use the graph of y=sin theta to find the value of 2theta for theta = pi/4 radians
Answers
y=sin x
for x=2theta
theta = pi/4 radians
so
x=2*pi/4-----> x=pi/2
using a graph tool
see the attached figure
for x=pi/2
y=sin pi/2------> y=1
the solution is
1
Related Questions
1. What is the median of the following set of numbers?
48.4, 47, 43, 47, 43.6, 41.6, 45, 51.4, 38.6
Hint: Order the numbers from least to greatest first!
A. 48.4 B. 43.6 C. 45
2. Each of the five math teachers are comparing the number of students in their homeroom classes. The number of boys and girls in each teachers’ classes are recorded in the table below.
Hint: Mean is the average.
Which statement best describes the means of the two sets of data?
A. The mean number of girls in 7 times greater than the mean numbers of boys in the homeroom classes.
B. The mean number of girls is the same as the mean number of bboys in the homeroom classes.
C. The mean number of girls is 7 more than the mean number of boys in the homeroom classes.
Answers
The middle number (median) is 47.
2.The table is not displayed so will explain how you can solve the problem.
→ Mean is the average. Find the sum and divide by the quantity of numbers you added to find the sum.
If you still need help with #2, upload the image of the table or type in the data.
Answer:b
Step-by-step explanation:divided look around the chart
Given: ABCD is a trapezoid, AC ⊥ CD AB = CD, AC=the square root of 75 , AB = 5 Find: AABCD
Answers
In this attached picture according to the conditions of the problem we have an isosceles trapezoid and since we know that legs are equal (AD=BC=5 cm), we have to calculate bases and height in order to find the area. Working with the triangle BCD, we apply Pythagoras theorem and find that CD = [tex] \sqrt{75+25} [/tex] = 10 cm. Since BDC is a right triangle, applying theorem for the area of triangles, we find that [tex] \frac{1}{2} * BF = \frac{1}{2} * 5 * \sqrt{75} [/tex] and BF= [tex] 0.5\sqrt{75} [/tex]. Since ABCD is an isosceles trapezoid, triangles ADE and BFC are congruent with Angle Side Angle theorem. Then, DE=FC and with the help of Pythagoras theorem, DE=FC=2.5 cm. Then, AB=EF=5 cm and the area of the trapezoid is [tex]A= BF * \frac{AB+CD}{2} = 0.5 \sqrt{75} * \frac{5+10}{2} = 18.75 \sqrt{3} cm^{2} [/tex]
The area of the given trapezoid will be [tex]\frac{75}{4} \sqrt{3}[/tex].
It is given that
In trapezoid ABCD
AE ⊥ CD
AC = √75
AD=BC =5
AB =5
In the triangle ADC
From Pythagoras theorem
AC²+AD²=DC²
(√75)² +5² = DC²
DC=10
Let DE=CF=x (Isosceles trapezoid)
What is isosceles Trapezoid?
Trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal.
AB=EF= DC-2x
5 = DC-2x
x=5/2
AE = [tex]\sqrt({5^{2} } -(5/2)^2)\\\\[/tex]
AE = [tex]\sqrt{75} /2[/tex]
So, the area of the trapezoid ABCD = [tex]\frac{1}{2} *(AB+CD)*AE[/tex]
Area of the trapezoid ABCD = [tex]\frac{1}{2} *(5+10)*\frac{\sqrt{75} }{2}[/tex]
Area of the trapezoid ABCD = [tex]\frac{75}{4} \sqrt{3}[/tex]
Therefore, The area of the given trapezoid ABCD will be [tex]\frac{75}{4} \sqrt{3}[/tex].
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Find the approximate circumference of a circle with a radius of 2.6 millimeters. Use = 3.14.
Answers
For which of the inequalities below is v = 4 a solution? A v + 5 ≥ 9 B v + 5 > 9 C v + 5 < 8 D v + 5 ≤ 8
Answers
What is -1 3/5 x -2/3 as a mixed number?
