The path of a rocket ship is given by the parametric equations x(t)=3t and y(t)=4t^2+1, where t is the time in seconds after launch. Where is the ship after 10 seconds?
A.) (3,4)
B.) (3,5)
C.) (30,401)
D.) (30,501)

Answers

Answer 1

x(t)=3t
y(t)=4t^2+1

Time (seconds):

Where is the ship after 10 seconds?
t=10→Position: Point: P=(x(t), y(t))=(x(10), y(10))=?

t=10→x(10)=3(10)→x(10)=30
t=10→y(10)=4(10)^2+1=4(100)+1=400+1→y(10)=401

Position: P=(x(10), y(10))=(30, 401)

Answer: Option C.) (30, 401)

Related Questions

Finish the pattern, 1, 2, 6, 22, __, __?

Answers

The pattern is times 4, minus 2. So, 22 x 4 = 88-6 = 86, then 86 x 4 = 344-2 = 342
So,
1, 2, 6, 22, 86, 342 is your answer

I think the pattern goes like this 1, 2, 6, 22, 86, 342

The path of a rocket ship is given by the parametric equations x(t)=3t and y(t)=4t^2+1, where t is the time in seconds after launch. Where is the ship after 10 seconds?
A.) (3,4)
B.) (3,5)
C.) (30,401)
D.) (30,501)

Answers

For this case we have the following equations that represent the position of the rocket:
x (t) = 3t
y (t) = 4t ^ 2 + 1
Substituting t = 10 in both equations we have:
x (10) = 3 (10) = 30
y (10) = 4 (10) ^ 2 + 1 = 400 + 1 = 401
Therefore, the position of the rocket is:
(x, y) = (30, 401)
Answer:
the ship after 10 seconds is at:
C.) (30,401)

The answer is C. (30,401) I already checked.

Compute the sales tax on the following transactions. An article retails for $37.50. The city sales tax is 6%, and the federal excise tax is 8%. How much does the article cost altogether?

Answers

First you must find the rate of both taxes. Since its 8% and 6%, you must add them both together, then divide them by 100.

14/100 = .14

Then for both rates you must add 1 because it is a tax increase.

1 + .14 = 1.14

Finally times 37.50 with 1.14

37.50(1.14) = 42.75

$42.75 is the answer.

Answer:

The article will cost altogether:

$ 42.75

Step-by-step explanation:

It is given that:

The retail price of the article is: $ 37.50.

Also, the article will hold a city tax of 6% and a federal excise tax of 8%.

Hence, the total percent tax on article is: 6+8=14%

This means that the cost price of the article is:

Retail Price of article+14% of retail price.

= 37.50+14% of 37.50

= 37.50+0.14×37.50

= 37.50+5.25

= 42.75

Hence, the article will cost: $ 42.75

How to find an area of a circumbscribed hexagon using the diameter?

Answers

The formula for the area of a circumscribed hexagon = 1/2 * 6 * a * r where a = side length and r = radius of the circle ( = 1/2 the diameter) so in terms of the diameter and side length its 1/2 * 1/2 * 6 *d * a = 1.5 ad.

You can calculate the value of a by using trigonometry You consider one of the 6 isosceles triangles that make up the hexagon. The vertex angle of these triangles = 60 degrees so:-

tan 30 = 1/2 a / r = 1/2 a / 1/2 d = a/d

a = d tan 30 = sqrt3 d / 3

Substituting for a :-

So the required formula for the area of the hexagon = 1.5 ad

= 1.5 * sqrt3 d * d / 3 = 1/2 sqrt3 d^2 Answer

You play darts with a friend. The board is a circle with a 6-inch radius. The “Bull’s Eye” is a smaller circle in the center of the board with an 0.25-inch radius. You throw darts (small metal arrows) at the board. At the end of six weeks, she has thrown 500 darts. She hit the board every time and hit the Bull’s Eye 1 time If you throw 500 darts, how many times should you expect to hit the Bull’s Eye by random chance? Compare this result to your friend’s result. Is she a skilled player for hitting the bull’s eye or is the result of hers expected?

