Answer:
Step-by-step explanation:
in complementary angles sum of two angles is always 90 degree .
2x+18+6x-8=90
8x+10=90
8x=90-10
x=80/8
x=10
angle B=6x-8
=6*10-8
=60-8
=52 degree
therefore angle B is 52 degree
Consider the following functions. (See attachment)
Find the area of the region.
Answer:
Area: [tex]\displaystyle \frac{1}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationGraphing FunctionsExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Area - Integrals
Area under a curveArea between 2 curvesIntegration 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 [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
U-Substitution
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify functions
[tex]\displaystyle f(x) = \sqrt[3]{x - 9}[/tex]
[tex]\displaystyle g(x) = x - 9[/tex]
Step 2: Identify Info
Graph the functions - See Attachment
[1st Integral] Bounds: [8, 9], g(x) top function/f(x) bottom function
[2nd Integral] Bounds: [9, 10], f(x) top function/g(x) bottom function
Step 3: Find Area Pt. 1
Set up integrals [Area of a Region Formula]: [tex]\displaystyle A = \int\limits^9_8 {[(x - 9) - \sqrt[3]{x - 9}]} \, dx + \int\limits^{10}_9 {[\sqrt[3]{x - 9} - (x - 9)]} \, dx[/tex]Rewrite integrals [Integration Property - Addition/Subtraction]: [tex]\displaystyle A = \int\limits^9_8 {(x - 9)} \, dx - \int\limits^9_8 {\sqrt[3]{x - 9}} \, dx + \int\limits^{10}_9 {\sqrt[3]{x - 9}} \, dx - \int\limits^{10}_9 {(x - 9)} \, dx[/tex]Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = (x^2 - 9x) \bigg| \limits^9_8 - \int\limits^9_8 {\sqrt[3]{x - 9}} \, dx + \int\limits^{10}_9 {\sqrt[3]{x - 9}} \, dx - (x^2 - 9x) \bigg| \limits^9_8[/tex]Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle A = \frac{-1}{2} - \int\limits^9_8 {\sqrt[3]{x - 9}} \, dx + \int\limits^{10}_9 {\sqrt[3]{x - 9}} \, dx - \frac{1}{2}[/tex]Subtract: [tex]\displaystyle A = -\int\limits^9_8 {\sqrt[3]{x - 9}} \, dx + \int\limits^{10}_9 {\sqrt[3]{x - 9}} \, dx - 1[/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle A = -\int\limits^9_8 {(x - 9)^{\frac{1}{3}}} \, dx + \int\limits^{10}_9 {(x - 9)^{\frac{1}{3}}} \, dx - 1[/tex]Step 4: Identify Variables
Identify variables for u-substitution.
u = x - 9
du = dx
Step 5: Find Area Pt. 2
[Integrals] U-Substitution: [tex]\displaystyle A = -\int\limits^0_{-1} {u^{\frac{1}{3}}} \, du + \int\limits^1_0 {u^{\frac{1}{3}}} \, du - 1[/tex][Integrals] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = -(\frac{3}{4}u^{\frac{4}{3}}) \bigg| \limits^0_{-1} + (\frac{3}{4}u^{\frac{4}{3}}) \bigg| \limits^1_0 - 1[/tex]Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle A = -(\frac{-3}{4}) + \frac{3}{4} - 1[/tex]Simplify: [tex]\displaystyle A = \frac{1}{2}[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integrals - Area between 2 curves
Book: College Calculus 10e
Please help me find DOMAIN/RANGE and the EQATION
Answer:
Domain of the function → (-6, ∞)
Range of the function → (-∞, ∞)
Step-by-step explanation:
Domain of a function is the set of x-values of the function.
Similarly, Range of the function is the set of y-values.
From the graph attached,
Domain of the function → (-6, ∞)
x-values of the function starts from x = -6 (excluding x = -5) and tends to the positive infinity.
Range of the function → (-∞, ∞)
y-values starts from negative infinity and tends to positive infinity.
Can someone please help me on this!!
Answer:
(Look at image)
Step-by-step explanation:
(Also look at image)
Three friends arrive at a party. Their arrival increases the number of people at the party by 20%. In total, how many people are now at the party
Answer:
18
Step-by-step explanation:
No of people joined=3
let x be people in begning
atq 3= 20/100x
x=20/100*3=15
no of people now=15+3=18
When Mr Lee was given a raise of 20%, his new salary was $1980.How much was his increase in his salary?
