Evaluate the following integral (Calculus 2) Please show step by step explanation!
Answers
Answer:
[tex]\dfrac{1}{2} \left(25 \arcsin \left(\dfrac{x}{5}\right) -x\sqrt{25-x^2}\right) + \text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given indefinite integral:
[tex]\displaystyle \int \dfrac{x^2}{\sqrt{25-x^2}}\:\:\text{d}x[/tex]
Rewrite 25 as 5²:
[tex]\implies \displaystyle \int \dfrac{x^2}{\sqrt{5^2-x^2}}\:\:\text{d}x[/tex]
Integration by substitution
[tex]\boxed{\textsf{For }\sqrt{a^2-x^2} \textsf{ use the substitution }x=a \sin \theta}[/tex]
[tex]\textsf{Let }x=5 \sin \theta[/tex]
[tex]\begin{aligned}\implies \sqrt{5^2-x^2} & =\sqrt{5^2-(5 \sin \theta)^2}\\ & = \sqrt{25-25 \sin^2 \theta}\\ & = \sqrt{25(1-\sin^2 \theta)}\\ & = \sqrt{25 \cos^2 \theta}\\ & = 5 \cos \theta\end{aligned}[/tex]
Find the derivative of x and rewrite it so that dx is on its own:
[tex]\implies \dfrac{\text{d}x}{\text{d}\theta}=5 \cos \theta[/tex]
[tex]\implies \text{d}x=5 \cos \theta\:\:\text{d}\theta[/tex]
Substitute everything into the original integral:
[tex]\begin{aligned}\displaystyle \int \dfrac{x^2}{\sqrt{5^2-x^2}}\:\:\text{d}x & = \int \dfrac{25 \sin^2 \theta}{5 \cos \theta}\:\:5 \cos \theta\:\:\text{d}\theta \\\\ & = \int 25 \sin^2 \theta\end{aligned}[/tex]
Take out the constant:
[tex]\implies \displaystyle 25 \int \sin^2 \theta\:\:\text{d}\theta[/tex]
[tex]\textsf{Use the trigonometric identity}: \quad \cos (2 \theta)=1 - 2 \sin^2 \theta[/tex]
[tex]\implies \displaystyle 25 \int \dfrac{1}{2}(1-\cos 2 \theta)\:\:\text{d}\theta[/tex]
[tex]\implies \displaystyle \dfrac{25}{2} \int (1-\cos 2 \theta)\:\:\text{d}\theta[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating $\cos kx$}\\\\$\displaystyle \int \cos kx\:\text{d}x=\dfrac{1}{k} \sin kx\:\:(+\text{C})$\end{minipage}}[/tex]
[tex]\begin{aligned} \implies \displaystyle \dfrac{25}{2} \int (1-\cos 2 \theta)\:\:\text{d}\theta & =\dfrac{25}{2}\left[\theta-\dfrac{1}{2} \sin 2\theta \right]\:+\text{C}\\\\ & = \dfrac{25}{2} \theta-\dfrac{25}{4}\sin 2\theta + \text{C}\end{aligned}[/tex]
[tex]\textsf{Use the trigonometric identity}: \quad \sin (2 \theta)= 2 \sin \theta \cos \theta[/tex]
[tex]\implies \dfrac{25}{2} \theta-\dfrac{25}{4}(2 \sin \theta \cos \theta) + \text{C}[/tex]
[tex]\implies \dfrac{25}{2} \theta-\dfrac{25}{2}\sin \theta \cos \theta + \text{C}[/tex]
[tex]\implies \dfrac{25}{2} \theta-\dfrac{5}{2}\sin \theta \cdot 5 \cos \theta + \text{C}[/tex]
[tex]\textsf{Substitute back in } \sin \theta=\dfrac{x}{5} \textsf{ and }5 \cos \theta = \sqrt{25-x^2}:[/tex]
[tex]\implies \dfrac{25}{2} \theta-\dfrac{5}{2}\cdot \dfrac{x}{5} \cdot \sqrt{25-x^2} + \text{C}[/tex]
[tex]\implies \dfrac{25}{2} \theta-\dfrac{1}{2}x\sqrt{25-x^2} + \text{C}[/tex]
[tex]\textsf{Substitute back in } \theta=\arcsin \left(\dfrac{x}{5}\right) :[/tex]
[tex]\implies \dfrac{25}{2} \arcsin \left(\dfrac{x}{5}\right) -\dfrac{1}{2}x\sqrt{25-x^2} + \text{C}[/tex]
Take out the common factor 1/2:
[tex]\implies \dfrac{1}{2} \left(25 \arcsin \left(\dfrac{x}{5}\right) -x\sqrt{25-x^2}\right) + \text{C}[/tex]
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Related Questions
what is the value of x= and y=
Answers
Answer:
x = 18
y = 18
Step-by-step explanation:
We are given a right triangle (notice the 90 degree angle), with one of the angles being 45°.
