9514 1404 393
Answer:
θC = π/4
Step-by-step explanation:
To find the desired angle, subtract multiplies of 2π until the angle is in the desired range.
9π/4 -2π = (9-8)π/4 = π/4
The angle θC = π/4 is coterminal with θ = 9π/4.
In the first 1/6 hour of a rainstorm, 1/10 inch of rain fell. If the rain continued to fall at the same rate, how much rain fell in 2 1/2 hours?
Answer:
you should multiply or add
Step-by-step explanation:
help how to do this due in a few hours
Answer:
x=52 y=116
Step-by-step explanation:
because they give you the angle 116.
those two are actually equal.
y=116
since that is true, you can do 180-116=64.
now, you subtract 64-12
which is 52.
Kiki has 1/6 pound of blueberries and 5/8 pound of raspberries.
What is the most accurate estimate for the difference between the pounds of berries?
Drag and drop an answer into each box to correctly complete the statements.
1/6 is closest to _____, and 5/8 is closest to_____. So the difference is closest ____.
0
1/2
1
Answer: Did this all by myself 1/6 is closer to 0 and 5/8 is closer to 1/2 so the answer is 1/2 0 then 1/2 then 1/3 again
Step-by-step explanation:
1/ 6 -5 /8 =(1 × 4 6 × 4) – (5 × 3 8 × 3) = 4 /24 – 15 /24 = 4 – 15 24 = – 11 24
Allison went to the store to buy some walnuts. The price per pound of the walnuts is
$4 per pound and she has a coupon for $3.25 off the final amount. With the coupon,
how much would Allison have to pay to buy 3 pounds of walnuts? Also, write an
expression for the cost to buy p pounds of walnuts, assuming at least one pound is
purchased.
Cost of 3 pounds:
Cost of p pounds:
HELP ASAP
Answer:
Step-by-step explanation:
Simran has a bag containing white and yellow marbles. Simran randomly selects one marble from the bag,
records the result, and returns the marble to the bag. The results of the first 65 selections are shown below.
A white marble was selected 41 times.
A yellow marble was selected 24 times.
Based on these results, what is the probability that the next marble Simran selects, rounded to the nearest
Answer:
d. 63%
Step-by-step explanation:
percent, will be white?
A41% b50% c59% d63%
The probability of white = P (w) = 41/65= 0.63
The probability of yellow = P (y)= 24/65= 0.369=0.37
The probability of choosing white is 0.63 . When rounded to nearest percent gives
0.63*100/100
=0.63*100 percent
= 63 percent
= 63%
the probability of getting the next marble white is the same as the probability of getting a white.
Consider the initial value problem my''+cy'+ky=F(t), y(0)=0, y'(0)=0, modeling the motion of a spring mass dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m=2 kilograms, c=8 kilograms per second, k=80 Newtons per meter, and F(t)=20 sin(6t) Newtons.
1. Solve the initial value problem. y(t)=?
2. Determine the long term behavior of the system. Is lim as t goes to infinity of y(t)=0? If it is, enter zero. If not, enter a function that approximates y(t) for very large positive values of t. For very large positive values of t, y(t) is approximately.. ?
Answer:
Hence, the [tex]y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t))\end{array}[/tex] and approximately value of [tex]y(t)[/tex] is [tex]-0.844[/tex].
Given :
[tex]my''+cy'+ky=F(t), y(0)=0, y'(0)=0,[/tex]
Where [tex]m=2[/tex] kilograms
[tex]c=8[/tex] kilograms per second
[tex]k=80[/tex] Newtons per meter
[tex]F(t)=20\sin (6t)[/tex] Newtons
Explanation :
(1)
Solve the initial value problem. [tex]y(t)[/tex]
[tex]my''+cy'+ky=F(t), y(0)=0, y'(0)=0,[/tex]
[tex]\Rightarrow 2y''+8y'+80y=20\sin (6t)[/tex]
[tex]\Rightarrow y''+4y'+40y=10\sin (6t)[/tex]
Auxilary equations :[tex]F(t)=0[/tex]
[tex]\Rightarrow r^2+4r+40=0[/tex]
[tex]\Rightarrow r=\frac{-4\pm\sqrt{4^2-4\times 1\times 40}}{2\times 1}[/tex]
[tex]\Rightarrow r=\frac{-4\pm\sqrt{16-160}}{2}[/tex]
[tex]\Rightarrow r=\frac{-4\pm\sqrt{-144}}{2}[/tex]
[tex]\Rightarrow r=\frac{-4\pm12i}{2}[/tex]
[tex]\Rightarrow r=-2\pm6i[/tex]
The complementary solution is [tex]y_c=e^{-2t}\left(c_1\cos 6t+c_2\sin 6t\right)[/tex]
The particular Integral, [tex]y_p=\frac{1}{f(D)}F(t)[/tex]
[tex]y_{y} &=\frac{1}{D^{2}+4 D+40} 25 \sin (6 t) \\\\ y_{y} &=\frac{25}{-6^{2}+4 D+40} \sin (6 t) \quad\left(D^{2} \text { is replaced with }-6^{2}=-36\right) \\\\y_{y} &=\frac{25}{4 D+4} \sin (6 t) \\\\y_{y} &=\frac{25}{4(D+1)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4(D+1)(D-1)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4\left(D^{2}-1\right)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4(-36-1)} \sin (6 t) \\\\y_{y} &=-\frac{25}{148}(D-1) \sin (6 t) \\y_{y} &=-\frac{25}{148}\left(\frac{d}{d t} \sin (6 t)-\sin (6[/tex]
Hence the general solution is :[tex]y=y_c+y_p=e^{-2t}(c_1\cos 6t+c_2\sin 6t)-\frac{25}{148}(6\cos 6t-\sin 6t)[/tex]
Now we use given initial condition.
