ASAP.
jack goes for a ride on a ferris wherl thst has a radius of 51 yards. the center of the ferris sherl is 61 yards above the ground. he starts bis rifr at the 9 oclock position and travels counter clockwise. define a function g that tepresents jacks verticL distance above the grihdn in yards in terms of the angel ( meassured in radians) jack has swept out measured grom the 9 oclock positions
Answer:
112 yards
Step-by-step explanation:
The center of the Ferris wheel is 61 yards above the ground and the radius is 51 yards. When Jack is at the 9 o'clock position, he is at a distance of 112 yards from the center of the Ferris wheel (51 yards from the center plus 61 yards above the ground). Let θ be the angle that Jack has swept out measured from the 9 o'clock position, in radians.
The function g that represents Jack's vertical distance above the ground in yards in terms of the angle θ is:
g(θ) = 61 + 51sin(θ)
where sin(θ) represents the vertical component of the distance Jack has traveled.
Note that when θ = 0, sin(θ) = 0, which means Jack is at the very top of the Ferris wheel, 112 yards above the ground. When θ = π/2, sin(θ) = 1, which means Jack is at the 12 o'clock position, 112 + 51 = 163 yards above the ground. Similarly, when θ = π, sin(θ) = 0, which means Jack is at the very bottom of the Ferris wheel, 112 yards above the ground.
7.35 km = _______ mm
Answer: 7.35 km = 7350000 mm
Step-by-step explanation:
Multiply km by 1000000
7.35 * 1000000 = 7350000 mm
Select the correct answer. Determine which statement is true about the zeros of the function graphed below. An upward parabola f on a coordinate plane vertex at (1, 4) and intercepts the y-axis at 5 units. A. Function f has one real solution and one complex solution. B. Function f has exactly one real solution and no complex solutions. C. Function f has exactly two real solutions. D. Function f has exactly two complex solutions.
The correct option is D, the equation has two complex solutions.
Which is the correct statement about the quadratic equation?Here we can see that we have the graph of a quadratic equation.
It opens upwards, and we can see that it has a vertex at (1, 4), which intercepts the y-axis at y = 5.
Now, we say that the solutions of a quadratic are the values of x such that the function becomes zero.
Particualrly, in this graph we can see that the graph never intercepts the x-axis, that means that this equation has no real roots.
Then the correct option is:
"Function f has exactly two complex solutions."
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if f(x)=x³-1 and g(x)=x²
find (gof) ( x) and (fog) (x)
Answer:
(x²)³ - 1 = x^6 - 1
Step-by-step explanation:
To find (gof)(x), we first need to evaluate g(x), which is x², and then use the result as input to f(x), giving us f(g(x)).
So, we have:
g(x) = x²
f(g(x)) = f(x²) = (x²)³ - 1 = x^6 - 1
Therefore, (gof)(x) = g(f(x)) = (f(x))² = (x³ - 1)² = x^6 - 2x^3 + 1.
To find (fog)(x), we first need to evaluate f(x), which is x³ - 1, and then use the result as input to g(x), giving us g(f(x)).
So, we have:
f(x) = x³ - 1
g(f(x)) = g(x³ - 1) = (x³ - 1)² = x^6 - 2x^3 + 1
Therefore, (fog)(x) = f(g(x)) = (x²)³ - 1 = x^6 - 1.
How do l do this? Help please
By expanding and simplifying the algebraic expression (y + 7)(y - 5), we have the result y² + 2y - 35
How to expand and simplify algebraic expression in bracketsTo expand an algebraic expression in brackets, we need to use the distributive property to make is easy for simplification, thus we expand and simplify the expression as follows:
(y + 7)(y - 5) = y(y - 5) + 7(y - 5) {distributive property}
(y + 7)(y - 5) = y² - 5y + 7y - 35
by simplification, we have;
(y + 7)(y - 5) = y² + 2y - 35
Therefore, the expansion and simplification of the algebraic expression (y + 7)(y - 5), gives the result y² + 2y - 35.