We also know that the hypotenuse (the side opposite of the 90° angle) is 18√2.
We want to find the value of x and y.
First, let's figure out what the value of the other angle is.
The angles in a triangle all add up to 180 degrees.
Let's call the value of the angle we don't know s.
s + 45 + 90 = 180
Add 45 and 90 together.
s + 135 = 180
Subtract 135 from both sides.
s = 45
So the value of the other angle is 45 degrees.
When a right triangle is a 45-45-90 triangle (the numbers referring to the measures of the degrees), there is actually something special about it; if the legs (the sides that make up the 90 degree angle) have the value a (they would both be congruent because a 45-45-90 triangle is isosceles), then the hypotenuse will be a√2.
Keeping this in mind, let's solve for a.
Set 18√2 equal to a√2.
18√2=a√2
Divide both sides by √2.
18 = a
The value of a, aka the legs is a.
Both x and y would be equal to a in this case.
Therefore, x = 18, and y = 18.
(a 2n - a n - 6) (a n + 8)
Answers
2an-an=an
then (an-6)(an+8)
=asqnsq+8an-6an+48
=asqnsq+2an+48answer
sq is square and first We should add or subtract like terms
In an analysis of variance study, we consider 3 treatments. We have 4 observations for the first treatment, 5 observations for the second treatment, and 6 observations for the third treatment. What are the degrees of freedom associated with SSE
Answers
In the analysis of variance study, if we consider 3 treatments, in which we have 4 observations for the first treatment, 5 observations for the second treatment, and 6 observations for the third treatment. Then, the degrees of freedom associated with SSE in each case is 2, 3, and 4, respectively.
Degrees of Freedom Associated with SSE
The number of degrees of freedom in statistics refers to the quantity of values that can fluctuate in a statistic's final calculation. Various amounts of data or information can be used to estimate statistical parameters.
In order to find the degrees of freedom associated with SSE in an Analysis of Variance (ANOVA) study, we subtract 2 from the number of observations. In n is the number of observations, then (n-2) gives the degrees of freedom associated with SSE.
Thus, for the first treatment, n = 4
⇒ Degrees of freedom = 4-2
= 2
For the second treatment, n = 5
⇒ Degrees of freedom = 5-2
= 3
For the third treatment, n = 6
⇒ Degrees of freedom = 6-2
= 4
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The table above shows four numeric expressions. Which expression is an integer when it's evaluated?
Question 6 options:
A)
G
B)
F
C)
H
D)
E
Answers
Answer: H
Step-by-step explanation:
[tex]9(-3)=-27[/tex], which is an integer.
Describe what a line with zero rate of change looks like.
Answers
Answer:
Step-by-step explanation:
rate of change = change in y/ change in x
The rate of change is 0 if the change in y = 0
0 = 0 / change in x
The graph is a horizontal line since the y values do not change.
Evaluate 5(14 – 23) + 8 ÷ 2. (1 point) 26 34 44 56
Answers
Answer:
-41
Step-by-step explanation:
5(14-23)+8 ÷ 2
=5(-9)+4
=-45+4
=-41
The solution of the given expression 5(14-23)+8 ÷ 2 is -41.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Example; 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
Simplification usually involves making the expression simple and easy to use later.
WE have given an expression as;
5(14-23)+8 ÷ 2
Solve the bracket then division;
=5(-9) + 4
=-45+4
=-41
Therefore, the solution of the given expression is -41.