[tex]y(t) &=e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\\y(0) &=e^{-\alpha 0)}\left(c_{1} \cos (0)+c_{2} \sin (0)\right)-\frac{25}{148}(6 \cos (0)-\sin (0)) \\\\0 &=\left(c_{1}\right)-\frac{25}{148}(6) \\\\c_{1} &=\frac{75}{74} \\\\y(t) &=e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\[/tex]
[tex]y^{\prime}(t)=-2 e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)+e^{-2 t}\left(-6 c_{1} \sin 6 t+6 c_{2} \cos 6 t\right)-\frac{25}{148}(-36 \sin (6 t)-6 \cos (6 t)) \\\\y^{\prime}(0)=-2 e^{0}\left(c_{1} \cos 0+c_{2} \sin 0\right)+e^{0}\left(-6 c_{1} \sin 0+6 c_{2} \cos 0\right)-\frac{25}{148}(-36 \sin 0-6 \cos 0) \\\\0=-2\left(c_{1}\right)+\left(6 c_{2}\right)-\frac{25}{148}(-6) \\\\0=-2 c_{1}+6 c_{2}+\frac{75}{74} \\\\0=-2\left(\frac{75}{74}\right)+6 c_{2}+\frac{75}{74} \\\\[/tex][tex]\begin{array}{l}0=-\frac{150}{74}+6 c_{2}+\frac{75}{74} \\\\\frac{150}{74}-\frac{75}{74}=6 c_{2}\end{array}[/tex]
[tex]\begin{array}{l}c_{2}=\frac{25}{148}\\\\\text { Substitute } c_{1} \text { and } c_{2} \text { in } y(t) \text { . Then }\\\\y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t))\end{array}[/tex]
(2)
[tex]y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\y(t)=\left(\frac{75}{74} e^{-2 t} \cos 6 t+\frac{75}{148} e^{-2 t} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\y(t)=\frac{75}{74}\left(e^{-2 t}-1\right) \cos 6 t+\frac{25}{148}\left(3 e^{-2 t}+1\right) \sin 6 t \\\\|y(t)| \leq \frac{75}{74} e^{-2 t}-1|\cos 6 t|+\frac{25}{148}\left|3 e^{-2 t}+1\right||\sin 6 t| \\\\[/tex]
[tex]|y(t)| \leq \frac{75}{74}\left|e^{-2 t}-1\right|+\frac{25}{148}\left|3 e^{-2 t}+1\right| \\\\\lim _{t \rightarrow \infty} y(t) \leq \lim _{t \rightarrow \infty}\left\{\frac{75}{74}\left|e^{-2 t}-1\right|+\frac{25}{148}\left|3 e^{-2 t}+1\right|\right\} \\\\\lim _{t \rightarrow \infty} y(t)=\left\{\frac{75}{74}\left|\lim _{t \rightarrow \infty}\left(e^{-2 t}-1\right)\right|+\frac{25}{148}\left|\lim _{t \rightarrow \infty}\left(3 e^{-2 t}+1\right)\right|\right\} \\[/tex]
[tex]\lim _{t \rightarrow \infty} y(t)=\left\{\frac{75}{74}(-1)+\frac{25}{148}(1)\right\}=-\frac{75}{74}+\frac{25}{148}=-\frac{-150+25}{148}=-\frac{125}{148} \approx-0.844[/tex]
Which of the following names the figure in the diagram below?
A. pentagon
B. prism
C. triangle
D. polygon
E.pyramid
F. square
Answer: Prism
Step-by-step explanation:
Find the length of the leg x. Enter the exact value, not a decimal approximation.
Find the length of arc AB.