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what is this pls help
David is trying to pick out an outfit for the first day of school. He can choose from 8 pairs of pants, 8 t-shirts, 4 sweaters or hoodies, and 3 pairs of shoes. How many different outfits does David have to choose from?
The number of the different outfits do David have to choose is 768.
Here we will use the concept of Combinations,
Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
Different outfits do Damian have to choose, will be;
⇒ 8C₁×4C₁×8C₁×3C₁
⇒ 8×4×8×3
⇒ 768
Hence, the number of the different outfits do David have to select is 768.
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Answers for these test question
The missing lengths and angles in the geometric systems are listed below:
Case 8: x = 60
Case 9: x = 48
Case 10: x = 5.535
Case 11: x = 5.665
Case 12: x = 9.103
Case 13: θ = 60°
Case 14: θ = 23.025°
How to find missing lengths and angles in triangles
In this problem we find two cases of geometric systems formed by triangles:
Systems of two similar triangles with a common unknown side.A triangle with an unknown side or an unknown angle.First case is analyzed by means of proportionality ratios and second case done by trigonometric functions:
Case 8
100 / x = x / 36
x² = 3600
x = 60
Case 9
x / 36 = 64 / x
x² = 36 · 64
x = 48
Case 10
x = 17 · sin 19°
x = 5.535
Case 11
x = 11 · cos 59°
x = 5.665
Case 12
x = 13 · tan 35°
x = 9.103
Case 13
cos θ = 7 / 14
cos θ = 1 / 2
θ = 60°
Case 14
tan θ = 17 / 40
θ = 23.025°
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If m/8 = 133°, find m/1.
Answer:
1064
Step-by-step explanation:
If m/8 = 133°, find m/1.
m/1 = m (Any number, except zero, divided by itself is 1)
m : 8 = 133 : 1
m = 8 * 133 : 1
m = 1064
----------------------
check
1064 : 8 = 133 : 1
133 = 133
the answer is good
If Ton spend $76.25 on food for a party. And he is having 4 friends over what average amount of money he will spent for food per person?
Answer: He would be spending $15.25 for each person including himself
Step-by-step explanation:
step 1. you need to find out how many people are getting food
step 2. divide that number (5) by how much the total cost is ($76.25) to get 15.25
The admission fee at an amusement park is $2.25 for children and $5.60 for adults. On a certain day, 269 people entered the park, and the admission fees collected totaled 1091 dollars. How many children and how many adults were admitted?
For a population growing at 3% a year, what is the yearly growth factor?
A beaker is shaped like a cylinder with a radius of 1.8 inches and a height of 4.6 inches. It is filled to the top with a solution. Caleb wants to pour it into a different beaker with a radius of 1.25 inches. What is the minimum height the second beaker must be so it does not overflow? Round to the nearest tenth.
The minimum height of the second beaker must be approximately 13.5 inches to hold the solution without overflowing.
Now, For the minimum height of the second beaker, we need to find its volume first.
The volume of the first beaker is given by;
⇒ V₁ = πr₁²h₁
where r₁ is the radius and h₁ is the height.
Substituting the given values, we get:
V₁ = π(1.8)²(4.6)
V₁ ≈ 66.85 cubic inches
Since, the first beaker is filled to the top, its volume equals the volume of the solution.
Therefore, the volume of the solution is also 66.85 cubic inches.
To find the minimum height of the second beaker, we need to use the formula for the volume of a cylinder:
V₂ = πr₂²h₂
where r₂ is the radius and h₂ is the height of the second beaker.
We want to find h₂ such that V₂ is equal to 66.85 cubic inches.
Dividing both sides of the equation by πr₂², we get:
h₂ = V₂ / (πr₂²)
Substituting the given value for r₂, we get:
h₂ = 66.85 / (π(1.25)²)
h₂ ≈ 13.5 inches
Therefore, the minimum height of the second beaker must be approximately 13.5 inches to hold the solution without overflowing.
