2z ÷ [z – (z – 4)]
Sub z=8 into the expression
2(8) ÷ [8 – (8 – 4)] = 16 ÷ 4
= 4
Find g(x) if the indefinite integral of f(x) need little help
Answer:
g(x) = 4x² - x
General Formulas and Concepts:
Algebra II
Functions
Function NotationPiecewise FunctionsCalculus
Integration
IntegralsIntegral NotationIntegration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/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:
*Note:
Integrating a piecewise function requires you to integrate both parts.
Step 1: Define
Identify.
[tex]\displaystyle f(x) = \left \{ {{8x - 1 ,\ x \leq 4} \atop {31 ,\ x \geq 4}} \right.[/tex]
[tex]\displaystyle \int {f(x)} \, dx = \left \{ {{g(x) + C ,\ x \leq 4} \atop {31x + C ,\ x \geq 4}} \right.[/tex]
Step 2: Find function g(x)
We can see that the 2nd part of the piecewise function already has been integrated:
[Integral] Set up: [tex]\displaystyle \int {f(x)} \, dx ,\ x \geq 4 = \int {31} \, dx ,\ x \geq 4[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {f(x)} \, dx ,\ x \geq 4 = 31 \int {} \, dx ,\ x \geq 4[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle \int {f(x)} \, dx ,\ x \geq 4 = 31x + C ,\ x \geq 4[/tex]To find function g(x), we simply have the same setup:
[Integral] Set up: [tex]\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = \int {8x - 1} \, dx ,\ x \leq 4[/tex][Integral] Rewrite [Integration Rule - Addition/Subtraction]: [tex]\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = \int {8x} \, dx - \int {1} \, dx ,\ x \leq 4[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = 8 \int {x} \, dx - \int {} \, dx ,\ x \leq 4[/tex][Integrals] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = 8 \bigg( \frac{x^2}{2} \bigg) - x + C ,\ x \leq 4[/tex]Simplify: [tex]\displaystyle \int {f(x)} \, dx ,\ x \leq 4 = 4x^2 - x + C ,\ x \leq 4[/tex]Redefine: [tex]\displaystyle g(x) = 4x^2 - x + C ,\ x \leq 4[/tex]The integration constant C is already included in the answer, so our answer is g(x) = 4x² - x.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration (Applications)
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
[tex]x = 2 \sqrt{3y} [/tex]
[tex]x = 0[/tex]
[tex]y = 7[/tex]
; about the y-axis
on this one, we proceed the same as the other, we start off by graphing them, Check the picture below. Now, we have a solid horizontal line at y = 7, that'd be our boundary, and a parabola that has a vertex at the origin, that's our other boundary, from 0 to 7.
In this case, is a solid area from the curve to the axis of rotation, so we can simply use the "disk" method to get the volume, lemme do it in the same way as "area under the curve", assuming h(y) = 0 for the axis of rotation
[tex]\textit{area under the curve}\\ \stackrel{f(y)}{2\sqrt{3y}}~~ - ~~\stackrel{h(y)}{0}\qquad \implies 2\sqrt{3y} \\\\\\ \displaystyle\int_{0}^7\pi \left( 2\sqrt{3y} \right)^2 dy\implies \int_{0}^7\pi(12y)dy\implies 12\pi \int_{0}^7 y\cdot dy \\\\\\ 12\pi \cdot \left. \cfrac{y^2}{2} \right]_{0}^7\implies12\pi \cdot \cfrac{49}{2}\implies 294\pi[/tex]
Write 1.96 as a percent and as a fraction,
help pls
solve the equation
4 to the power of 3x ÷ 2 to the power of 4x =32
Answer:
x = 5/2
Step-by-step explanation:
(4^3x)/(2^4x) = 32
(2^6x)/(2^4x) = 32
2^2x = 32
2^2x = 2^5
2x = 5
x = 5/2
Shen borrowed $8000 at a rate of 17%, compounded quarterly. Assuming he makes no payments, how much will he owe after 6 years?
Solve for x: 5x + 15 = 28
A: 43/5
B: 13/5
C: 13
D: 43
[tex]\mathfrak{5x + 15 = 28} [/tex]
[tex]\mathfrak{5x = 28-15} [/tex]
[tex]\mathfrak{5x = 13} [/tex]
[tex]\boxed{\mathfrak{x = \dfrac{13}{5}}} [/tex] → option B.