Answer:
11.17
Step-by-step explanation:
arc length = 2πr(θ/360)
= 2π(8)(80/360)
= 11.1701072...
= 11.17 to nearest hundredth
Evaluate f(x) = 2x - 7 when x = 8.
Answer:
9
Step-by-step explanation:
Substitute 8 in place of x
f(x) = 2*8-7
f(x) = 9
Answer:
9
Step-by-step explanation:
plug in 8 where x is so it would look like
2(8)-7 = 9
do 2 *8 first which is 16
then do 16-7 which gives you 9
5% equals what fraction, in lowest terms?
Answer:
1/20
Step-by-step explanation:
According to G0ogle 5 percent equals 1/20 in lowest terms.
Answer:
5% equals 5/100 which is 1/20 in lowest terms.
Step-by-step explanation:
5% is basically equivalent to 5/100. 5/100 in lowest terms is 1/20 since you divide the numerator and denominator by 5.
I hope this helps, have a nice day.
An isosceles right triangle has legs of equal length. If the
hypotenuse is 10 centimeters long, find the length of each leg.
Answer:
[tex] \displaystyle 5\sqrt{2}[/tex]
Step-by-step explanation:
we have a right angle isosceles triangle
in order to figure out the length of each leg we can consider Pythagoras theorem given by
[tex] \displaystyle {a}^{2} + {b}^{2} = {c}^{2} [/tex]
remember that,
isosceles triangle has two equal legs so a=b and given that the the hypotenuse is 10
substitute:
[tex] \displaystyle {a}^{2} + {a}^{2} = {10}^{2} [/tex]
simplify addition:
[tex] \displaystyle {2a}^{2}= 100[/tex]
simplify square:
divide both sides by 2:
[tex] \displaystyle {a}^{2}= 50[/tex]
square root both sides:
[tex] \displaystyle {a}^{}= \sqrt{50}[/tex]
[tex] \displaystyle {a}^{}= 5\sqrt{2}[/tex]
hence,
the length of each leg is 5√2
solve for x. topic: pythagorean theorem
Answer: 44.59 or 44.6
Step-by-step explanation:
30^2+33^2= 900+ 1089
= 1989^2
square root = 44.6
hope this helps
Voce 2x-u - 1x2-3x+3 = 2
Answer:
u=−x2−x+1
Step-by-step explanation:
Let's solve for u.
2x−u−1x^2−3x+3=2
Step 1: Add x^2 to both sides.
−x2−u−x+3+x2=2+x2
−u−x+3=x2+2
Step 2: Add x to both sides.
−u−x+3+x=x2+2+x
−u+3=x2+x+2
Step 3: Add -3 to both sides.
−u+3+−3=x2+x+2+−3
−u=x2+x−1
Step 4: Divide both sides by -1.
−u/−1=x2+x−1
−1/u=−x2−x+1
Answer:
u=−x2−x+1
The difference between one-half of a number and one-sixth of the number is equal to ten more than one-eighth of that number.
Which equation could be used to find the number?
n - = 10 + n
- n = 10 + n
n - n = 10 + n
Answer:
equ no second option is correct
What steps to get the principle of a 30 year loan at 5.5%?
PLEASE HELP FAST WILL MARK BRAINLIEST PLEASEEE
Answer:
[tex]\frac{8x^{18} }{y^{2} }[/tex]
Step-by-step explanation:
100% A bookstore sells book covers in 4 colors; pink, blue, purple, green. The owner surveys 60 customers at random. The table shows the colors people prefer. color number pink 25 blue 13 purple 12 green 10 What percent of the customers prefer the purple book cover? O A. 2% OB. 20% O C. 5% OD. 7.2% O E. 22%
Answer:
a 2%
Step-by-step explanation:
Hi, i need to calculate roots x1 and x2 using the vieta theorem, can anyone help me? I have found the answer for x1 and x2, its 1,5 and 2, all i need is a solution on how to get this answer, the equation is in the picture, will give you brainliest if you type down the correct solution for me, thanks.
I have left a similar equation that i did. The only thing why i cant do the equation, because in front of x2 there’s an number, so i don’t understand.
Answer:
Solution given:
x²-12x+11=0
Comparing above equation with ax²+bx+c
we get
a=1
b=-12
c=11
By using Vieta's theorem
X1+X2=[tex] \frac{-b}{a} [/tex]=[tex] \frac{- -12}{1} [/tex]=12
again
X1X2=[tex] \frac{c}{a} [/tex]=[tex] \frac{11}{1} [/tex]=11
x1.x2=11
x1+x2=12
Is the line a good fit for the data points plotted in the scatter plot below?
One angle of a right triangle measures 71°. What is the measure of the other acute angle?