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Rachel works at a lemonade stand at the park on Monday. She used 1 2/5 bags of lemons on Tuesday. She used 1 1/4 times as many lemons as on Monday. How many bags of lemons did Rachel use on Tuesday?
Let's start by finding how many bags of lemons Rachel used on Monday. We know she used a whole number of bags plus a fraction, so we'll need to convert the mixed number to an improper fraction:
1 2/5 = 7/5
So Rachel used 7/5 bags of lemons on Monday.
On Tuesday, Rachel used 1 1/4 times as many lemons as on Monday. To find out how many bags of lemons that is, we can multiply the amount Rachel used on Monday by 1 1/4:
1 1/4 = 5/4
5/4 times 7/5 = 35/20 = 7/4
So Rachel used 7/4 bags of lemons on Tuesday, which is the same as 1 3/4 bags of lemons.
Therefore, Rachel used 1 3/4 bags of lemons on Tuesday.
What is the value of x in this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answer:
58.85°
Step-by-step explanation:
You want to know the measure of the angle in the right triangle that has hypotenuse 29 and adjacent side 15.
CosineThe cosine function relates angles and sides by ...
Cos = Adjacent/Hypotenuse
cos(x) = 15/29
The inverse function is used to find the angle value:
x = arccos(15/29) ≈ 58.85°
The value of x is about 58.85°.
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Please help !!!!!!!!!!!!!!!!
length LD = 6 units
length DF = 9 units
length HF = 6 units
length LH = 9 units
length L'D' = 2 units
length D'F' = 3 units
length H'F' = 2 units
length L'H' = 3 units
What is dilation?Dilation is the scaling of an object, where it gets bigger or smaller.
Scale factor = new dimension/old dimension
length LD = 15-9 = 6units
length DF = 6-(-3) = 9units
length HF = 15-9 = 6 units
length LH = 6-(-3) = 9 units
Since the scale factor is 1/3, we divide the preimage dimension by 3 to get the dimensions of the new image.
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A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. Find P (4) and Find P (More than 2)
Probability of answering exactly 4 questions correctly = 0.206
P (More than 2) = 0.475
How to solve for the probability1.
ind P(4): Probability of answering exactly 4 questions correctly.
P(X=4) = (10C4) * (0.25^4) * (0.75^6)
10C4 = 10! / (4! * (10-4)!) = 210
P(X=4) = 210 * (0.25^4) * (0.75^6)
= 0.206
2. P(More than 2):P(X=0) = (10C0) * (0.25^0) * (0.75^10) ≈ 0.056
P(X=1) = (10C1) * (0.25^1) * (0.75^9) ≈ 0.187
P(X=2) = (10C2) * (0.25^2) * (0.75^8) ≈ 0.282
Now, calculate P(X>2):
P(X>2)
= 1 - (P(X=0) + P(X=1) + P(X=2))
= 1 - (0.056 + 0.187 + 0.282)
= 1 - 0.525
= 0.475
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what is the value of sin B?
8/17
17/15
15/17
8/15
The sine of angle B is obtained dividing the length of the opposite side to angle B by the length of the hypotenuse.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined on the bullet points below:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse of the triangle.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse of the triangle.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle of the triangle.Missing InformationThe problem is incomplete, hence the general procedure to obtain the sine of angle B is presented.
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Let u = -2i+9j, v = 2i- j, and w= -4i. Find 3u - (2v-w).
3u - (2v-w) =
(Type your answer in terms of i and j.)
The value of 3u - (2v-w) is -6i + 25j.
We have,
u = -2i+9j, v = 2i- j, and w= -4i.
Now, 3u - (2v - w)
= 3(-2i + 9j) - [ 2(2i - j) - (-4i)]
= -6i + 27j - [4i - 2j + 4i]
= -6i + 27j - 4i - 2j + 4i
= -6i + 25j
Thus, the value of 3u - (2v-w) is -6i + 25j.
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find the area of the figure (hint don’t forget units!)
