An arrow is shot vertically upward at a rate of 160 feet per second from ground level. Use the projectile formula
h
=
−
16
t
2
+
v
0
t
+
h
0
h
=
-
16
t
2
+
v
0
t
+
h
0
to determine when the height of the arrow will be 114 feet.
Answers
Answer:
0.772 seconds; 9.228 seconds
Step-by-step explanation:
The given projectile formula with the given numbers filled in is ...
[tex]\displaystyle h=-16t^2+v_0t+h_0\\\\114=-16t^2+160t[/tex]
We can "complete the square" to solve this for t, the times at which the height is 114 feet.
16(t² -10t) = -16(7.125) . . . . . rearrange, showing factor of 16
t² -10t +25 = -7.125 +25 . . . . divide by 16, add 25 to complete the square
t = 5 ±√17.875 ≈ 5 ± 4.228 . . . . take the square root, add 5
t ∈ {0.772, 9.228}
The arrow is 114 feet high after 0.772 seconds and again after 9.228 seconds.
Related Questions
Solve the problem 4747+38383
Answers
4747+38383=43,130
Answer:
4747
+38383
=43130 that is my answer
A large grocery store chain pays all workers time and a half on Saturdays and double time on Sundays. If an employee's regular pay is $10.75 per hour, use the expression 10.75(1.5)(x) + 10.75(2)(y) to find their gross income if they worked 4.5 hours on Saturday and 5 hours on Sunday. (4 points)
A.. $156.72
B. $177.38
C. $180.06
D. $257.44
Answers
The gross income earned by the workers if paid time and a half on Saturdays and double time on Sundays is $180.06
How to find gross incomeTotal = 10.75(1.5)(x) + 10.75(2)(y)
where,
x = hours worked on Saturday = 4.5 hoursy = hours worked on Sunday = 5 hoursTotal = 10.75(1.5)(4.5) + 10.75(2)(5)
= 72.5625 + 107.5
= $180.0625
Approximately,
$180.06
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MATH
NATION
Question 6 of 10
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A cup is 6.4 cm tall, not including a 0.6 cm lip. Cups are stacked inside one another. You may want to draw a diagram t
you see how the height of the stack of cups increases. Select the function that represents the height of a stack of cups
terms of the number of cups in the stack.
Answers
Answer:
If you ever need help on a question and you don’t know the answer just remember this quote “ purple is always the answer”.
Step-by-step explanation: Hope this helps u!
Mario loaned Robert $390 at an interest rate of 18% for 229 days. How much will Robert pay Mario at the end of 229 days? Round your answer to the nearest cent.
Answers
Answer:
Amount Robert will pay back = $434.04
Step-by-step explanation:
Formula for interest is;
I = (P * R * T)/100
We are given;
P = $390
Rate = 18%
Time; T = 229 days = 229/365
Thus;
I = (390 * 18 * (229/365))/100
I = $44.04
Thus, total amount Mario will pay back = $390 + $44.04 = $434.04
The demand equation for a manufacturer's product is:
p = 50 x [tex](151 - q)^{0.02\sqrt{q+19} }[/tex]
(a) Find the value of dp/dq when 150 units are demanded.
(b) Using the result in part (a), determine the point elasticity of demand when 150 units are demanded. At this level, is demand elastic, inlastic, or of unit elasticity?
(c) Use the result in part (b) to approximate the price per unit it demand decreases from 150 to 140 units.
(d) If the current demand is 150 units, should the manufacturer increase or decrease price in order to increase revenue?
