if a ball is thrown directly upward with a velocity of 40 ft/s, its height (in feet) after t seconds is represented by 40t-16t^2. what is the maximum height attained by the ball?
Answers
[tex]\bf h(t)=40t-16t^2\implies h(t)=-16t^2+40t+0 \\\\\\ \begin{array}{llll} \qquad \textit{in feet}\\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\textit{initial velocity of the object}\\ \qquad 40\\ h_o=\textit{initial height of the object}\\ \qquad 0\\ h=\textit{height of the object at "t" seconds} \end{cases}[/tex]
[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llll} y = &{{ -16}}x^2&{{ +40}}x&{{ +0}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left( \stackrel{\textit{it took this long}}{-\cfrac{40}{2(-16)}}~~,~~\stackrel{\textit{to get this high}}{0-\cfrac{40^2}{4(-16)}} \right)\qquad \stackrel{\textit{maximum height}}{0-\cfrac{40^2}{4(-16)}}[/tex]
The maximum height attained by the ball is 25 feet.
Explanation:The maximum height attained by the ball can be found by determining the vertex of the quadratic equation representing the height of the ball. In the given equation 40t - 16t^2, the coefficient of t^2 is negative, indicating a parabolic shape with a maximum point. The formula for the x-coordinate of the vertex is -b/2a, which in this case is -40/(2*(-16)) = 1.25 seconds. Substituting this value into the equation gives the maximum height: 40(1.25) - 16(1.25^2) = 25 feet.
Related Questions
x3-27i=0 solve for the root equation
Answers
Add 27i to both sides
x * 3 - 27i + 27i = 0 + 27i
Then simplify
The form x * 3 = 27i
Divide both sides by 3
x * 3 27i
____ = ____
3 3
And now simplify to get your final answer
x = 9i
Line IJ has an equation of a line y = −3x − 8. Which of the following could be an equation for a line that is parallel to line IJ?
A) y=3x+7
B) y=1/3x+7
C) y= -3x+7
D) y= -1/3x+7
Answers
C) y = -3x +7
Step-by-step explanation:It's all about recognizing patterns.
The form of the equation is ...
... y = mx + b
In this form, the coefficient of x, which we called "m" in the above, is the slope of the line. When two lines have the same slope, they are parallel. So, we're looking for an equation that has an x-coefficient of -3, the same as in the given equation.
The coefficient of x in selection C is -3, so that is our answer choice.
... C) y = -3x +7
Answer:
y = -3x +7 which is option C
got it right on my test.
Jane has a 5 × 7-inch photograph that she wants enlarged to a 10 × 14-inch photograph.
What is the scale factor from the original photograph to the enlarged photograph?
Answers
compare the 5 and 10 dimension then the 7 and 14 dimensions
10/5 =2
14/7 =2
they both are the same ratio/factor
the factor is 2
Answer:
2:1
Step-by-step explanation:
it asks for the scale since 5 x 2 = 10 and 7 x 2 = 14
the scale is 2 : 1
Billy wants to live in the area defined by y < 3x − 6. Explain how you can identify the houses in which Billy is interested in living. (2 points)
Answers
to graph an inequality, you pretty much first off, need to graph the "equality" or equation, so for y < 3x − 6, first off, graph the line y = 3x − 6.
and then you do a "true" or "false" check.
now, if you look at the line below, it splits the grid in two sections, so, let's check a point in either section, if one is false, the other is true and the other way around.
so, let's check the region on the left-hand-side, hmmmm say point 0,0, the origin.
y < 3x - 6
y = 0, x = 0 thus
0 < 3(0) - 6
0 < -6 <--- now, is that really true? is 0 lesser than -6? not quite, is false.
recall that on the negative side, the closer to 0, the larger the value, so -1 is much larger than -1,000,000.
because the point 0,0 yielded a false inequality, that region is the "false region" and thus not shaded, therefore, the other side must be the "true region", and thus we shade that then.