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Find all numbers whos absolute value is 8
Answers
Answer:
8 and -8.
Step-by-step explanation:
Absolute value is the magnitude of quantity, irrespective of sign; the distance of a quantity from zero. The absolute value of a number is symbolized by two vertical lines, as |8| or |-8| is equal to 8.
The absolute value of number a:
⇒ |a| = a for a ≥ 0⇒ |a| = -a for a < 0|a| = 8 ⇔ a = 8 or a = -8
Which expression is equivalent to 21\root(3)(15)-9\root(3)(15)
Answers
The equivalent expression of 21√(3)(15) - 9√(3)(15) is 36√5
How to determine the equivalent expression?The expression is given as:
21√(3)(15) - 9√(3)(15)
Express 15 as 3 * 5
21√(3)(15) - 9√(3)(15) = 21√(3)(3 * 5) - 9√(3)(3 * 5)
Evaluate the product of 3 and 3
21√(3)(15) - 9√(3)(15) = 21√(9 * 5) - 9√(9 * 5)
Take the square root of 9
21√(3)(15) - 9√(3)(15) = 21*3√(5) - 9*3√5)
Evaluate the product
21√(3)(15) - 9√(3)(15) = 63√(5) - 27√5)
Evaluate the difference
21√(3)(15) - 9√(3)(15) = 36√5
Hence, the equivalent expression of 21√(3)(15) - 9√(3)(15) is 36√5
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The terminal side of an angle
intersects the unit circle at point
Answers
Answer:
[tex] - \frac{ \sqrt{2} }{2} [/tex]
Step-by-step explanation:
The sine of an angle is equal to the y coordinate point where the terminal side of the angle intersects the unit circle.
Identify the indicated sum for the geometric series.
S7 for 162 − 54 + 18 − 6 + .....
Answers
The indicated sum for the geometric series is 121.5
How to identify the indicated sum for the geometric series?The series is given as:
162 − 54 + 18 − 6 + .....
Start by calculating the common ratio of the geometric series.
This is calculated using
r = -54/162
Evaluate
r = -1/3
The indicated sum for the geometric series is then calculated as:
S = a(1 - r^n)/1 - r
Substitute the known values in the above equation
S = 162(1 - (-1/3)^7)/1 + 1/3
Evaluate the exponent and the sum
S = 162(1 + 1/2187)/4/3
Evaluate the sum
S = 162(2188/2187)/4/3
Express as products
S = 162 * (2188/2187)* 3/4
Evaluate the product
S = 162 * 547/729
Evaluate the product
S = 121.5
Hence, the indicated sum for the geometric series is 121.5
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If u=(-5,3) and v=(-15,25) with an angle theta between the vectors, are u and v parallel or orthogonal? Explain
Answers
Answer:
Option (2)
Step-by-step explanation:
[tex]\mathbf{u} \cdot \mathbf{v}=(-5)(-15)+(3)(-25)=0[/tex]
So, the vectors are orthogonal.
Ekaete collected 12 raffle tickets. Roseline collected twice as many. How many raffle tickets did they collect in all?
Answers
Answer:
36
Step-by-step explanation:
12 times 2 which is 24 then u add 12 cause it's the amount they have together so you get 36
12/31/2021 and 3 million shares at 12/31/2020 (81 million) (59 million) total shareholders’ equity $ 774 million $ 603 million how many of levi's common shares were outstanding on 12/31/2020
Answers
The number of Levi's common shares that were outstanding on 12/31/2020 is 16,000,000 shares.
What is an Outstanding common shares?This refers to the number of shares of common stock that a company has issued to investors and company executives.
Total common shares
= $95million / $5 par shares
= 19 million shares
Outstanding common shares = 19 million shares - 3 million shares
Outstanding common shares = 16,000,000 shares
Therefore, the number of Levi's common shares that were outstanding on 12/31/2020 is 16,000,000 shares.
Full information
The following partial information is taken from the comparative balance sheet of Levi Corporation:
Shareholders’ equity 12/31/2021 12/31/2020
Common stock, $5 par; 29 million shares authorized; 24 million shares issued and 19 million shares outstanding at 12/31/2021; and ____million shares issued and ____shares outstanding at 12/31/2020.
