Answer:
x=57
Step-by-step explanation:
To solve this problem we need to make an equation to use to solve x.
The sum of 88 and x will equal 145 so the equation will look like this, 88 + x = 145.
Whatever x is, it has to add with 88 to make 145 so we have to use reverse operations.
The opposite of addition is subtraction so we subtract 88 from 145 like so. 145 - 88 = 57, which means x = 57.
If you need me to explain further don’t hesitate to ask me and I hope I helped! :)
How do I evaluate this using trigonometric substitution?
∫dx/(81x^2+4)^2
Answer:
[tex]\displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C[/tex]
General Formulas and Concepts:
Alg I
Terms/CoefficientsFactorExponential Rule [Dividing]: [tex]\displaystyle \frac{b^m}{b^n} = b^{m - n}[/tex]Pre-Calc
[Right Triangle Only] Pythagorean Theorem: a² + b² = c²
a is a legb is a legc is hypotenuseTrigonometric Ratio: [tex]\displaystyle sec(\theta) = \frac{1}{cos(\theta)}[/tex]
Trigonometric Identity: [tex]\displaystyle tan^2\theta + 1 = sec^2\theta[/tex]
TI: [tex]\displaystyle sin(2x) = 2sin(x)cos(x)[/tex]
TI: [tex]\displaystyle cos^2(\theta) = \frac{cos(2x) + 1}{2}[/tex]
Calc
Integration 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]
IP [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
U-Substitution
U-Trig Substitution: x² + a² → x = atanθ
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int {\frac{dx}{(81x^2 + 4)^2}}[/tex]
Step 2: Identify Sub Variables Pt.1
Rewrite integral [factor expression]:
[tex]\displaystyle \int {\frac{dx}{[(9x)^2 + 4]^2}}[/tex]
Identify u-trig sub:
[tex]\displaystyle x = atan\theta\\9x = 2tan\theta \rightarrow x = \frac{2}{9}tan\theta\\dx = \frac{2}{9}sec^2\theta d\theta[/tex]
Later, back-sub θ (integrate w/ respect to x):
[tex]\displaystyle tan\theta = \frac{9x}{2} \rightarrow \theta = arctan(\frac{9x}{2})[/tex]
Step 3: Integrate Pt.1
[Int] Sub u-trig variables: [tex]\displaystyle \int {\frac{\frac{2}{9}sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[(2tan\theta)^2 + 4]^2}} \ d\theta[/tex][Int] Evaluate exponents: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4tan^2\theta + 4]^2}} \ d\theta[/tex][Int] Factor: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4(tan^2\theta + 1)]^2}} \ d\theta[/tex][Int] Rewrite [TI]: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{[4sec^2\theta]^2}} \ d\theta[/tex][Int] Evaluate exponents: [tex]\displaystyle \frac{2}{9} \int {\frac{sec^2\theta}{16sec^4\theta} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{1}{72} \int {\frac{sec^2\theta}{sec^4\theta} \ d\theta[/tex][Int] Divide [ER - D]: [tex]\displaystyle \frac{1}{72} \int {\frac{1}{sec^2\theta} \ d\theta[/tex][Int] Rewrite [TR]: [tex]\displaystyle \frac{1}{72} \int {cos^2\theta} \ d\theta[/tex][Int] Rewrite [TI]: [tex]\displaystyle \frac{1}{72} \int {\frac{cos(2\theta) + 1}{2}} \ d\theta[/tex][Int] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{1}{144} \int {cos(2\theta) + 1} \ d\theta[/tex][Int] Rewrite [Int Prop - A/S]: [tex]\displaystyle \frac{1}{144} [\int {cos(2\theta) \ d\theta + \int {1} \ d\theta][/tex]Step 4: Identify Sub Variables Pt.2
Determine u-sub for trig int:
u = 2θ
du = 2dθ
Step 5: Integrate Pt.2
[Ints] Rewrite [Int Prop - MC]: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} \int {2cos(2\theta) \ d\theta + \int {1 \theta ^0} \ d\theta][/tex][Int] U-Sub: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} \int {cos(u) \ du + \int {1 \theta ^0} \ d\theta][/tex][Ints] Integrate [Trig/Int Rule - RPR]: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} sin(u) + \theta + C][/tex][Expression] Back Sub: [tex]\displaystyle \frac{1}{144} [\frac{1}{2} sin(2 \theta) + arctan(\frac{9x}{2}) + C][/tex][Exp] Rewrite [TI]: [tex]\displaystyle \frac{1}{144} [\frac{1}{2}(2sin(\theta)cos(\theta)) + arctan(\frac{9x}{2}) + C][/tex][Exp] Multiply: [tex]\displaystyle \frac{1}{144} [sin(\theta)cos(\theta) + arctan(\frac{9x}{2}) + C][/tex][Exp] Back Sub: [tex]\displaystyle \frac{1}{144} [sin(arctan(\frac{9x}{2}))cos(arctan(\frac{9x}{2})) + arctan(\frac{9x}{2}) + C][/tex]Step 6: Triangle
Find trig values:
[tex]\displaystyle tan\theta = \frac{9x}{2}[/tex]
[tex]\displaystyle \theta = arctan(\frac{9x}{2})[/tex]
tanθ = opposite / adjacent; solve hypotenuse of right triangle, determine trig ratios:
sinθ = opposite / hypotenuse
cosθ = adjacent / hypotenuse
Leg a = 2
Leg b = 9x
Leg c = ?