Answers
-8 -2
--- * ----- = 16/15 (an improper fraction), or 1 1/15 (a mixed number)
5 3
1 3/5=8/5x2/3=16/15=1 1/15
Find two number whose sum is 60 such that the sum of the square of one number plus 12 times the other number is a minimum
Answers
x^2=48
x=6.93
Hope this helps
FACTORIZE PLEASE, A LOT OF POINTS
64x^(3)-48x^(2)+12xy^(2)-y^(3)
Answers
=> (4x)³ - 3(4x)²(y) + 3(4x)(y)² - y³
We know the formula: (a - b)³ = a³ - 3a²b + 3ab² - b³
By applying this formula above, we will get
=> (4x - y)³. (Ans)
Hope this helps!
or you can just put it in a smaller form by saying (4x - y)³
Which expression is equivalent to square root 55x^7 y^6/11x^11 y^8? Assume x > 0 and y > 0.
Answers
[tex] \sqrt{ \frac{5 x^{7} y^{6} }{ x^{11} y^{8} } } [/tex]
Now reduce the fraction with [tex] x^{7} [/tex].
[tex] \sqrt{ \frac{5 y^{6} }{ x^{4} y^{8} } } [/tex]
Reduce the fraction one more time with [tex] y^{6} [/tex].
[tex] \sqrt{ \frac{5}{ x^{4} y^{2} } } [/tex]
To take the root of a fraction,, we must take the root of the numerator and denominator separately. This rule will change the expression to the following:
[tex] \frac{ \sqrt{5} }{ x^{2} y} [/tex]
Since we cannot simplify this fraction any further,, the final answer is going to be [tex] \frac{ \sqrt{5} }{ x^{2} y} [/tex].
Let me know if you have any further questions.
:)
Answer:
Basically the answer is C.
Tim bought 5 pencils for .25 cents each. he also bought 2 packs of paper for $1.25 each. he paid with a $10.00 bill. how much change could tim receive
Answers
.25 • 5 = 1.25
1.25 • 2 = 2.50
2.50 + 1.25 = 3.75
10 - 3.75 = 6.25
Identify the type of sequence AND provide the next 3 terms:
5 , 9, 13, 17…
-1, 2, -4, 8…
8, 1, -6, -13…
Answers
-16, 32, -64
not sure about the last one
What is the vertex form, f(x) = a(x − h)2 + k, for a parabola that passes through the point (4, −3) and has (5, 2) as its vertex. What is the standard form of the equation?
Answers
[tex]\text{therefore we have:}\ f(x)=a(x-5)^2+2[/tex]
[tex]\text{a parabola that passes through the point (4, −3)}[/tex]
[tex]\text{substitute the coordinates of the point (4;-3) to the equation:}[/tex]
[tex](4;-3)\to x=4;\ y=-3\\\\-3=a(4-5)^2+2\\\\-3=a(-1)^2+2\\\\-3=a+2\ \ \ |-2\\\\a=-5[/tex]
[tex]f(x)=-5(x-5)^2+2=-5(x^2-2\cdot x\cdot5+5^2)+2=-5(x^2-10x+25)+2\\\\=-5x^2+50x-125+2=-5x^2+50x-123[/tex]
Answer:
y = x² - 10x + 27
Step-by-step explanation:
Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the slope of the line through the origin and the center.
Answers
y_2 - y_1/x_2 - x_1
Fill in:
0 - r/0 - r
r/r
1
The answer to this problem is 1.
The value of slope of the line through the origin and the center is,
⇒ Slope = 1
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Circle P is tangent to the x-axis and the y-axis.
And, the coordinates of the center are (r, r),
Now, The value of slope of the line through the (0, 0) and the center (r, r) is,
⇒ Slope = (r - 0) / (r - 0)
⇒ Slope = r/r
⇒ Slope = 1
Thus, The value of slope of the line through the origin and the center is,
⇒ Slope = 1
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HELP ASAP
What are the coordinates of the vertices of the triangle after a dilation by a scale factor of
1
4
, centered at the origin?