$120million $95million
Additional paid-in capital on common stock 529million 401million
Retained earnings 206million 166million
Treasury common stock, at cost, 5 million shares at 12/31/2021 and 3 million shares at 12/31/2020 (81million) (59million)
Total shareholders’ equity $774million $603million
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1. Find the length of a.
Answers
a^2 = b^2 + c^2 - 2bc*cos(A)
a^2 = 15^2 + 12^2 - 2*12*15*cos(110)
a^2 = 225 + 144 - 360*-0.342
a^2 = 369 + 123.13
a^2 = 492.13
a = 22.18
What is the greatest possible error if irina measured the length of her window as 3.35 feet? 0.5 0.05 0.005 0.0005
Answers
3.35 feet have a maximum inaccuracy of 0.005 feet.
The correct option is C.
What is error analysis?When students consistently commit mistakes, an approach known as error analysis is frequently employed to determine the root of the problem. Reviewing student work is the first step in the process, after which misunderstood patterns are sought out. Mathematics mistakes can be conceptual, procedural, or factual, and they can happen for a variety of reasons.
Given:The window is 3.35 feet long.
Find the biggest error you can
According to the given data:Half of the measuring unit is considered to be the maximum amount of measurement error.
3.35 feet are calculated to the nearest centimeter, or 0.01 feet
Consequently, the largest conceivable error is equal to half of the measurement unit.
= .01/2
= .005
Therefore, the maximum inaccuracy for 3.35 feet is 0.005 feet.
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Which equation describes the circle having center point (3,7) and radius r = 4
in standard form?
A. (x-3)²+(y-7)² = 4
B. (x+3)² + (y+7)² =4
c. (x-3)²+(y-7)² = 16
D. (x+3)² + (y+7)² = 16
Answers
What is the value of x
Answers
A boat heading out to sea starts out at Point A, at a horizontal distance of 1315 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 12^{\circ}. At some later time, the crew measures the angle of elevation from point B to be 8^{\circ}. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Answers
Bearing is a topic that deals with distance and measure of the angle in locating the position of an object. The distance required in the question is 692 feet.
Bearing is a topic that relates the distance and measure of an angle so as to determine the accurate position of a given object. The angle with respect to the object is measured clockwise with respect to the North pole.
From the first part of the question, the height of the lighthouse, h, can be determined by applying the trigonometric function. So that;
Tan θ = [tex]\frac{Opposite}{Adjacent}[/tex]
Tan 12 = [tex]\frac{h}{1315}[/tex]
h = Tan 12 x 1315
= 279.51
Thus the height of the lighthouse is approximately 280 feet.
Thus, let the distance between points A and B be represented by l. This implies that the distance from point B to the lighthouse is (l + 1315) ft.
So that;
Tan θ = [tex]\frac{Opposite}{Adjacent}[/tex]
Tan 8 = [tex]\frac{280}{(l+1315)}[/tex]
Tan 8 x (l + 1315) = 280
0.141l + 185.415 = 280
0.141 l = 280 - 185.415
= 97.585
l = [tex]\frac{97.585}{0.141}[/tex]
= 692.092
l = 692 feet
Therefore, the distance between points A and B is 692 feet.
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Simplify this expression √x4y12
Answers
Answer:
4[tex]\sqrt{3xy}[/tex]
Step-by-step explanation:
4 is a perfect square. We can pull 2 out from under the square root symbol.
The prime factor of 12 is 2.2.3. We can pull another 2 outside of the square root symbol. 2 x2 is 4 that will be outside of the square root symbol and the x, y and 3 will be left under the symbol.
At time t, the position of a body moving along the s-axis is s=t^3 -18t^2+60t m. Find the displacement of the body from t=0 to t=3.
a. 56 m
b. 67 m
c. 105 m
d. 45 m
Answers
The displacement between t = 0 and t = 3 is 45 meters, so the correct option is d.
How to find the displacement?The displacement is defined as the difference between the final position and the initial position.
The initial position is what we get when we evaluate in t = 0.
s = 0^3 -18*0^2+60*0 = 0
The initial position is 0 meters.