we can run a quick check on that btw, say on point 4,4
y =4, x = 4 thus
4 < 3(4) - 6
4 < 12 - 6
4 < 8 <---- yeap, is true, 4 is lesser/smaller than 8.
hmm ohh yes, the line needs to be dashed for a < or >, because it "has that boundary but it does not include it", unlike ⩽ and ⩾, which is a solid line, because it has that boundary and it includes it too.
what is the sum of (1-5q)+2(2.5q+8)
Answers
Answer:
17
Step-by-step explanation:
Eliminating parentheses, we have ...
... 1 - 5q +2·2.5q +2·8
... = 1 -5q +5q +16 . . . . . carry out the multiplication
... = q(-5+5) +(1 +16) . . . . group like terms
... = q·0 +17 . . . . . . . . . . . combine like terms
... = 17
What produces a graph in a straight line
Answers
For ex: x = 3, y = 4, x = -1.5, y = -2/3
Also two variables linear equations with degree of 0 or 1 (Each term) shows always graph in straight line,
For ex: x + y = 5, 2x - 4y = 7 etc.
Which ordered pairs are solutions to the inequality y−4x≥−5 ?
Select each correct answer.
(−2, 1)
(−4, 2)
(4, 0)
(5, −2)
(1, −1)
Answers
y - 4x ≥ - 5
To find the correct answer, we should test each answer as shown below.
Test (-2. 1):
y - 4x = 1 - 4(-2) = 9
It is ≥ -5.
CORRECT
Test (-4, 2)
y - 4x = 2 - 4(-4) = 18
It is ≥ -5
CORRECT
Test (4,0)
y - 4x = 0 - 4(4) = -16
It is < -5
INCORRECT
Test (5,-2)
y - 4x = -2 - 4(5) = -22
It is < -5
INCORRECT
Test (1,-1)
y - 4x = -1 - 4(1) = -5
It is ≥ -5.
CORRECT
Answer: The correct answers are
(-2,1)
(-4,2)
(1,-1)
Answer:
The correct answers are
(-2,1)
(-4,2)
(1,-1)
Step-by-step explanation:
hope dis help u guys, habe a good rest of ya day!
put these in order from the smallest
6² 3 to the power of 4 2 to the power of 5 5³
Answers
A = 6 to the power of 2, which is 36
B = 3 to the power of 4, which is 81
C = 2 to the power of 5, which is 32
D = 5 to the power of 3, which is 125
Therefore, the order is C, A, B, D
Hope that helped!
From least to greatest.
1. 6^2= 36
2. 3^4 = 81
3. 5^3 = 125
4. 2^5 = 128
What is the value of x?
Answers
Alice leaves her house and walks to school. She walks 45 meters south and 336 meters east. How far is Alice from her house?
Answers
Select all numbers that are irrational. 1049−−√ 3.14 π 0.5
Answers
The answer would be 10/49 and π which are irrational numbers from the definition of the irrational number.
What is an irrational number?It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.
A rational number is a sort of real number that has the form p/q and does not equal zero.
It is given that:
The numbers are:
10/49, 3.14, π, 0.5
As we know, from the definition of the irrational, the numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.
The numbers 10/49 and π are irrational numbers.
Thus, the answer would be 10/49 and π which are irrational numbers from the definition of the irrational number.
Learn more about the irrational number here:
brainly.com/question/17450097
#SPJ2
Emma uses 5 ounces of milk to make a shake.she want to buy enough milk to make 7 shake and she want to buy the smallest size container ok milk that she can.should she buy a pint a quart or gallon of milk?justify your answer Help
Answers
Sam opened a savings account with an initial deposit of $2,000. Since then, he has never made any other deposits or withdrawals. His savings account earns 0.4% interest monthly and an annual bonus of 1.5% interest. Which equation gives the approximate amount, A(x), he has in his savings account as a function of x, the number of years since his initial deposit?