Answers

The area of the board = πr² = 36 π square inches
Area of the Bull's eyes = πr² = 0.0625 π square inches

If a dart is thrown at random, the probability that it will hit the bull's eye can be calculated as:

Area of Bulls's Eyes divided by Area of Complete Board

So, probability of hitting the bulls'e eye = 1/576 = 0.001736

The friend hit Bull's eye once in a 500 throws. So the probability of hitting the Bull's eyes will be = 1/500 = 0.002

If we compare the two probabilities, they are close to each other. So we can conclude that the friend is not a skilled player and she hit the bull's eye just by chance.

the distance between bay town and oak glen is 175 miles. if the equation y=-x+175 represents the distance left to travel to oak glen, what does the domain represent? what is the domain?

a) time left to reach oak glen; x>0
b) distance left to reach oak glen; x>0
c) time it takes to travel oak glen; x>0
d) distance traveled since leaving bay town; x>0

Answers

The domain is
the distance traveled since leaving bay town; x>0.

The set of input values is distance traveled and it will make the 175 miles decreaxse.

The correct option is D, distance traveled since leaving bay town; x>0.

What is the domain and range of a function?

The domain of a function is the set of x values for which it is defined, whereas the range is the set of y values for which it is defined.

Given that the distance between bay town and oak glen is 175 miles. If the equation y=-x+175 represents the distance left to travel to oak glen.

Since the distance left to travel to oak glen can be 0 this will be when you reach Oak glen, while the minimum will be when the journey is just started and you haven't travelled even a single mile.

Therefore, the domain of the function is from 0 to 175, and the domain represents the distance traveled since leaving the bay town.

Hence, the correct option is D, distance traveled since leaving bay town; x>0.

Learn more about Domain and Range here:

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Please help me with this

Answers

Number of Art 2 students who entered digital pieces = 24
%( Art 2 students who entered digital pieces)=(24/300)*100%=8%
Number of all entries that were painted by Art 1 students = 34
%( painted by Art 1 students)=(34/300)*100%≈11.3%
%( clay pieces by Art 3 students)= (20/300)*100%=6.7%

From least to greatest,
6.7% - clay pieces by Art 3 students
8%- Art 2 students who entered digital piece
11.3%-painted by Art 1 students

Graph BCD with vertices.

Answers

first you need to plot the coordinates given first (along the corridor, up the stairs if you forget which order the directions come in) then join them together.

when you've drawn that, draw on the line x=1

to draw that go to the x axis and go along one, then flip the triangle as though it were in a mirror (use a real mirror if it helps you visualize)

1. In the figure, m DE = 106 degrees and m BC = 62 degrees. The diagram is not to scale.

What is m< A?

A) 44 degrees

B) 22 degrees

C) 75 degrees

D) 85 degrees

2. In the figure, m AB = 45 degrees and m CD = 23 degrees. The diagram is not drawn to scale.

What is the value of x?

A) 34 degrees

B) 56.5 degrees

C) 22 degrees

D)68 degrees

Can someone please check my work and tell me if I'm correct or not and explain.

Answers

For question 1, the formula for that is m1= 1/2(a-b). 106 being A and 62 being B. You should get m1=.5*(106-62) which equals B.22

The measure of the missing angles in both instances is; m∠A = 22 degrees and x = 34 degrees

How to find the angles in the triangle?

1) For question 1, the formula for the missing angle from triangle is;

m∠A = ¹/₂(∠DE - ∠BC).

Thus;

m∠A = ¹/₂(106 - 62).

m∠A = 44/2

m∠A = 22 degrees

2) To get the missing angle, we will use the formula;

x = ¹/₂(AB + CD)

This is because the measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

x = ¹/₂(45 + 23)

x = 34 degrees

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Each letter of the alphabet is written on a piece of paper and put in a hat. If a piece of paper is chosen at random, what is the probability that it will be a vowel?

The number of favorable outcomes is .

The number of possible outcomes is .

So P(vowel) = , or about percent.

Answers

Number of favourable outcomes = 5

Number of possible outcomes = 26

P(vowel) = 5/26

Answer: 5/26

The probability of pulling a vowel out of the hat is [tex]\frac{5}{26}[/tex]

The number of favorable outcomes is [tex]5[/tex]

The number of possible outcomes is [tex]26[/tex]

The number of possible outcomes is the size of the sample space.