Answers
From the given price function, we have;
(a) [tex] \frac{dp}{dq} = - 13[/tex]
(b) The point elasticity of demand is 0.0256; inelastic demand
(c) $46.6
(d) Increase
How can the elasticity of demand be found?a. The given function is presented as follows;
[tex]p = 50 \times (151 - q) ^{0.02 \times \sqrt{q + 19} } [/tex]
Differentiating the above function with a graphing calculator and setting q = 150 gives;
[tex] \frac{dp}{dq} = - 13[/tex]
b. The point elasticity of demand is given by the formula;
[tex] e \: = \frac{dq}{dp} \times \frac{p}{q} [/tex]
When q = 150, we have;
P = 50
Which gives;
[tex]e \: = \frac{1}{13} \times \frac{50}{150} = 0.0256[/tex]
The point elasticity of demand, E = 0.0256
The demand is inelastic (less than 1) when the quantity demanded is 150 unitsc. If the quantity demanded decreases from 150 to 140 units, we have;
[tex]0.0256 \: = \frac{1}{13} \times \frac{p}{140} = [/tex]
Which gives;
p = 46.6
The price when the quantity demanded decreases to 140 is $46.6d. Given that increase in price, from 46.6 to 50, increases the quantity demanded from 140 to 150, therefore;
The manufacturer should increase the price, p to increase the revenue, R.R = p × q
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x -5 = 2x -8 solve this equation
Answers
Answer:
x = 3
Step-by-step explanation:
x - 5 = 2x - 8
First subtract x from both sides: -5 = x - 8
Finally, add 8 to both sides: 3 = x
Hope this helps!
List and describe the characteristics of a perfectly competitive market.
Answers
A market system with perfect competition is one in which there are several buyers and sellers interacting with the same goods.
A perfectly competitive market structure is widely found a market in the Indian economy. This market often accepts prices as a single seller cannot change the market price in the economy. Together with other characteristics, this trait sets this market apart from other types of markets.
Let's discuss the characteristics of the perfectly competitive market in detail which are as follows:
1. Large number of buyers and sellers- A commodity has a high number of buyers and sellers when there is ideal competition. Because there are so many customers, each one only purchases a very little portion of the available supply.
2. Homogeneous Products- Products in this market are homogenous in nature which means the products are identical in nature. This suggests that each company's output, in terms of quantity, quality, colour, size, features, etc., is a perfect substitute for the work of the others. This suggests that consumers don't care about what different companies produce.
3. Free entry and exit of firms- In the economy, there are 2 periods: long run and short run. In the long run, there is completely free entry and exit of firms while in the short run, some factors may contribute to the obstruction of entry and exit of firms. This guarantees that all businesses will ultimately make a regular profit or no economic profit, which evaluates the opportunity cost of the business to either continue operating or close.
4. Perfect Knowledge- In this market structure both the sellers and buyers have perfect knowledge of the market factors like price prevailing in the market because of this feature no seller can charge a higher price in the market to any customer.
5. No transportation cost- The products sold in this market structure are generally sold locally so there incur no transportation cost. Also because the same price is prevailing in the market sellers not require to transport anything.
6. No promotion cost- Homogeneous product is sold and uniform prices prevail so the sellers do not need to incur any selling cost like advterisemt for such a product. So the promotional cost incurred by firms is zero.
7. Price Taker- Firms are generally price takers in this structure of the market as sellers cannot influence the price of the goods so they need to accept the price that is prevailing in the market.
8. Perfect mobility of factors of production- Factors of production like Land, Labour and Capital are perfectly mobile in this market structure. These factors can freely move in and out of industry making demand and supply equal to each other.
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Read the question and enter your response in the box prc
How do you write an equivalent expression -1/4(-8x+12y
Answers
Explanation: distribute -1/4 into 8x and 12y
5 Vera is a shop manager. 5 She has this information about the income in her shop for eight weeks this year. Week 1 2. 3 4 5 6 7 8 Income (thousands of £) 53.5 42.3 39.8 45.1 52.4 19.4 47.9 42.5 The median income for the same eight weeks last year was £49 300 Vera knows that the median income for these eight weeks has decreased this year compared to last year. (a) Work out the percentage decrease of the median income. Give your answer to 2 decimal places.
Answers
Using the median concept, it is found that it suffered a 11.16% decrease.
What is the median of a data-set?It is the 50th percentile of the data-set, which is the value that separates the lower 50% from the upper 50%.