Sub variables [PT]: [tex]\displaystyle 2^2 + (9x)^2 = c^2[/tex]Evaluate exponents: [tex]\displaystyle 4 + 81x^2 = c^2[/tex][Equality Property] Square root both sides: [tex]\displaystyle \sqrt{4 + 81x^2} = c[/tex]Rewrite: [tex]c = \sqrt{81x^2 + 4}[/tex]Substitute into trig ratios:
[tex]\displaystyle sin\theta = \frac{9x}{\sqrt{81x^2 + 4}}[/tex]
[tex]\displaystyle cos\theta = \frac{2}{\sqrt{81x^2 + 4}}[/tex]
Step 7: Integrate Pt.3
[Exp] Sub variables [TR]: [tex]\displaystyle \frac{1}{144} [\frac{9x}{\sqrt{81x^2 + 4}} \cdot \frac{2}{\sqrt{81x^2 + 4}} + arctan(\frac{9x}{2}) + C][/tex][Exp] Multiply: [tex]\displaystyle \frac{1}{144} [\frac{18x}{81x^2 + 4} + arctan(\frac{9x}{2}) + C][/tex][Exp] Distribute: [tex]\displaystyle \frac{1}{144}arctan(\frac{9x}{2}) + \frac{x}{8(81x^2 + 4)} + C[/tex]The perimeter of a rectangular e room is 24 feet. Twice the length
decreased by three times the width is 4 feet. What are the dimensions e of
thg room?
Please help me
Answer:
i am gessing to divide
Step-by-step explanation:
⦣G and ⦣H are complementary. If the measure of ⦣H is 72°, what is the measure of ⦣G?
9514 1404 393
Answer:
∠G = 18°
Step-by-step explanation:
Complementary angles total 90°. The measure of G is ...
∠G = 90° -72° = 18°
Tyler has $125.00 to spend on books and CDs. He buys one book for $30.00. He wants to spend the rest on CDs that are on sale for $9.00 each. Which of these statements is true?
Group of answer choices
He can't buy any CDs.
He can buy 11 CDs.
He can buy 10 CDs.
He can buy more than 11 CDs.
Answer:
He can buy 10 cds
Step-by-step explanation:
125-30=95
95 divided by 9 = 10.5555555556
Write the missing decimal so that each pair adds to 1/2 + ...= 1
Answer:
0.5
Step-by-step explanation:
1/2 + 0.5 = 1
Paisley works on her drawings for 2 hours. She spends 1/6 hour on each drawing. How many drawings does she work on in 2 hours? HELP FAST!!!!
Answer:
1/12
Step-by-step explanation:
1/6 divided by 2 = 1/12
What's the place value of 3 in 19.364?
Answer:
Tenths
Hope this helps :)
Answer:
tenths
Step-by-step explanation:
Complete the table of values.
X
-1
NIW
0
d
e
4
f
d =
e =
f=
Answer:
Step-by-step explanation:
d=4
e=2
f=6
Mother shared 60 sweets among her 2 daughters in the ratio 2:3. If Janice gets 20, how many do Kayla gets?
Answer:
40
Step-by-step explanation:
Because if janice getd 20 and kayla also 40 gets Sweets among
PLS HELP!!!! :))) BDHDHSJWJDJD
Answer:
Your answer is "H"
Step-by-step explanation:
A plane travels 1820 meters at a speed of 260 m/sec. How long did it
take to reach its destination? PLEASE HELP!
Answer:
7 seconds
Step-by-step explanation:
1820/260=7.