Since the sample space

[tex]S=\{\text{all the letters of the alphabet in the hat}\}[/tex]

then, the number of possible outcomes is

[tex]|S|=26[/tex]

The number of favorable outcomes is possible number of vowels that can be gotten from the hat. Since the set of vowels

[tex]V=\{a,e,i,o,u\}[/tex]

then, the number of favorable outcomes is

[tex]|V|=5[/tex]

The probability of pulling a vowel out of the hat

[tex]P(V)=\frac{\text{number of favorable outcomes}}{number of possible outcomes}=\frac{5}{26}[/tex]

Learn more about probability here: https://brainly.com/question/1286075

The number of assists per match for the setter on your school's volleyball team has a mean of 58 and a standard deviation of 7. if in the last game he made 77 assists, how many standard deviations is that from the mean? 1.36 standard deviations below the mean 2.71 standard deviations above the mean 1.36 standard deviations above the mean 2.71 standard deviations below the mean

Answers

Given that mean=58
standard deviation=7
thus
77 is (77-58)=18 away from 58
This will be:
19/7=2.71

standard deviations from the mean.

Answer: 2.71 standard deviations above the mean

Answer:

(B)

Step-by-step explanation:

It is given that The number of assists per match for the setter on your school's volleyball team has a mean of 58 and a standard deviation of 7.

Also, in the last game he made 77 assists, therefore

[tex]77-58=19[/tex] assists away from the mean.

Thus, To get the number of standard deviation that 77 is from the mean, we get the z-score which is given as:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Substituting the given values, we get

[tex]z=\frac{77-58}{7}[/tex]

[tex]z=\frac{19}{7}[/tex]

[tex]z=2.71[/tex]

Thus, there are 2.71 standard deviations above the mean.

Hence, option B is correct.

Joylin receives a 50 gift card for the local movie theater for her birthday. She uses the card to purchase tickets and snacks for her family.if joylin spends $6more on tickets than she does on snacks, how much does joylin spend on tickets.

Answers

Let amount spent on snacks be x
amount spent on tickets be x+6

So, x+(x+6) = 50
2x = 44
x = 22 (44/2)
so, (x+6) = 22+6 = 28

Final answer is $28

Answer:

Step-by-step explanation:

edge 2020

Jon has 8 blue marbles and 4 red marble sin a bag. he took 1 marble from the bag na fthen a second marble without replacing the first one. assuming a red marble was selected first, what is the probability that jon selected a red marble both times

Answers

Since there are 12 marbles in total, he takes only one of them.

4/12, and he gets a red one.

If he doesn't replace the first one, the next one would be 3/11. The probability that Jon selected a red marble both times is 1/11.

(I kind of forgot this lesson, but here's my guess.

I am struggling with Parts B and D of this calculus question. I think that Parts A and C are OK. I wonder if Parts B and D require the graph that I drew for Part A?

Answers

For part B, you are correct as far as you've gone. There is no algebraic solution to your equation. A graphing calculator or Newton's Method iteration can get you to a solution fairly quickly.
a ≈ 1.114157141

For part C, you need to consider your answer. For a=0, the equation is that of a straight line, so there is no inflection point at x=1. For cos(a)=0, there are an infinite number of possible values of [tex]a[/tex] that will put a point of inflection at x=1. As you have noted, a=π/2 is only one of them in the range 0 < a < 4.

For part D, again you have stopped part way to the answer. Consider what values of [tex]a[/tex] will make [tex]a \sin(ax)[/tex] strictly greater than 1. There aren't any. The sine function always crosses zero. This part of the question has no solution.

Find the value of each variable. If your answer is not an integer, express it in simplest radical form. Please explain how you got the answer! I can't figure it out.

Answers

For y we have:
sine (60) = y / 14
Clearing y we have:
y = 14 * sine (60)
Rewriting:
y = 14 * (root (3) / 2)
y = 7 * root (3)

For x we have:
cosine (60) = x / 14
Clearing x we have:
x = 14 * cosine (60)
x = 14 * (1/2)
x = 7

Answer:
the value of each variable is:
y = 7 * root (3)
x = 7

In the given right triangle, x and y are 7 and 7√3 respectively.

