Where x is the horizontal distance in feet from the point at which the ball is thrown.How far from the child does the ball strike the ground?
Answers
To calculate the maximum distance that the ball takes, we can use the first and second derivatives of y to find out this. We have:
[tex]\begin{gathered} y=-\frac{1}{14}x^2+4x+3 \\ \Rightarrow y^{\prime}=-\frac{2}{14}x+4=-\frac{1}{7}x+4 \\ \Rightarrow y^{\doubleprime}=-\frac{1}{7} \end{gathered}[/tex]Using the second derivative criterion, we have that y'' < 0, therefore, we have a maximum in the root of the first derivative. For that, we get the following:
[tex]\begin{gathered} y^{\prime}=0 \\ \Rightarrow-\frac{1}{7}x+4=0 \\ \Rightarrow\frac{1}{7}x=4 \\ \Rightarrow x=7\cdot4=28 \\ x=28 \end{gathered}[/tex]Therefore, at x=28 is where the maximum distance is. Now we only substitute x=28 in y to find out:
[tex]\begin{gathered} y=-\frac{1}{14}(28)^2+4(28)+3 \\ \Rightarrow y=-\frac{1}{14}(784)+112+3 \\ \Rightarrow y=-56+112+3=59 \\ y=59 \end{gathered}[/tex]Finally, we have that the ball will go 59 feet from the child
Related Questions
A homeowner has decided to fill in his pool. The pool is rectangular and measures 20ft wide, 40ft long, and 5.5ft deep throughout. Each cubic yard of fill dirt cost $12. How much will it cost to fill the pool?
Answers
The volume of the pool is
[tex]20ft\text{ }\times40ft\text{ }\times5.5ft=4400ft^3[/tex]a cubic foot is 0.037 cubic yards.
thus
[tex]4400ft^{3^{}}^{}=4400\times0.037=162.8yd^3[/tex]but a cubic yard of dirt costs $12, and we need 162.8 cubic yards.
that would cost
[tex]12\times162.8=\text{ \$1953.6}[/tex]Assume that random guesses are made for six multiple-choice questions on a test with five choices for each question so that there are n equals six trials each with the probability of success (correct) given by P equals 0.20. Find the probability of no correct answers.
Answers
Given in the question:
a.) Random guesses are made for six multiple-choice questions.
b.) There are five choices for each question.
c.) There are n equals six trials each with the probability of success (correct) given by P equals 0.20.
We will be using the Binomial Probability Formula:
[tex]P(X=k)=(_nC_k)(p^k)(1-p)^{n-k}[/tex]Where,
n = Number of trials = 6
P = Probability of success = 0.20
X = Correct answers
Let's evaluate the definition of binomial probability at k = 0 since we are tasked to find the probability of no correct answers.
[tex]P(X=0)=(_6C_0)(0.20^0)(1-0.20)^{6-0}[/tex][tex]P(X=0)\text{ = (}\frac{6!}{0!(6-0)!})(0.20^0)(0.80^6)^{}^{}[/tex][tex]P(X=0)\text{ = }0.262144\text{ }\approx\text{ 0.26}2[/tex]Therefore, the probability of no correct answers is 0.262 or 26.20%.
-(1 – 7a) = 3(8a - 6)
Answers
ANSI’s bought 3 1/2 yards of ribbon she had 2 feet 10 inches of ribbon left after trimming some curtains how many inches did she used to trim the curtains
Answers
With the help of conversion units, we know that 56 inches of ribbon was used in the curtains.
What is a conversion unit?If you want to change the units of a measured quantity without changing the value, you can do so by using a conversion factor, which is an expression representing the relationship between the units. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).So, inches of ribbon Ansi used in curtains:
1 yard = 36 inches
Now,
3½6+1/25/22.5Now, 2.5 yards in inches:
2.5 × 36 = 90 inchesNow, 1 foot = 12 inches.