In this problem, the ordered data-set, in thousands of £, is given by:
{19.4, 39.8, 42.3, 42.5, 45.1, 47.9, 52.4, 53.5}
It has even cardinality, hence the median is the mean of the 8/2 = 4th and 5th terms, so:
M = (42.5 + 45.1)/2 = £43800.
It decreased from £49300 last year. The percentage decrease is the change divided by initial amount and multiplied by 100%, hence:
P = (49300 - 43800)/49300 x 100% = 11.16%.
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in november 1958 the cover scientific american showed this diagram on its cover. Each of the interior rectangles is a square. if square D is 81 spuare units and square c is 64 square units what is the area of the other seven squares? what is the area of the of the entire figure? what is the perimeter of the figure
Answers
From the 32 by 33 rectangular figure, having interior squares, we have
The area of the squares in square units are;
A = 324 B = 225E = 100F = 196G = 16H = 49I = 1Area of the entire figure = 1056The perimeter of the figure = 130 unitsHow can the area and perimeter be found?The areas in square units are;
Area of square A = 18 × 18 = 324
Area of square B = 15 × 15 = 225
Area of square E = 10 × 10 = 100
Area of square F = 14 × 14 = 196
Area of square G = 4 × 4 = 16
Area of square H = 7 × 7 = 49
Area of square I = 1 × 1 = 1
Area of a rectangle = Length × Breadth
Therefore;
Area of the entire figure = 32 × 33 = 1056
Area of the entire figure = 1056 square unitsThe perimeter, P, of the rectangular figure is therefore;
P = 2 × 32 + 2 × 33 = 130
The perimeter of the figure = 130 unitsLearn more about finding the area of plane figures here;
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Frank ate 2/8 of the apple pie and
Jose at 3/8 of the cherry pie. How
much pie did Frank and Jose eat
altogether?
Answers
Answer:
answer 5/8 because 2/8 + 3/8= 5/8
Moose left a $7.50 tip for his waitress on a $50 restaurant bill. What percent of his bill did he leave as a tip?
Answers
Answer:
he left 15 % of his bill as a tip
Step-by-step explanation:
7.5/50 x 100
0.15 x 100
15
Percentage
7.5/50×1000.150(100)15.0%Frankie is saving up to have spending money for her family vacation. If Frankie's current monthly net pay is $490.00 and her monthly expenses are $396.90 what percent of her net pay is left for savings?
19%
23%
67%
81%
Answers
$490-$396.90= $93.70
Now we’ll go for cross multiplication
100% $490
? $93.70
? = 100 x 93.7/490
? = 19.1 %
So the answer is 19.1% which rounded to the nearest whole number is 19%. The answer is the first option.
Hope it helped you
Special Right Triangles
Isosceles Right Triangle
30-60-90 Triangle
help 1-12 please
Answers
Step-by-step explanation:
remember, the sum of all angles in a triangle is always 180°.
1.
since it is a right-angled triangle, and one of the leg angles is 45°, then the other leg angle is also 45°.
which makes this an isoceles triangle.
so, the second leg is 6 too.
the baseline (Hypotenuse) is then per Pythagoras
baseline² = 6² + 6² = 36 + 36 = 72 or 2×36
baseline = sqrt(72) = 6×sqrt(2)
2.
this is then a 30-60-90 triangle.
the left leg (a) is then 2a/2 = 10/2 = 5.
and the bottom leg is 5×sqrt(3).
3.
isoceles triangle.
so, left and right legs (a) are both 3 (from the 3×sqrt(2)).
4.
30-60-90 triangle
upper leg is then 6×sqrt(3).
the baseline is 2 times the left leg : 2×6 = 12
5.
isoceles triangle
both legs are 2 (from the 2×sqrt(2)).
6.
30-60-90 triangle
left leg is 4 (from the 4×sqrt(3)).
the baseline is 2×4 = 8.
7.
isoceles triangle.
6 = a×sqrt(2)
a (both legs) = 6/sqrt(2)
8.
30-60-90 triangle
9 = a×sqrt(3)
a (left leg) = 9/sqrt(3)
baseline = 2a = 2×9/sqrt(3) = 18/sqrt(3)
9.
due to the equal leg angles this is an isoceles triangle.