U → U'
V → V'
W → W'
Answers
U' = (-1,2)
V' = (2,2)
W' = (0,-2)
Explanation:
The given dilation factor is 1/4
This means that each coordinate point is multiplied by 1/4 to get its dilated image.
For point U:
Point U = (-4,8)
x coordinate of U' = 1/4 * x coordinate of U
x coordinate of U' = 1/4 * -4 = -1
y coordinate of U' = 1/4 * y coordinate of U
y coordinate of U' = 1/4 * 8 = 2
This means that: U' = (-1,2)
For point V:
Point V = (8,8)
x coordinate of V' = 1/4 * x coordinate of V
x coordinate of V' = 1/4 * 8 = 2
y coordinate of V' = 1/4 * y coordinate of V
y coordinate of V' = 1/4 * 8 = 2
This means that: V' = (2,2)
For point W:
Point W = (0,-8)
x coordinate of W' = 1/4 * x coordinate of W
x coordinate of W' = 1/4 * 0 = 0
y coordinate of W' = 1/4 * y coordinate of W
y coordinate of W' = 1/4 * -8 = -2
This means that: W' = (0,-2)
Hope this helps :)
The coordinates of a triangle's vertices after a dilation by a scale factor of 1/4, centered at the origin, are found by multiplying each of the original vertex coordinates by 1/4.
The coordinates of the vertices of the triangle after a dilation by a scale factor of 1/4, centered at the origin, can be found by multiplying the original coordinates of each vertex by 1/4. If the original coordinates are (x, y), then the coordinates after the dilation will be (x/4, y/4).
This applies to all vertices of the triangle, so the transformed triangle, denoted by U', V', and W', will have vertices with coordinates calculated by taking the original vertex coordinates of U, V, and W and scaling them down by a factor of 1/4.
Which point best represents the square root of 15?
A. Point A
B. Point B
C. Point C
D. Point D
Answers
So point B is the answer it’s between 2 and 4
A jet plane is descending at a rate of 200 feet per second from an altitude of 36000 feet let x represent the number of seconds of descent and y represent the jet plane’s altitude in feet.
Which expression represents this situation?
A. y = 200x - 36000
B. y = 200x + 36000
C. y = -200x - 36000
D. y = -200x + 36000
Answers
In x second, the plane will have descended by 200*x ft = 200x ft
The altitude of the plane, y after x seconds will be 36000 - 200x. That is,
y= 36000-200x = -200x + 36000.
Therefore, the correct expression representing this situation is D.
y=ax+b
where:
a=slope=rate
b=y-intercept or initial valuegiven:
from the question
a=200 ft per second
b=36000 ft
thus the expression representing the situation will be:
y=200x+36000
where x is time in seconds
thus the answer is:
B. y = 200x + 36000
The tank shown is a cylinder with diameter equal to 4 feet and height equal to 12 feet. the tank holds 1130 gallons of rainwater when full. how many gallons of water are in the tank when the depth of the water is 9 feet?
Answers
volume of the tank=1130 gal
step 1
find the volume of the tank with deep 9 ft
volume of the tank with deep 9 ft=pi*r²*h
r=4/2-----> 2 ft
h=9 ft
volume of the tank with deep 9 ft=pi*2²*9-----> 113.04 ft³
step 2
convert to gal
1 ft³------------------> 7.48052 gal
113.04 ft³--------> x
x=113.04*7.48052-----> x=845.60 gal
the answer is
845.60 gal
alternative method
if the volume of the tank is 1130 gal for ----------> a height of 12 ft
X volume-----------------------------------> 9 ft
x=9*1130/12-----> 847.5 gal
There are 158 fourth grade studnets and 139 fifth grade students going on a field trip. There needs to be one caperone for every 8 kids. Explain how to find the number of caperones needed for the trip.
