Answer:
[tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx = 32[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^6_0 {g(x)} \, dx = 20[/tex]
[tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx[/tex]
Step 2: Integrate
[Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx = \int\limits^6_0 {g(x)} \, dx + \int\limits^6_0 {2} \, dx[/tex][2nd Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx = \int\limits^6_0 {g(x)} \, dx + 2\int\limits^6_0 {} \, dx[/tex][1st Integral] Substitute in value: [tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx = 20 + 2\int\limits^6_0 {} \, dx[/tex][Integral] Reverse Power Rule: [tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx = 20 + 2(x) \bigg| \limits^6_0[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx = 20 + 2(6)[/tex]Simplify: [tex]\displaystyle \int\limits^6_0 {[g(x) + 2]} \, dx = 32[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Answer:
32
(I think I remember your other information correctly.)
Step-by-step explanation:
I think you said you were given
*Integral from x=-5 to x=0 of g was -14
*Integral from x=-5 to x=6 of g was 6
Asked to find integral( g(x) + 2 , from x=0 to x=6)
Yes this can be split into two integrals:
Integral(g(x), x=0 to x=6) + Integral(2, x=0 to x=6)
The last integral is easier... the antiderivative or 2 is 2x. So evaluate 2x as the limits and subtract. Always plug in the top limit first. 2(6)-2(0)=12-0=12
Let's start with the bigger interval from x=-5 to x=6 which was 6... and since we want to get rid of the interval from x=-5 to x=0 to find the integral of g from x=0 to 6, all we must do is do 6-(-14)=20.
Integral( g(x) + 2 , from x=0 to x=6)
=
Integral(g(x), x=0 to x=6) + Integral(2, x=0 to x=6)
=
20+12
=
32
f(x) =-x^2+x+13
find f(9)
Answer:
f(9) = - 59
Step-by-step explanation:
Substitute x = 9 into f(x) , that is
f(9) = - (9)² + 9 + 13
= - 81 + 22
= - 59
Answer:
-59
Step-by-step explanation:
f(x) =-x^2+x+13
Let x = 9
f(9) = - (9)^2 +9+13
= -81 +9+13
= -59
Kristian spends 45% of his $ 75 on a game. What is the price of the game
Answer:
The price of the game is 33.75
Step-by-step explanation:
45% of 75
.45 * 75
33.75
The price of the game is 33.75
The polygons in each pair are similar. Find the scale factor of the smaller figure to the larger figure.
Answer:
8/12 or 2/3
Where the first number is on the top and vice versa.
Step-by-step explanation:
Chloe rolled 2 dice. Given that one die showed a 6, what is the probability that she rolled double 6? (Hint: Conditional Probability)
Answer:
1/6
Step-by-step explanation:
since they already tells us six has been rolled already, we depend on the second which can only show 1-6. There are six numbers so the answer is 1/6
Find the value of z.
Answer:
Option D, 110
Step-by-step explanation:
first we find x
10x+20-80=2(2x+15)
or, x=15
now, 10x+20 = 170
so, z = 360-170-80 = 110
A house was bought for $450 000 and 3 years later was valued at $540 000. Find: a. The new value as a percentage of the old value b. The increase in value over the three year period c. The increase in value as a percentage of the original value
Answer:
A) The percentage is given by (The new value)/(The old value)*100 = 120%
B) The increase in value is $90000
C) The increase as a percentage is (90000/450000)*100=20%
a. The new value is 120% of the old value.
b. The increase in value over the three-year period is $90 000.
c. The increase in value over the three-year period is 20% of the original value.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
a. To find the new value as a percentage of the old value, we can divide the new value by the old value and multiply by 100 to get a percentage:
New value as a percentage of old value = (New value / Old value) x 100%
= ($540 000 / $450 000) x 100%
= 120%
Therefore, the new value is 120% of the old value.
b. To find the increase in value over the three-year period, we can subtract the old value from the new value:
Increase in value = New value - Old value
= $540 000 - $450 000
= $90 000
Therefore, the increase in value over the three-year period is $90 000.
c. To find the increase in value as a percentage of the original value, we can divide the increase in value by the old value and multiply by 100 to get a percentage:
Increase in value as a percentage of original value = (Increase in value / Old value) x 100%
= ($90 000 / $450 000) x 100%
= 20%
Therefore, the increase in value over the three-year period is 20% of the original value.