A(x) ≈ 2,000 + (1.059)x3
A(x) ≈ 2,000(1.019)x2
A(x) ≈ 2,000(1.065)x
A(x) ≈ 2,000(1.059)x2
Answers
Answer:
Third option:
[tex]A(x)\approx 2,000(1.065)^x[/tex]
Step-by-step explanation:
Notice if we invest 2,000 then the first month then after the first 0.4% interest is earned we will have in the account:
2,000(1+0.004) = 2,000(1.004)
I just applied the simple interest formula.
Then after the second month we will have:
[tex]2,000(1.004)(1.004) = 2,000(1.004)^2[/tex]
And so on each month.
So at the end of the first year (12 months) we have:
[tex]2,000(1.004)^{12}[/tex]
But we also earn an additional 1.5% in the year, so we will have:
[tex]2,000(1.004)^{12}(1.015)[/tex]
At the end of the second year we will have:
[tex]2,000[(1.004)^{12}(1.015)]^2[/tex]
At the end of the third year:
[tex]2,000[(1.004)^{12}(1.015)]^2[/tex]
And so on,
So if the number of years is denoted with x, at the end of x years we will have the following amount in the savings:
[tex]2,000[(1.004)^{12}(1.015)]^x[/tex]
We use our calculator to simplify that inside the brackets:
[tex](1.004)^{12}(1.015)=1.06481[/tex]
Rounding to the third decimal place we get: 1.065
So notice the amount in the savings after x years will be:
[tex]2,000(1.065)^x[/tex]
Since they want it in function notation we just write the A(x) that denotes the amount in the savings:
[tex]A(x)\approx 2,000(1.065)^x[/tex]
A scatterplot is produced to compare the size of a lake to the number of fish that are in it. There are 15 data points, each representing a different lake. The points are widely dispersed on the scatterplot with no pattern of grouping. Interpret what the results of the scatterplot tell you about the relationship between the two variables.
Answers
Based on the dispersion of the scatterplot, we can infer that there is no relationship between the variables.
Relationships in scatterplots Data points are used to predict relationships. If a line can be drawn based on these data points, then a relationship exists.The fact that these data points are dispersed however and offer no form of grouping, means that the variables are not related and show no correlational trend.
Find out more on scatterplots at https://brainly.com/question/2749543.
kalen's truck has a 60 gallon fuel tank The fuel gauge points to 1/4 how much fuel does he need to buy to fill the tank show Your work
Answers
One canned juice drink is 25% orange juice; another is 10% orange juice. How many liters of each should be mixed together in order to get 15L that is 17% orange juice
Answers
likewise, we'll use "y" of the 10% OJ, and it will end up with (10/100) *y or 0.10y of juice in it.
whatever "x" and "y" are, they must add up to 15 Liters, and the juice concentration on that mixture, must also be the sum of their sum concentration.
[tex]\bf \begin{array}{lccclll} &\stackrel{liters}{amount}&\stackrel{juice~\%}{quantity}&\stackrel{juice}{quantity}\\ &------&------&------\\ \textit{25\% juice}&x&0.25&0.25x\\ \textit{10\% juice}&y&0.10&0.10y\\ ------&------&------&------\\ mixture&15&0.17&2.55 \end{array} \\\\\\ \begin{cases} x+y=15\implies \boxed{y}=15-x\\ 0.25x+0.10y=2.55\\ ----------\\ 0.25x+0.10\left(\boxed{15-x} \right)=2.55 \end{cases} \\\\\\ 0.25x-0.10x+1.5=2.55\implies 0.15x=1.05\implies x=\cfrac{1.05}{0.15} \\\\\\ x=7[/tex]
how much will be it of the 10% juice? well, y = 15 - x.