Answers
(158 + 139)/8
297/8 = 37.125
You will need a minimum of 38 chaperones for the 297 students. If there is any remainder(decimal) you will need an extra chaperone so the groups do not exceed 8.
Express 0.0037 as a power of 10.
Answers
To express 0.0037 as a power of 10, we move the decimal point 3 places to the right, resulting in 3.7 × 10⁻³.
Explanation:To express 0.0037 as a power of 10, we need to count the number of places we have to move the decimal point to get a number between 1 and 10. In this case, we have to move the decimal point 3 places to the right, so the power of 10 is -3.
0.0037 = 3.7 × 10-3
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HURRY PLZ
Determine whether each set of side lengths could be the sides of a right triangle. Drag and drop each set of side lengths to the correct box. Right Triangle Not a Right Triangle.
Determine whether each set of side lengths could be the sides of a right triangle.
Drag and drop each set of side lengths to the correct box.
Right Triangle Not a Right Triangle.
6cm, 22.9cm, 20.1cm.
10.5cm, 20.8cm, 23.3cm
Answers
36 + 404 does NOT equal 524.41
These do NOT form a right triangle.
10.5^2 + 20.8^2 =? 23.3^2
110.25 + 432.64 = 542.89
Therefore, it is a right triangle.
Answer:
Second option is the correct answer.
Step-by-step explanation:
To know if the given set of numbers can be possible lengths for a right triangle, we will use the Pythagorean theorem that states:
[tex]a^{2}+b^{2} =c^{2}[/tex]
a and b are smaller lengths.
Option first:
6cm, 22.9cm, 20.1cm.
[tex]6^{2}+20.1^{2} =22.9^{2}[/tex]
=> [tex]36+404.01=524.41[/tex]
=> [tex]440.01\neq 524.41[/tex]
This is not a right triangle.
Option second:
10.5cm, 20.8cm, 23.3cm
[tex]10.5^{2}+20.8^{2} =23.3^{2}[/tex]
=> [tex]110.25+432.64=542.89[/tex]
=> [tex]542.89=542.89[/tex]
This is a right triangle.
The table shows the calories burned during exercise.
(picture of the table attached)
Which statement is true?
A)The y-intercept of the function is (15, 75).
B)The rate of change is 15 calories burned per minute.
C)A linear function to model the calories burned, y, as a function of time in minutes, x, is y = 5x.
D)An exponential function to model the calories burned, y, as a function of time in minutes, x, is y = 5x.
Answers
We have then that the slope of the line is:
[tex]m = \frac{y2-y1}{x2-x1} [/tex]
Substituting values:
[tex]m = \frac{150-75}{30-15} m = 5[/tex]
Then, the equation of the line is:
[tex]y = 5x [/tex]
Answer:
C) A linear function to model the burned calories, and, as a function of time in minutes, x, is y = 5x.
Answer: C. A linear function to model the calories burned, y, as a function of time in minutes, x, is y = 5x.
Step-by-step explanation:
What is the percent chance a coin lands on heads with 3 tosses?
Answers
then you convert it into a percent
12.5%
help please
Sammy is planning a trip to Nashville. He knows the hotel costs $125 per night and the round trip flight is $159. He has a budget of $900 to spend on his trip. Which of the following inequalities represents his budget to determine how many nights he can stay in Nashville?
125n + 159 ≥ 900
125n + 159 ≤ 900
159n + 125 ≤ 900
159n + 125 ≥ 900
Answers
In short, the second option is correct. Hope this helps!
What is the length of AC?
Answers
[tex]\bf \cfrac{small}{large}\qquad \cfrac{DE}{BA}=\cfrac{EC}{CA}\implies \cfrac{7}{84}=\cfrac{x}{156-x}\implies 1092-7x=84x \\\\\\ 1092=91x\implies \cfrac{1092}{91}=x\implies 12=x\qquad \quad \qquad \boxed{AC=156-12}[/tex]
PLEASE HELP 20 POINTS
Answers
looking at the graph there is a peak on x= 1 and then a peak on x= 4
4-1 = 3 so the peak is 3
the amplitude is the midpoint between the highest point and lowest point
on the graph
the high point is y=1 and the low point is y = -2
1 + -3 = 3 spaces, midpoint = 3 / 2 = 1.5 so the amplitude = 1.5
the answer is the first one.
