Given the same type of golf ball scenario with an equation
y=-0.005x2 +1.8x, horizontal distance of 360 feet, maximum
height of 162 feet, and using the helpful projectile motion formulas
below, answer the following.
x(t)=v, cos(6)y(t)= h, + v, - sin(0).4-1612
. 0
a.) What is the angle at which the ball takes off?
[ Select]
b.) How long is the ball in the air? (Select]
c.) What is the ball's speed when it hits the ground?
[ Select
The angle at which the ball takes off, distance the ball in the air, the ball's speed is mathematically given as
theta=60d=6.3658vo=116.486What is the angle at which the ball takes off?Generally, the equation for the verticle component is mathematically given as
[tex]y=xtan\theta-\frac{16x^2}{v0cos^2\theta}\\\\Therefore\\\\\theta=tan^{-1}(1.8)[/tex]
theta=60
b)
hmax=vo^2sin^2\theta/2g
vo=116.486
Therefore, distance the ball in the air
[tex]d=\frac{2*114.486*0.874*2}{32}[/tex]
d=6.3658
c)
The ball's speed when it hits the ground will be vo
vo=116.486
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The cost of a barrel of beans, b, fluctuates (changes) by 17% in both
directions during a three-month period.
Match the verbal description of the high cost of a barrel of beans with all equivalent expressions for b is increased by 17%.
A. b + 0.17b
B. b - 0.17b
C. b - 1.17b
D. -0.17b
E. 0.83b
F. 1.17b
Answer:
b increased by 17% =b + 17% of b =b + 0.17b =1.17bCorrect ones A and F
------------------------------------------
b decreased by 17% =b - 17% of b =b - 0.17b =0.83bCorrect ones H and K
Circle A has a center of (2,3) and a radius of 5, and circle B has a center of (1,4) and a radius of 10. What steps will help show that circle A is similar to circle B?
-Dilate circle A by scale factor of 2
- Translate circle A using the rule (x+1, y-1)
-Rotate circle A 180 degrees about the center.
-Reflect circle A over the Y axis
Answer:
-Dilate circle A by scale factor of 2
Got it right on the test (see picture)
Circle A is translated using the rule (x + 1, y - 1). Then the correct option is B.
What is a circle?It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
Circle A has a center of (2,3) and a radius of 5, and circle B has a center of (1,4) and a radius of 10.
Circle B is translated as 1 unit leftward in the x-direction and 1 unit upward in the y-direction.
Then circle B is dilated by a factor of 2.
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An investment of $1,000 earns an annual interest rate of 2%. How much more interest is earned in Year 5 with compound interest than with simple interest?
An additional interest of $ 4.08 is earned in year 5 by using compound interest and in comparison with simple interest method.
How to determine money gain by simple interest
Simple interest (C) is the amount of money gained and solely related to the initial capital ([tex]C_{o}[/tex]), in monetary units. The money earned by simple interest is determined by the following formula:
[tex]C = \frac{C_{o}\cdot r\cdot t}{100}[/tex] (1)
Where:
r - Interest rate, in percentaget - Time, in yearsCompound interest (C) takes into account the capital throughout time and its formula is presented below:
[tex]C = C_{o}\cdot \left[\left(1+\frac{r}{100} \right)^{t}-1\right][/tex]
Now we proceed to determine the simple and compound interest: ([tex]C_{o} = 1000[/tex], r = 2, t = 5)
Simple interestC = [(1000) · (2) · (5)]/100
C = $ 100
Compound interestC = (1000) · {[1+(2/100)]⁵-1}
C = $ 104.08
An additional interest of $ 4.08 is earned in year 5 by using compound interest and in comparison with simple interest method. [tex]\blacksquare[/tex]
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The distance between the Earth and the Moon is approximately 1,260,000,000 feet, and a rocket can travel there at a speed of about 1,540,000 ft/min. How long will it take the rocket ship to travel to the moon and back, in minutes? Express your final answer in minutes and round to the nearest minute. Be sure to convert each number to scientific notation first, before performing any operations. show your work.
