I would appreciate it if you could answer the questions please- A ball is thrown upward at 48ft/s from a building that is 100 feet high the function h(t)= -16+84t + 100 expresses the balls height,h in feet given the time t, in seconds since the ball was thrown.please answer the questions if you know the answer I would appreciate it
Answers
Problem 8
Answer: 1.5 seconds----------------
Work Shown:
h(t) = -16t^2+48t+100 is the same as y = -16x^2+48x+100, just with different variables.
Compare this to y = ax^2+bx+c to find that a = -16, b = 48, c = 100
Then compute the x coordinate of the vertex -b/(2a) getting
h = -b/(2a)
h = -48/(2*(-16))
h = 1.5
It takes 1.5 seconds for the ball to reach its peak height. The vertex represents the max height since the parabola opens downward.
==============================================
Problem 9
Answer: 136 feet----------------
Work Shown:
Plug the result from problem 8 into the function
y = -16x^2 + 48x + 100
y = -16(1.5)^2 + 48(1.5) + 100
y = 136
The vertex is (1.5, 136)
This means at 1.5 seconds, the ball is 136 feet off the ground at its highest point.
==============================================
Problem 10
Answer: approximately 4.415 seconds----------------
Work Shown:
Plug in y = 0 and solve for x
y = -16x^2 + 48x + 100
0 = -16x^2 + 48x + 100
-16x^2 + 48x + 100 = 0
Apply the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(48)\pm\sqrt{(48)^2-4(-16)(100)}}{2(-16)}\\\\x = \frac{-48\pm\sqrt{8704}}{-32}\\\\x \approx \frac{-48\pm93.29523032}{-32}\\\\x \approx \frac{-48+93.29523032}{-32}\ \text{ or } \ x \approx \frac{-48-93.29523032}{-32}\\\\x \approx \frac{45.29523032}{-32}\ \text{ or } \ x \approx \frac{-141.2952303}{-32}\\\\x \approx -1.41547593\ \text{ or } \ x \approx 4.41547595\\\\[/tex]
A negative x value makes no sense because time cannot be negative, so we ignore the first solution. The only practical solution is roughly x = 4.415
It takes approximately 4.415 seconds for the ball to reach the ground.
==============================================
Problem 11
2 Answers: At 0.5 seconds and at 2.5 seconds----------------
Work Shown:
Use the same idea as problem 10. Instead of y = 0, use y = 120
y = -16x^2 + 48x + 100
120 = -16x^2 + 48x + 100
-16x^2 + 48x + 100 = 120
-16x^2 + 48x + 100-120 = 0
-16x^2 + 48x - 20 = 0
-4(4x^2 - 12x + 5) = 0
4x^2 - 12x + 5 = 0
Now apply the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-12)\pm\sqrt{(-12)^2-4(4)(5)}}{2(4)}\\\\x = \frac{12\pm\sqrt{64}}{8}\\\\x = \frac{12\pm8}{8}\\\\x = \frac{12+8}{8}\ \text{ or } \ x = \frac{12-8}{8}\\\\x = \frac{20}{8}\ \text{ or } \ x = \frac{4}{8}\\\\x = 2.5\ \text{ or } \ x = 0.5\\\\[/tex]
There are two moments in time when the ball is 120 feet in the air. Those two moments are at x = 0.5 seconds and at x = 2.5 seconds.
At x = 0.5, the ball is going upward. At x = 2.5, the ball is coming back down.
Answer:
(I'm not sure if your teacher is nit-picky about significant figures, but here I go...)
8) 1.5 seconds
9) 136 feet
10) 4.415 seconds
11) 2.5 seconds (also 0.5 seconds)
Step-by-step explanation:
See attached screenshot of Desmos graph showing y(t) = -16t² + 48t + 100, y = 120 and respective points.