The initial position is what we get when we evaluate in t = 3.
s = 3^3 -18*3^2+60*3 = 45
The final position is 45 meters.
Then the displacement is:
D = 45m - 0m = 45m
The correct option is d.
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A prism is created using 2 regular pentagons as bases. The apothem of each pentagon is 2.8 centimeters.
A regular pentagonal prism is shown. The apothem of each pentagon is 2.8 centimeters. The height of the prism is (2 x + 1). All sides of the pentagon are congruent.
Which expression represents the volume of the prism, in cubic centimeters?
9x2 + 7x
14x2 + 7x
16x2 + 14x
28x2 + 14x
Answers
the expression that represents the volume of the prism is 14x² + 7x cubic centimeters. Option 2
What is the volume of a pentagonal prism?The volume of a pentagonal prism is determined using the formula;
V = 5/2abh
where
a is the apothemh is the height of the prismb is the base of the prismNow, let's substitute the values given
Let the base be 'x'
The apothem is 2. 8 centimeters
height is 2x + 1
Volume = 5/ 2 × 2. 8 × x × (2x + 1)
Volume = 14/ 2 × x(2x + 1)
Volume = 7x(2x + 1)
Volume = 14x² + 7x
Thus, the expression that represents the volume of the prism is 14x² + 7x cubic centimeters. Option 2
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PLEASE HELP ME QUICK!! I"M BEING TIMED
Carter and Ari had $240 altogether. Ari had twice as much as Carter after Carter gave him $16. How much more money did Ari have than Carter in the beginning?
Answers
Answer: $48 more
Step-by-step explanation: We use algebra. Let c = Carter and a = Ari. C+A = 240. A+16 = 2(C-16). 2C-32 + C-16 = 240. 3C - 48 is 240. 240+48 is 288. So, C is 96 and a is 144. 144- 96 = 48 more.
70 POINTS !! Charlotte has a map of the village. The scale on the map is such that 1cm represents 25m.
a) On the map, the church is 7cm from the village store. What is the real distance from the church to the village store?
b) Charlotte calculates her car is parked approximately half a kilometer from the church. On the map, how many cm would represent this distance?
Answers
Answer:
A. 175 m
B. 20 cm
Step-by-step explanation:
[tex]\frac{1 cm}{25 m} =\frac{7 cm}{x m}[/tex]
x = 175 m
[tex]\frac{25 m}{1 cm} = \frac{500 m}{x cm}[/tex]
x = 20 cm
Answer:
No1. 175 m
no2. 20 cm
The graph f(x) = (x + 2) ^ 2 - 7 is translated 3 units up, resulting in the graph g(x) . Which equation represents the new function, g(x) ?
Answers
Step-by-step explanation:
x^2 +4x +4 -7 is
y=x^2+4x-3
Answer: g(x)=(x+2)²-4.
Step-by-step explanation:
g(x)=f(x)+3
g(x)=(x+2)²-7+3
g(x)=(x+2)²-4.
which expression is equivalent to (125^2/ 124^4/3)
Answers
The answer is 25.
What is numerator and denominator?The value above the horizontal line is the numerator in a fraction. It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the vinculum. It indicates the overall total of all of the equal portions.For instance, the fraction bar is the line that separates the numbers 4 and 5, and 45 is a fraction. Here, the numerator is the number above the fraction bar, and the denominator is the number below the fraction bar. The denominator, or the number of pieces out of the whole, is represented by a numerator.Multiplying the numerator times the numerator and denominator. Denominator. The answer should be lowered to a mixed number in the simplest form.The expression is equivalent to [tex]\frac{125^{2} }{125^{\frac{4}{3}} }[/tex] :
[tex]\frac{125^{2} }{125^{\frac{4}{3}} } =125^{2-(\frac{4}{3}) }[/tex]
[tex]=125^{\frac{2}{3} }[/tex]
[tex]125=5x^{3}[/tex]
[tex](5^{3} )^{\frac{2}{3}} =5\frac{6}{3} =5^{2} =25[/tex]
Therefore, The answer is 25.