Then, 2 feet and 10 inches:2 × 12 + 1024 + 1034 inchesInches of ribbon used:
90 - 34 = 56 inchesTherefore, with the help of conversion units, we know that 56 inches of ribbon was used in the curtains.
Know more about conversion units here:
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Select the correct answer. What is the difference of the values of the two variables in this system of equations? y= 2x + 1 x + 3y = 10 O A. 0 B. 1 KD C. 2 KD D. 3
Answers
According to the given data we have the following equation:
2x + 1 x + 3y = 10
There are two types of variables in the equation above.
The variable x and the variable y
In order to calculate the difference of the values of the two variables we would make the following:
First we would sum elements of variable x
variable x=2x + 1x=3x
variable y=3y
Therefore, the difference of the values=3x-3y=0
So, The right answer would be A, the value is 0.
J is the midpoint of HK . What are HJ, JK, and HK?
Answers
HJ=25
JK=25
HK=50
Explanation
Step 1
J is the midpoint, it means
[tex]HJ=JK[/tex]Step 2
replace andsolve for x
[tex]\begin{gathered} HJ=JK \\ 9x-2=4x+13 \\ \text{subtract 4x in both sides} \\ 9x-2-4x=4x+13-4x \\ 5x-2=13 \\ add\text{ 2 in both sides} \\ 5x-2+2=13+2 \\ 5x=15 \\ divide\text{ both sides by 5} \\ \frac{5x}{5}=\frac{15}{5} \\ x=3 \\ \end{gathered}[/tex]Step 3
finally replace the valure of X to find HJ and JK
[tex]\begin{gathered} HJ=JK=9x-2=9\cdot3-2=27-2=25 \\ HJ=25 \\ JK=25 \\ then \\ HK=HJ+JK=25+25 \\ \\ HK=50 \end{gathered}[/tex]I hope this helps you
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each series with the equivalent series written in sima notation.
Answers
Step 1
Given;
Step 2
[tex]3(5)^0+3(5)^1+3(5)^2+3(5)^3+3(5)^4[/tex][tex]3+15+75+375+1875[/tex][tex]\begin{gathered} 4(8)^0+4(8)^1+4(8)^2+4(8)^3+4(8)^4 \\ 4+32+256+2048+16348 \end{gathered}[/tex][tex]\begin{gathered} 2(3)^0+2(3)^1+2(3)^2+2(3)^3+2(3)^4 \\ 2+6+18+54+162 \end{gathered}[/tex][tex]\begin{gathered} 3(4)^0+3(4)^1+3(4)^2+3(4)^3+3(4)^4 \\ 3+12+48+192+768 \end{gathered}[/tex]Answer:
Marc se come un sándwich de huevo para el desayuno y una hamburguesa grande para el almuerzo todos los días.
El sándwich de huevo tiene 250 calorías. Si Marc come 5,250 calorías en el desayuno y almuerzo en toda la
semana en total, ¿cuántas calorías tiene una hamburguesa grande?
lón de juegos la primera vez ella ganó 60 boletos. La segunda vez,
Answers
Answer:Hay 500 calorías en una Big Burger.
Step-by-step explanation:
En una semana (7 días), Mark come 7 sándwiches de huevo, que son 1750 calorías. Reste la cantidad total de calorías que consumió por la cantidad de calorías consumidas a través de sándwiches de huevo; 5250-1750=3500. 3500 es el número total de calorías que Mark consumió al comer una Big Burger todos los días durante 7 días. Divide 3500 entre 7 = 500. Hay 500 calorías en una Big Burger.
A skating rink attendant monitored the number of injuries at the rink over the past year. He tracked the ages of those injured and the kinds of skates worn during injury. In-line skates Roller skates Age 8 11 10 Age 10 4 9 Age 12 3 16 What is the probability that a randomly selected injured skater was not age 12 and was not wearing roller skates? Simplify any fractions.