It will take approximately 169 minutes for a the rocket to travel a distance of 1,260,000,000 feet at 1,540,000 ft/min
Speed, Distance and TimeGiven Data
Distance = 260,000,000 feetSpeed = 1,540,000 ft/minApplying the relationship between speed, distance and time we have
Speed = Distance/Time
Substituting our given data into the expression we have
1,540,000 = 260,000,000/time
Making time subject of formula
time = 260,000,000/1,540,000
time = 169 miniutes
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For each of the following expressions, identify the base and the exponent. 2× ,10² , x×
Answer:
2 is the base, 10 is the base, and x is the base. X is the exponent of 2, x is the exponent of 10, and x is the exponent of x.
Step-by-step explanation:
f ( x ) = x 2 + 6 x and g ( x ) = x − 8 , calculate. f ( g ( − 5 ) ) =
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
First we have to calculate g (-5) :
[tex]\qquad \tt \dashrightarrow \:x - 8[/tex]
[tex]\qquad \tt \dashrightarrow \: - 5 - 8[/tex]
[tex]\qquad \tt \dashrightarrow \: - 13[/tex]
Now, let's find f (g (-5)) :
[tex]\qquad \tt \dashrightarrow \: {x}^{2} + 6x[/tex]
[tex]\qquad \tt \dashrightarrow \:( - 13) {}^{2} + (6 \times - 13)[/tex]
[tex]\qquad \tt \dashrightarrow \:169 + ( - 78)[/tex]
[tex]\qquad \tt \dashrightarrow \:169 - 78[/tex]
[tex]\qquad \tt \dashrightarrow \:91[/tex]
An amount of 47,000 is borrowed for 12 years at 8.25% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
Use the calculator provided and round your answer to the nearest dollar.
Answer:
$121,683.79
Step-by-step explanation:
A= P(1+ r)^t
A= Amount, P = Principal, r = Rate (decimal form), t= time
A = 47000(1+0.0825)^12
A = 47000(1.0825)^12
A = 47000(2.589016751)
A = 121683.7873
Rounded Answer = $121,683.79
(If there is meant to be no cents then $121,684). Good luck :)
A boat is heading towards a lighthouse, where Meena is watching from a vertical
distance of 120 feet above the water. Meena measures an angle of depression to the
boat at point A to be 18º. At some later time, Meena takes another measurement and
finds the angle of depression to the boat (now at point B) to be 44º. Find the distance
from point A to point B. Round your answer to the nearest foot if necessary.
Answer:
245 ft
Step-by-step explanation:
The geometry of the problem can be modeled by a right triangle in which Meena's height is the side opposite the angle of depression, and the distance to the boat is the side adjacent to the angle of depression. The mnemonic SOH CAH TOA reminds us of the relation ...
Tan = Oppsite/Adjacent
__
The more useful trig function for this problem is the inverse of the tangent function, the cotangent. Using that function, we have ...
cot(angle) = (distance to boat)/(Meena's height)
Then the distance to the boat is ...
distance to boat = (Meena's height)×cot(angle)
The change in distance from A to B is then ...
A -B = (120 ft)(cot(18°) -cot(44°))
= (120 ft)(3.0777 -1.0355) ≈ 245.06 ft
The distance from point A to point B is about 245 feet.
Isabel wants a coat that costs $60. She has saved $42. What fraction of the
amount she needs has she saved?
A) 21/30
B) 4/6
C) 8/12
D) 1/3
coat cost= $60.
to find:the fraction of amount she needs to save.
solution:saved/ actual cost
= $42/ $60 ÷ 2/2
= 21/30
answer= option a) 21/30
If you drive 23 miles south, make a turn and drive 39 miles east, how far are you, in a straight line, from
your starting point? Round your answer to the nearest tenth of a mile.
Answer:
45.27 miles
Step-by-step explanation:
Pythagorean theorem
23^2 + 39^2 = d ^ 2
d = 45.27 miles
If a person drives 23 miles south and make a turn to east and drive 39 miles then the distance between starting point and person is 45.27 miles.
What is pythagoras theorem?Pythagoras theorem applies in a right angled triangle. It says that in a right angled triangle the square of hypotenuse is equal to sum of squares of perpendicular and base of that triangle.
[tex]H^{2} =P^{2} +B^{2}[/tex]
How to find distance?When person drives towards south and then east , it forms a right angled triangle. We have to find the distance of person from the starting point. If we see the figure then we will come to know that we are require to find hypotenuse of triangle.
H=[tex]\sqrt{P^{2} +B^{2} }[/tex]
Distance=[tex]\sqrt{23^{2} +39^{2} }[/tex]
=[tex]\sqrt{1521+529}[/tex]
=[tex]\sqrt{2050}[/tex]
=45.27
Hence the distance of person from starting point is 45.27 miles.
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Select the correct answer from each drop-down menu.
The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0.
The equation of this circle in standard form is
. The center of the circle is at the point
, and its radius is
units.
Step-by-step explanation:
[tex](x - 2) {?}^{2} + (y + 3) { = 18} [/tex]
PLEASE HELP PLEASE PLEASE
Answer:
4 degrees is the closest thing i could think of while looking at this.
Use ABC to find the value of sin A
12/35
35/37
37/12
12/37
Answer:
The correct answer is 12/37
Given vectors, a= (-2 -3) and b= ( 1 -1 ) find 2a-3b
Answer:
(-10,0)
Step-by-step explanation:
2a =[2(-2) , 2(-3)] = (-4 -6) <--- add them
-3b = [-3(1) . -3(-1)] = (-3 +3) <--- add them
2a - 3b =
[(-4 -6), (-3 +3)] =
(-10,0)
Willie runs 4 miles in 44 minutes. If Willie runs at the same rate, how many miles can he run in 66 minutes?
Answer:
6 miles in 66 mins
Step-by-step explanation:
4 miles = 44 mins
simplify to the lowest point
1 mile = 11 mins
? = 66 mins
? = 1 x 6
you can run 6 miles in 66 mins
Answer:
Step-by-step explanation:
4/44= 0.0909090909...*66=6
find the propotunate value by dividing each initial value and multiply it by the listed secondary value
The graph shows the vertical position of a ball attached to a spring oscillating between a low point and a high point as a function of time.
Select all statements that describe the graph.
The amplitude is 24 cm.
The ball travels 24 cm in 1 s.
It takes the ball 2 s to complete a cycle.
The midline is at f(x)=0.
Step-by-step explanation:
The statements that describe the graph are,
The ball travels 24 cm in 1s.
It takes the ball 2s to complete a cycle
The midline is at f(x)=0
I hope it helped you
This exercise uses Newton's Law of Cooling.
Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6°F. Immediately following death, the body begins to
cool. It has been determined experimentally that the constant in Newton's Law of Cooling is approximately k - 0.1947, assuming time is measured in hours. Suppose that the
temperature of the surroundings is 60°F.
(a) Find a function TCC) that models the temperature t hours after death.
TL)
х
(6) If the temperature of the body is now 78°F, how long ago was the time of death? (Round your answer to the nearest whole number.)
Xhr
By applying the Newton's law of cooling and performing the neccessary calculations, the time of death of the body is about 4 hours ago.
Newton's law of coolingAccording to the Newton's law of cooling;
T(t) = T(s) + (To - Ts)e^-kt
T(t) = temperature at time t
T(s) = temperature of the surroundings
To = Initial temperature
k = cooling constant
t = time taken
Substituting the values;
T(t) = 60 + (98.6 - 60)e^- 0.1947t
To find the time taken to attian a temperature of 78°F;
78 = 60 + (98.6 - 60)e^- 0.1947t
78= 60 + 38.6e^- 0.1947t
78 - 60 = 38.6e^- 0.1947t
18/38.6 = e^- 0.1947t
0.466 = e^- 0.1947t
ln0.466 = lne^- 0.1947t
ln0.466 =- 0.1947t
t = ln0.466 /- 0.1947
t = 4 hours
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What is value of x?
Enter your answer in the box.
X=
Answer: 10
Step-by-step explanation:
1. Quinn's test scores are 95, 90, and 83. What must she score on the next test to have an average
score of 90 on the four tests?
Answer:
92
Step-by-step explanation:
Add 95, 90, and 83 all together
add 92 to that total
divide by 4
please help!!!!!!!!!!!!!!!
Answer:
There are 8 oz of soup per can : True
In 8 cans, there are 21 oz of soup : False
There are 2 oz of soup in 16 cans : False
In 1/8 of a can, there is 1 oz of soup : True
Step-by-step explanation:
To start, we know we have 168 oz of soup and 21 cans that are all the same size. To find how much is each can, (We know that they will all have the same amount since it says equally sized cans.) we can simply divide the amount we have of soup in oz by the amount of cans we have.
168 / 21 = 8.
This means that all the cans will be filled with 8 oz of soup. Making the first statement true.