Related Questions
if we need to decrease the standard deviation of the sampling distribution by half what do we need to do to the sample size
Answers
Answer:
The answer is below
Step-by-step explanation:
For a normal distributed population with a mean (μ), and a standard deviation (σ), if a sample size of n is selected from the population, the mean of the sample ([tex]\mu_x[/tex]) = μ and the standard deviation of the sample ([tex]\sigma_x[/tex]) = [tex]\frac{\sigma }{\sqrt{n} }[/tex]
Let the normal distribution population have a standard deviation of σ. If the standard deviation is to be decreased by half, the sample size (n) needed is:
[tex]Using:\\\\\sigma_x=\frac{\sigma}{\sqrt{n} } \\\\but\ \sigma_x=\frac{\sigma}{2}\\\\Hence:\\\\ \frac{\sigma}{2}=\frac{\sigma}{\sqrt{n} }\\\\Divide\ through\ by \ \sigma\ to\ get:\\\\ \frac{1}{2}=\frac{1}{\sqrt{n} }\\\\\sqrt{n}=2\\\\square\ both\ sides:\\\\(\sqrt{n} )^2=2^2\\\\n=4\\\\[/tex]
To decrease the standard deviation of the sampling distribution by half we need a sample size of 4
How many boys are there in an introductory engineering course if 416 students are enrolled and there are seven boys to every nine girls?
Answers
Answer:
182 boys
Step-by-step explanation:
Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)
The one-to-one functions g and h are defined as follows.
HELP PLEASE
Answers
Answer:
2, (x+13)/6, -7
Step-by-step explanation:
The -1 bit means do it backwards, so look the for the output of the function with the value given.
In g, when we put in 2 we get 9 out, so g^-1(9) is 2.
For the second one we need to rearrange it to get x = something.
h(x) + 13 = 6x
x = (h(x) + 13)/6
Then replace the h(x) with x and the x with h^-1(x) to get
h^-1(x) = (x + 13)/6
The last one is a trick. Note that h and h^-1 are opposites. If we do something then do the opposite of it, we haven't done anything at all! So the number stays the same.
Solve the equation.
5/6b = 1 7/8
Answers
Step-by-step explanation:
5/6b=17/8
Cross multiple
40=102b
divide through by 102
b=20/51
Find the value of x and the length of each side—- geometry
Answers
Answer:
I think x = 7
but I'm not sure
.. :-))
Find the indicated probability. In one town, 71% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance
Answers
Answer:
0.254
Step-by-step explanation:
Given that:
Percentage of those having health insurance = 71%
p = 71 / 100 = 0.71
Number of adults selected at random, n = 4
Probability that 4 selected have health insurance :
p^n = 0.71^4 = 0.25411681
= 0.254
Can someone help me with this please
What is the right answer for it?
Answers
120=10x(10+AB)
12-2=AB
132 is what percent of 880
Answers
Answer:
Step-by-step explanation:
132 is what percent of 880? = 15.
find the value of trigonometric ratio
Answers
Answer:
they all are the same but the 2nd one has more of a lumnicution so thats the answer
Step-by-step explanation:
Solve this equation 5x-3+x=21
Answers
Answer:
x = 4
Step-by-step explanation:
5x - 3 + x = 21
6x - 3 = 21
6x = 24
x = 4
A fifth grade teacher gives homework every night in both mathematics and language arts. The time to complete the mathematics homework has a mean of 30 minutes and a standard deviation of 3 minutes. The time to complete the language arts homework has a mean of 40 minutes and a standard deviation of 4 minutes. Assuming both distributions of homework time are Normally distributed, what is the probability that the average time it takes to complete both homework assignments is greater than 82 minutes?
Answers
Answer:
0.82% probability that the average time it takes to complete both homework assignments is greater than 82 minutes
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Math homework:
[tex]\mu_M = 30, \sigma_M = 3[/tex]
Arts homework:
[tex]\mu_A = 40, \sigma_A = 4[/tex]
What is the probability that the average time it takes to complete both homework assignments is greater than 82 minutes?
Here, we have a sum of normal variables. The mean will be the sum of the means, while the standard deviation is the square root of the sum of the variances. So
[tex]\mu = \mu_M + \mu_A = 30 + 40 = 70[/tex]
[tex]\sigma = \sqrt{\sigma_M^2 + \sigma_A^2} = \sqrt{3^2+4^2} = 5[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 82. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{82 - 70}{5}[/tex]
[tex]Z = 2.4[/tex]
[tex]Z = 2.4[/tex] has a pvalue of 0.9918
1 - 0.9918 = 0.0082
0.82% probability that the average time it takes to complete both homework assignments is greater than 82 minutes
Simplify: 6√3 + 2√75 - 4√27
do you know the answer?
