A rocket is launched with an initial velocity of 360 ft/s. The height of the rocket in meters is modeled by the function shown below, where t is time in seconds. h(t)=‒10t2 + 360t Which statement is true?
A. The rockets maximum height is 324 feet.
B. The rockets maximum height is 3240 feet.
C. In the interval from 9 seconds to 18 seconds, the rocket is descending.
D. The rocket hits the ground in 18 seconds.
What is the nth term for 1 7 15 25 37
Answer:
51 hope this helps!!!!!!!!!!
Step-by-step explanation:
Final answer:
The nth term for the given sequence 1, 7, 15, 25, 37 is derived to be n² + n - 1, which fits the pattern of the sequence accurately.
Explanation:
The sequence given is 1, 7, 15, 25, 37. To find the nth term of this sequence, let's first identify the pattern of differences between the terms. Observing the differences, we see they are 6, 8, 10, and 12, which suggests an arithmetic sequence in the differences. This indicates the original sequence is quadratic.
Using the general formula for the nth term of a quadratic sequence, An² + Bn + C, we can substitute the first few terms to solve for A, B, and C. However, there's a quicker method given the pattern of differences seen in the second layer (6, 8, 10, 12, ...) that increases by 2 each time, suggesting that 2n is involved.
Through analysis, the nth-term formula can be derived as n² + n - 1.
Here's why:
considering n=1 for the first term, we get 1+1-1=1;
for n=2, the formula yields 2^2+2-1=7; and so forth, matching the given sequence precisely.
Suppose r contains a reference to a new rectangle(5, 10, 20, 30). which of the following assignments is legal? (look inside the api documentation to check which interfaces the rectangle class implements.)
a. rectangle a = r;
e. measurable e = r;
b. shape b = r; f. serializable f = r;
c. string c = r; g. object g = r;
d. actionlistener d = r;
The Java Rectangle class implements both the Shape and Serializable interfaces. Therefore, Rectangle r can be legally assigned to Rectangle, Shape, Serializable, and Object data types. It can't be assigned to a String, Measurable, and ActionListener as Rectangle doesn't implement these.
Explanation:In Java, the Rectangle class implements the Shape and Serializable interfaces. Therefore, the legal assignments would be:
Rectangle a = r; because r is a Rectangle, you can assign r to another Rectangle object.Shape b = r; because Rectangle implements the Shape interface, you can assign r to a Shape object.Serializable f = r; because Rectangle implements the Serializable interface, you can assign r to a Serializable object.Object g = r; because all classes in Java extend the Object class implicitly, you can assign r to an Object.The rest assignments are not legal because the Rectangle class doesn't implement Measurable, ActionListener interfaces and it cannot be assigned to a String.
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How many terms are in the arithmetic sequence 7, 0, −7, . . . , −175?
Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference
Derrick's garden is 18 1/2 feet long. He plants 3/8 of a foot apart. How many bulbs can Derrick plant in one row?
The shadow of a vertical tower is 50 m long when the angle of elevation of the sun is 35°. find the height of the tower. © k12 inc. 2. an airplane is flying 12,330 feet above level ground. the angle of depression from the plane to the base of a building is 11°. how far must the plane fly horizontally before it is directly over the building?
Betsy and 3 of her friends are splitting a whole watermelon. There are 6 circular slices of watermelon. How many slices of watermelon will each person get?
The slices of watermelon each person will get is 1.5 slices.
If the watermelon is divided equally, the number of slices each person would get can be determined by dividing the total slices of watermelon by the total number of friends.
Slice each person would get = total slices / total number of friends
6 / 4 = 1.5 slices
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Right triangle ABC is shown below.
Use the distributive property in two different ways to find the product of 127 and 32.
Answer and explanation:
Use the distributive property in two different ways to find the product of 127 and 32.