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pls help!
using the numbers 1-9 fill in the boxes so that it meets the criteria. use each number only once per red box and once per blue box
Answers
The way to solve this is to try to get the vales that would best fill the empty spaces in the diagram. This has been done below
a. log6⁰, log 2 . 1, log 8/3
b. log 1 .4 , 1 , log 4. 6
c. log 9/2, log 3. 5 , log 5⁷
How to find the logarithm of a numberTo do this, you have to decide on that specific number whose logarithm you are trying to determine. Next you have to find the base of that number.
The logarithm of the number is the power that it would have to be raised for us to obtain a different number.
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f(x)=x^2-6. find the inverse
Answers
Answer:
f-1(x) = +- sqrt(x + 6)
Step-by-step explanation:
f(x) = x^2 - 6
y = x^2 - 6
x = y^2 - 6
x + 6 = y^2
y = +- sqrt(x + 6)
f-1(x) = +- sqrt(x + 6)
Hi :)
Let's find the inverse of the function
——————————Remember, inverse functions do the opposite things in the opposite order.
To find the inverse,
replace [tex]\boldsymbol{f(x)}[/tex] with [tex]\boldsymbol{y}[/tex]swap x's and y'ssolve for yReplace f(x) with y. (one step)
Then
[tex]\boldsymbol{y=x^2+6}[/tex]
Swap x's and y's (one step)
Then
[tex]\boldsymbol{x=y^2+6}[/tex]
Solve for y (several steps)
[tex]\boldsymbol{x-6=y^2}[/tex] > square root both sides
[tex]\boldsymbol{\sqrt{x-6}=y}[/tex] > swap y and √x-6
[tex]\boldsymbol{y=\sqrt{x-6}}[/tex]
[tex]\tt{Learn~More;Work~Harder}[/tex]
:)
X
3.
What is the value of x to the nearest tenth?
6
24
Answers
Answer:
C. 13.4=======================
Connect the center with one end of the chord, this gives us a right triangle with hypotenuse of x, one leg of 6 and another leg of 24/2 = 12.
Use Pythagorean to find the value of x:
x² = 6² + 12²x² = 36 + 144x² = 180x = √180x = 13.4 (rounded)Correct choice is C.
Answer:
x = 13.4
Step-by-step explanation:
Definitions
Radius: a straight line from the center of the circle to its circumference.
Chord: a straight line joining two points on the circle.
Perpendicular: at a right angle (90°).
Isosceles triangle: a triangle with 2 sides of equal length and 2 congruent base angles.
From inspection of the given diagram:
radius = xchord = 24 unitssegment of the radius perpendicular to the chord = 6 unitsIf lines are drawn from the center of the circle to the endpoints of the chord, an isosceles triangle is created with base of 24 units and height of 6 units.
The isosceles triangle is made up of two right triangles with base of 12 units and height of 6 units. The radii are the hypotenuse of these right triangles. Therefore, to calculate the radius of the circle (x), use Pythagoras Theorem.
Pythagoras Theorem
[tex]\sf a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right trianglec is the hypotenuse (longest side) of the right triangleTherefore:
[tex]\sf \implies 6^2+12^2=x^2[/tex]
[tex]\implies \sf x^2=36+144[/tex]
[tex]\implies \sf x^2=180[/tex]
[tex]\implies \sf \sqrt{x^2}=\sqrt{180}[/tex]
[tex]\implies \sf x=\pm 6\sqrt{5}[/tex]
As length is positive:
[tex]\implies \sf x = 6\sqrt{5}=13.4\:units\:(nearest\:tenth)[/tex]
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34.
The drawing shows parallel lines L and m intersected by transversal t.
Which statement best describes angles 1 and 5?
A They are interior angles.
B They are vertical angles.
C They are complementary angles.
D They are corresponding angles.
Answers
Answer:
D
Step-by-step explanation:
1=5 ( being corresonding angle)
3. What are the solutions to the system of equations graphed below?
Answers
Answer:
(-1, 5) and (3, -3)
Step-by-step explanation:
The solutions are all the points where the two functions intersect. Since the lines intersect at two different points, there are two solutions.
The two points at which the functions appear to intersect are (-1, 5) and (3, -3).