5.2 ft 3 ft 2.4
Answer:
A = 11.4 ft²
Step-by-step explanation:
the area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the height between the bases
here h = 3 , b₁ = 2.4 , b₂ = 5.2 , then
A = [tex]\frac{1}{2}[/tex] × 3 × (2.4 + 5.2) = 1.5 × 7.6 = 11.4 ft²
After running a 100 meter dash, Jane turns left 40 degrees and walks 60 meter. True or false: she is closer now to her starting position than when she crossed the finish line. What about if Jane turns left 90 degrees or 120 degrees?
False. When Jane turns left 40 degrees and walks 60 meters, she is farther away from her starting position than when she crossed the finish line.
If Jane turns left 90 degrees or 120 degrees, then she will also be farther away from her starting position than when she crossed the finish line. Turning left 90 degrees or 120 degrees will take her in a different direction, and thus she will be farther away from her starting position than when she crossed the finish line.
Therefore, the given statement is false.
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The list represents the ages of students in a gymnastics class. 10, 10, 11, 12, 12, 13, 13, 14, 14, 15 If another student of age 15 joins the class, how is the mean affected? The mean will remain the same at 13. The mean will remain the same at about 12.4. The mean will increase to about 12.6. The mean will decrease to about 11.
The required mean will increase to about 12.6 when another student of age 15 joins the class, and the correct answer is C.
The original mean is the sum of the ages divided by the number of students:
Mean = (10 + 10 + 11 + 12 + 12 + 13 + 13 + 14 + 14 + 15) / 10
Mean = 124 / 10
Mean = 12.4
If another student of age 15 joins the class, the new sum of the ages is:
Sum = 10 + 10 + 11 + 12 + 12 + 13 + 13 + 14 + 14 + 15 + 15
Sum = 139
The new mean is the new sum of ages divided by the new number of students:
New mean = Sum / (Number of students + 1)
New mean = 139 / 11
New mean = 12.63636... or about 12.6 (rounded to one decimal place)
Therefore, the mean will increase to about 12.6 when another student of age 15 joins the class, and the correct answer is C.
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Solve the following for θ, in radians, where 0≤θ<2π.
−sin2(θ)−4sin(θ)+4=0
Select all that apply:
1.1
2.52
0.98
0.69
1.43
2.17
Answer:0.98
2.17 are correct
Step-by-step explanation:
-u^2 - 4u + 4 = 0
Multiplying both sides by -1, we get:
u^2 + 4u - 4 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 4, and c = -4. Substituting these values, we get:
u = (-4 ± sqrt(4^2 - 4(1)(-4))) / 2(1)
u = (-4 ± sqrt(32)) / 2
u = (-4 ± 4sqrt(2)) / 2
u = -2 ± 2sqrt(2)
Therefore, either:
We can approximate the amount of current in amps I
The measure of the third outgoing current will be 0.5 amperes.
We know that,
The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing currents measure 0.8 amps and 0.55 amps.
Then the measure of the third outgoing current will be
We know that the sum of the incoming current will be equal to the sum of the outgoing current at a junction.
Let the incoming current be I₁, I₂, and I₃. And the outgoing current is I₄, I₅, and I₆.
Then we have
I₁ + I₂ + I₃ = I₄ + I₅ + I₆
0.7 + 0.68 + 0.47 = 0.8 + 0.55 + I₆
1.85 = 1.35 + I₆
I₆ = 0.5
Thus, the measure of the third outgoing current will be 0.5 amperes.
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complete question:
The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing current measure 0.8 amps and 0.55 amps find the measure of the third outgoing current
PLEASE HURRY!!!!
The height h in feet of an object shot straight up with initial velocity v in feet per second is given by h = −16t^2 + vt + c, where c is the initial height of the object above the ground. A model rocket is shot vertically up from a height of 6 feet above the ground with an initial velocity of 22 feet per second. Will it reach a height of 10 feet? Identify the correct explanation for your answer.
A. No; The discriminant is positive so the rocket will reach a height of 10 feet.
B.Yes; The discriminant is positive, so the rocket will reach a height of 10 feet.
C.No; The discriminant is negative, so the rocket will not reach a height of 10 feet.