Answer:
7m/sec
Step-by-step explanation:
A white-tailed deer is running from a black bear at 20 miles per hour. It is 1/3 miles in front of the bear. The bear is running at 30 miles per hour. How many minutes will it take the bear to catch the deer? Assume both continue running at a constant pace.
Answer:
Step-by-step explanation:
d=20t+1/3, b=30t
20t+1/3=30t
10t=1/3
t=1/30 hr
t=(1/30)60=2 min
URGENT NEED ANSWERS •_•
Plzzzzzz help meeee plz I am timed
Answer:
multiplication property of equality. Hope this help and maybe a brainlist?
Step-by-step explanation:
Answer:
multiplication property of equality
Step-by-step explanation:
d/10=12
Multiply both sides by the equation by 10
10× d/10=10×12
Reduce the numbers by the greatest common factor which is 10
d=10×12
Multiply 10 and 12
d=120
So using multiplication to solve this equation
List three decimal values between 2.5 and 2.6
Answer:
2.55 2.56 2.57
Step-by-step explanation:
Answer:
2.51, 2.52, 2.59
Step-by-step explanation:
Ay yo whats good bro
A mistake was made in the steps shown to simplify the expression. Which step includes the mistake?
9/2+ 3(4 – 1) – 7 + 23
Step 1: = 9/2+ 3(3) — 7 + 23
Step 2: = 9/2 + 3(3) - 7 + 8
Step 3: =15/2 (3) — 7+8
Step 4: =45/2 - 7+8
Step 5: =31/2 +8
Step 6: =47/2
Answer: step 3 maybe?
Step-by-step explanation:
12
A model maker wants to make a model of a
ship
He will use a scale of 1:50
The ship was 100ft long
1 foot = 0.3 m
How long will the ship be in cm?
9514 1404 393
Answer:
60 cm
Step-by-step explanation:
The model ship will be x feet long, where ...
x/100 = 1/50
x = 100/50 = 2
In meters, that is ...
2(0.3 m) = 0.6 m
A meter is 100 cm, so the length in centimeters is ...
(0.6)(100 cm) = 60 cm
Solve the inequality: l 2x + 5 l > 15
Help plsss I’m stressing out
please help me please
Answer:
It won't let me see the picture
Step-by-step explanation:
pls help me.........
Answer:
36 m^2
Step-by-step explanation:
A trapezoid's area can be found by (side 1 + side 2) * (height ÷ 2)
Answer:
tama po yan sa taas pareho kami ng sagot
What quadrilateral's diagonals are perpendicular and they bisect each other?
Answer:
Rhombus
Step-by-step explanation:
The diagonals of Rhombus bisect each other and form 4 right triangles. Since they are right triangles, they measure 90 degrees so the diagonals are perpendicular.
The students in a class were asked which hand they preferred to use
for writing. The bar graph shows the results. Find the total number of
students who had a preference.
Answer:25
Step-by-step explanation:
At Davidson's Bike Rentals, it costs $41 to rent a bike for 8 hours. How many hours of bike use does a customer get per dollar?
Answer:
0.192 hour
Step-by-step explanation:
41$ / 8 = 0.192 hours = 11.703 minutes
2.4= -5y + 14.9. Solve for y
Pls help I’ll mark brainliest
Answer:
2=72 4=148 6=222 10=370 15=555 16=592
sorry about the second part i didnt see it
Answer:
148, 3 , 740, 1110, 8.
Step-by-step explanation:
Miles: 148 + 740 + 1,110 = 1,998
Gallons: 2 + 4 + 3 + 10 + 15 + 8 = 42
Use the Distributive Property to expand the following expressions.
a.) 2 ( y + 5x) = _______________
b.) 0.4 ( x + 2) = ______________
Answer:
Step-by-step explanation:
Distributive property: a(b +c)=(a*b )+(a*c)
a) 2(y + 5x) = y*2 + 5x*2
= 2y + 10x
b) 0.4(x + 2) = x*0.4 + 2*0.4
= 0.4x + 0.8
Triangle XYZ with vertices X (1,-2) Y (3,-5) and Z (4,1) translated 5 units left and 3 units up
Answer:
x= (4,-7)
y= (6,-10)
z= (7,-4)
Step-by-step explanation:
solve for x
8x+12=48-3(x+1)
Answer:
hello! :) have a good day!
X = 3
What is - or how do you find answer to:
12 1/2 - (-4 1/2) =
Answer:
8
Step-by-step explanation:
12 times 1/2=6
(-4(1/2))= -2
6-(-2)
6+2
=8