4 = a×sqrt(2)
a (both legs) = 4/sqrt(2)
10.
30-60-90 triangle
the bottom leg (a) = 2a/2 = 6/2 = 3
the left leg is then 3×sqrt(3)
11.
isoceles triangle
left leg is also 5.
baseline is 5×sqrt(2)
12.
30-60-90 triangle
12 = a×sqrt(3)
a (left leg) = 12/sqrt(3)
the baseline is then 2a = 2×12/sqrt(3) = 24/sqrt(3)
1
Leslie earned $12 Friday, $20 Saturday, and $56 Sunday selling bracelets. If she sold each bracelet for the same amount of money what is the most she could charge for each bracelet?
Answers
Answer:
$4
Step-by-step explanation:
For this, you want to find the greatest common factor
This basically means what number can be divided out of all of these.
So, you can find the factors for all of them and find which one appears in all three numbers and which is the greatest number
for 12:
1, 2, 3, 4, 6, 12
For 20:
1, 2, 4, 5, 10, 20
For 56:
1, 2, 4, 7, 8, 14, 28, 56
The numbers that appear in all of there are:
1, 2, and 4
And since we want to find the greatest amount she can charge for bracelet, the answer is:
$4
if tan=5/12
Find sinx/cosx+tanx
Answers
Answer:
[tex] \frac{10}{12} [/tex]
Step-by-step explanation:
given,
tanX = 5/12
sinX/cosX + tanX
= tanX + tanX ( sinX/cosX = tanX)
= 5/12 + 5/12
=
[tex] \frac{10}{12} [/tex]
Step-by-step explanation:
[tex] \tan(x) = \frac{5}{12} \\ \hookrightarrow \: \frac{p}{b} = \frac{5}{12} [/tex]
As,
[tex] \hookrightarrow \: \frac{ \sin(x) }{ \cos(x) } = \tan(x) [/tex]
Now,
[tex] \hookrightarrow \: \frac{ \sin(x) }{ \cos(x) } + \tan(x) \\ \hookrightarrow \: \tan(x) + \tan(x) \\ \hookrightarrow \: \frac{5}{12} + \frac{5}{12} \\ \hookrightarrow \frac{5 + 5}{12} \\ \hookrightarrow \frac{10}{12} [/tex]
Suppose that y varies inversely with x. Write a function that models the inverse function.
x = 6 when y = 8
Answers
8=k/6
k=48
:y=48/x
[tex] \qquad \qquad \huge\text{Anѕwer}♨[/tex]
Let's Solve ~❖ Aѕ givєn in thє quєѕtiσn, ч vαriєѕ invєrѕєlч with х, thiѕ єхprєѕѕiσn cαn вє rєprєѕєntєd αѕ :
[tex] \qquad \Rrightarrow \rm y \propto \dfrac{1}{x} [/tex]
➻ To rєplαcє prσpσrtiσnαlitч ѕign with єquαlѕ tσ, wє hαvє tσ uѕє α cσnѕtαnt (k)
[tex] \qquad \Rrightarrow \rm y = k \times\dfrac{1}{x} [/tex]
[tex] \qquad \Rrightarrow \rm \dfrac{}{} xy = k[/tex]
➻ nσw, plug in vhє vαluєѕ σf х αnd ч fσr α ѕpєcific inѕtαnt, thαt'ѕ givєn in thє quєѕtiσn ~
х = 6, whєn ч = 8[tex] \qquad \Rrightarrow \rm \dfrac{}{} 6 \times 8 = k[/tex]
[tex] \qquad \Rrightarrow \rm \dfrac{}{} k = 48[/tex]
thєrєfσrє, vαluє σf prσpσrtiσnαlч cσnѕtαnt iѕ 48
➼ ѕσ, thє rєquirєd єхprєѕѕiσn will вє :
[tex] \qquad \Rrightarrow \rm \dfrac{}{} xy = 48[/tex]
A car is traveling at a constant speed of 45 miles per hour. How many feet does it travel in 6 seconds?