Learn more about the percentages here:
brainly.com/question/24159063
#SPJ2
Would √x+6 -4 = x be an extraneous solution? The x + 6 are under the radicands line.
[tex] \sqrt{x + 6 } = x + 4[/tex]
now square both side
help me please :( just tell me the answer :'3
The 2nd choice is the correct statement.
The maximum is 149 inches.
PLS HELP NE ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Answer:
314 in³
Step-by-step explanation:
Volume of a cone,
(1/3)×πr²h
= (1/3)×3.14×5²×12
= 314 in³
the product of two number is 105. if one number is -3 what is the other number
Answer: -35
Step-by-step explanation:
You can check it by multiplying -3 and -35 you should get 105
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The data value that occurs most often in the data set is the ____________.
A. mean
B. median
C. mode
D. range
Which of the following numbers are irrational numbers? Please choose all that apply.
Question 2 options:
−67−−√
13
0.6
π
A parallelogram has one angle that measures 93°. What are the measures of the other three angles in the parallelogram?
Answer:
huhuhuhhu
Step-by-step explanation:
ubuuhuhhuhuhuhuhuhuuuhu
Answer: 93, 87 and 87
Explanation:
The given angle is 93 degrees. The angle opposite this is also 93 degrees. Opposite angles of any parallelogram are always the same measure.
Another rule to keep in mind is that: any two adjacent angles add to 180
So if x is adjacent to 93, then 93+x = 180 solves to x = 87. The other two angles, opposite one another, are 87 degrees each.
The diagram is below.
85°
4x + 21°
what do I am suppose
Answer:
x= 16
4x+21 = 85 degrees
Step-by-step explanation:
The angles shown are vertical angles and vertical angles are equal
85 = 4x+21
Subtract 21 from each side
85 -21 = 4x+21-21
64 = 4x
Divide by 4
64/4 = 4x/4
16 = x
Answer:
16degrees
Step-by-step explanation:
As these angle are (vertically opposite angles)
So,85=4x+21,
85-21=4x
x=64/4
x=16degrees
4. 19 feet to inches
There is 10% salt solution and a 30% salt solution. How much of each is needed to make 10L mixture that is 25% salt solution?
Answer:
2.5L of 10% salt solution and 7.5L of the 30% salt solution
Step-by-step explanation:
let the amount of L in the 10% solution be 'x'
let the amount of L in the 30% solution be '10-x'
* because they add up to a total of 10L
10%(x) + 30%(10-x) = 25%(10)
0.1x + 3 - 0.3x = 2.5
-0.2x = -0.5
x = 2.5
x =2.5
10-x = 7.5
2.5 of 10% solution and 7.5% of 30% solution
what is an equation of the line that passes through the points (-6,-5) and (-4 -6)
Answer:
y=-2x-15
Step-by-step explanation:
first find the slope. the formula for finding slope is (y_1 - y_2)/(x_1 - x_2) (rise over run) so we plug in the values and get (-6+4)/(-5+6)= -2/1=-2 so m=-2 and we have y=-2x+b. then plug in either point for x and y and solve for b. -5= -2*-5 +b, -5= 10+b, b=-15, y=-2x-15
Answer:
y=-0.5x-8
Step-by-step explanation:
i got it right
Write your answer as a polynomial or a rational fraction in simplest form
Answer:
- 4x^2-15x
Step-by-step explanation:
(f-g)(x) = f(x) - g(x) = - 3x^2-8x-x^2-7x = - 4x^2-15x
Pleaseeeeee
Within 9 hours, the number of stars seen went from 190 to 33 as the sun started to rise. Find out how many stars are getting hidden by the sunlight each hour.
