Answer:
Amplitude = -3
Period = [tex]\frac{2\pi}{4}=\frac{\pi}{2}[/tex]
Frequency = [tex]\frac{1}{\pi/2}=\frac{2}{\pi}[/tex]
Vertical Shift = 6.
Step-by-step explanation:
Consider the function:
[tex]y=A\ sin (B(x+C))+D[/tex]
Here,
A = amplitude; It is the measure of how high is the peak from the center line.
2π/B = period; A period is the distance between one peak to the next.
C = phase shift; it represents how far the function is shifted horizontally from the initial point.
D = vertical shift; it represents how far the function is shifted vertically from the initial point.
The frequency of a function is the number of times something happens per unit time.
[tex]\text{Frequency}=\frac{1}{Period}[/tex]
The function provided is:
[tex]y=-3\ cos\ 4x+6[/tex]
On comparing the provided function with the general one it can be determined that:
Amplitude = -3
Period = [tex]\frac{2\pi}{4}=\frac{\pi}{2}[/tex]
Frequency = [tex]\frac{1}{\pi/2}=\frac{2}{\pi}[/tex]
Vertical Shift = 6.
YEAR 9 MATHS- PLEASE HELP
The shape A has been reflected on the line drawn to give shape B.
State the equation of the line.
Answer:
y=2
Step-by-step explanation:
since the line is horizontal, on the point 2 on the y axis, the equation is 2. If, however the line were to be diagonal, it would have been different, as would it if the line were vertical(in which case, the equated would start x =)
Hope this helps
Answer: y =2
Step-by-step explanation:
The diameter of a bicycle wheel is 50 cm. How many complete rotations does it make over a distance of 3km?
Answer:
47.12388
Step-by-step explanation:
Wheel Diameter = Wheel 2 x Radius; 50 cm / 2 = 25 cm.
For one rotation of the wheel, the distance travelled = circumference of the wheel.
Circumference = 2 x pi x radius = 2 x 3.1415926858 x 25 cm = 157.07 cm approx.
Distance travelled with 30 turns of the wheel = 30 x 157.07 = 4712.39cm approx.
Distance in meters = 4712.39cm / 100 = 47.12388 meters approximate (1 cm = 1/100th of a meter).
hope it helps you
The requried bicycle wheel makes approximately 1910 complete rotations over a distance of 3 km.
What is the circumference?The circumference of the bicycle wheel is equal to its diameter multiplied by π (pi).
Here
Circumference = diameter x π = 50 cm x 3.14 ≈ 157 cm
To find the number of rotations, we need to divide the distance traveled by the circumference of one rotation:
Number of rotations = Distance ÷ Circumference
Number of rotations = 300000cm ÷ 157 cm = (3000 m ÷ 157 cm) ÷ (100 cm ÷ 1 m) = 1910.82
Therefore, the bicycle wheel makes approximately 1910 complete rotations over a distance of 3 km.
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how to find the distance from a velocity-time graph?
Answer:
Calculating the distance travelled
Calculate the total distance travelled by the object - its motion is represented by the velocity-time graph below.
Here, the distance travelled can be found by calculating the total area of the shaded sections below the line.
½ × base × height.
½ × 6 × 2 = 12 m 2
(10 – 6) × 2 = 8 m 2
Answer:
Calculate the total distance travelled by the object - its motion is represented by the velocity-time graph below.
Here, the distance travelled can be found by calculating the total area of the shaded sections below the line.
½ × base × height.
½ × 4 × 8 = 16 m 2
(10 – 4) × 8 = 48 m 2
Step-by-step explanation:
The day after her birthday party 1/3 of Emma’s birthday cake is left is the remaining cake is shared equally among Emma her brother Owen and their mother and father what fraction of the original Kikoo each of them get
Answer:1/4
Step-by-step explanation:
Answer:
1/12
Step-by-step explanation:
1/3 ÷ 4
1/3 x 1/4 = 1/12
What is the vertical asymptote for the reciprocal of y=8x-4
Answer:
The vertical asymptote for the reciprocal of y=8x-4 is [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given Equation : [tex]y = 8x-4[/tex]
Reciprocal of given equation =[tex]\frac{1}{y}=\frac{1}{8x-4}[/tex]
Now to find the vertical asymptote
[tex]\frac{1}{y}=\frac{1}{8x-4}[/tex]
Equate denominator to 0
8x-4=0
8x=4
[tex]x=\frac{4}{8}[/tex]
[tex]x=\frac{1}{2}[/tex]
So, The vertical asymptote is[tex]\frac{1}{2}[/tex]
Hence the vertical asymptote for the reciprocal of y=8x-4 is [tex]\frac{1}{2}[/tex]
Which statement best describes f (x) = negative 2 StartRoot x minus 7 EndRoot + 1?