Distributive property says that,
[tex]a(b+c)=ab+ac[/tex]
We have to find product of 127 and 32,
1) Split 127 as 100+27
[tex]127\times32=(100+27)\times 32[/tex]
Apply distributive property,
[tex]127\times32=100\times 32+27\times 32[/tex]
[tex]127\times32=3200+864[/tex]
[tex]127\times32=4064[/tex]
2) Split 32 as 30+2
[tex]127\times32=127\times (30+2)[/tex]
Apply distributive property,
[tex]127\times32=127\times 30+127\times 2[/tex]
[tex]127\times32=3810+254[/tex]
[tex]127\times32=4064[/tex]
Describe t-test and explain how to interpret its results?
s=n(a1+an)/2 gives the partial sum of an arithmetic sequence. What is the formula solved for an?
What is 31/2 times 3 1/2
What is the value of the range of the function f(x)=x^2+2 for the domain value 1/4?
write 784 miles per 40 gallons as a rate in simplest form?
I believe it would be
784 miles/40 gallons = 19.6 miles per gallon
David is playing a trivia game where he gains points for correct answers and loses points for incorrect answers. At the start of round 3 his score is −1500 points. During round 3 he answered five 1000 point questions correctly and three 500 points questions incorrectly. What is his score at the end of round 3?
A) −2000
B) −500
C) 2000
D) 3500
Answer:
2000 points
Step-by-step explanation:
Topic: Substraction, Addition and Products
You have to organize the problem, as you can see
at Start of Round 3 David Has: - 1500
During Round 3:
5 Questions: 1000 each correctly
so 5 x 1000 = 5000
3 Questions: - 500 each incorrectly
so 3 x -500 = -1500
at the End of Round 3:
Starting: -1500
During Round 3: 5000 - 1500 = 3500
the end of round 3: -1500 + 3500 = 2000
Solve the simultaneous equations
5x-4y=19
x+2y=8
Which of the following is the best example of a characteristic of an experiment?
Participants should be selected into the treatment group randomly.
Participants are rarely aware that they are part of an experiment.
Participants are observed without researchers making changes to their behaviors.
The results of an experiment are based on a questionnaire given to a random sample of the population.
19+X=17 What is X pls tell me!
John has painted 4/5 of his house the next day he painted 2/3 of what he had left what fraction of the house is left to paint
A major league baseball pitcher throws a pitch that follows these parametric equations:
x(t) = 143t
y(t) = –16t2 + 5t + 5.
Recall that the speed of the baseball at time t is
s(t)=√ [x '(t)]2 + [y ' (t)]2 ft/sec.
What is the speed of the baseball (in mph) when it passes over homeplate?
The speed of the baseball when it passes over the home plate is 97.67 mph.
Given :
[tex]x(t) = 143t[/tex] ---- (1)[tex]y(t) = -16t^2+5t+5[/tex] ---- (2)The distance between the pitcher's plate and the home plate is 60.5 ft.Differentiate the function x(t) and y(t) with respect to t.
[tex]x'(t)=143[/tex]
[tex]y'(t)= -32t+5[/tex] ---- (3)
Now, put the value of x(t) in equation (1).
60.5 = 143t
t = 0.423 sec
Now, put the value of t in equation (3).
[tex]y'(t) = -32(0.423)+5=-8.536[/tex]
Now, [tex]s(t) = \sqrt{(x'(t))^2+(y'(t))^2}[/tex]
[tex]s(t)=\sqrt{143^2+(-8.536)^2}[/tex]
[tex]\rm s(t)=\sqrt{20521.8633} = 143.2545\;ft/sec[/tex]
[tex]\rm s(t) = 97.67 mph[/tex]
Therefore, the speed of the baseball when it passes over the home plate is 97.67 mph.
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Solve the problem as directed. The rate traveled from Amarillo to Austin by a bus averages 65 miles per hour. The bus arrived in Austin after eight hours of travel. An automobile averages 80 miles per hour. Using the inverse variation relationship, show what the time would be for the automobile to complete the trip. a0 hours
65*8 = 520 miles traveled
520/80 = 6.5 hours for the car
Answer:
The automobile would take 6.5 hours to complete the trip.
Step-by-step explanation:
This is a case of a inverse variation relationship because when you increase the speed of traveling the time of arriving will reduce, now we have to define the equation and the variables:
Inverse variation equation: [tex]x1y1=x2y2[/tex]
[tex]x1[/tex]: speed of the bus, 65 miles per hour
[tex]y1[/tex]: time to Austin by bus, 8 hours
[tex]x2[/tex]: speed of the automobile, 80 miles per hour
[tex]y2[/tex]: time to Austin by automobile, unknown
Now we can replace the values in the equation and clear [tex]y2[/tex], this is:
[tex]65*8=80*y2\\y2=\frac{65*8}{80} =\frac{520}{80} =6.5\\[/tex]
The automobile would take 6.5 hours to complete the trip.
Select "Rational" or "Irrational" to classify each number. Rational Irrational 0.25 √ 0.25 √0.33
Jessica wants to serve 3/4 of a pint of orange juice to each of her guests. Her juice jar can hold 12 full pints of juice. Jessica can serve the juice to guest
Answer:16
Step-by-step explanation:
Let P=(x,y) be a point on the graph of y=x2−9. (a) Express the distance d from P to the origin as a function of x.
Explanation on finding distance from a point to the origin as a function of x and showing invariance under rotations.
Distance from point P to the origin as a function of x:
Given point P(x, y) on y = x² – 9.
The distance d from P to the origin is d = √(x² + y²).
Substitute y = x² - 9 into the distance formula to express d as a function of x: d = √(x² + (x² - 9)²).
Invariance of distance under rotations:
The distance from P to the origin remains constant regardless of the rotation, as it depends only on the coordinates of the point and not the orientation of the coordinate system.
Prove that f(x) = x^3 – 1000x^2 + x – 1 is ω(x^3) and o(x^3).
To prove that [tex]f(x) = x^3 - 1000x^2 + x - 1[/tex] is [tex]\omega(x^3)[/tex] and [tex]o(x^3)[/tex], we must show how the function grows in comparison to x^3 asymptotically.
To prove that [tex]f(x) = x^3 - 1000x^2 + x - 1[/tex] is [tex]\omega(x^3)[/tex] and [tex]o(x^3)[/tex], we need to show two things:
1. Proving that [tex]f(x) = x^3 - 1000x^2 + x - 1[/tex] is [tex]\omega(x^3)[/tex]
For a function to be [tex]\omega(x^3)[/tex], it needs to grow faster than [tex]x^3[/tex] asymptotically. This requires that the ratio of the function to [tex]x^3[/tex] tends towards infinity as x approaches infinity.
Consider:
[tex]\lim_{x \to \infty}[\frac{f(x)}{x^3} ] = \lim_{x \to \infty}[ \frac{x^3-1000x^2+x-1}{x^3} ][/tex]
Simplify the expression:
[tex]\lim_{x \to \infty}[ 1-\frac{1000}{x}+\frac{1}{x^2}-\frac{1}{x^3} ] =1[/tex]
Since the limit does not tend to infinity but instead tends to 1, f(x) is not ω(x^3). We made a mistake in our earlier assumption; let's correct this in the next point.
2. Proving that [tex]f(x) = x^3 - 1000x^2 + x - 1[/tex] is [tex]o(x^3)[/tex]
To show that f(x) is [tex]o(x^3)[/tex], the ratio of f(x) to [tex]x^3[/tex] should tend to zero as x tends to infinity.
Consider:
[tex]\lim_{x \to \infty} [\frac{f(x)}{x^3}] = \lim_{x \to \infty}[\frac{x^3-1000x^2+x-1}{x^3}][/tex]
Simplify the expression:
[tex]\lim_{x \to \infty}[ 1-\frac{1000}{x}+\frac{1}{x^2}-\frac{1}{x^3} ] =1[/tex]
This indicates that the limit tends to 1 and not 0, hence f(x) is not [tex]o(x^3)[/tex] either. We can see in both cases that the limits did not meet the required criteria for [tex]\omega(x^3)[/tex] or [tex]o(x^3)[/tex], implying a misunderstanding in the problem setup.