Answer:
Approximately 17
Step-by-step explanation:
Number of starts getting hidden in 9 hours = 190 - 33
= 157
Therefore the nun of starts getting hidden in 9 hours is 157
9 hours = 157 stars
1 hours = x
Cross multiply
9 × x = 157 × 1
9x = 157
Divide both sides by 9
x = 157 ÷ 9
x = 17.4
Therefore 17.4 stars are getting hidden every hour.
Answer:
17 4/9 stars per hour
Step-by-step explanation:
First find the decrease in the number of stars
190-33 = 157
Divide by the hours that passed
157/9
17 4/9 stars per hour
Simplify 2m^2 – 2m + 3m^2
Answer:
5m^2-2m
Step-by-step explanation:
2m^2-2m + 3m^2
5m^2-2m
Answer:
5m² - 2m
Step-by-step explanation:
Given
2m² - 2m + 3m² ← collect like terms
= (2m² + 3m²) - 2m
= 5m² - 2m
Someone please helppp
Answer:
112
Step-by-step explanation:
A quadratic can be written in the form
ax^2 +bx +c
-3x^2 +4x+8
a = -3 b = 4 c = 8
the discriminant is
b^2 -4ac
(4)^2 - 4(-3) (8)
16+96
112
Answer:
112
Step-by-step explanation:
Discriminant = b² - 4ac
Substitute the values for the variables.
[tex](4)^2-4(-3)(8)\\16-4(-24)\\16-(-96)\\16+96\\112[/tex]
Pls Help, Thanks
According to the partial construction shown, what is the next step in constructing a line perpendicular to a point on the line?
Place compass at point D, and draw an arc that intersects the arc above line DF.
Place compass at point F, and draw an arc that intersects the arc above line DF.
Place compass at point P, and draw an arc above line DF
Place compass at point P, and draw an arc below line DF
Step-by-step explanation:
First draw a lign segment like DF
Next keep the point on D make an arc by increasing the length of compass
As same keep the point on F make an arc lile same as before
Next there is apoint name it as any meeting on drew arc
connect it to the point with P
hello could you please help me with this math problem with full explanation which I am unable to solve? Thank you.
Answer:
14 cm
Step-by-step explanation:
from the right triangle we know that:
- A leg is 8 cm
- B leg is 11 cm
- angle between A and B leg is 90'
If we have one angle which is 90' we can use the following formula:
[tex]c = \sqrt{a^{2} + {b^{2} }[/tex]
[tex]c = \sqrt{8^{2} + {11^{2} }[/tex]
[tex]c = 13.60147[/tex]
The length of a room is two times its breadth and three times its height . if the cost of white wash on the 4 wall at Rs. 50 per m² is Rs. 7200, find the cost of carpeting its floor at Rs. 325 per m²
Answer:
Step-by-step explanation:
let the height of the room(h) = x
Length(l) = 3*x = 3x
length = 2 * breadth
breadth(b) = length /2 = 3x/2
Cost of whitewashing the 4 walls = ₹ 7200
Area of 4 walls = 7200 ÷ 50 = 144 m² ------(I)
Area of walls = 2lh + 2bh
= 2*3x*x + 2 *[tex]\frac{3x}{2}[/tex] * x
= 6x² + 3x²
= 9x²
9x² = 144 {From (I)}
x² = 144/9
x² = 16
x = [tex]\sqrt{16}=\sqrt{4*4}[/tex]
x = 4 m
height = 4 m
length = 3*4 = 12m
Breadth = [tex]\frac{3}{2}*4=3*2=6 \ m[/tex]
Area of floor = l*b
= 12 * 6
= 72 m²
Cost of carpeting the floor = 72 * 325 = ₹ 23400
v+19= 36
----------------
Answer:
17
Step-by-step explanation:
v+19=36
v=36-19
v=17
Can you answer this, please?