Answers
Answer:
4√3 or Decimal form 6.928203
Step-by-step explanation:
ofc i know the answer, ima different breed
A coin is weighted so that the probability of heads is 0.64. On average, how many coin flips will it take for the tails to first appear
Answers
Answer:
1.563
Step-by-step explanation:
Given :
Probability of head, p = 0.64
Number of flips it would take for tail to appear first :
Treatting the question as a geometric function :
Using the relation :
1 / p
Expected number of flips until first tail :
1 / P = 1/ 0.64 = 1.5625
E(x) = expected number of flips until first tail = 1.563
A model of a rectangular stove top with four circular burners is shown. The side lengths of the stove top and the diameters of the burners are labeled.
Which measurement is the best estimate of the area in square inches of the stove top that does not include the area of the burners?
A) 108 in.2
B) 492 in.2
C) 420 in.2
D) 528 in.2
Answers
The required estimate of the area in square inches of the stove top that does not include the area of the burners is 415 square inches.
What is surface area?Surface area is defined as the measure of a region or surface is called as surface area.
The best estimate of the area of the stovetop that does not include the area of the burners can be obtained by subtracting the total area of the four burners from the total area of the stovetop.
The total area of the stove top is given by the product of its length and width:
Length = 24 inches
Width = 22 inches
Area = Length × Width = 24 × 22 = 528 square inches
The area of each burner is given by the formula for the area of a circle:
= π × (diameter/2)²,
where π is approximately equal to 3.14
Since the diameter of each burner is 6 inches, the radius of each burner is 6/2 = 3 inches.
Area of one burner = Pi × (3)² = 3.14 × 9 = 28.26 square inches
The total area of the four burners is 4 × 28.26 = 113 square
The area of the stove top = 528 - 113
= 415 square inches.
Thus, the required estimate of the area in square inches of the stove top that does not include the area of the burners is 415 square inches.
Learn more about the surface area here:
https://brainly.com/question/2835293
#SPJ6
An open-top box with a square base is to have a volume of 4 cubic feet. Find the dimensions of the box (in ft) that can be made with the smallest amount of material.
Answers
Answer:
The dimension of box=[tex]2ft\times 2ft\times 1ft[/tex]
Step-by-step explanation:
We are given that
Volume of box=4 cubic feet
Let x be the side of square base and h be the height of box
Volume of box=[tex]lbh=x^2h[/tex]
[tex]4=x^2h[/tex]
[tex]h=\frac{4}{x^2}[/tex]
Now, surface area of box,A=[tex]x^2+4xh[/tex]
[tex]A=x^2+4x(\frac{4}{x^2})=x^2+\frac{16}{x}[/tex]
[tex]\frac{dA}{dx}=2x-\frac{16}{x^2}[/tex]
[tex]\frac{dA}{dx}=0[/tex]
[tex]2x-\frac{16}{x^2}=0[/tex]
[tex]2x=\frac{16}{x^2}[/tex]
[tex]x^3=8[/tex]
[tex]x=2[/tex]
[tex]\frac{d^2A}{dx^2}=2+\frac{32}{x^3}[/tex]
Substitute x=2
[tex]\frac{d^2A}{dx^2}=2+\frac{32}{2^3}=2+4=6>0[/tex]
Hence, the area of box is minimum at x=2
Therefore, side of square base,x=2 ft
Height of box,h=[tex]\frac{4}{2^2}=1 ft[/tex]
Hence, the dimension of box=[tex]2ft\times 2ft\times 1ft[/tex]
Hi, can you please help me? 1 Over a period of 3 hours, 190 leaves fell from a tree. At this rate, about how many leaves fell every hour? (Round your answer to the nearest whole number.)
A. 60 leaves per hour
B. 72 leaves per hour
C. 75 leaves per hour
D. 63 leaves per hour
question 2:Mrs. Hill drove a total of 252 miles and used 12 gallons of gasoline. What is the unit rate?
A. 16 miles per gallon
B. 12 miles per gallon
C. 21 miles per gallon
D. 32 miles per gallon
Answers
Answer:
D.63 leaves
Step-by-step explanation:
Divide the given number of leaves by the time it took that many to fall
190/3=63.33 which rounds down to 63
Question #2
21 Miles per gallon
Divide the number of gallons by the amount of gas to get miles per gallon.
252/12=21 miles per gallon
michiko bought pens for $3.85 and pencils for $1.25 how much did she spend all together?