–6 is in the domain of f(x) but not in the range of f(x).
–6 is not in the domain of f(x) but is in the range of f(x).
–6 is in the domain of f(x) and in the range of f(x).
–6 is neither in the domain of f(x) nor in the range of f(x).
Answer:
Option B.
Step-by-step explanation:
The given function is
[tex]f(x)=-2\sqrt{x-7}+1[/tex]
The above function is defined if (x-7) is greater than 0.
[tex]x-7\geq 0[/tex]
Add 7 on both sides.
[tex]x\geq 7[/tex]
It is means domain of the function is [tex][7,\infty)[/tex]. So, -6 is not in domain.
We know that
[tex]\sqrt{x-7}\geq 0[/tex]
Multiply both sides by -2. So, the sign of inequality will change.
[tex]-2\sqrt{x-7}\leq 0[/tex]
Add 1 on both sides.
[tex]-2\sqrt{x-7}+1\leq 0+1[/tex]
[tex]f(x)\leq 1[/tex]
It is means range of the function is [tex](-\infty,1][/tex]. So, -6 is in Range.
Since –6 is not in the domain of f(x) but is in the range of f(x), therefore the correct option is B.
Answer:
B
Step-by-step explanation:
I need help .... can y’all help me
6. C.
7. B.
8. B.
9. B.
10. C
solve the inequality
[tex]2(4 + 2x) \geqslant 5 + 5[/tex]
Answer:
Step-by-step explanation:
8 + 4x ≥ 10
4x ≥ 2
x ≥ 2/4
x ≥ 1/2
which expression is equivalent to 7/12?
if i understand correctly what you mean by this question the answer could be
14/24
28/48
you can just keep multiplying the top and the bottom by the same number to get an equivalent fraction
im sorry if i understood the question wrong, i hope this helped a little bit
Disclaimer: The options are missing. The options to the question are:
A.7x1/12; B.7/7x12/12; C.1/7x7/12; D.12x1/7
The expression equivalent to 7/12 is 7x1/12. So, option A. is the right choice.
What are equivalent fractions?Two fractions are said to be equivalent fractions when they both give the same value in their reduced or simplest form.
How do we solve the given question?We are asked to find the expression equivalent to 7/12 from the given options.
To solve the question, we reduce all the options to their simplest form. The option = 7/12 will be our answer.
A. 7 * 1/12 = 7/12B. 7/7 * 12/12 = 1*1 = 1C. 1/7 * 7/12 = 1/12D. 12 * 1/7 = 12/7As we can see only option A. 7 * 1/12 = 7/12 in its simplest form, so it is the right option.
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Daniel, Clarence, and Matthew split a $20.20 dinner bill so that Daniel pays half of what Clarence pays. If Daniel pays $6.06, what is the ratio of Clarence's pay to Matthew's pay?
Answer:
grgrtgdegtrt
Step-by-step explanation:
etetetetrdgtfrrgdergdrg
Simplify 3x(2x + 4y)
Answer:
[tex]6x^2+12xy[/tex]
Step-by-step explanation:
By the distributive property:
[tex]3x(2x+4y)= \\\\3x(2x)+3x(4y)=\\\\6x^2+12xy[/tex]
Hope this helps!
Find the surface area of a cylinder with a diameter of 4 cm, and a height of
8 cm. (use 3.14 for Pi) *
Answer:
125.66
Step-by-step explanation:
What’s the answer to this ??
Answer:
Option C
Step-by-step explanation:
zero's are
(2, 0) and (0, -2)
y= x-2, x<3
(3, 2) and (4,3)
y=x-1, x≥3
These are covered in Option C
URGENT PlZ Help
which statement is an example of the transitive property of congruence
[tex]the \: answer \: is \: of \: option \: a \\ \\ for \: example \\ \\ if \: a = b \: and \: b = c \\ then \: we \: can \: say \: a = c \\ hope \: it \: helps[/tex]
Answer:
A is the answer
Step-by-step explanation:
The transitive property is if ABC=DEF and DEF=GHI, then ABC=GHI. The concept is the same here, just with different letters.