Answer:
$330
Step-by-step explanation:
to find how much he earned before raise:
1.2x = 1980
x = 1980/1.2
x = 1650
current salary: 1980
former salary: 1650
he makes $330 more
Answer:
330
Step-by-step explanation:
it doesn't let me post pitures
Answer:
me neither!
what's wrong with this app?
birdseed cost $1.25 per pound how much does 6 pounds of birdseed cost
Answer:
7.5 for 6 pounds
Step-by-step explanation:
Find all zeros. Choose all answers that apply.
f(x) = -x3 + 4x² + 5x
O A. X = -5
B. X = -1
O C. x = 0
O D. x = 1
The angle measurements in the diagram are represented by the following expressions
ZA = 8r+6
B = 4.1 +38
Solve for x and then find the measure of B:
_B =
answer:
∠B = 70°
step-by-step explanation:
as you can see, the angle are alternate exterior anglestherefore, they are EQUALwe can set them equal to each and solve for x first∠A = ∠B
8x + 6 = 4x + 38
4x + 6 = 38
4x = 32
x = 8
now, we will plug in x in the expression for B to find B4(8) + 38
32 + 38
= 70
therefore, ∠B = 70° and x = 8What is the volume of a
cube that has one side of ||
cm?
Answer:
5
Step-by-step explanation:
633 yess sjs this is rhe im doing this for points
Answer: V=a3
Step-by-step explanation:
In the diagram, the sum of the values of r and z is 116.
bo/20
xo
What is the value, in degrees, of y?
Enter a number in the space provided.
Answer: 122 degrees
Step-by-step explanation:
Don’t feel like explaining.
Plzzzzz helppppppp teachersssss
Answer:
1. tan(x) = 9/20
arctan(9/20) ≈ 24.23°
2. cos(x) = 17/32
arccos(17/32) ≈ 57.91°
3. tan(x) = 13/18
arctan ≈ 35.84°
4. sin(x) = 21/28
arcsin(21/28) ≈ 48.59°
Answer:
1 x = 24.2°
2 x = 57.9°
Step-by-step explanation:
You must memorize the definitions of the trig functions and then these problems are easy
1: tan = opposite side/adjacent side
opp side to x is 9 and adjacent side is 20
So, tan x = 9/20
x = arctan (9/20) = 24.2°
2: cos = adjacent side/hypotenuse
adjacent side = 17 and hypotenuse = 32
cos x = 17/32
x = arccos (17/32)
x = 57.9°
You do 3 and 4. Hint: Use the tan function in 3 and the sine function in 4
OK? You can do it!!!!
In her assignment, Pat is representing the populations of cities using circles. The area of
each circle is directly proportional to the population of the city it represents.
(a) If a city of population 20 000 is represented by a circle of radius 1.5 cm, what would
be the radius of the circle representing:
(i) City A, population 10 000?
(ii) City B, population 36 500?
(b) Would Pat be able to use a circle to represent a city of population 4 500 000? Explain
your answer.
Answer:
n
Step-by-step explanation:
n
Find the area of the circle.
Use 3.14 for pi
d = 10 cm
A = [?] cm2
A=Pi r2
Step-by-step explanation:
the only thing youre missing is
radius = diameter / 2
Answer:
78.54 cm squared
Step-by-step explanation:
A=πr^2
Since they only give the diameter, divide the diameter by 2
π*25 = 78.54
Have a good day :)
3x^2+3x^2=42
xy=-15
Find the value of (x-y)^2
Answer:
wrong question
Step-by-step explanation:
[tex]wrong question[/tex]
Find the length of y
Answer:
From SOHCAHTOA
Cos17=73/y
y=73/cos17
y=76.34cm
Option B
Tom is tiling a wall.
He needs to buy at least 100 tiles. The tiles are sold in large packs and small packs.
Large pack = 40 tiles £18
Small pack = 28 tiles £14
Special offer = 25% reduction when you buy 3 or more large packs.
Work out the cheapest cost for Tom to buy the packs of tiles he needs.
Answer £
Answer:
The correct answer is - £ 40.5 for 3 large packs.
Step-by-step explanation:
Given:
Large pack = 40 tiles £18
Small pack = 28 tiles £14
Special offer = 25% reduction when you buy 3 or more large packs.