3. Is XY Tangent to circle Z?
Y
12 X
(20
Z
18
Answer:
XY is a tangent
Step-by-step explanation:
Given
[tex]XY = 12[/tex]
[tex]WY = 20[/tex]
[tex]WZ = 8[/tex]
Required
Is XY a tangent?
XY is a tangent if:
[tex]WY^2 = XY^2 + WX^2[/tex]
Because XY should make a right angle at point X with the circle
Where
[tex]WX = 2 * WZ[/tex]
So, we have:
[tex]WY^2 = XY^2 + WX^2[/tex]
[tex]WY^2 = XY^2 + (2*WZ)^2[/tex]
[tex]WY^2 = XY^2 + (2WZ)^2[/tex]
[tex]WY^2 = XY^2 + 4WZ^2[/tex]
This gives:
[tex]20^2 = 12^2 + 4*8^2[/tex]
[tex]400 = 144 + 256[/tex]
[tex]400 = 400[/tex]
Yes, XY is a tangent
Which phrase describes the expression 505n ?
Answer:
I believe it would be "505 times n"
Step-by-step explanation:
If tis is not what you are looking for I am sorry, but the question was vague.
Your pool is 80 ft long by 40 ft wide and the depth is 3ft to 8ft what is the pool volume?
Answer:
Since there are 7.5 gallons in each cubic foot, multiply the cubic feet of the pool by 7.5 to arrive at the volume of the. 3.14 x 25 ft x 3 ft x 7.5 = 1766.25 gallons
Step-by-step explanation:
If you toss three coins, what are the odds in favor of getting exactly two tails and one head?
Answer:
I think the answer is 3:5
Answer:
3.5
Step-by-step explanation:
Find the exact value of sin A in simplest radical form.
Using the sine rule,
[tex] \frac{a}{sin(a)} = \frac{b}{sin(b)} = \frac{c}{sin(c)} [/tex]
Here we are going to use the values of A and C,
[tex] \frac{12}{sin(a)} = \frac{14}{sin(90)} \\ \frac{12}{sin(a)} = \frac{14}{1} \\ sin(a) = 12 \div 14 \\ sin(a) = 0.8571[/tex]
So sin(A) = 12/14 = 6/7 = 0.8571, but since the question says in its simplest radical form, I think the closest answer to it should be
[tex] \frac{ \sqrt{3} }{2} [/tex]
Which statement describes whether the function is continuous at x = 2?
O The function is continuous at x = 2 because f(2) exists.
O The function is continuous at x = 2 because lim f(x) exists.
X-2
The function is not continuous at x = 2 because f(2) does not exist.
The function is not continuous at x = 2 because lim f(x) does not equal f(2).
X-2
Answer: (b)
Step-by-step explanation:
Given
The function is given as
[tex]f(x)=\dfrac{x^2-12x+20}{x-2}[/tex]
Solving the function
[tex]f(x)=\dfrac{x^2-2x-10x+20}{x-2}\\\\f(x)=\dfrac{(x-2)(x-10)}{(x-2)}\\\\f(x)=x-10[/tex]
for [tex]x=2[/tex]
[tex]f(2)=2-10\\f(2)=-8[/tex]
The function is continuous at [tex]x=2[/tex] because [tex]\lim_{x \to 2} f(x)[/tex] exists.
If the limit exists at a point, then the function is continuous.
Answer:
on edge its fs not b or c
Step-by-step explanation:
A babysitter earns the same amount per hour. She earned $36 for 3 hours of babysitting. Which equation describes the relationship between x, the number of hours spent babysitting, and y, the total amount
in dollars earned?
Answer:
y= 12x
Step-by-step explanation:
36/3=12
12× x =y
________________________
Convert the rectangular coordinates (-9, 3V3) into polar form. Express the angle
using radians in terms of te over the interval 0
Answer:
[tex](6\sqrt{3},\,\frac{5\pi}{6})[/tex]
Step-by-step explanation:
The radius r can be found from the relationship
[tex]r^2=x^2+y^2\\r^2=(-9)^2+(3\sqrt{3})^2\\r^2=81+27=108\\r=\sqrt{108}\\r=6\sqrt{3}[/tex]
The point is in Quadrant II (-, +), so use the inverse cosine function to find the angle.
[tex]\cos{\theta}=\frac{x}{r}=\frac{-9}{6\sqrt{3}}\\\cos{\theta}=-\frac{9}{6\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}\\\cos{\theta}=-\frac{9\sqrt{3}}{6\cdot3}\\\cos{\theta}=-\frac{\sqrt{3}}{2}\\\\\cos^{-1}\frac{-\sqrt{3}}{2}}=\frac{5\pi}{6}[/tex]
See the attached image.
algebra 2 question. need help
Answer:
d. x²+2
Step-by-step explanation:
x²+2x+1-2x-2+3 = x²+2