Answers
Answer:
5.1 :)
Step-by-step explanation:
what a ratio of 4 days to 36 hours
Answers
Answer:
4:36
24 x 4:36
96:36
8:4
1day = 24 hours
Step-by-step explanation:
You are skiing down a mountain with a vertical height of 650 feet. The distance from the top of the mountain to the base is 1300 feet. What is the angle of elevation from the base to the top of the mountain
Answers
Answer:
The angle of elevation from the base to the top of the mountain is 30°.
Step-by-step explanation:
Given: Vertical height of mountain is 650 feet and the distance from the top of the mountain to the base is 1300 feet.
To find: The angle of elevation from the base to the top of the mountain.
Let AB be the height of mountain and BC be the base.
Then, according to question, AB=650 feet and AC=1300 feet.
Let ∠ACB=[tex]\Theta[/tex].
Then, in ΔABC,
[tex]sin\Theta=\frac{AB}{AC}[/tex]
⇒[tex]sin\Theta=\frac{650}{1300}[/tex]
⇒[tex]sin\Theta=\frac{1}{2}[/tex]
⇒[tex]\Theta=30[/tex]°
Hence, the angle of elevation from the base to the top of the mountain is 30°.
Tay used 52 fruits altogether,
Here are two equations, where x is the number of apples
and y is the number of strawberries:
y = 3x
52 = x+y
How many of each type of fruit did Tay use?
I need helpppppppp
Answers
Answer: x=13,y=39
Step-by-step explanation: y=3x,x+y=52
x+3x=52
4x=52
x=52/4
x=13
y=3(13)
y=39
Evaluate the expression 9-3÷1/3+1
A. 9
B. 3
C. 1
D. 19
Answers
P- none
E- none
M- none
D- (3/1/3=1)
AS- 9-1+1=9
The answer is A.
Mrs. Campos is making cupcakes for a bake sale. She uses the equation c = 0.55x to determine the cost, c, for x cupcakes. Which best represents the constant rate at which cupcakes are sold at the bake sale?
55 cupcakes per dollar
$0.55 per cupcake
$4 per cupcake
4 cupcakes per dollar
Answers
A dog walker charges a flat fee of $20 to all of his clients for coming to walk their
dogs. He then charges a fee of $12 per dog he has to walk. Write a linear equation to
model this scenario.
Answers
Answer:
12(x) + 20
Step-by-step explanation:
x represents the amont of dogs and the +20 is the flat fee.
Which is the simplified form of ,-7 +5-12?
구
12
0 - - s12
s12
0 +11
s12
Answers
Yeah I think
Brayden is going to an amusement park. The price of admission into the park is $35,
and once he is inside the park, he will have to pay $2 for every ride he rides on. How
much money would Brayden have to pay in total if he goes on 15 rides? How much
would he have to pay if he goes on r rides?
Answers
35+30=65
He would pay 65 if he rode 15 rides
Answer: $65; $35+r•2
Step-by-step explanation:
So if every ride Brayden goes on costs $2 and he rides 15 rides, 2•15= $30 from rides alone. Then you add the $35 from admission to that number to get $65. This works for any amount of rides, just change the number to how many rides he goes on and use the same formula, 35+r•2 where r equals the number of rides ridden.
Find the surface area of this triangular prism 18cm 30cm 24 cm 7cm
Answers
Answer:
936
Step-by-step explanation:
18*24=432
24*7=168
30*7=210
18*7=126
432+168+210+126
=936
20 POINTS (Again) Helppp Hurry!!
Answers
Answer:
6
Step-by-step explanation:
Answer:
m∠5=34°
Step-by-step explanation:
angle 1 is a corresponding angle to angle 5 therefore they are congruent
Write a four digit whole number that is divisible by 2. Use a divisibility rule and explain how you know that your number
Is divisible by 2
Answers
Answer:
4894
Step-by-step explanation:
I know that it is divisible by 2, because it is an even number, and also the one's digit has 4, which is divisible by 2.
hope this helps :3
Answer:
2344
Step-by-step explanation:
I know that it is divisible by 2 because the digit in the ones place
2344
is an even number so that makes it divisible by 2.
I HOPE IT HELPS!
WILL GIVE BRAINLIEST
Answers
the answer is 162
(to add more letters)
help pleeaseee? ty babez
Answers
Answer: I think it’s 1/10
Step-by-step explanation:
Answer:
1/5
Step-by-step explanation:
3-2=1
10-5=5
hope this helps