What is the sine of an angle?

Sine of an angle = [tex]\frac{OPPOSITE SIDE}{HYPOTENUSE}[/tex]

From the diagram, we can see that y is the opposite side to angle B while x is the adjacent side while 14 is the hypotenuse.

Sin α = opposite side/ hypotenuse

Sin 60° = y/14(given)

y = 14sin60

y=7√3

Cos α = adjecent side / hypotenuse

Cos60° = x/14(given)

x = 14cos60

x= 7

So, for the given right triangle x and y are 7 and 7√3 respectively.

Therefore, In the given right triangle, x and y are 7 and 7√3 respectively.

To get more about trigonometric ratios visit:

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If a triangle’s original dimensions are 24 cm by 40 cm, which triangle would be an enlargement of the original by a scale factor of 2.2?

Answers

we have that
a triangle’s original dimensions are 24 cm by 40 cm
scale factor=2.2
then
a triangle’s enlargement dimensions=[scale factor]*original dimensions

a triangle’s enlargement dimensions=[2.2]*24------> 52.8 cm
a triangle’s enlargement dimensions=[2.2]*40------> 80 cm

the answer is
a triangle’s enlargement dimensions will be 52.8 cm by 80 cm

Answer:

52.8cm

88com

Step-by-step explanation:

The length of a rectangular floor is 2 feet more than its width. The area of the floor is 168 square feet. Kim wants to use a rug in the middle of the room and leave a 2-foot border of the floor visible on all sides. What should the length (the longer side) of the rug be?

Answers

if the area is 168& the length is 2 feet more so length is 14& width is 12 (14*12= 168), the rug is 8feet in total less from all sides so it gives an area on 160. To come out with length& width knowing the length should be less than 14, so it could be either (10*16, 8*20)

Elijah is going to spin a spinner 180 times. mc008-1.jpg He predicts that 60 of those spins will result in the spinner landing on the section labeled 3. Based on the theoretical probability, which best describes Elijah’s prediction?

Answers

Answer:

its C on Edge

Answer:c

Step-by-step explanation:

Anyone know the answer?

Answers

3. Both are supplementary to angle BCE
4. Angle 2 = Angle 1

A test consists of 10
a. True
b. False questions. to pass the test a student must answer at least 9 questions correctly. if a student guesses on each question, what is the probability that the student will pass the test?

Answers

the answer will be 1/2^9

Trey's mom planted an 18 feet by 20 feet garden in his back yard. this new garden reduced the area of trey's backyard by 24%. which answer choice best represents the total area of the back yard

Answers

Ok so the answer should be 1500 square feet

The garden area is given by:

[tex] A = (18) * (20)

A = 360
[/tex]

We are looking for the backyard area now.

For this, we make the following rule of three:

360 ---------------------> 24%

x -------------------------> 100%

From here, we must clear the value of x.

We have then:

[tex] x = (100/24) * (360)

x = 1500 ft ^ 2
[/tex]

Answer:

The total area of the back yard is:

[tex] x = 1500 ft ^ 2 [/tex]

which statement most accurately explains why x^5/x^2 is equal to x^3?

Answers

[tex]\bf \cfrac{x^5}{x^2}\implies \cfrac{x^{3+2}}{x^2}\implies \cfrac{x^3\underline{x^2}}{\underline{x^2}}\implies x^3[/tex]

The answer you are looking for would be C.

When you divide varibles with exponents, you subtract the exponents. Since there are no numbers in front of the x, we can assume there is only 1 x. 1x/1x = 1x. Since the top has the largest exponent, you'd subtract the bottom exponent to the top, leaving a power of 3. Thus meaning, the answer of x^3 is explained in C.

I hope this helps!

Find the geometric mean of 125 and 5.

Answers

The geometric mean would have to be 25.

