A 12 ft. ladder is leaning against a house. The ladder makes a 60° angle with the ground. Use special right triangles to find how far up the building the ladder will reach.
Answers
Given:
The length of the ladder = 12 ft
The angle of ladder with ground = 60 degrees
To find:
How far up the building the ladder will reach.
Solution:
Using the given information draw a figure as shown below.
We need to find the vertical distance between the top of ladder and the ground.
Let x be the required distance.
In a right angle triangle,
[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
In the below triangle ABC,
[tex]\sin A=\dfrac{BC}{AC}[/tex]
[tex]\sin 60^\circ=\dfrac{x}{12}[/tex]
[tex]\dfrac{\sqrt{3}}{2}=\dfrac{x}{12}[/tex]
Multiply both sides by 12.
[tex]\dfrac{\sqrt{3}}{2}\times 12=x[/tex]
[tex]6\sqrt{3}=x[/tex]
Therefore, the ladder will reach [tex]6\sqrt{3}[/tex] ft far up the building.
Related Questions
Hello I need this quickly pls
Answers
Answer:
Area = x² + 10x + 21
Step-by-step explanation:
Area = L * W
Length = (x + 7)
Width = (x + 3)
=> Area = (x + 7) * (x + 3)
=> Area = x² + 3x + 7x + 21
Combining like terms would result in;
=> Area = x² + 10x + 21
Hope this helps!
Find all x-intercepts of the function.
y = x³ - 9x² + 18x
Answers
Answer:
Step-by-step explanation:
X-intercepts mean y=0 so we have
y = x³ - 9x² + 18x = 0
Factoring
x³ - 9x² + 18x = 0
x*(x² - 9x +18) = 0
x*(x-3)*(x-6) = 0
So x-intercepts are at x=0, x=3 and x=6
Answer:
Step-by-step explanation:
see plot, intercepts at 0, 3, 6
Out of 400 people sampled, 56 had kids. Based on this, construct a 90% confidence interval for the true population proportion of people with kids.
Give your answers as decimals, to three places
___ < p < ___
Answers
Answer:
because having 90% means big
hellp plsssss i need it
Answers
A store purchased a DVD for $12.00 and sold it to a customer for 50% more than the purchase price. The customer was charged a 7% tax when the DVD was sold.
What was the customer’s total cost for the DVD?
Answers
Answer:
$19.26
Step-by-step explanation:
12 × .5 = 6
6 + 12 = 18
18 × 0.07 = 1.26
1.26 + 18 = 19.26
Explaination:
Math and I took the test
Write an explicit formula for am, the nth term of the sequence 5, 30, 180, ....
Answers
Answer:
Am = 5 * 6^(m-1)
Step-by-step explanation:
30/5 = 6
180/30 = 6
Am = 5 * 6^(m-1)
PLEASE HELP QUICK!!!
COMPOUND INTEREST!!!
$600 is deposited in an account that pays 7% annual interest, compounded continuously. What is the balance after 5 years?
Answers
9514 1404 393
Answer:
$851.44
Step-by-step explanation:
The balance is given by the formula ...
A = Pe^(rt) . . . . principal P, interest rate r, t years
Using the given numbers, we find the balance to be ...
A = $600·e^(0.07·5) ≈ $851.44
h(-4), h(0), h(4), h(8)
h(x)= {-(x+1)^2 + 7, x<2
{ -1/3x, x>4
h(-4)=
h(0)=
h(4)=
h(8)=
PLEASE HELP
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The first two x-values, -4 and 0, fall in the first part of the function definition.
There is no function definition for x = 4, as the second part only applies for x > 4.
The last x-value, 8, falls in the second part of the function definition.
The function is evaluated by putting the x-value where x is in the expression and doing the arithmetic. For example, ...
h(-4) = -(-4+1)^2 +7 = -(-3)^2 +7 = -9 +7 = -2
h(0) = 6
h(4) = undefined
h(8) = -8/3
The
exact solusion of the IVP
Answers
Answer:
[tex]\displaystyle y = \sqrt{2}e^{\frac{1}{2} ln|2 + x^2|}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
|Absolute Value|FunctionsFunction NotationExponential Rule [Multiplying]: [tex]\displaystyle b^m \cdot b^n = b^{m + n}[/tex]Algebra II
Logarithms and Natural LogsEuler's number eCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Differential Equations
Separation of VariablesAntiderivatives - Integrals
Integration Constant C
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
Logarithmic Integration
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y' = \frac{xy}{2 + x^2}[/tex]
[tex]\displaystyle y(0) = 2[/tex]
Step 2: Rewrite
Separation of Variables
Rewrite Derivative Notation: [tex]\displaystyle \frac{dy}{dx} = \frac{xy}{2 + x^2}[/tex][Division Property of Equality] Isolate y's: [tex]\displaystyle \frac{1}{y} \frac{dy}{dx} = \frac{x}{2 + x^2}[/tex][Multiplication Property of Equality] Rewrite Derivative Notation: [tex]\displaystyle \frac{1}{y} dy = \frac{x}{2 + x^2} dx[/tex]Step 3: Find General Solution Pt. 1
Integration
[Equality Property] Integrate both sides: [tex]\displaystyle \int {\frac{1}{y}} \, dy = \int {\frac{x}{2 + x^2}} \, dx[/tex][1st Integral] Integrate [Logarithmic Integration]: [tex]\displaystyle ln|y| = \int {\frac{x}{2 + x^2}} \, dx[/tex]Step 4: Identify Variables
Identify variables for u-substitution for 2nd integral.