Dr.Chavez drew a rectangle on a coordinate plane to estimate the size of a lake. Each unit represents 1 mi. The coordinates of the rectangle are the origin, (0,7.65), (12.8, 7.65) and (12.8,0). Based on the information, what is the perimeter of the lake?
Answer:
40.9 mi
Step-by-step explanation:
The four points will make the rectangle, and each pair of points in sequence will create a side of the rectangle. So, to find the length of each side, we need to find the distances between each pair of points in sequence:
distance between (0,0) and (0, 7.65) -> |7.65 - 0| = 7.65 mi
distance between (0,7.65) and (12.8, 7.65) -> |12.8 - 0| = 12.8 mi
distance between (12.8, 7.65) and (12.8, 0) -> |0 - 7.65| = 7.65 mi
distance between (12.8, 0) and (0, 0) -> |0 - 12.8| = 12.8 mi
So the perimeter is 7.65 + 12.8 + 7.65 + 12.8 = 40.9 mi
Answer:
40.9 mi
Step-by-step explanation:
will make it simple and short
in a surveying measurements with coordinates, we always take it from the Zero. So each coordinates must be subtracted from Zero to get the length of each point.
therefore the perimeter = 0 + 7.65 + 12.8 + 7.65 + 12.8 + 0 = 40.9 mi
factorise 32 x cube minus 8 y square
Answer: [tex]8(4x^3-y^2)[/tex]
Step-by-step explanation:
[tex]32x^3-8y^2[/tex]
[tex]8(4x^3-y^2)[/tex]
Triangle L N P has centroid S. Lines are drawn from each point to the midpoint of the opposite side to form line segments N R, L P, and Q M. The length of line segment N S is 7 x minus 3 and the length of line segment S R is 5 x minus 3. What is the length of segment NS? 1 unit 2 units 4 units 6 units
Answer:
6 units
Step-by-step explanation:
Given: Triangle L N P has centroid S.
[tex]NS=7x-3, SR=5x-3[/tex]
To find: NS
Solution:
Centroid is the point of intersection of the medians of the triangle such that it divides each of the median in ratio [tex]2:1[/tex]
So,
[tex]NS:SR=2:1\\\frac{NS}{SR}=\frac{2}{1} \\[/tex]
Put [tex]NS=7x-3, SR=5x-3[/tex]
[tex]\frac{7x-3}{5x-3}=\frac{2}{1}\\ 7x-3=10x-6\\10x-7x=-3+6\\3x=3\\x=1[/tex]
Therefore,
[tex]NS=7x-3=7(1)-3=4\,\,units\\SR=5x-3=5(1)-3=2\,units[/tex]
So,
[tex]NS=NS+SR=4+2=6\,\,units[/tex]
Answer:
The answer is 4
Step-by-step explanation:
It asks for the length of NS not the length of NR
May someone please help me with this question
Answer:
2+i or 2-i (D)
Step-by-step explanation:
First you use the quadratic formula. X= (-b +/- [tex]\sqrt{b^{2}-4ac }[/tex])/2a
a=1
b=-4
c=5
X= (4 +/- [tex]\sqrt{16-20}[/tex])/2
X=(4 +/- [tex]\sqrt{-4}[/tex])/2
The square root of -4 is 2i. i=√-1. Therefore 2i= 2√-1 .If you simplify that, it becomes √-4i.
X= (4+/- 2i)/2
X= 2+/-i
X= 2+i or 2-i
A sequence is defined by the recursive function f(n + 1) = –10f(n). If f(1) = 1, what is f(3)?
Answer:
f(3) = 100
Step-by-step explanation:
Using the recursive formula and f(1) = 1 , then
f(2) = - 10 f(1) = - 10 × 1 = - 10
f(3) = - 10 f(2) = - 10 × - 10 = 100
Answer:
100
Step-by-step explanation:
what is the number of possible permutations of 8 objects Taken 3 at a time
The number of possible permutations of 8 objects taken 3 at a time is 336.
The formula for PermutationThe formula to calculate the permutation of 'n' object taken 'r' at a time is [tex]P_{r}=\dfrac{n!}{(n-1)!}[/tex].
How to find the number of possible permutations?The formula for calculating the permutation is [tex]P_{r}=\dfrac{n!}{(n-r)!}[/tex] where 'n' is the number of distinct objects taken 'r' at a time.