Solution:
Following combinations are possible for tom to get the tiles he needs:
1. 3 large packs
40*3 = 120 tiles with 25% discount
cost = 18*3 - 0.25*18*3 = 40.5
2. 4 small packs
28*4 = 112 tiles
cost = 14*4 = 56
3. 2 large packs and 1 small pack
40*2 + 28 = 108 tiles
cost = 18*2 + 14 = 50
4. 1 large pack and 3 small packs
40 + 28*3 = 124 tiles
cost = 18 + 14*3 = 60
Thus, the correct answer is - 1st case with three large packs.
What is 2.785571 rounded to the nearest cent?
marking brainliest
Answer:
2.7
or
2.75
or
2.8
What system of equations is shown on the graph below?
The different kinds of beads Jen is using to make purses come in packages of 4 and 12. What is the least number of each kind of bead Jen can buy to have an equal number of each of the different kinds of beads?
Answer:
You should buy 3 packages of beads that come in packages of 4 and 1 package of beads that come in packages of 12 to have an equal number of each of the different kinds of beads.
Step-by-step explanation:
Since the different kinds of beads Jen is using to make purses come in packages of 4 and 12, to determine what is the least number of each kind of bead Jen can buy to have an equal number of each of the different kinds of beads the following calculation must be performed:
12/4 = 3
4 x 3 = 12
Thus, you should buy 3 packages of beads that come in packages of 4 and 1 package of beads that come in packages of 12 to have an equal number of each of the different kinds of beads.
You went to the barber to get your hair cut. The haircut cost $30. You tipped the barber 20%. How much money did you give the barber for a tip? What is the total amount you paid all together?
Answer:
Tip $6
Total Amount $36
Step-by-step explanation:
20% of $30 is 6
$30 + $6 = 36
PLEASE HELP!
can you help me with these math questions im struggling on :,)?
Answer:
Step-by-step explanation:
Multiply by 2
Help me!!!!!!!!!!!!!!!
Answer:
look at the picture i have sent
Answer:
BHM = 64°
x = 16°
Step-by-step explanation:
BHL is 90° and MLH is 26°. This means to find BHM, we have to subtract 26 from 90.
90 - 26 = 64°
BHM = 64°
BHM is also equal to 4x.
So, to find x, divide 64 by 4. (64 = 4x --> 64 ÷ 4 = x)
64 ÷ 4 = 16
x = 16°
Find the EXACT shaded Area
Answer:
Step-by-step explanation:
area of sector=πr²/4=π ×6²/4=9 π ft²
area of one triangle= 1/2×6×6=18 ft²
area of three triangles=3×18=54 ft²
area of sector +area of three triangles=54+9 π ft²
area of circle=π×6²=36 π ft²
area of shaded region=36 π-9π-54=27 π-54=27(π-2) ft²
Which expression represents the value of y
Answer:
C
Step-by-step explanation:
sin33° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{19}[/tex] ( multiply both sides by 19 )
19 × sin33° = y → C
Answer: c
Step-by-step explanation: sin 33=x/19 x=19sin33
which two integers does √5 go between?
Answer:
The two integers are 2 and 3
Step-by-step explanation:
√5
=2.2
Given m||n, find the value of x , please help me I don't understand , I'm stressed lol
Answer:
x = 2
Step-by-step explanation:
because m || n, you can assume the two angles are congruent.
set them equal to each other:
5x - 4 = 4x - 2
solve
add 4 to both sides: 5x + (-4 + 4) = 4x + (-2 + 4) --> 5x = 4x + 2
subtract 4x from both sides: (5x - 4x) = (4x - 4x) + 2 --> x = 2
1250
€ 125oo
Q8 A taxi company charges £5 standing charge and £1.50 per mile for a journey.
A man travels in a taxi for 12.2 miles.
What is the cost of his journey?
Show your working
Answer:
£23.30
Step-by-step explanation:
First, find the cost from traveling 12.2 miles. Since the cost is £1.50 per mile, multiply 12.2 by 1.5:
12.2(1.5)
= 18.3
Add the standing charge to this:
18.3 + 5
= 23.3
So, the cost of his journey is £23.30
Can someone do 11-12?
Solve this problem...!
Answer:
a) 66 degrees
b) 32 degrees
Step-by-step explanation:
a) 90+24
=114
180-114
=66 degrees
b) 180-51= 129
x= 129+19
148
180-148
= 32
mark me brainliestt :)) i worked hard