Find the area of the region that lies under the parabola y=5x - x^2, where 1≤x≤4. I would definitely like to see some work :)
Answer:
16.5 square units
Step-by-step explanation:
You are expected to integrate the function between x=1 and x=4:
[tex]\displaystyle\text{area}=\int_1^4{(5x-x^2)}\,dx=\left.\left(\dfrac{5}{2}x^2-\dfrac{1}{3}x^3\right)\right|_{x=1}^{x=4}\\\\=\dfrac{5(4^2-1^2)}{2}-\dfrac{4^3-1^3}{3}=37.5-21=\boxed{16.5}[/tex]
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Additional comment
If you're aware that the area inside a (symmetrical) parabola is 2/3 of the area of the enclosing rectangle, you can compute the desired area as follows.
The parabolic curve is 4-1 = 3 units wide between x=1 and x=4. It extends upward 2.25 units from y=4 to y=6.25, so the enclosing rectangle is 3×2.25 = 6.75 square units. 2/3 of that area is (2/3)(6.75) = 4.5 square units.
This region sits on top of a rectangle 3 units wide and 4 units high, so the total area under the parabolic curve is ...
area = 4.5 +3×4 = 16.5 . . . square units
Which equation does the graph below represent?
I kinda really need help with this lol
Thanks :)
Answer:
y-intercept, where the graph crosses y-axiss is 0. that means in the equation: y = mx + b
b = 0
the m, is slope. looking at the graph you can see the points on the line are connect up 4 right 1. rise/run = slope = 4
y = 4x
Step-by-step explanation:
Pls somone help me pls
Answer:
This is a right answer. You can check it
How many feet of fencing are needed to enclose the garden? 54 feet 68 feet 108 feet 140 feet.
Answer:
140
Step-by-step explanation:
30+30=60
40+40=80
60+80=140
Answer:
140
Step-by-step explanation:
I got it right on edge
growing from 1.4m to 1.6m in one year what’s the rate to change
Answer:
1.6 - 1.4 = 0.2
0.2 / 1.4 = 0.14 = 14%
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs.
Simplify the mathematical expressions to determine the product or quotient in scientific notation. Round so the first factor goes to the tenths place.
1) (3.8 * 10^3) * (9.4 * 10^-5) = 0.3572 = 3.6 * 10^-1
2) (4.2 * 10^7) * (7.4 * 10^-2) = 3.1 * 10^6
3) (8.6 * 10^-6) * (7.1 * 10^9) / (4.1 * 10^ -2) * ( 2.8 * 10 ^-7) = 5.3 * 10^-6
4) 4.2 * 10^-1
Sorry for not putting my work for number 4. Hope this helps!
would - (-2) 4 be negative or positive
Would - (-2) 4 be negative or positive ?
- x - = +
Therefore -(-2)4 = 2*4= 8 which is positive
PositiveWhich ratio is larger, 18/5 or 72/25 ?
Answer:
Step-by-step explanation:
LCM of 5 and 25=25
Now,
18/5=18x5/5x5=90/25
72/25=72/25
Since 90/25>72/25
Hence,
18/5 is greater than 72/75
A jar is full of 100 coins. All of the coins are either nickels or dimes.
a. The value of the coins is $6.35. Write a linear system representing this equation.
b. Solve the system to determine how many of each type of coin is in the jar.
Answer:
73 nickels, 27 dimes
Step-by-step explanation:
x+y=100
5x+10y=635
x=100-y
5(100-y)+10y=635
500-5y+10y=635
500+5y=635
5y=135
y=27
5x+10(27)=635
5x+270=635
5x=365
73
73+27=100
Solve for x. The problem is in the picture!!
Answer:
According to the given Attachment
we know sum of all angles in a triangle is 180° .
Sum of all angles in ∆ = 180°On substituting the given value we obtain
➥ x + 61° + 70° + 61° = 180°
➥ x + 192° = 180°
➥ x = 180° - 192°
➥ x = -12°
So, the value of x is -12°
Step-by-step explanation:
[tex]x + 61 + 70 + 61 = 180(sum \: of \\ \: triangle) \\ \\ x + 192 = 180 \\ \\ x = 180 - 192 \\ \\ x = - 12[/tex]
# be careful#
Hi Everyone! Please draw a regular bar graph with x and y axis, along with all components of a bar graph!
that the bar graph with all components
Three times a number is 24 less than the number. What is the number?