Thus we will substitute n=8 and r=3, we will get
[tex]P_{3}=\dfrac{8!}{(8-3)!}\\P_{3}=\dfrac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{5!}\\P_{3}=\dfrac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{5\times 4\times 3\times 2\times 1}\\P_{3}=8\times 7\times 6\\P_{3}=336[/tex]
So, the number of possible permutations of 8 objects taken 3 at a time is 336.
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-7/10+7/15+1/-20+-9/10+11/15+11/-20
what is the answer please help me .....!!!!
Answer:
-1
Step-by-step explanation:
-7/10+7/15+1/-20+-9/10+11/15+11/-20
= -7/10 + -9/10 + 7/15 + 11/15 + 1/-20 + 11/-20
= -16/10 + 18/15 + 12/-20
= -8/5 + 6/5 + -3/5
= (-8+6-3)/5
= -5/5
= -1
when a number,n is increassed by two and then the result is divided by five the quotient is equal to 14. write an equation and solve it to find the value of n.
Answer:
68
Step-by-step explanation:
(n+2)/5=14
n+2=14*5
n+2=70
n=70-2
n=68
Answer:
68
Step-by-step explanation:
Find the area of the shaded region. Can I have the steps explained please?
Answer:
76.3 cm²
Step-by-step explanation:
step 1
area of circle= πr²= 3.14*5²= 78.6 cm²step 2
area of 60° sector= 60/360*area of circle= 1/6*78.6= 13.1 cm²step 3
Area of equilateral triangle = √3/4a²= √3/4*5²= 10.83 cm²step 4
Area of circle - area of sector + area of triangle= 78.6 - 13.1 + 10.8= 76.3 cm²Is the real number rational or irrational? rational irrational
Answer:
rational
Step-by-step explanation:
Answer:
Rational.
Step-by-step explanation:
A real number is rational.
cos (x/2) = -sqrt2/2 in (0,360) looking for two values ?? Can someone please help me I can’t seem to figure out how to solve this problem, I’m looking at other examples but I’m still confused please help
Answer:
135° and 225°
Step-by-step explanation:
basically you want to find the value of x between 0 and 360 in this equation
cos x/2 = -(√2)/2
assume x/2 as n, so
cos n = -(√2)/2
n = 45°
then remember the quadrant system
0-90 1st quadrant, all is POSITIVE
90-180 2nd quadrant, only SIN has positive value
180 - 270 3rd quadrant, only TAN has positive value
270 -360 4th quadrant, only COS positive here.
so if you try to find negative value look into 2nd and 3rd quadrant that related 45° to x-axis (0°or 180°)
so the value of x is
180 - 45 = 135° (2nd quadrant) and
180 + 45° = 225° (3rd quadrant)
The interior angles of a triangle are 42°,56° and 2x°. Find the value of x.
Answer:
41 degrees
Step-by-step explanation:
Since the sum of the interior angles of a triangle will always be 180 degrees:
42+56+2x=180
2x=82
x=41
Hope this helps!
Answer:
X=41°[tex]solution \\ 42 + 56 + 2x = 180(sum \: of \: angle \: in \: triangle) \\ or \: 98 + 2x = 180 \\ or \: 2x = 180 - 98 \\ or \: 2x = 82 \\ or \: x = \frac{82}{2} \\ x = 41[/tex]
hope this helps...
Good luck on your assignment...
Suck at maths! HELP!
Answer:
Step-by-step explanation: you can use a protractor if you have 1 or seeing as the bottom left is 65, the bottom right will be the same, mostly a guess but half 65 and try that.
What is the slope of the line represented by the equation f(t)=2t-6
Answer:
The slope would be 2
Step-by-step explanation:
Your slope-intercept form is always y=mx + b
The b is always your constant
The mx is your slope
The y is your output
Answer: Slope: 2 & Y-int: -6.
Step-by-step explanation:
I will try to explain it in my own simple way for you to understand, however, I may be wrong.
The form, y=mx+b, think of f(t) as y, the 2t as m, the t as x, and the -6 as the y-intercept. Since the -6 is the opposite of +b, in the y=mx+b, it would be -6.
Hope this helped.
use the discriminant to determine the nature of the roots of the quadratic equation
The given equation is in the form ax^2 + bx + c = 0, where
a = 2
b = -12
c = 18
Those a,b,c values are plugged into the discriminant formula below
d = b^2 - 4ac
d = (-12)^2 - 4(2)(18)
d = 144 - 144
d = 0
The discriminant is zero, so there is only one real root. This root is specifically a rational number.
-5/2(-2+11/8)=-5/2×-5/8=25/16
Answer:
x=-1/4
Step-by-step explanation: