If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 ft per second, then its height h after t seconds is given by the equation h(t) = -16t ^2 + 128t. What is the height after 60 seconds?
Answers
Answer:
undefined
Step-by-step explanation:
t=60 is outside the domain of the function, which is t ∈ [0, 8].
_____
If you take the function and the time at face value, ...
... h(60) = -49920 . . . feet, more than 9.4 miles below ground level*
___
*The deepest hole ever drilled into the Earth is 40,230 feet deep, so this is almost 2 miles deeper.
Answer:
C) 8 seconds
Step-by-step explanation:
Related Questions
533÷41 long division
Answers
Answer: 41
Step-by-step explanation:
533÷41 = 533/41
Se photo for step -by-step of ling division
The answer to the long division of 533 by 41 is 13. This is reached by multiplying 13 by 41 which results in 533, the original dividend. The remainder is 0.
Explanation:Let's perform a long division of 533 by 41. First, write the number 533, which is the dividend, inside the long division bracket and the number 41, the divisor, outside of it. Now we need to see how many times 41 fits into 533.
It fits 13 times because 13 times 41 equals 533. Therefore, write 13 above on your long division bracket.
When you multiply 13 (your answer) by 41 (your divisor), you get 533, which is your dividend. Subtract 533 from 533 and you get a remainder of 0. The answer of the long division of 533 by 41 is 13.
Done correctly, long division is a reliable method of dividing large numbers. The important thing is to ensure all steps are followed orderly and accurately.
Learn more about Long Division here:https://brainly.com/question/28824872
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Please help with this question:)
Answers
Answer:
x=1
Step-by-step explanation (this way is not the shortest one):
if 2x-3>0, then the equation 2x-3=2x-1 has no roots.
if 2x-3<0 (x<1,5), then the equation 3-2x=2x-1 has one root, x=1
Could someone help me to solve this pls!
Answers
Answer:
15 ft²
Step-by-step explanation:
The volume of a cone is given in terms of the base area (B) and height (h) by the formula ...
... V = (1/3)Bh
Putting in the given numbers, you have ...
... 35 ft³ = (1/3)B(7 ft)
... B = (35·3/7) ft² = 15 ft² . . . . . . solve for B
Select all radical expressions that are equivalent to 5 2/3
Answers
Answer:
1 and 3
Step-by-step explanation:
(5^(1/3))^2 = 5^(2/3)(5^2)^(1/2) = 5^(2/2) = 5(5^2)^(1/3) = 5^(2/3)(5·3)^(1/2) = 5^(1/2)·3^(1/2)(5^(1/2))^3 = 5^(3/2)(5·2)^(1/3) = 5^(1/3)·2^(1/3)___
Applicable rules are ...
[tex]\sqrt[n]{x^{m}}=x^{\frac{m}{n}}\\\\(x^{b})^{c}=x^{bc}\\\\(ab)^{c}=a^c\cdot b^c[/tex]
Simplify (2p+3)2 - (2p-3)2 (Give proper detailed answer with all steps,the 2 is the symbol of square)
Answers
Answer:
24p
Step-by-step explanation:
This is the difference of 2 squares:- a^2 - b^2 = (a + b)(a - b).
So here we have:-
(2p + 3)^2 - (2p - 3)^2
= (2p + 3 + (2p - 3))(2p + 3 - (2p - 3))
= (2p + 3 + 2p - 3)(2p + 3 - 2p + 3
= 4p * 6
= 24p (answer)
Final answer:
To simplify the expression (2p+3)² - (2p-3)², apply the difference of squares formula to get ((2p+3) + (2p-3)) * ((2p+3) - (2p-3)), which simplifies to 24p.
Explanation:
To simplify the expression (2p+3)² - (2p-3)², we need to apply the difference of squares formula, which is
a² - b² = (a+b)(a-b).
Here, a is (2p+3) and b is (2p-3). The result will be the product of the sum and difference of a and b.
Let's perform the simplification step-by-step:
Simplify both products:
(4p) * (6)
Finally, multiply the results to get the simplified expression:
24p
The simplified result of the expression (2p+3)² - (2p-3)² is 24p.
Line segment ABCD is split into unequal segments by points A, B, C, and D. The length of segment AD is 28 cm, and the distance between the midpoints of segments AB and CD is 16 cm. Find the length of segment BC.
Answers
Answer:
4 cm
Step-by-step explanation:
The midpoint segment has length ...
... L = AB/2 + BC + CD/2 = 16 cm
The entire segment has length ...
... AD = AB + BC + CD = 28 cm
If we subtract AD from 2L, we have ...
... 2L - AD - 2L = 2(AB/2 +BC + CD/2) - (AB +BC +CD) = 2(16 cm) -28 cm = 4 cm
... AB +2BC + CD -AB -BC -CD = 4 cm . . . . remove parentheses
... BC = 4 cm . . . . simplify
What is the effect on the graph of the function f(x)=x when f(x) is replaced with -1/2f(x)?
Answers
Answer:
For negative sign , the graph reflects over x -axis and for 1/2 there will be a vertical compression
Step-by-step explanation:
Parent function is f(x)= x
We need to find the effect of the graph when f(x) is replaced with -1/2f(x)
When negative sign is multiplied outside f(x) like -f(x), then there will be a reflection over x-axis
When negative sign is multiplied inside f(x) like f(-x) then there will be a reflection over y-axis
When a number is multiplied outside f(x) then there will be a vertical stretch or compression
Here 1/2 is multiplied outside f(x). [tex]\frac{1}{2}[/tex] is less than 1 so there will be a vertical compression
For negative sign , the graph reflects over x -axis and for 1/2 there will be a vertical compression
James took 22 seconds to run the 200yard dash. How many feet per minute is that? Show work.
Answers
Answer:
1636.4 ft/min
Step-by-step explanation:
Multiply by the conversion factors that change the units you have to the units you want.
(200 yd)/(22 s) × (3 ft/yd) × (60 s/min) = 18000/11 ft/min ≈ 1636.4 ft/min
What is the volume of a sphere with a diameter of 15 cm? Round the answer to the nearest whole number.
Answers
Answer:
1767 cm³
Step-by-step explanation:
We can use volume V = 4/3 π r³
We have diameter of 15 cm. To get radius, we need to divide diameter by 2.
r = 7.5 cm
So now plug in r = 7.5 then calculate V:
V = 4/3 π ( 7.5 )³
V = 4/3 π * 421.875 ≈ 1767.145 ≈ 1767
Hope this helps.
Hari’s weekly allowance varies depending on the number of chores he does. He received $16 an alarm once a week he did 12 chores, and $14 in allowance the week he did 8 chores. Write an equation for his allowance in slope-intercept form.
Answers
Answer:
y = ($0.5/ch) x + $10
Step-by-step explanation:
Let
x = number of chores
y = allowance
The relationship between y and x can be expressed in a linear equation in the slope-intercept form.
y = mx + b
where
m is the slope
b is the y-intercept
We have the ordered pairs (8, 14) and (12, 16). We can calculate the slope using the following expression.
m = Δy/Δx = $16-$14/12ch-8ch = $0.5/ch
The equation is
y = ($0.5/ch) x + b
We will replace the first point in the previous equation.
$14 = ($0.5/ch) 8ch + b
b = $10
The final equation is
y = ($0.5/ch) x + $10
This equation can be used to predict Hari's allowance for any number of chores. For example, if Hari does 10 chores, his allowance will be $12.50. The final equation is y = ($0.5/ch) x + $10.
We are given that Hari's allowance varies depending on the number of chores he does.
We are also given two points, (8, 14) and (12, 16), that represent the relationship between the number of chores and the allowance.
We can use these two points to find the slope of the line.
The slope is equal to rise over run, which in this case is equal to
$16 - $14 / 12 - 8 = 0.5/ch.
We can now plug the slope and one of the points into the slope-intercept form of the equation to find the value of b, the y-intercept.
We will use the point (8, 14).
y = mx + b
14 = ($0.5/ch) 8ch + b
14 = $4 + b
b = $10
The final equation is y = ($0.5/ch) x + $10.