Answer:
Step-by-step explanation:
i put a awnser and that person hacked me lol
Jack Watkins earns a base salary of $1500 a month, plus a 4% commission on the sales he makes. What is his gross pay of his sales for the month are $8000.
A. 1520
B. 1532
C. 1700
D. 1820
Answers
solution:
Gross pay=(salary)+(commissions)
base salary=$1500
commission=4%
monthly sales=$8000
commissions earned in cash
=4/100×8000
=$320
thus
Gross salary=320+1500=$1820
What is the smallest natural number that 2, 10, 14, and 36 will divide evenly?
Answers
Written Answer: The smallest Natural number that 2, 10, 14, and 36 is divide evenly by is 2.
On Tuesday, Mrs. Myles assigned 7 more problems than she did on Monday. If she assigned x problems on Monday, write an expression to represent how many problems Mrs. Myles assigned on Tuesday
Answers
Answer:
Number of problems assigned on Tuesday = x+7
Step-by-step explanation:
Number of problems assigned on Monday = x.
Number of problems assigned on Tuesday is 7 more than that assigned on Monday.
Number of problems assigned on Tuesday = x+7. [In Matha we use + sign for more than]
The expression that will represent the number of problems Mrs. Myles assigned on Tuesday is x+7.
Answer: actually it 7 + x the other way around
Step-by-step explanation:
grant is rolling a standard six sided number die eight times. how many outcomes are possible
Answers
There are 6 possible outcomes for each roll; 6^8 = 1679616
We have been given that Grant is rolling a standard six sided number die eight times and we have to find the total number of outcomes.
Grant is rolling six sided number die. Hence, we can say that
Number of outcomes if rolled once = 6
Number of outcomes if rolled twice = [tex]6\times 6= 6^2[/tex]
Number of outcomes if rolled thrice= [tex]6\times 6 \times 6= 6^3[/tex]
We can see that if rolled twice then we have exponent 2, when rolled trice then we have an exponent 3.
Hence, if rolled 8 times then we have an exponent 8 on 6.
Therefore, the possible number of outcomes should be [tex]6^8= 1679616[/tex]
Hence, the number of possible outcomes is 1679616
The local weather person has been accurate in her predictions within 2 degrees temperature forecast 80% of the time. Find the probability that she is accurate...
a) exactly 3 out of the next 5 days
b) at least 4 of the next 5 days
Answers
B) 0.7373
To find the probability that she is correct exactly 3 days, we have
[tex]_5C_3(0.8)^3(1-0.8)^{5-3} \\ \\\frac{5!}{3!2!}(0.8)^3(0.2)^2=0.2048[/tex]
To find the probability that she is right at least 4 of the 5 days, we find the probability she is right 4 days, the probability she is right 5 days, and add them together:
[tex]_5C_4(0.8)^4(1-0.8)^{5-4}+_5C_5(0.8)^5(1-0.8)^{5-5} \\ \\\frac{5!}{4!1!}(0.8)^4(0.2)^1+\frac{5!}{5!0!}(0.8)^5(0.2)^0 \\ \\5(0.8)^4(0.2)+0.8^5=0.4096+0.32768=0.73728\approx0.7373[/tex]
Find the value of the lesser root of x 2-8x+7=0
Answers
[tex] {x}^{2} - 8x + 7 = 0[/tex]
[tex](x - 7)(x - 1)[/tex]
Rule AB = 0, gives A = 0 or B = 0
[tex]x - 7 = 0 \: \: or \: \: x - 1 = 0 \\ x = 7 \: \: \: \: \: \: \: \: \: or \: \: x = 1[/tex]
Therefore, the smallest of both roots is x = 1.