Answer:
Don't know the number.
Step-by-step explanation:
Tell me also.
HELP (0,-3) and (5,-5) what is the slope
Answer:
-2/5
Step-by-step explanation:
To find the slope, we use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -5 - -3)/( 5 - 0)
= ( -5+3)/( 5-0)
= -2/5
Hi! I can help you with joy! :)
Use the slope formula:[tex]\displaystyle\frac{y2-y1}{x2-x1}[/tex]Wherey2 is the y-coordinate of the second point (in this case, it's equal to -5)y1 is the y-coordinate of the first point (in this case, it's equal to -3)x2 is the x-coordinate of the 2nd point (in this case, x2=5)x1 is the x-coordinate of the 1st point (in this case, x1=0)Plug in the values:[tex]\displaystyle\frac{-5-(-3)}{5-0} \\\frac{-5+3}{5}[/tex][tex]\displaystyle\frac{-2}{5}[/tex][tex]\displaystyle-\frac{2}{5}[/tex]Answer:
[tex]\huge\boxed{\bold{Slope=\displaystyle-\frac{2}{5} }}[/tex]
Hope it helps!
~Nature~
which math expression means 52 more than an unknown number
Find the value of the power.
0.92 =
Answer:
hello the correct answer is x=6
Step-by-step explanation:
What is the value for x?
Jojo likes to paint. She estimates the number of paintings she completes using the function P of w equals two thirds times w minus two, where w is the number of weeks she spends painting. The function J(y) represents how many weeks per year she spends painting. Which composite function would represent how many paintings Jojo completes in a year? P of J of y equals J times the quantity two thirds times w minus two P of J of y equals two thirds times J of y minus two J of P of w equals two thirds times J of y minus two J of P of w equals J times the quantity two thirds times w minus two.
Composite functions are functions of functions. The needed composite function for given context is: [tex]P(J(y)) = \dfrac{2}{3}J(y) - 2[/tex]
What are function of functions and how are they represented?Function of function, as the name suggests, are functions applied over functions themselves. This is also called function composition.
We have input. We apply one function on that input. Then we apply another function on the output obtained by the first function. This whole function application on first input is called function of functions. The resultant function which maps the input x to the final output is called function of function.
If first function is g( and the other function is f, then we can write the resultant function of function as [tex](f\circ g)(x)[/tex]input to first function.
Thus, we have;
[tex](f\circ g)(x) = f(g(x))[/tex]
For the given case, it is given that:
[tex]P(w) = \dfrac{2}{3}w - 2[/tex][tex]J(y)[/tex]To evaluate how many paintings Jojo completes in a year, we need [tex]P(J(y))[/tex] (since, we need number of paintings and input is year, so we convert year to number of weeks by function J, and then give the output to P function to evaluate number of paintings)
Thus,
[tex]P(w) = \dfrac{2}{3}w - 2\\\\P(J(y)) = \dfrac{2}{3}J(y) - 2[/tex]
Thus,
The needed composite function for given context is: [tex]P(J(y)) = \dfrac{2}{3}J(y) - 2[/tex]
Learn more about composite functions here:
https://brainly.com/question/24780056
Constance is drawing a map of the block on which she lives, using a scale of 1 inch to 160 feet. The actual length of her block is 1800 feet.
What is the exact length of the block on Constance's map
Answer:
788947
Step-by-step explanation:
I'm just here for answers
solve for X and y
60°
14 3
Answer:
X = 28
Y = 14
Step-by-step explanation:
+++++++++++++++++++++++++++++++++++++
Write the next three terms of the arithmetic sequence.
0.2, 0.6, 1, 1.4,
help please
Solve the problem and explain the steps taken.
There are four students working on a project in math class. Miguel has completed 1/8 of the project, Gina has completed 13% of the project, Jatziry has completed 0.10 of the project, and Kwa has completed 1/9 of the project. Make a list of the students in order from least to greatest by the amount of the project they have completed.