Answers
Answer:
The car will travel at 198 feet in 3 seconds. The speed of the car = 45miles/ hour. To convert miles to feet;. 1 mile = 5280 feet.
Step-by-step explanation:
The car will travel at 198 feet in 3 seconds. The speed of the car = 45miles/ hour. To convert miles to feet;. 1 mile = 5280 feet.
Given m \| nm∥n, find the value of x. (7x-10)° (6x-5)°
Answers
7x-10=6x-5
We simplify the equation to the form, which is simple to understand
7x-10=6x-5
We move all terms containing x to the left and all other terms to the right.
+7x-6x=-5+10
We simplify left and right side of the equation.
+1x=+5
We divide both sides of the equation by 1 to get x.
x=5
pythag test. question in screenshot
Answers
196-81=x^2
115=x^2
x=10.7238
25^2-10.7238^2=(j+9)^2
625-115=(j+9)^2
510=(j+9)^2
510=j^2+9^2
510-9^2=j^2
510-81=j^2
j=13.6
Today Zack sold twice as many bags of popcorn at the ball game as he sold last Saturday. In the 2 days he sold a total of 96 bags. Write a system of equations to determine s, the number of bags Zack sold last Saturday, and t, the number of bags he sold today?
Answers
Answer:
[tex]s=32\\t=64[/tex]
Zack sold 32 bags of popcorn last Saturday, and 64 bags of popcorn today.
Step-by-step explanation:
Start by determining what information the question gives us, and what we need to find.
Given:
Zack sold twice as many bags of popcorn as he sold last Saturday
He sold 96 bags altogether in the 2 days
Find:
s, number of bags he sold last Saturday
t, number of bags he sold today
Equation/System of Equations:
[tex]t=2s[/tex] (OR "number of bags he sold today = number of bags he sold last Saturday multiplied by 2, or twice the amount he sold last Saturday)
[tex]t+s=96[/tex] (OR "number of bags he sold today + number of bags he sold last Saturday is equivalent to the amount of bag he sold altogether which is 96 bags as given by the question)
Solve:
We can solve this system of equations using substitution. In this case, we can substitute "2s" for "t" into the second equation giving us...
[tex]2s+s=96\\3s=96[/tex]
Divide both sides by 3. Notice that the Division Property of Equality states that if you divide on side of the equation by something, you must divide the other side by the same quantity.
[tex]s=\frac{96}{3}\\s=32[/tex]
Substitute 32 in for "s" to solve for "t"...
[tex]t=2s\\t=2(32)\\t=64[/tex]
Answer:
Zack sold 32 bags of popcorn last Saturday, and 64 bags of popcorn today.
To earn a B on his quiz, John needs to get between 80%-89% of the questions correct. There are 30 questions on the quiz. What is the least number of questions John needs to get correct for his grade to be a B
Answers
Answer:
24 he can get 24 at the very minimum
Step-by-step explanation:
f(x)=3x^3 + 4x^2 - 6x -7
g(x)= 2x-4
Find (f-g)(x)
Answers
Answer:
f(x)-2x+4
Step-by-step explanation:
f(x)-g(x)
f(x)-g(x)=f(x)-(2x-4)
f(x)-(2x-4) remove parentheses for addition or subtraction
f(x)-2x+4
can someone please help me
Answers
Answer:
(2, 4)
Step-by-step explanation:
All you have to do is hop up 10 units on the grid from point P. 10 units up from -6 is 4. Therefore, your answer is (2, 4).
I hope this helps! Have a lovely day!! :)
Answer:
i belive its c
Step-by-step explanation:
you are shifting up 5 squares so you arrive at (2,4)
What is the perfect square of the root 3x^4
Answers
Answer:
the perfect square is 9x²
Step-by-step explanation:
√(3×)⁴
=(3x)²
=9x²
If the mass of an object on Earth is 9 grams, what would the mass of the same object be on
the Moon?
Answers
Answer:
1.49 Grams
Step-by-step explanation:
Answer:
9 gms.
Step-by-step explanation:
mass will be same.
weight will be different.