Answer:
-x² + 13x + 2
Step-by-step explanation:
you are on ambitious level, and you cannot answer that yourself ? that is trivial. truly. no hidden traps, just straight forward adding and simplifying. what is the problem, please ?
-7x² + 6x² = -x²
5x + 8x = 13x
-1 + 3 = 2
Answer:
3rd option
Step-by-step explanation:
Given
(- 7x² + 5x - 1) + (6x² + 8x + 3) ← remove parenthesis
= - 7x² + 5x - 1 + 6x² + 8x + 3 ← collect like terms
= - x² + 13x + 2
-x/c=6.5
I need to solve for x first then c
Answer:
[tex]x = -6.5c[/tex]
[tex]c = -\frac{x}{6.5}[/tex]
Step-by-step explanation:
In both cases, you are simply isolating the variable you are trying to solve for:
[tex]\frac{-x}{c} = 6.5[/tex]
Solve for x. Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. First, multiply c to both sides, and then divide -1 from both sides:
[tex]\frac{-x}{c} = 6.5\\\frac{-x}{c} * c = 6.5 * c\\-x = 6.5c\\\frac{-x}{-1} = \frac{6.5c}{-1}\\x = -6.5c[/tex]
Solve for c. Isolate the variable, c. Note the equal sign, what you do to one side, you do to the other. Multiply -1/x to both sides of the equation:
[tex]\frac{-x}{c} = 6.5\\\frac{-x}{c}(c)) = 6.5(c) \\-x = 6.5c\\\frac{-x}{6.5} = \frac{6.5c}{6.5}\\c = -\frac{x}{6.5}[/tex]
Answer:
x = -6.5c
-x/6.5 = c
Step-by-step explanation:
-x/c=6.5
Multiply each side by -c
-x/c * -c=6.5*-c
x = -6.5c
-x/c=6.5
Multiply each side by c
-x/c *c=6.5*c
-x = 6.5c
Divide each side by 6.5
-x/6.5 = 6.5c/6.5
-x/6.5 = c
can someone please help me? this is confusing
Answer:
S=(-2, -9)
T=(-8, -9)
U=(-9, -5)
V=(-6, -5)
Step-by-step explanation:
rotating counter clockwise 90 degrees has a simple formula: (-y, x) simply take your ordered pair and rearrange it to match this formula.
ex. (3, 4) would become (-4, 3)
(-y, x) the negative symbol in front of the y means to switch the sign from either positive or negative to its opposite. since there is no symbol in front of the x you keep that numbers sign the same.
The Anderson family wants to look at their cash flow over a year. They decide to write out their cash flow for 4 months as given in the spreadsheet below. In which of the months did they have the greatest net cash flow? A 5-column spreadsheet showing cash inflows and outflows over a year. Total cash inflow: January, 2,760 dollars; April, 3,060 dollars; August, 2,760 dollars; December, 2,900 dollars. Total cash outflow: January, 2,435 dollars; April, 2,675 dollars; August, 2,670 dollars; December, 3,000 dollars. a. January b. April c. August d. December
Answer:
It is B. April
Step-by-step explanation:
The Anderson family greatest cash flow for the year is April
How to find greatest cash flowTotal cash inflow:
January, 2,760 dollarsApril, 3,060 dollarsAugust, 2,760 dollarsDecember, 2,900 dollarsTotal cash outflow:
January, 2,435 dollarsApril, 2,675 dollarsAugust, 2,670 dollarsDecember, 3,000 dollarsCash flow:
January = 2,760 dollars - 2,435 dollars
= $325
April = 3,060 dollars - 2,675 dollars
= $385
August = 2,760 dollars - 2,670 dollars
= $90
December = 2,900 dollars - 3,000 dollars
= $ -100
Learn more about cash cash flow:
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look at the image below
Answer: what’s the question ?