Answer:
13%, 1/8, 1/9, 0.10 13>1/8>1/9>0.10
Step-by-step explanation:
John's bicycle covers 60 inches in one revolution. What
is the radius of his tire?
Answer:
The radius is equal to [tex]\frac{30}{pi}[/tex] or about 9.5 inches
Step-by-step explanation:
A revolution is the same as the circumference,
which can be found using C = 2πr
C = 2πr
60 = 2πr
(2π)r = 60
r = [tex]\frac{60}{2pi}[/tex]
r = [tex]\frac{30}{pi}[/tex] or about 9.5 inches
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.
- Heather
How are humans impacting Earth's climate?
Answer:
technology because of our building style or oil
Step-by-step explanation:
A car travels 625km using 25L of fuel (km/L)
Answer:
Step-by-step explanation:
625km divide by 25L =25
Hoped it helped u
In terms of x, what is the length of the side of a square whose area is represented by the expression 25x^2 + 40x + 16?
Answer:
Step-by-step explanation:
25x2 − 40x + 16 = (5x)² - 2*5*4 + 4² { (a - b)² = a² - 2ab + b² }
= (5x - 4)² { here a = 50 and b = 4}
Side of the square = 5x - 4 units
Part B:
25x2 − 16y2 = (5x)² - (4y)² { a² - b² = (a + b) * (a - b) }
= (5x + 4y) * (5x - 4y) { here a = 5x and b = 4y}
Dimensions of Rectangle: (5x + 4y) ; (5x - 4y)
Answer:
Step-by-step explanation:
25x²+40x+16=25x²+20x+20x+16
=5x(5x+4)+4(5x+4)
=(5x+4)(5x+4)
=(5x+4)²
length of side=5x+4
What number is halfway between –3 and 4 ?
Answer:
0.5
Step-by-step explanation:
4-(-3)
4+3=
7
Half of 7 is 3.5
4-3.5=0.5
Answer:
The number 0.5 is halfway between -3 and 4.
Step-by-step explanation:
To find the halfway point between two numbers, add them together and divide by 2.
-3 + 4 = 1
1/2 = 0.5
HELP A store had apples on sale for $1.20 a pound. Joan spent $5.28 on apples. How many pounds did she buy?
Answer:
4.4 and almost a half
Step-by-step explanation:
Because he can't but 5 because if he bought 5 it would be 6$
But 4 he can if you add taxes.
1.20 for 1
2.40 for 2
3.60 for 3
4.80 for 4
PLSSSSS HELP WILL MARK BRAINLIEST
If the expression is expanded, what is the coefficient of x?
4 (3x + 5)
Coefficient of x =
Answer:
12
Step-by-step explanation:
Start by expanding the expression:
4(3x+5)
Distribute the 4 to each of the numbers in the parentheses
12x+20
The coefficient of x is basically what is being multiplied by x. In this scenario, we can expand 12x to be...
12*x
Which means that the coefficient of x is 12
12x+20
12x+20=0
12x=-20.
12÷12x=-20÷12
x=-5/3
x=negative five over three
Find the area of the shaded region. Use 3.14 as an approximation.
Answer:
shaded area = 113.64 cm²
Step-by-step explanation:
To find the shaded area, subtract the area of the circle from the area of the triangle.
Area of a triangle = 1/2 x base x height
⇒ area of triangle = 1/2 x 25 x 21.4 = 267.5 cm²
Area of a circle = [tex]\pi r^2[/tex] (where r is the radius)
From inspection, we can see that the diameter of the circle = 14 cm
Therefore, as the diameter = 2r, then r = 14 ÷ 2 = 7 cm
⇒ area of circle = 3.14 x 7² = 153.86 cm²
Shaded area = area of triangle - area of circle
⇒ shaded area = 267.5 - 153.86 = 113.64 cm²
Solve for f.
4 = fover3
Answer:
f = 12
Step-by-step explanation:
Step 1: Multiply both sides by 3.
4 × 3 = (f/3) × 3 12 = fStep 2: Check if solution is correct.
4 = 12/34 = 4Have a lovely rest of your day/night, and good luck with your assignments. ♡