This equation can be used to predict Hari's allowance for any number of chores. For example, if Hari does 10 chores, his allowance will be $12.50.
Learn more about slope-intercept form here:
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The baseball team is making a circle graph to keep track of this year's games. So far, they have entered the data you see. How many games have they played this year?
A 5 games
B 15 games
C 20 games
D 25 games
Answers
Answer:
The baseball team plays 25 games
Step-by-step explanation:
If they have lost 5 games and that is 20 %, we can make a ratio.
games/ total = 20/100
5 20
------ = -----------
total 100
Using cross products
5*100 = 20*total
500 = 20* total
Divide by 20 on each side
500/20 = 20/20 * total
25 = total
Answer:
its D which is also 25 games
Step-by-step explanation:
write a quadratic function whose graph has the given characteristics x-intercepts: -4,2 point on graph (0,-9)
Answers
y = (9/8)(x +4)(x -2)
Step-by-step explanation:When the x-intercepts are "a" and "b", you know factors of the function are (x-a) and (x-b). So, we can write the function as ...
... y = k(x -(-4))(x -2) = k(x +4)(x -2) . . . . . for some scale factor k
We can find k using the given point.
... -9 = k(0 +4)(0 -2) = -8k
Dividing by -8 gives ...
... 9/8 = k
The desired function is ...
... y = (9/8)(x +4)(x -2)
... = (9/8)(x² +2x -8)
a model is made of a car. please help.
Answers
Answer:
10.8 : 1
Step-by-step explanation:
In raw terms the ratio of car length to model length is ...
... 9 ft : 10 in
As a pure number this will be ...
... 108 in : 10 in = 10.8 : 1
se the drawing tool to form the correct answers on the provided grid. For the sequence (1, 2, 4, 8, . . .), the index starts at 1. Let f be the function that describes this sequence. Graph as much of function f as will fit on the grid.
Answers
Answer:
See attached
Step-by-step explanation:
For each increase of 1 in the index, the function value doubles. The size of the function value rapidly exceeds the limit of any linear grid.
We've shown a few points plotted. Perhaps it will give you the idea of what you need to do.
Answer:
The index starts at 1, so the domain of the function is D = {1, 2, 3, 4, 5, 6, . . .}. The sequence is based on the add 3 rule. So, to get more terms of the sequence, add 3 to the last term to get the next one. The range values include the terms of the sequence, so the range is R = {1, 4, 7, 10, 13, 16, . . .}.
To graph the function of this sequence on a coordinate plane, pair the domain values with the corresponding range values to get {(1, 1), (2, 4), (3, 7), (4, 10), (5, 13), (6, 16), . . .}. Then plot these points on the graph.
Step-by-step explanation:
Tim ran 5 miles in 35 minutes. Dan rund 7 miles in 70 minutes. If they are running a marathon 26 miles, who will finish first?
Answers
Answer:
they will tie
Step-by-step explanation:
if you divied 7 in to 70 you get 7 and if you divied 5 into 35 it 7
It takes both of them 7 mins to complet a mile
find the length of arc shown in red.
Answers
Answer:
≈10.99525 cm.
Step-by-step explanation:
1. The length of the circle is L=2πr, where π≈3.1415 and r- radius of the circle.
2. if the given arc is 45° and full circle is 360°, then the length of the arc is 45/360=0.125 of full circle, that is L(arc)=0.125L=0.25πr; ⇒ L(arc)≈0.25*3.1415*14=10.99525 (cm).
Answer:
10.99 ≈ 11cm
Step-by-step explanation:
To find the length of the arc, first we need to find the circumference of the circle, which we find with the following formula :
[tex]c=2\pi r[/tex]
where [tex]r[/tex] is the radius which is indicated in the image: [tex]r=14cm[/tex].
so the circumference is:
[tex]c=2\pi(14cm)\\c=87.96cm[/tex]
This is the measure of the entire perimeter of the circle, it is the measure of the 360 ° arc.
Because we only want 45 ° of those 360 °, we divide the value of the circumference by 360 and multiply po 45:
[tex]\frac{87.96cm(45)}{360}=\frac{3958.2}{360}=10.99cm[/tex]
which can be rounded to 11cm
The length of the arc is 11cm
Max delivers 8520 pieces of mail in one year. If he delivers the same number of pieces of mail each month, about how many pieces of mail does he deliver in two months? Explain your steps
Answers
Answer:
1420 pieces of mail he delivered in 2 months.
Step-by-step explanation:
If he delivered the same amount each month, you would divide 8520 by 12 (number of months in a year). Then once you divide it, the number you get is 710 now multiply 710 by 2 (because they ask how many he delivered in 2 months). And the answer would be 1420
Answer:
Max delivers 1420 in two Months because 8520 divided by 12 is 710 and thats just one month so 710 x 2 = 1420.
Step-by-step explanation:
In the figure on the right, STWC space is a square centered at the origin with side length 2a What are the coordinates of the vertices?
Answers
D. S(-a, -a), T(-a, a), W(a, a), Z(a, -a)
Step-by-step explanation:Point S is in the 3rd quadrant, where both coordinates are negative. That eliminates choices A and B.
The distance between points is 2a, so the distance from a corner point to either axis is "a". That is, the magnitude of any coordinate value is "a", not "2a." That eliminates choice C.
Remaining is the correct choice: D.
Should I round 13.9876652 to 14 or 13.99?
Answers
Answer:
14.
Unless your assignments tells you not to round to whole numbers or to round to the nearest decimal places, then 13.99. But, in most cases, you'd round to 14.
A company estimates its total profit (profit = total revenue minus total cost) as P(x) = 2x5 − 3x4 − 5x2 − 2, where P is in thousands of dollars and x is the number of years elapsed since the company was founded. How many times can the total profit become exactly zero? Hint: Use Descartes's rule of signs.
A.
2 or 0
B.
5 or 3 or 1
C.
3 or 1
D.
1
Answers
Answer:
D. 1
Step-by-step explanation:
The signs of the terms are +---, so there is 1 change of sign. That means there is 1 positive real root. Profit is zero exactly one time.
The table of values below represent an exponential function. Write an exponential equation that models the data.
x y
-2 21
-1 14.7
0 10.29
1 7.203
2 5.0421
a. y = 21(0.7) b. y = 14.7(1.7) c. y = 10.29(0.7) d. y = 10.29(1.3)
Answer: c
Answers
y = 10.29·0.7^x . . . . . selection c seems the closest
Step-by-step explanation:For most any exponential function, the exponential multiplier will be 1 when x=0, so the y-intercept is the overall multiplier for the function.
The values decrease as x increases, so the base of the exponential term must be less than 1.
These considerations narrow your choice to C.
... y = 10.29·0.7^x
_____
If you actually want to determine the equation, you can do it several ways. One is to make use of the exponential regression function of your graphing calculator. (See attached). Another is to take the logarithms of the y-values and find a best-fit line through them.
_____
Comment on the answer choices
You may notice that none of the offered answers appears to be anything but the product of two numbers. There are no x-variables involved, and no exponents indicated. Cutting and pasting answers like this does not work.
Answer:
c
Step-by-step explanation:
Help me pretty pleaseeee
Answers
7 . . . . . inches per week
Step-by-step explanation:The average rate of change of height is ...
... (change in height)/(change in time)
The height changes from 41 inches to 83 inches when the time changes from 3 weeks to 9 weeks. Then the rate of change is ...
... (83 -41) inches/((9 -3) weeks) = (42/6) inches/week = 7 inches/week
It seems likely that the required answer will just be a number: 7.
Solve the inequality for b.
Answers
Answer:
-2 ≥ b
Step-by-step explanation:
10 ≤ -2 ( 9 + 12b ) / 3
10 ≤ -2 ( 3 + 4b )
-10 ≥ 2 ( 3 + 4b )
-10 ≥ 6 + 8b
-16 ≥ 8b
-2 ≥ b
the rhombus, m<1 = 168. what are m<2 and m<3?
Answers
Answer:
∠2 = 168°
∠3 = 6°
Step-by-step explanation:
Opposite angles of a rhombus are congruent, so ∠2≅∠1 = 168°.
∠3 is the base angle of the isosceles triangle with an apex angle of 168°. Hence it will be (180° -168°)/2 = 6°.
In ΔABC, AC = BC side CD is the median of side AB with d belonging to side AB,AB = 4 in and CD = sqaure root of 3 in. find AC.
Answers
Answer:
AC = √7 in
Step-by-step explanation:
ΔABC is isosceles, so ΔADC is a right triangle with AD = 2 in and CD = √3 in. The length of hypotenuse AC is found using the Pythagorean theorem.
... AC² = AD² +CD² = (2 in)² +(√3 in)² = (4 +3) in²
... AC = √7 in . . . . take the square root
are theese rational
11/12 times 9/22
x + (-2x)
Answers
Answer:
11/12 times 9/22 - rational
x + (-2x) unknown
Step-by-step explanation:
11/12 is a rational number (the ratio of integers)
9/22 is a rational number (the ratio of integers)
11/12 * 9/22 is a rational number
The product of 2 rational numbers is rational
x+-2x = x but we do not know if x is rational or irrational , so we cannot say if it is rational or not. If x is rational, the sum is rational. If r is irrational, the sum is irrational.
Write each polynomial function in standard form, then classify it by degree and number of terms and describe its end behavior.
y = 2x(x^2 – 3)(x^2 + 2)
Answers
Answer:
y = 2x^5 -2x^3 -12xdegree 5, 3 terms, end behavior: (-∞, -∞), (+∞, +∞)Step-by-step explanation:
I like to form the product of something like this by multiplying binomial pairs first. The distributive property applies for that (as does FOIL).
... (x^2 -3)(x^2 +2) = x^2·x^2 + x^2·2 + (-3)·x^2 + (-3)·2
... = x^4 -x^2 -6 . . . . . the two x^2 terms combine
Now, it is a simple matter to multiply each term by 2x:
... y = 2x^5 -2x^3 -12x
_____
The highest-degree term has degree 5. There are 3 terms. (All are odd-degree, so this is an odd function, symmetrical about the origin.)
As with any odd-degree function (with positive leading coefficient) the overall shape has a positive slope (/), tending toward -∞ for large negative values of x, and tending toward +∞ for large positive values of x.
you have a job raking leaves. You charge 10 dollars plus .50 for each bag you fill with leaves. the equation y=0.50x+10 models this situation,where x is the number of bags and y is your total amount earned. how many bags do you fill if you earn 17 dollars
Answers
Answer:
14 bags
Step-by-step explanation:
If you earn $17, to find the number of bags substitute 17 for y in the equation y=0.50x+10. Then use inverse operations to solve for x.
17 = 0.50x+10 Subtract 10 from both sides.
17-10 = 0.50x
7=0.50x Divide both sides by 0.50
7/0.50 = x
14 =x
i will give brainliest thanks
Answers
Answer:
The correct answer is A which is
[tex]\:<\:1[/tex]
Step-by-step explanation:
The angle of elevation from the submarine to the boat is [tex]\:<\:1[/tex].
This is the angle through which an observer from the submarine will raise the head before seeing the boat.
See diagram in the attachment for illustration.
Classify the following as Linear or Quadratic. Then identify the quadratic, linear, and constant terms.
x + 2x(x-3)
Answers
Answer:
This is quadratic since it has an x^2
The quadratic term is 2x^2, the linear term is -5x and the constant term is 0
Step-by-step explanation:
x + 2x(x-3)
Distribute the 2x
x + 2x^2 -6x
Combine like terms
2x^2 -5x
This is quadratic since it has an x^2
The quadratic term is 2x^2, the linear term is -5x and the constant term is 0
Answer:
quadratic, 2, -5, 0
Step-by-step explanation:
x + 2x(x-3)
= x + 2x^2 - 6x
= 2x^2 - 5x
so the eqn is quadratic
the quadratic term is 2,
the linear term is -5, and
the constatnt term is 0