A washer and dryer cost a total of $1280. The cost of the washer is three times the cost of the dryer. Find the cost of each item. Cost of washer: $ Cost of dryer: $
Answers
Answer:
Dryer = 320
Washer = 960
Step-by-step explanation:
Washer + Dryer = 1280
Let,
Dryer = x
Washer = 3x
3x + x = 1280
4x = 1280
x = 320
Washer = 3x = 3(320)=960
960 + 320 = 1280
Thus,
Dryer = 320
Washer = 960
~lenvy~
Evaluate UV if possible.
Answers
Answer: B
Step-by-step explanation:
Multiply U and V:
[tex]\begin{pmatrix}-9&1&0\\ \:4&0&2\\ \:0&1&5\end{pmatrix}\begin{pmatrix}2\\ \:-2\\ \:1\end{pmatrix}[/tex]
[tex]\mathrm{Multiply \ the \ rows \ of \ the \ first \ matrix \ by \ the \ columns \ of \ the \ second \ matrix:}[/tex]
[tex]\begin{aligned}&\left(\begin{array}{ccc}-9 & 1 & 0\end{array}\right)\left(\begin{array}{c}2 \\-2 \\1\end{array}\right)=(-9) \cdot 2+1 \cdot(-2)+0 \cdot 1 \\&\left(\begin{array}{ccc}4 & 0 & 2\end{array}\right)\left(\begin{array}{c}2 \\-2 \\1\end{array}\right)=4 \cdot 2+0 \cdot(-2)+2 \cdot 1 \\&\left(\begin{array}{lll}0 & 1 & 5\end{array}\right)\left(\begin{array}{c}2 \\-2 \\1\end{array}\right)=0 \cdot 2+1 \cdot(-2)+5 \cdot 1\end{aligned}[/tex]
[tex]=\begin{pmatrix}\left(-9\right)\cdot \:2+1\cdot \left(-2\right)+0\cdot \:1\\ 4\cdot \:2+0\cdot \left(-2\right)+2\cdot \:1\\ 0\cdot \:2+1\cdot \left(-2\right)+5\cdot \:1\end{pmatrix}[/tex]
[tex]\mathrm{Simplify\:each\:part:}[/tex]
[tex]=\begin{pmatrix}-20\\ 10\\ 3\end{pmatrix}[/tex]
Therefore, the correct answer is B
Mrs. Williams' desk is located at (-5,2). The wireless internet box is halfway between her desk and the door. If the box is located at the coordinates (8, -8), what are the coordinates of the door?
Answers
Topic : Midpoint between points
desk = (-5,2)box = (8, -8)door = (x, y)formula:
[tex]\sf \bold{(x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})}[/tex]
=====================================
[tex]\hookrightarrow \sf \dfrac{x+(-5)}{2} ,\dfrac{y+2}{2} = (8, -8)[/tex]
separate taking coefficients:
[tex]\rightarrow \sf \dfrac{x-5}{2} =8, \ \dfrac{y+2}{2} = -8[/tex]
[tex]\rightarrow \sf x-5 =16, \ y+2 = -16[/tex]
[tex]\rightarrow \sf x =16+5, \ y= -16-2[/tex]
[tex]\rightarrow \sf x =21, \ y= -18[/tex]
coordinates of door: (21, -18)
Let that be (x,y)
So
[tex]\\ \rm\rightarrowtail (8,-8)=(\dfrac{x-5}{2},\dfrac{y+2}{2})[/tex]
[tex]\\ \rm\rightarrowtail \cfrac{x-5}{2}=8\implies x-5=16\implies x=21[/tex]
[tex]\\ \rm\rightarrowtail \cfrac{y+2}{2}=-8\implies y+2=-16\implies y=-18[/tex]
(x,y)=(21,-18)A High School’s football Stadium holds a total of 7,000 fans. A survey shows that of the total number of fans, 68% root for the home team. How many fans attending a football game are rooting for the home team? Please help!
Answers
Explanation: 7,000 x .68 =4,760
Hope this helps and please mark brainliest!!!