[tex]\mathbb{MIREU} [/tex]
Answer:
B
Step-by-step explanation:
The first thing you need to do is,
28 - 15
which is 13.
Now look at the answer choices and multiply them by 5.
It cannot be C or D because it would not fit the equation.
If anyone of them equal 13 then it is the answer.
Now lets try it.
43/5 = 8.6
13/5 = 2.6
8.6 times 5 is way to big so A is not it.
2.6 times 5 is 13.
So it is B.
(I WILL GIVE BRAINLIEST) PLEASE HELP!
Answer:
Option D
Step-by-step explanation:
Step 1: Determine the correct option
Option A, this option doesn't work because -3.46 is not greater than -2 1/3. Although the number 3 is greater than 2, these numbers are negative therefore the bigger the negative number, the smaller the number actually is.
Option B, this option doesn't work because 16/5 is not greater than 6. If we convert 16/5 into a decimal we get 3.2 and this number isn't bigger than 6.
Option C, this option doesn't work because once again it states that -3.46 is greater than -2 1/3 when in reality it's actually smaller.
Option D, this option does work because everything goes according the way it should. -3.46 is smaller than -2 1/3 and -2 1/3 is smaller than -3/4 and -3/4 is smaller than 16/5 and 16/5 is smaller than 6.
Answer: Option D
Graph the equation. y= - 2x
Answer: The picture
Step-by-step explanation: if you mean graph that means graph the coordantes.
PLEASE HELP ME!!!!!!
B or D so sorry these ones are confusing written like this.
Gave a lovely weekend.
How many types of windows does Python use? Correct answer will get brainliest.
a.
four
b.
five
c.
one
d.
two
Answer:
A. 4
Step-by-step explanation:
i guess it A. 4 i dunno
Four types
Explanation:-The python supported windows starts form windows 7 (32bit)All types of python windows are
Windows 7Windows 8Windows 10Windows 11please help me on this
Answer:
10/9
Step-by-step explanation:
Find the least common denominator for these fractions.
Answer:
15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
Find sin(a-B), if cosa=1/3, cosB=1/4, a=(0;180), B(-90;0)
Give me some hint please
Travis has hired Charlie and Dora to plant flowers. Dora can plant 150 flowers in the same time it takes Charlie to plant 120 flowers, which can be shown using the following relationship where d and c are the respective rates at which Dora and Charlie can plant flowers:
150 over d equals 120 over c
Also, Dora can plant 18 flowers more per day than Charlie.
How many flowers can Charlie plant per day?
Answer:
72
Step-by-step explanation:
If the rates d and c are flowers per day, we have ...
150/d = 120/c
d -c = 18
__
Multiplying the first equation by cd/30, we have ...
5c = 4d
Multiplying the second equation by 4 gives ...
4d -4c = 72
Adding these equations together, we get ...
5c +4d -4c = 4d +72
Simplifying and subtracting 4d leaves ...
c = 72
Charlie can plant 72 flowers per day.
lost on this a little
Answer:
the answer would be 7/5
Step-by-step explanation:
2 of them would already make a whole, and if you add another one, it's going to be more than just one pitcher of lemonade.
Simplify:(4x2 - 2x) - (-5x2 - 8x)
Answer 6x+18
Step-by-step explanation:
This is my question I need the answer to
what is an equation of the line that passes through points (4,-8) (-4,2)?
Answer:The equation of the line that passes through the points (–12, –8) and (–17, –16) is y + 16 = 8/5(x + 17). slope = (-16 + 8)/(-17 + 12) = -8/-5 = 8/5 y + 16 = 8/5(x + 17)
Step-by-step explanation:
A plane is flying at an elevation of 21000 feet. It is within sight of the airport and the pilot finds that the angle of depression to the airport is 17 ∘ . Find the distance between the plane and the airport. Find the distance between a point on the ground directly below the plane and the airport.
Answer:
Answer:x=79,202.77 ft
6. Gloria has 7 yellow pencils. She has 9 red pencils. Which strategy
would NOT help you find 9 -
- 7?