D.Yes; The discriminant is zero, so the rocket will reach a height of 10 feet.
Answer:
B.
Step-by-step explanation:
We can use the given formula to find the time it takes for the rocket to reach a height of 10 feet:
10 = -16t^2 + 22t + 6
Rewriting the equation in standard quadratic form:
16t^2 - 22t + 4 = 0
Using the quadratic formula:
t = (22 ± sqrt(22^2 - 4(16)(4)))/(2(16))
t = (22 ± sqrt(36))/32
t = 3/4 or 1/4
Since the rocket reaches a height of 10 feet at two different times (3/4 and 1/4 seconds), it must pass through that height twice during its flight. Therefore, the rocket will reach a height of 10 feet. The correct answer is B.
A boat heading out to sea starts out at Point A, at a horizontal distance of 1035 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 8°. At some later time, the crew measures the angle of elevation from point B to be 5°. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Note that given the angle of elevation, the distance from pont A to Point B is approximately 627.6ft.
See the attached image.
As shown in the attached figure:
L = AO Tan 8°
L = 1035 * Tan 8°
L = 1035 * 0.14054083470239144683811769343281
L = 1035 * 0.14054083470239144683811769343281
L = 145.46 Feet
BO = L/Tan 5°
BO = 145.459763917 / 0.08748866352592400522201866943496
BO = 1662.61270952
BO = 1662.6 Feet
Since AB = BO-AO
AB = 1662.6-1035
AB = 627.6 Ft.
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Find the area of the composite figure.
2 ft
F
4.5 ft
K
6.5 ft
1 ft
1 ft
Answer:
The area is 13 feet squared.
Step-by-step explanation:
To find the area, first separate the composite figure into two shapes: a rectangle and a triangle.
Find the area of each shape separately, and then add the areas together.
First, the rectangle:
length= 4.5 feet
width = 2 feet
[tex]2*4.5=9 ft^{2}[/tex]
The area of the rectangle is 9 feet squared.
Next, the triangle:
The base is 2 feet + 1 foot + 1 foot = 4 feet
The height is 6.5 feet - 4.5 feet = 2 feet
The formula to find the area of a triangle is [tex]\frac{h*b}{2}[/tex] (height times base over two)
[tex]\frac{2*4}{2}=4ft^{2}[/tex]
the area of the triangle is 4 feet squared.
Add the two areas together to find the total area of the composite figure:
[tex]9ft^{2} +4ft^{2}=13ft^{2}[/tex]
The area is 13 feet squared.
Which relation is a function?
The only graph that represents a function is: Graph D
How to identify a function?A function is defined as a relationship or expression that involves one or more variables. It typically has a set of input and outputs. Each input has only one output. The function is the description of how the inputs relate to the output.
A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.
From the graphs, we can see that:
Graph A has 2 outputs at x = -2
Graph B has 2 outputs at x = 0
Graph C has two outputs at x = -1
Graph D has a unique output for every input and as such it is a function
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The endpoints of WX are W(-5,-1) and X(2,6).
What is the length of WX?
A. 7
B. 14
C. 4√2
D. 7/2
Use a half-angle identity to find the exact value of tan5π/12
The required exact value of tan(5π/12) is (2 + √3) / 3.
We can use the half-angle identity for a tangent:
tan(x/2) = [1 - cos(x)] / sin(x)
to find the exact value of tan(5π/12), since 5π/12 is a half-angle of 5π/6.
First, we find the values of sin(5π/6) and cos(5π/6) using the unit circle:
sin(5π/6) = sin(π - π/6) = sin(π/6) = 1/2
cos(5π/6) = cos(π - π/6) = -cos(π/6) = -√3/2
Now we can use the half-angle identity for a tangent with x=5π/6:
tan(5π/12) = tan[(5π/6)/2] = [1 - cos(5π/6)] / sin(5π/6)
= [1 - (-√3/2)] / (1/2)
= (2 + √3) / 3
Therefore, the exact value of tan(5π/12) is (2 + √3) / 3.
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