . . . . . . . . . . add 3z+2
z = 3/8 . . . . . . . . . .divide by 8
_____
* This is equivalent to equating exponents of the same base. You're making use of the rules of exponents ...
(a^b)^c = a^(bc)
(a^b)(a^c) = a^(b+c)
1/a = a^-1
and the logarithm relations ...
logb(b^x) = x
log(xy) = log(x) +log(y)
Rachel has bought 24 pounds of dog food. She feeds her dog 3/4 pounds for each meal. For how many meals will the food last?
Answer:
32 meals
Step-by-step explanation:
24/.75 = 32
- Please let me know if you need a further explanation
The sum of the measures of a regular 25 sided polygon is 4140 degrees. What is the measure of each interior angle?
Answer: 165.6
Step-by-step explanation:
The formula for finding the interior angle of a polygon is
= (2n - 4) x right angle
= (2n - 4)90 ,or
(n - 2)180
Now since the sum total of the interior angle of the 25 sided regular polygon = 4140 using the formula above,
Therefore, the value of each of the interior angle will be
= 4140/25
= 165.6
Final answer:
Each interior angle of a regular 25-sided polygon, with sum of the interior angles at 4140 degrees, measures 165.6 degrees.
Explanation:
The sum of the measures of a regular 25-sided polygon is 4140 degrees. To find the measure of each interior angle of a regular polygon, we use the formula:
(n - 2) × 180° = Sum of interior angles,
where n is the number of sides in the polygon. Since we are given that the sum of the interior angles is 4140 degrees for a 25-sided polygon, we can plug in the values into our formula:
(25 - 2) × 180° = 4140 degrees,
which simplifies to:
23 × 180° = 4140 degrees.
This confirms the given sum of the interior angles. To find the measure of one interior angle, we divide the sum by the number of angles:
4140 degrees ÷ 25 = 165.6 degrees.
So the measure of each interior angle in a regular 25-sided polygon is 165.6 degrees.
A jewellery shop sells 240 neck less in a month.180 of the neck less were sold via the shop website, the rest were sold in a high street shop. work out the ratio of online sales to shop sales.
Answer:
The ratio is 3:1
Step-by-step explanation:
Let
x --->number of neck less sold via the shop website
y --->number of neck less sold in a high street shop
we know that
To find out the ratio of online sales to shop sales, simply divided the number of neck less sold via the shop website by the number of neck less sold in a high street shop
so
[tex]ratio=\frac{x}{y}[/tex]
we have
[tex]x+y=240[/tex] ----> equation A
[tex]x=180[/tex] ---> given value
substitute the value of x in the equation A
[tex]180+y=240[/tex]
solve for y
[tex]y=240-180=60[/tex]
Find the ratio
[tex]ratio=\frac{180}{60}[/tex]
[tex]ratio=\frac{3}{1}[/tex]
charlie can make 125 pizzas in 5 hours. how many pizzas can he make in one hour?
Answer:
25
Step-by-step explanation:
125 in 5 hours
125/5= 25
25 in 1 hour
Final answer:
To find out how many pizzas Charlie can make in one hour, divide the total number of pizzas he can make by the total number of hours he spends making them. Charlie can make 25 pizzas in one hour.
Explanation:
To find out how many pizzas Charlie can make in one hour, we need to divide the total number of pizzas he can make (125) by the total number of hours he spends making them (5).
So, the calculation would be: 125 pizzas / 5 hours = 25 pizzas per hour
Therefore, Charlie can make 25 pizzas in one hour.
determine which of the following are functions. select all that apply
Relation (A) and polynomial (D) y = -4x² + 45x + 9 are functions rest are not function.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
In another word, a linear function is a function that varies linearly with respect to the changing variable.
In option (A) ;
For every single unique input, there is single unique output so it will function.
In option (B) ;
Here for x = 0,2 and y = 5 so it means for two inputs one output so it will not be a function.
In option (C) ;
For x = 0 , y = 2 , 4 so two output for one input it means it is also not a function.
In option (D) ;
y = -4x² + 45x 9 it gives one input for one output.
Hence "Relation (A) and polynomial (D) y = -4x² + 45x + 9 are functions rest are not function".
For more about the linear function,
brainly.com/question/21107621
#SPJ6
Given question is incomplete so image has been attached