A Make 10
(B
Think Addition
Count to Subtract
My Way
The strategy that won't help her to calculate 9 - 7 is (a) Make 10
The given parameters are:
[tex]Yellow = 7[/tex]
[tex]Red = 9[/tex]
To determine 9 - 7,
She can use addition, as in 9 + (-7)She can subtract directly by countingHowever, she cannot make 10.
This is so, because 9 and 7 are not up to 10
Hence, the strategy that won't help her to calculate 9 - 7 is (a)
Read more about subtraction at:
https://brainly.com/question/4700137
Karen, Trey, and Dante have a total of 75 in their wallets. Karen has 5 more than Trey. Dante has 2 times what Karen has. How much do they have in their wallets?
Answer: Karen has 20, Trey has 15, Dante has 40
Step-by-step explanation:
Karen=x+5 Trey=x Dante=2x+10
x+x+5+2x+10=75
4x+15=75
4x=60
x=15
The wavelength of yellow light in a spectrum is about 0.00002 inches. Which number best approximates this length as a power of 10? O A. 2x 10-5 O B. 2 x 105 O C. -2x 105 O D. 2 x 10-4 SUBMIT help me please fast
Answer:
A
Step-by-step explanation:
You have to move the decimal 5 places to the left to get 2
the number of Significant Figures in 13410000 *
Answer:
hhhhhhhhhhhhhhhhhhh
Step-by-step explanation:
hhhhhhhhhhhh
Answer:
4
Step-by-step explanation:
13410000
Sig Figs4
13410000
Decimals0
Scientific Notation1.341 × 107
E-Notation1.341e+7
Words thirteen million four hundred ten thousand
4. You have 36 pairs of running shoes. Let x be the
number of Nikes and y be the number of Adidas shoes
you own. You own twice as many Nikes as Adidas
shoes.
d
Write and solve a linear system of equations to find the
number of each brand of shoes.
Answer:
Nikes: 24 pairsAdidas: 12 pairsStep-by-step explanation:
The system of equations can be written ...
x + y = 36
x = 2y
__
The system can be solve by substituting for x:
(2y) +y = 36
y = 12 . . . . . . divide by 3
x = 2(12) = 24
There are 24 pairs of Nikes and 12 pairs of Adidas.
jorden claims that x^2+3=12 is exponential equation. is jorden correct
There are 400 bricks used to build a wall that's 15 feet high. How many bricks will be used to build a wall that's 36 feet high?
factorise
28q+35
pls help
Answer:
7(4q+5)..................
Find the slope of the line y=−5x−4
Answer:
-5
Step-by-step explanation:
I hope this helps!
Answer:
-5
Step-by-step explanation:
The slope of the line in this format is the coefficient of x, or the number in front of x.
PLEASE HELP ME WITH GEOMETRY
What composition of rigid motions maps STR to MNP?
Answer:
first option
Translate seven left followed by mirror over y = 2
Step-by-step explanation:
The solution is Option A.
The translation of triangle MNP to triangle STR is a translation of 7 units to the right and a reflection along R = 2
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the triangle be represented as MNP
Now , the transformed triangle be STR
Now , the translation is given as
Step 1 :
The coordinates of triangle is MNP
M = M (-5 , 2 )
N = N ( - 8 , 5 )
P = P ( -2 , 4 )
Now , the translation of 7 units to the right will result in
M' = M' ( 2 , 2 )
N' = N' ( -1 , 5 )
P' = P' ( 5 , 4 )
Step 2 :
The coordinates of the translated triangle M'N'P' is
M' = M' ( 2 , 2 )
N' = N' ( -1 , 5 )
P' = P' ( 5 , 4 )
Now , on reflection of triangle M'N'P' by R = 2 , we get
S = S ( 2 , 2 )
T = T ( -1 , -1 )
R = R ( 5 , 0 )
Hence , the translation of triangle MNP to triangle STR is a translation of 7 units to the right and a reflection along the R = 2
To learn more about transformation of function click :
https://brainly.com/question/26896273
#SPJ2
PLS PLS PLS HELP ON GEOMETRY PLS
Answer:
40 degrees
Step-by-step explanation:
Since triangle HJL is isosceles, angle HJL is congruent to HLJ, so it is 75 degrees.
Angle HLM is linear with HLJ, so they add up to 180, so HLM = 105 degrees.
Triangle HLM adds to 180 degrees, so 180 - 35 - 105 = 40