Answers
Given data:
The given table is shown.
The expression for the probability of that a randomly selected injured skater was not age 12 and was not wearing roller skates is,
[tex]undefined[/tex]Students in a science class recorded lengths of a stretched spring as shown in the table. Find the rate of change and explain what it means for this situation.
Answers
To find the rate of change;
Rate of change = change in y / change in x
= 10-0/ 2-0
=10/2
=5/1
=5
This means that the increase in w
Dustin boat traveled 36 miles downstream in three hours. The same boat traveled 30 miles upstream in five hours. What is the speed of the boat and the speed of the current
Answers
Answer:
The speed of the boat is 9 miles/hour and the speed of the current is 3 miles/hour
Explanation:
Let's call x the speed of the boat and y the speed of the current.
The distance traveled is equal to the speed times the time, so the boat traveled 36 miles in three hours and we can write the following equation
(x + y)3 = 36
3(x + y) = 36
because when the boat traveled downstream, the total speed is the sum of x and y.
On the other hand, the boat traveled 30 miles upstream in 5 hours, so
(x - y)5 = 30
5(x - y) = 30
Therefore, the system of equations is
3(x + y) = 36
5(x - y) = 30
Solving the first equation for x, we get
[tex]\begin{gathered} 3(x+y)=36 \\ \\ \frac{3(x+y)}{3}=\frac{36}{3} \\ \\ x+y=12 \\ x+y-y=12-y \\ x=12-y \end{gathered}[/tex]Now, we can replace this expression on the second equation as follows
[tex]\begin{gathered} 5(x-y)=30 \\ \\ {\frac{5(x-y)}{5}}=\frac{30}{5} \\ \\ x-y=6 \\ \\ \text{ Replacing x = 12 - y} \\ 12-y-y=6 \\ 12-2y=6 \\ 12-2y-12=6-12 \\ -2y=-6 \\ \\ \frac{-2y}{-2}=\frac{-6}{-2} \\ \\ y=3 \end{gathered}[/tex]Then, the value of x is
x = 12 - y
x = 12 - 3
x = 9
So, the speed of the boat is 9 miles/hour and the speed of the current is 3 miles/hour
due today, i will mark as brainliest!
Answers
Step-by-step explanation:
y=2x-20 is the right answer mark brainliest
Answer:
[tex]\sf Y=2X-20[/tex]
Step-by-step explanation:
Given linear equation:
[tex]\sf X=\dfrac{1}{2}(20+Y)[/tex]
To express Y in terms of X, rearrange the equation to isolate Y.
Apply the distributive property of multiplication over addition:
[tex]\implies \sf X=\dfrac{1}{2} \cdot 20+\dfrac{1}{2} \cdot Y[/tex]
[tex]\implies \sf X=\dfrac{20}{2}+\dfrac{Y}{2}[/tex]
[tex]\implies \sf X=10+\dfrac{Y}{2}[/tex]
Subtract 10 from both sides of the equation:
[tex]\implies \sf X-10=10+\dfrac{Y}{2}-10[/tex]
[tex]\implies \sf X-10=\dfrac{Y}{2}[/tex]
Multiply both sides of the equation by 2:
[tex]\implies \sf 2(X-10)=2 \cdot \dfrac{Y}{2}[/tex]
[tex]\implies \sf 2(X-10)=Y[/tex]
[tex]\implies \sf Y=2(X-10)[/tex]
Apply the distributive property of multiplication over subtraction:
[tex]\implies \sf Y=2\cdot X- 2\cdot 10[/tex]
[tex]\implies \sf Y=2X- 20[/tex]
Which is the better deal? Cheerios12 oz. for $ 1.9936 oz. for $2.5948 oz. for $3.9960 oz. $4.59
Answers
To calculate which is the best deal we must standardize all prices and compare them.
To do this we will divide the value by the number of ounces they have and thus choose the best one.
1.