Write an equation of the graph:

y = |x| translated two units downward

Answers

Y = |x| - 2. Nothing too complicated for this transformation

y = |x| - 1 is the answer

ur mom

PLS HELP ME ASAP WITH C!! (SKETCH A LINE THAT REPRESENTS THE DIFF SHAPES)

- ALSO INDICATE WHICH LINE IS WHAT FUNCTION

THANK YOU!!

(Random answers gets moderated!)

Answers

Since the cross section is of uniform width (front to back), the fill rate (rate of change of depth vertically) is inversely proportional to the horizontal (side-to-side) dimension.

a) The horizontal width is narrow near the bottom, so the fill rate will be relatively fast until the depth where the width changes. Then the fill rate will slow to perhaps 1/3 of what it was.

b) The horizontal width is a linearly decreasing function of depth, so the fill rate will be increasing on a hyperbolic curve--increasingly fast as the depth increases.

c) This is the reverse of case (a). The fill rate is initially slow, then jumps dramatically when the depth reaches the point where the horizontal width suddenly narrows.

It is not clear whether you are supposed to graph fill rate as a function of depth or as a function of time. The desriptions are for fill rate. If you want to graph versus time, these descriptions apply to the slope of the curve, not its level.

What is the total amount and the amount of interest earned on $6,500 at 6% for 25 years?

Answers

Here's the equation for one year:
0.06(6500) + 6500
But because it is 25 years:
25(0.06(6500)) + 6500
1.5(6500) + 6500
We can make it simpler:
2.5(6500)
The total amount is $16350

To calculate the total amount and interest earned on $6,500 at 6% simple interest for 25 years, you use the formula I = P × r × t, which gives you interest (I) of $9,750. Adding the interest to the principal, the total amount after 25 years is $16,250.

To calculate the total amount and the interest earned on $6,500 at a simple interest rate of 6% for 25 years, we can use the simple interest formula:

I = P × r × t

Where:

I is the interestP is the principal amount ($6,500)r is the annual interest rate (6%, or 0.06)t is the time in years (25)

Using this formula:

I = $6,500 × 0.06 × 25

I = $9,750

The total amount after 25 years will be the principal plus the interest:

Total Amount = P + I

Total Amount = $6,500 + $9,750

Total Amount = $16,250

The interest earned on the investment after 25 years is $9,750.

Isabel divided 32 by 8 and got 4. She says that if she divides 32 by 4,the quotient will be greater than 4. Is she correct? Explain.

Answers

Yes, she is absolutely correct because 32/4=8

8>4 so it make sense.

Which graph represents g(x)=(x−3)2−5 ?

Answers

The graph has vertex (3, -5),
and it is looking upward because it is positive coefficient in front of (x-3)²
Correct answer is A.

Final answer:

The graph of g(x) = (x-3)^2 - 5 is a parabola that opens upwards. The vertex is located at (3, -5) and the function values are negative when x is less than 3.

Explanation:

The graph of the equation g(x) = (x-3)^2 - 5 is a parabola. The vertex of the parabola is located at the point (3, -5), and the parabola opens upwards because the coefficient of the quadratic term is positive. When x is less than 3, the function values are negative, and when x is greater than 3, the function values are positive.

Factor x2 – 8x + 15.
Which pair of numbers has a product of ac and a sum of b?

Answers

-5 and -3 are your numbers.

The greatest common factor of 24and 36 is the least common multiple of a pair of numbers.which two number could they be ? Pls make sure to explain this specifically!!
A.3 and 6
B.4 and 6
C.8 and 9
D.8 and 12

Answers

4, and 6. Because 4 is a common factor of 24, and it is also the least factor. Same thing with 36. Remember: 4 x 6 = 24 and 6 x 6 = 36. Hope this helps!

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The path of a rocket ship is given by the parametric equations x(t)=3t and y(t)=4t^2+1, where t is the time in seconds after launch. Where is the ship after 10 seconds? A.) (3,4) B.) (3,5) C.) (30,401) D.) (30,501)

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The path of a rocket ship is given by the parametric equations x(t)=3t and y(t)=4t^2+1, where t is the time in seconds after launch. Where is the ship after 10 seconds?
A.) (3,4)
B.) (3,5)
C.) (30,401)
D.) (30,501)