Since there are 8 oz in each can, we can do 8 cans * 8 oz to find how many oz are in 8 cans of soup.
8 * 8 = 64 oz.
There are 64 oz of soup in 8 cans. Making the second statement false.
Now again, since there are 8 oz in each can, we can do 16 cans * 8 oz to find how many oz are in 16 cans of soup.
16 * 8 = 128 oz.
There are 128 oz of soup in 16 cans. Making the third statement false.
For the last question, to find 1/8 of a can of soup, we can take 8 oz (8 oz in one can) and divide it by 8.
8/8 = 1
Meaning 1/8 of a can of soup is 1 oz of soup. Making the fourth statement true.
You have been asked to design a rectangular box with a square base and an open top. The volume of the box must be 24cm3 . Determine the minimum surface area necessary to construct a box of this volume. Enter an exact answer.
Help will give thanks to the first to answer
our number is x
we add seven (+7) to x
x+7
What is the greatest common factor of 36 and 90 ?
A 6
B 18
C 36
D 180
Answer:
B
Step-by-step explanation:
It's 18! Obviously it's not 180 because it's too big. It can't be 36 because 36 doesn't go evenly into 90. 6 is too small, so the answer is 18.
While on vacation, the Garner family paid $120 for 3 tickets to a water park. How much money would they have spent on 5 tickets?
Answer:
$ 200
Step-by-step explanation:
$ per ticket = $ 120 / 3 tix
Price for 5 $120 / 3 tix * 5 tix = $ 200
The ratio of Wei Ling's age to Wei Xuan's age 5 years ago was 2: 5. In 9 years
time, the ratio of Welling's age to Wel Xuan's age will be 3:4 How old is Wei
Xuan now?
Answer:
15 years old
Step-by-step explanation:
Start by defining the variables that we are going to use throughout our working:
Let the current age of Wei Ling and Wei Xuan be L and X years old respectively.
Next, form equations using the given information.
5 years ago
Wei Ling: (L -5) years old
Wei Xuan: (X -5) years old
Given that the ratio of Wei Ling's age to that of Wei Xuan's is 2: 5,
[tex] \frac{ L - 5}{X - 5} = \frac{2}{5} [/tex]
Cross multiply:
2(X -5)= 5(L -5)
Expand:
2X -10= 5L -25
2X= 5L -25 +10
2X= 5L -15 -----(1)
9 years time
Wei Ling: (L +9) years old
Wei Xuan: (X +9) years old
Given that the ratio of Wei Ling's age to that of Wei Xuan is 3: 4,
[tex] \frac{L + 9}{X + 9} = \frac{3}{4} [/tex]
Cross multiply:
3(X +9)= 4(L +9)
Expand:
3X +27= 4L +36
3X= 4L +36 -27
3X= 4L +9 -----(2)
Let's solve using the elimination method.
(1) ×3:
6X= 15L -45 -----(3)
(2) ×2:
6X= 8L +18 -----(4)
(3) -(4):
6X -6X= 15L -45 -(8L +18)
0= 15L -45 -8L -18
0= 7L -63
7L= 63
L= 63 ÷7
L= 9
Substitute L= 9 into (1):
2X= 5(9) -15
2X= 45 -15
2X= 30
X= 30 ÷2
X= 15
Thus, Wei Xuan is 15 years old now.
Yan had 5 trading cards, and then his friend gave him more cards. Now he has 16 trading cards. Let t represent the number of cards his friend gave him. Write both an addition equation and a subtraction equation to model the problem.
PLEASE ANSWER IN THE NEXT 1 MINUTE.
SOLVE FOR X IN THE FOLLOWING EQUATION :-- -3(2X+3)+4X=4/3X+11
Answer:
-6
Step-by-step explanation:
-2x - 9 = 4/3x+11
-
-6x-27=4x+33
-
-6x-27-4x=33
-
=6x-4x=33+27
-
10x=33+27
-
-10x=60
-
x= -6
A total of 643 tickets were sold for the school play. They were either adult tickets or student tickets. There were 57 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
350 adult tickets
Step-by-step explanation:
If x is the number of adult tickets sold, then x-57 is the number of student tickets sold (57 fewer). The total number sold is ...
x +(x -57) = 643
2x = 700 . . . . . . . . collect terms, add 57
x = 350 . . . . . . . divide by 2
There were 350 adult tickets sold.
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