[tex]\frac{1.99}{12}=0.165[/tex]2.
[tex]\frac{2.59}{36}=0.071[/tex]3.
[tex]\frac{3.99}{48}=0.083[/tex]4.
[tex]\frac{4.59}{60}=0.076[/tex]The price list by ounces would be as follows.
0.165
0.071
0.083
0.076
Best deal is number 2 0.071
how do i find out if a table is a linear function? i know the formula i just dont know how to figure out if its linear, thanks!
Answers
Answer:
Table 3
Explanation:
A linear function has a constant slope.
To determine if the table represents a linear function, find the slope for two different pairs of points.
Table 1
Using the points (1,-2), (2,-6)
[tex]\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-6-(-2)}{2-1}=-6+2=-4[/tex]Using the points (2,-6), (3,-2)
[tex]\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-2-(-6)}{3-2}=-2+6=4[/tex]The slopes are not the same, thus, the function is not linear.
Table 3
Using the points (1,-2), (2,-10)
[tex]\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-10-(-2)}{2-1}=-10+2=-8[/tex]Using the points (2,-10), (3,-18)
[tex]\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-18-(-10)}{3-2}=-18+10=-8[/tex]The slopes are the same, thus, the function is linear.
Table 3 is the correct option.
1 1 2. Consider 2 divided by 2 (a) Write a real-world problem for the division. (b) Create a model or write an equation for the division. (C) Find the quotient for the real-world problem in part (a). Show your work or explain your reasoning. Answer:
Answers
We will have the following:
a) His parents spent:
[tex]2.49\cdot6=14.94[/tex]So they spent $19.94.
b) They will spent the following in rental:
[tex]\frac{150}{8}=18.75[/tex]So, the hourly rate $18.75.
c) We will determine the amount spent:
[tex]182.53-150-14.49=18.04[/tex]So, it would be $18.04.
The average temperature on the planet A is 162°C. Convert this temperature to degrees Fahrenheit. Round to the nearestdegreeUse the formula F =+ 32162° Celsius is equivalent toFahrenheit.
Answers
Using the formula:
[tex]F=\frac{9}{5}c+32[/tex]We get:
[tex]\begin{gathered} F=\frac{9}{5}(162)+32 \\ F=323.6 \end{gathered}[/tex]162°C is equal to 323.6 F
slove for y(13x-27)(9y + 19)(10x+6)
Answers
To obtain the value of y, we need to obtain the value of x first
Step 1: Finding x
(13x - 27) and (10x + 6) are equal (Alternate exterior angles)
so we can equate both angles
13x - 27 = 10x + 6
13x - 10x = 27 + 6
3x = 33
Divide both sides by 3
x = 33/ 3
x = 11
Step 2: Finding y
(9y + 19) and (10x + 6) are supplementary, hence they add up to 180
9y + 19 + 10x + 6 = 180
9y + 10x + 19 + 6 = 180
9y + 10x + 25 = 180
9y + 10x = 180 - 25
9y + 10x = 155
9y = 155 - 10x
substitute the value of x = 11 from step 1 into the equation
9y = 155 - 10 x 11
9y = 155 - 110
9y = 45
divide both sides by 9
y = 45/9
y = 5
what is 6 5/6 as a decimal
Answers
the answer for 6 5/6
6.83
Evaluate the expression when y= -4.y²-7y+2
Answers
Put y = -4 into the expression below:
[tex]y^2-7y+2[/tex]Hence,
[tex]\begin{gathered} y^2-7y+2=(-4)^2-7(-4)+2 \\ =16+28+2 \\ =46 \end{gathered}[/tex]Therefore, the value of the expression when y = -4 is 46
HELPPPP MEEEEEE PLEASEEEEhey tutor how you doing doing I struggle with math so much.