write the equation of the line MN, which is formed by the points M(-3,5) and N(2,0)
Answers
Step 1
Find the slope of the given line
Let
[tex]M(-3,5)\ N(2,0)[/tex]
we know that
the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{0-5}{2+3}[/tex]
[tex]m=\frac{-5}{5}[/tex]
[tex]m=-1[/tex]
Step 2
Find the equation of the line
we know that
the equation of the line into point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-1[/tex]
point N [tex](2,0)[/tex]
substitute the values
[tex]y-0=-1(x-2)[/tex]
[tex]y=-x+2[/tex]
therefore
the answer is
[tex]y=-x+2[/tex]
Jemma has 24 balls. Out of the 24 balls,
12 are yellow, 4 are pink, and the rest
are red. What is the ratio of the number
of red balls to the number of balls that
are either yellow or pink?
Answers
208,000,478 in expanded form
Answers
What are 2 ways three people can share fifths?
Answers
Final answer:
Three people can share fifths by dividing one pie into five slices and each taking three, or dividing three pies into fifteen slices and each person getting one slice from each pie. Both methods ensure each person receives three-fifths of a pie.
Explanation:
Two ways that three people can share fifths involve division and allocation of pie (or any other divisible whole). One way is to take a single pie, divide it into five equal slices, and each person takes three slices. However, since we need to divide these among three people and a pie has only five slices, we'll end up with a fraction of a slice per person. The second way is to start with three pies, divide them so that there are a total of fifteen slices (five slices per pie), and then each person gets one slice from each pie, totaling three slices per person.
Here are two arithmetic representations of the scenarios:
First method: (3 slices/person) / 5 slices = 3/5 per personSecond method: 1 slice from each of 3 pies / 5 slices per pie = 3/5 per personWhether we are dealing with one pie or three, each person ends up with the same fraction of the total available pie: three-fifths.
A person made an estimate for a three–minute interval. the estimate was 241.5 seconds. what was the error of this estimate?
Answers
A seafood company sold 9,125 pounds of fish last month. If 6 seafood companies sold the same amount of fish, how much fish did the 6 companies sell last month in all ?
Answers
Mark earns $135 for selling a $1500 refrigerator. Which sale listed has the same commission rate? $36 commission on a $400 dryer or B) $40 commission on a $500 dryer sale C) $210 commission on $1400 oven sale d) $30 commission on a $600 freezer sale?
salelisted has the same commssion rate. ?
Answers
36/400 * 3.8 = 136.6/1520
40/500 * 3 = 120/1500
210/1400 (not even close)
30/600 * 3 = 90/1800 (not even close)
so the two answer choices that are close are A and B, A has the closest numbers to the original commission rate.
Answer:
Option A is the correct choice.
Step-by-step explanation:
We have been given that Mark earns $135 for selling a $1500 refrigerator.
Since proportions states that two fractions are equal , so we will use proportions to find the same commission rate with the listed price from our given choices.
We can set proportion for commission and listed price as:
[tex]\frac{\text{Commission}}{\text{Listed price}}=\frac{135}{1500}[/tex]
Let us compare our given choices one by one.
A. $36 commission on a $400 dryer.
[tex]\frac{36}{400}=\frac{135}{1500}[/tex]
Upon simplifying our proportion we will get,
[tex]\frac{9}{100}=\frac{9}{100}[/tex]
[tex]0.09=0.09[/tex]
We can see that commission rates for both items are equal, therefore, option A is the correct choice.
B. $40 commission on a $500 dryer sale.
[tex]\frac{40}{500}=\frac{135}{1500}[/tex]
Upon simplifying our proportion we will get,
[tex]\frac{2}{25}=\frac{9}{100}[/tex]
[tex]0.08\neq 0.09[/tex]
We can see that both commission rates are different, therefore, option B is not a correct choice.
C. $210 commission on $1400 oven sale.
[tex]\frac{210}{1400}=\frac{135}{1500}[/tex]
Upon simplifying our proportion we will get,
[tex]\frac{3}{20}=\frac{9}{100}[/tex]
[tex]0.15\neq 0.09[/tex]
Since the commission rates are different, therefore, option C is not a correct choice.