What is the area of a parallelogram whose vertices are A(−4, 9) , B(11, 9) , C(5, −1) , and D(−10, −1) ?
Let
[tex]A(-4,9)\\B(11,9)\\C(5,-1) \\D(-10,-1)\\E(-4.-1)[/tex]
using a graphing tool
see the attached figure to better understand the problem
we know that
Parallelogram is a quadrilateral with opposite sides parallel and equal in length
so
[tex]AB=CD \\AD=BC[/tex]
The area of a parallelogram is equal to
[tex]A=B*h[/tex]
where
B is the base
h is the height
the base B is equal to the distance AB
the height h is equal to the distance AE
Step 1
Find the distance AB
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]A(-4,9)\\B(11,9)[/tex]
substitute the values
[tex]d=\sqrt{(9-9)^{2}+(11+4)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(15)^{2}}[/tex]
[tex]dAB=15\ units[/tex]
Step 2
Find the distance AE
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
[tex]A(-4,9)\\E(-4.-1)[/tex]
substitute the values
[tex]d=\sqrt{(-1-9)^{2}+(-4+4)^{2}}[/tex]
[tex]d=\sqrt{(-10)^{2}+(0)^{2}}[/tex]
[tex]dAE=10\ units[/tex]
Step 3
Find the area of the parallelogram
The area of a parallelogram is equal to
[tex]A=B*h[/tex]
[tex]A=AB*AE[/tex]
substitute the values
[tex]A=15*10=150\ units^{2}[/tex]
therefore
the answer is
the area of the parallelogram is [tex]150\ units^{2}[/tex]
The area of the parallelogram is 0 units.
Explanation:To find the area of a parallelogram, we can use the formula A = base * height. We can find the length of the base by finding the distance between points A and D, which is 11 units. To find the height, we can find the distance between points A and B, which is 0 units. Therefore, the area of the parallelogram is 0 units.
A rainstorm in Portland Oregon wiped out the electricity in 5% of the households in the city. Suppose that a random sample of 60 Portland households is taken after the rainstorm. a. Estimate the number of households in the sample that lost electricity by giving the mean of the relevant distribution (that is the expectation of the relevant random variable do not round your response.) b. Quantify the uncertainty of your estimate by giving the standard deviation of the distribution run your response to at least three decimal places.
Find the area of the shaded figure. To do so, subtract the area of the smaller square from the area of the larger square.
Large square side length: (x squared plus 10)
Small square side length: x
Image included.
What is the area of the shaded region?
The area of the shaded figure is (x⁴ + 19x² + 100) square meters after subtracting the area of the smaller square from the area of the larger square.
What is a square?It is defined as a two-dimensional geometry that has four sides and four vertices. The sides of the square are equal in length. It is a regular quadrilateral.
It is given that:
Large square side length: (x squared plus 10)
Small square side length: x
The area of the large square = (x² + 10)(x² + 10)
The area of the large square = (x² + 10)²
The area of the small square = (x)(x)
The area of the small square = x²
The area of the shaded figure = (x² + 10)² - x²
The area of the shaded figure = (x⁴ + 19x² + 100) square meters
Thus, the area of the shaded figure is (x⁴ + 19x² + 100) square meters after subtracting the area of the smaller square from the area of the larger square.
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The number of terms in a binomial expansion
is one less than the power
is equal to the power
is one more than the power
Answer:
(C) is one more than the power
Step-by-step explanation:
Let us consider a binomial expansion:
[tex](x+y)^2=x^2+2xy+y^2[/tex]
The power of the above expansion is [tex]2[/tex] and the number of the terms in the above binomial expansion are [tex]3[/tex], thus the total number of terms in the binomial expansion is one more than the power.
Hence, Option C is correct.
Which one of the following is an arithmetic sequence?
A. .35, .5, .85, 1.1, 1.22, . . .
B. 5, 0, −1, −3, −7, . . .
C. 2, 3, 5, 7, 11, 13, 17, . . .
D. −2, 1, 4, 7, 10, . . .