Answers
Answer:
[tex]m\measuredangle8=110^o[/tex]Explanation:
The angles 4 and 8 are equal; therefore,
[tex]m\measuredangle8=m\measuredangle4[/tex][tex]3x+20=x+80[/tex]Subtracting x from both sides gives
[tex]2x+20=80[/tex]Subtracting 20 from both sides gives
[tex]2x=80-20[/tex][tex]2x=60[/tex]Finally, dividing both sides by 2 gives
[tex]\boxed{x=30.}[/tex]With the value of x in hand, we now find the measure of angle 8.
[tex]m\measuredangle8=x+80[/tex][tex]m\measuredangle8=30+80[/tex][tex]\boxed{m\measuredangle8=110^o\text{.}}[/tex]Hence, the measure of angle 8 is 110.
I would appreciate some help here, i’m bad at math
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
Considering the given line,
m = - 3 and c = - 1
By substituting these values into the slope intercept equation, the equation of the line is
y = - 3x - 1
We would substitute values of x into the equation and solve for corresponding values of y. It is shown below
For x = - 2, y = - 3 * - 2 - 1 = 6 - 1 = 5
For x = - 1, y = - 3 * - 1 - 1 = 3 - 1 = 2
For x = 0, y = - 3 * 0 - 1 = 0 - 1 = - 1
For x = 1, y = - 3 * 1 - 1 = - 3 - 1 = - 4
For x = 2, y = - 3 * 2 - 1 = - 6 - 1 = - 7
We would plot the corresponding x and y values on the horizontal and vertical axes of the graph respectively. The graph is shown below
Sue receives $7 per hour when she works at the book store. Last week she earned $259.How many hours did she work at her job?
Answers
1 hour = $7
Number of hours = Amount/7
Therefore, 259/7 = 37 hours
Solution: Sue worked for 37 hours last week.
Find the 38th term 359,352,345
Answers
Let's begin by listing out the information given to us:
1st term = 359, 2nd term = 352, 3rd term = 345
[tex]\begin{gathered} 359,352,345\ldots x_n \\ x_1=359,x_2=352,x_3=345 \\ x_1-x_2=x_2-x_3\Rightarrow359-352=352-345\Rightarrow7=7 \\ 7=7 \end{gathered}[/tex]This is an Arithmetic Progression (A.P.)
[tex]\begin{gathered} x_1=359 \\ x_2=359-7(2-1)\Rightarrow359-7(1)=359-7=352 \\ x_3=359-7(3-1)\Rightarrow359-7(2)=359-14=345 \\ x_n=x_1-7(n-1) \\ n_{38}=x_1-7(38-1)=359-7(37)=359-259=100 \\ n_{38}=100 \end{gathered}[/tex]Your sock drawer has 4 pairs of pink socks, 2 pairs of white socks, and 7 pairs of black socks. What is the probability that if you choose at random withough replacement you will not choose black socks 2 days in a row? a 1/12b 2/13c 3/8d 5/26
Answers
SOLUTION:
Case: Probability
Method:
To select socks that are not black without replacement,
Since there are a total of 6 pairs that are not black (NB)
[tex]\begin{gathered} Pr(NB) \\ =\frac{6}{13}\times\frac{5}{12} \\ =\frac{5}{26} \end{gathered}[/tex]Final answer:
5/26
the chance of you having the same DNA as another person (other than an identical twin) is approximately 1 in 10 trillion (one trillion is a 1 by 12 zeros). Given the fraction,express this very small number using a negative power of 101/10,000,000,000,000
Answers
We are asked to write the quotient : 1/10,000,000,000,000 in a notation with powers of ten. This is called "scientific notation".
when we perform the division of 1 by that enormous number, we get:
0.0000000000001
This can be represented by a 10 to a negative exponent. Notice that we have 13 zeros in the denominator (which implies that we have to divide 13 times by ten)
so we can write the answer as: 1 * 10^(-13)
which with the appropriate equation editor becomes:
[tex]1\cdot10^{-13}[/tex]the base 10 with exponent -13 (negative 13)
1. An account is opened with a balance of $2800earning 4.25% simple interest. What will be thebalance in the account in 30 years?