D. $30 commission on a $600 freezer sale.
[tex]\frac{30}{1400}=\frac{135}{1500}[/tex]
Upon simplifying our proportion we will get,
[tex]\frac{3}{140}=\frac{9}{100}[/tex]
[tex]0.0214\neq 0.09[/tex]
Since the commission rates are different, therefore, option D is not a correct choice.
At an automobile factory, 1849 parts are made in 4 hours. What is the average rate at which parts are made per hour?
Answers
or 1849 parts/ 4 hours, or 462.25 parts/hour, or (rounded off) 462 parts/hour.
Answer:
462.25
Step-by-step explanation:
At an automobile factory, the number of parts are made in 4 hours = 1849.
We have to calculate the average rate of production per hour.
We will divide the production of parts in 4 hours by 4 to get the number of parts made per hour.
The average rate of production in one hour = [tex]\frac{1849}{4}[/tex]
= 462.25/hour
462.25 parts are made per hour.
Chris answered 61/66 questions correctly. What is his test average to the nearest thousandth?
Answers
x=61*100/66=92.424
-20,480 , -5,120 , -1280 , -320 what goes next
Answers
- 1280/4 = -320
- 320/4 = - 80
how many fossil kits with 10 samples each have the same number of fossils as 30 fossil kits with 8 samples each?
Answers
Answer:
24 fossil kits.
Step-by-step explanation:
Given,
The number of fossil kits = 30,
the number of samples each has = 8,
So, the total samples = number of fossil kits × the number of samples contained by each kit
= 30 × 8
= 240,
Let x be the number fossil kits with 10 samples each,
Total samples = 10x
According to the question,
10x = 240
[tex]\implies x =\frac{240}{10}=24[/tex]
Hence, there would be 24 fossil kits with 10 samples each.
write a word problem that can be solved by ordering three decimals to thousandths.
Answers
[Solution: 5 / 2.6 = 1.923076923076923 millimeters or approximately 1.923 millimeters]
Daniel dives into a swimming pool. The height of his head is represented by the function h(t) = -8t(squared) - 28t + 60, where t is the time in seconds and h(t) is the height of his head, in inches. How many seconds will it take for Daniel's head to reach the surface of the pool?
Answers
Therefore:
-8t² - 28t + 60 = 0 To simplify, divide both sides by -4
2t² + 7t - 15 = 0
Consider the trinomial ax² + bx + c
To factor by grouping, we must find two numbers that multiply to equal AC (-30) and add up to B (7)
Two numbers that satisfy this are 10 and -3:
2t² + 10t - 3t - 15 = 0 Rewrite the equation using 10t and -3t
2t (t + 5) -3 (t +5) = 0 Regroup, then rewrite
(2t -3) (t+5) = 0
2t-3 = 0
2t = 3
t = 3/2
OR
t + 5 = 0
t = -5
We know t cannot be a negative number, so the answer is:
t = 3/2, or 1 and a half seconds
differentiate please..
y= √x +6 ÷ √x-6
Answers
[tex]\bf \cfrac{dy}{dx}=\cfrac{\frac{1}{2}x^{-\frac{1}{2}}~(\underline{\sqrt{x}}-6~-~\underline{\sqrt{x}}-6)}{(\sqrt{x}-6)^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{1}{2}x^{-\frac{1}{2}}(-12)}{(\sqrt{x}-6)^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{\frac{-12}{2\sqrt{x}}}{(\sqrt{x}-6)^2}\implies \cfrac{dy}{dx}=\cfrac{\frac{-6}{\sqrt{x}}}{(\sqrt{x}-6)^2}\implies \cfrac{dy}{dx}=\cfrac{-6}{\sqrt{x}(\sqrt{x}-6)^2}[/tex]