u = 2 + x²
du = 2xdx
Step 5: Find General Solution Pt. 2
[2nd Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle ln|y| = \frac{1}{2}\int {\frac{2x}{2 + x^2}} \, dx[/tex][2nd Integral] U-Substitution: [tex]\displaystyle ln|y| = \frac{1}{2}\int {\frac{1}{u}} \, du[/tex][2nd Integral] Integrate [Logarithmic Integration]: [tex]\displaystyle ln|y| = \frac{1}{2} ln|u| + C[/tex][Equality Property] e both sides: [tex]\displaystyle e^{ln|y|} = e^{\frac{1}{2} ln|u| + C}[/tex]Simplify: [tex]\displaystyle |y| = e^{\frac{1}{2} ln|u| + C}[/tex]Rewrite [Exponential Rule - Multiplying]: [tex]\displaystyle |y| = e^{\frac{1}{2} ln|u|} \cdot e^C[/tex]Simplify: [tex]\displaystyle |y| = Ce^{\frac{1}{2} ln|u|}[/tex]Back-Substitute: [tex]\displaystyle |y| = Ce^{\frac{1}{2} ln|2 + x^2|}[/tex]Our general solution is [tex]\displaystyle |y| = Ce^{\frac{1}{2} ln|2 + x^2|}[/tex].
Step 6: Find Particular Solution
Substitute in point: [tex]\displaystyle |2| = Ce^{\frac{1}{2} ln|2 + 0^2|}[/tex]Evaluate |Absolute Value|: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln|2 + 0^2|}[/tex]|Absolute Value| Evaluate exponents: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln|2 + 0|}[/tex]|Absolute Value| Add: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln|2|}[/tex]|Absolute Value| Evaluate: [tex]\displaystyle 2 = Ce^{\frac{1}{2} ln(2)}[/tex][Division Property of Equality] Isolate C: [tex]\displaystyle \sqrt{2} = C[/tex]Rewrite: [tex]\displaystyle C = \sqrt{2}[/tex]Substitute in C [General Solution]: [tex]\displaystyle y = \sqrt{2}e^{\frac{1}{2} ln|2 + x^2|}[/tex]∴ Our particular solution is [tex]\displaystyle y = \sqrt{2}e^{\frac{1}{2} ln|2 + x^2|}[/tex].
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Differential Equations
Book: College Calculus 10e
I still need help! Please! Help me
Answers
Part A = 60
Part B is C
Find the circumference of a
circle with diameter, d = 10.8cm.
Give your answer rounded to 3
SF.
Answers
Answer:
33.9
Step-by-step explanation:
r = d/2
= 5.4
[tex]2\pi \: r[/tex]
[tex] = (2)(\pi)(5.4)[/tex]
=33.93
C=33.912
rounded 33.9
This is my first time doing this if it’s wrong literally Pretend this wasn’t even here
O capital de R$ 12.000,00 foi aplicado a juros compostos à taxa de 60% ao ano durante 2 anos. Determine o montante? *
Answers
?Answer:
Step-by-step explanation:
Which equation is true when x = 1/2?
Answers
Answer:
D
Explanation:
6/ 1/2 = 6*2, 6*2 not equal to 3
half of 8 is 4, not 16
1/2+2 = 2 1/2
10/ 1/2 = 10*2 = 20
In order to complete the square for the equation below, what value should be added to both sides of the equation?
x2 - 8x + ? = 42 + ?
Answers
Answer:
? = 16
Step-by-step explanation:
x2 - 8x + ? = 42 + ?
1. Take the coefficient of the middle term 8x, which is 8 and divide it by 2. [tex]\frac{8}{2} = -4[/tex]. Then square it [tex]-4^{2} = 16[/tex]
2. Take 16 and add it to both sides: [tex]x^2 - 8x + 16 = 42 + 16[/tex]
2. Take half of the coefficient 8 that you divided by 2, which is 4 and insert 4 into the equation [tex](x -4)^2 = 58[/tex]
3. ? = 16
The number of gallons of water left in a swimming pool at time t minutes can be modeled by w(1) = -7t+B50. Find the y-intercept and explain what it represents in this situation.