Answers
Answer:
$6370
Explanation:
The simple interest formula gives us the final amount A given the principal amount P:
[tex]A=P(1+rt)[/tex]where r is the interest rate and t is the time interval.
Now in our case we have
P = 2800
r = 4.25/100
t = 30 years
therefore, the above formula gives
[tex]A=2800(1+\frac{4.25}{100}\cdot30)[/tex]which simplifies to give
[tex]\boxed{A=\$6370}[/tex]Hence, the account balance after 30 years will be $6370.
Need help solving question 34 via expanding and simplifying thanks
Answers
34. The equation is given as
[tex](x+y)^2-x(2-y)[/tex]Solving the equation by expanding and simplifying.
Use the identity,
[tex](a+b)^2=a^2+b^2+2ab[/tex][tex]x^2+y^2+2xy-2x+xy[/tex][tex]x^2+y^2-2x+3xy[/tex]Hence the answer is
[tex]x^2+y^2-2x+3xy[/tex]T-Mobile charges a flat fee of $20 plus $10 per Gig of data used per month. AT&T charges $60 for an unlimiteddata use. How many Gigs of data would you have to use so that the cost will be the same for both companies?
Answers
For this case we can set uo an equation given by:
[tex]y=10x+20[/tex]Where y represent the final cost. x the number of Gig used and for this case we can set up the following equation:
[tex]60=10x+20[/tex]And solving for x we got:
[tex]x=\frac{60-20}{10}=\frac{40}{10}=4[/tex]And the final answer for this case woudl be 4 Gig of data used
diana and her classmates are reading the same book.on Monday, diana started to write down the number of pages she has left to read at the end of each day from Monday through Thursday, which person is reading the same number of pages per day as diana.
Answers
From the diana table we can conclude:
[tex]\begin{gathered} x1=187 \\ x2=181 \\ x3=175 \\ x4=169 \\ x2-x1=x4-x3=6 \end{gathered}[/tex]She's reading 6 pages per day.
Since:
[tex]\begin{gathered} y1=180 \\ y2=174 \\ y3=168 \\ y4=162 \\ y2-y1=y4-y3=6 \end{gathered}[/tex]Keith is also reading 6 pages per day.
Use the Trapezoidal Rule to approximate ∫43ln(x2+9) dx using n=3. Round your answer to the nearest hundredth.
Answers
The Trapezoidal rule formula is given to be:
[tex]\begin{gathered} \int_a^bf(x)dx\approx\frac{\triangle x}{2}(f(x_o)+2f(x_1)+2f(x_2)+2f(x_3)+...+2f(x_{n-1})+f(x_n) \\ where \\ \triangle x=\frac{b-a}{n} \end{gathered}[/tex]The question gives:
[tex]\begin{gathered} f(x)=\ln(x^2+9) \\ a=3 \\ b=4 \\ n=3 \\ \therefore \\ \triangle x=\frac{1}{3} \end{gathered}[/tex]Therefore, divide the interval into n = 3 subintervals of length 1/3 with the following endpoints:
[tex]a=3,\frac{10}{3},\frac{11}{3},4[/tex]Evaluate the function at the endpoints:
[tex]\begin{gathered} f(x_0)=f(3)=2.89 \\ 2f(x_1)=2f(\frac{10}{3})=6.00 \\ 2f(x_2)=2f(\frac{11}{3})=6.22 \\ f(x_3)=f(4)=3.22 \end{gathered}[/tex]Sum up the calculated values and multiply by Δx/2:
[tex]\Rightarrow\frac{1}{3\times2}(2.89+6.00+6.22+3.22)=3.06[/tex]Therefore, the answer will be:
[tex]\int_3^4\ln(x^2+9)dx\approx3.06[/tex]