Answers
Answer:
I'm not really sure
Step-by-step explanation:
soooooooory
13) A rectangular garden has an area of 45 square meters. The garden will be 4 meters longer than its width Write and sowe an equation to find the dimensions in meters.
Answers
Answer:
9m ×5m
Step-by-step explanation:
Area of a rectangle= length ×width
Let the width be W meters and the length be L meters.
2 equations can be written from the given information:
45= WL -----(1)
L= W +4 -----(2)
Substitute (2) into (1):
45= W(W +4)
Expand:
45= W² +4W
-45 on both sides:
W² +4W -45= 0
Factorise:
(W +9)(W -5)= 0
W+9=0 or W-5=0
W= -9 or W= 5
(reject)
Substitute W= 5 into (2):
L= 5 +4
L= 9
∴ The dimensions of the garden is 9m ×5m.
The table shows the mean number of minutes spent on homework last weekend. The MAD for both sets of data is 5. Which number correctly completes the statement: The difference between the means is _______ times the value of the MAD of each set of data. (Subtract the two means and then divide that difference by 5.)
Answers
Explanation:
23+15=7
29+21=8
12+15=6
74+12=?
Answers
Step-by-step explanation:
here are all the anwsers
SOMEONE PLEASE HELP ME ANSWER ALL THESE IM IN SUMMER SCHOOL NO LINKS OR FILES I WOULD DEEPLY APPRECIATE IT<33
Answers
1) 3:4
2)4:5
3)7:5
4)1:1
5)8:9
Wat is the average between 1,000, 2300,1000,2600
Answers
Answer:
1180.2
Step-by-step explanation:
The average of 1,000,2300,1000,2600 is 1180.2
HELPP!!! I need help ASAP
Answers
Answer:
the right answer is C
Step-by-step explanation:
___________
Please help just put answer
Answers
............
Ssszxsxxzjdnndnd dj shh dbd
The answer is: 15 ft
What is the solution of log; (3x+2) = log: (4x-6)?
Answers
Answer:
x = 8
Step-by-step explanation:
Answer:
x = 8
Step-by-step explanation:
Cancel the log from both sides and you'll get:
[tex]3x + 2 \: = 4x - 6 \: \\ 6 + 2 = 4x - 3x \: \\ x = 8[/tex]
Which set of equations shows a way to find 771 - 468?
Answers
Answer:
The one that has 303 as the answer is the correct one
Help me please will be appreciated thx
Answers
Answer:
-6 +8d -2c
Step-by-step explanation:
[tex]\frac{-2}{5} (15 -20d +5c) = \frac{-2}{5} \times 15 - \frac{-2}{5}\times20d +\frac{-2}{5}\times5c = -6 + 8d -2c[/tex]
1
Abdullah tracked the scores of his Science tests this year.
93, 71, 86, 95, 72, 81, ?
He lost the score from his final test, but knows he had a mean score of 82.
Calculate his missing score.
76 O
Activate Windows
Go to Settings to activate Windows.
11:30 AM
5/31/2021
Desktop
4») GG ENG
O
10
Answers
Answer:
76
Step-by-step explanation:
Answer:
I believe the answer is 76
What is the name of the following net?
Answers
Answer:
[tex]\large\colorbox{gold}{sǫᴜᴀʀᴇ ᴘʏʀᴀᴍɪᴅ}[/tex]
what is the mean absolute deviation for 9, 7, 6, 8, 7, and 5? (2 points) a 1 b 2 c 6 d 7
Answers
Answer: a. 1
Step-by-step explanation:
Given data: 9, 7, 6, 8, 7, and 5.
Mean absolute deviation: [tex]MAD=\dfrac1n\sum^n_{i=1}|x_i-m|[/tex], where m = mean
mean (m) = [tex]\frac{\text{Sum of values}}{\text{Number of values}}[/tex]
[tex]=\frac{42}{6}\\\\=7[/tex]
Now, [tex]MAD=\dfrac{|9-7|+|7-7|+|6-7|+|8-7|+|7-7|+|5-7|}{6}[/tex]
[tex]MAD=\dfrac{2+0+1+1+0+2}{6}[/tex]
[tex]MAD=\dfrac{6}{6}[/tex]
[tex]MAD=1[/tex]
Hence, the mean absolute deviation=1
Thus correct option is a. 1
which expression is equivalent to 6 (3x + 4)?
A) 9x + 4
B) 18x + 4
C) 18x + 24
D) 9x + 10
Answers
Answer:
c number is the ans
Step-by-step explanation:
multiply each term with 6
The habitable part of Earth's surface has been estimated to cover 60 trillion square meters. Estimate the percent of this area occupied by humans if Earth's current population stood packed together as people do in a crowded elevator.The habitable part of Earth's surface has been estimated to cover 60 trillion square meters. Estimate the percent of this area occupied by humans if Earth's current population stood packed together as people do in a crowded elevator. HINT
Answers
Answer:
yay
Step-by-step explanation: