A small toy rocket is launched from a 32-foot pad. The height ( h, in feet) of the rocket t seconds after taking off is given by the formula h=−2t2+0t+32 . How long will it take the rocket to hit the ground?t=______(Separate answers by a comma. Write answers as integers or reduced fractions.)
Answers
Given: A small toy rocket is launched from a 32-foot pad. The height (h, in feet) of the rocket t seconds after taking off is given by the formula
[tex]h=-2t^2+0t+32[/tex]Required: To find out how long will it take the rocket to hit the ground.
Explanation: When the rocket touches the ground its height will be zero i.e.,
[tex]\begin{gathered} -2t^2+0t+32=0 \\ 2t^2=32 \\ t^2=16 \end{gathered}[/tex]Which gives
[tex]t=\pm4[/tex]Neglecting the negative value of t since time cannot be negative. We have
[tex]t=4\text{ seconds}[/tex]Final Answer: Time, t=4 seconds.
Related Questions
A landscape supply business charges $35 to deliver mulch. The cost of the mulch is
$29 per cubic yard. Write a linear equation to find the cost of having x cubic yards of
mulch delivered to a site.
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The linear function to represent the number of mulch delivered to a site is y = 29x + 35
What is a linear function?In mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
For this question, we can represent the cost of having x cubic yards of mulch delivered to a site. For a standard linear function, it can be represented as y = mx + c
m = slope
c = intercept
We can use this concept to write a linear function to represent this problem:
y = mx + c
y = 29x + 35
In this case, the slope is 29 and the intercept is 35. The slope in this situation is the cost of the mulch and the amount charged by the business is the intercept.
The equation representing this problem is y = 29x + 35
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consider the function f(x) whose second derivative is f' '(x)=4x+4sin(x). If f(0)=3 and f'(0)=4, what is f(5)?
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Problem: consider the function f(x) whose second derivative is f' '(x)=4x+4sin(x). If f(0)=3 and f'(0)=4, what is f(5)?.
Solution:
Let the function f(x) whose second derivative is:
[tex]f^{\prime\prime}(x)\text{ = 4x+4sin(x)}[/tex]Now, the antiderivative (integral) of the above function would be:
EQUATION 1:
[tex]f^{\prime}(x)=\int f^{\prime\prime}(x)\text{ }dx\text{= }2x^2-4\cos (x)\text{ +C1}[/tex]where C1 is a constant because we have an indefinite integral. Now the antiderivative (integral) of the above function f´(x) is:
[tex]f(x)=\int f^{\prime}(x)\text{ }dx\text{=}\int \text{ (}2x^2-4\cos (x)\text{ +C1)}dx\text{ }[/tex]that is:
EQUATION 2:
[tex]f(x)=\text{ }\frac{2x^3}{3}-4\sin (x)+C1x+\text{ C2}[/tex]where C2 is a constant because we have an indefinite integral.
Now using the previous equation, if f(0)= 3 then:
[tex]3=\text{ C2}[/tex]Now, using equation 1 and the fact that f ´(0) = 4, then we have:
[tex]4=f^{\prime}(0)\text{= }^{}-4\text{ +C1}[/tex]That is:
[tex]4=\text{ }^{}-4\text{ +C1}[/tex]Solve for C1:
[tex]8=\text{ }^{}\text{C1}[/tex]Now, replacing the constants C1 and C2 in equation 2, we have an expression for f(x):
[tex]f(x)=\text{ }\frac{2x^3}{3}-4\sin (x)+8x+3[/tex]Then f(5) would be:
[tex]f(5)=\text{ }\frac{2(5)^3}{3}-4\sin (5)+40+3=\text{ }125.98[/tex]
then the correct answer is:
[tex]f(5)=\text{ }125.98[/tex]Valentina earned some money doing odd jobs last summer and put it in a savings account that earns 7% interest compounded quarterly after 5 years there is 500.00 in the account how much did valentina earn doing odd jobs
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HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
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By the midpoint formula, the real number - 5 / 12 is between the rational numbers - 1 / 3 and - 1 / 2.
How to find a rational number between two rational numbers
Rational numbers are real numbers of the form m / n, where m and n are integers and n is non-zero. There are more than one choice between the rational numbers - 1 / 3 and - 1 / 2, one option can be found by obtaining the midpoint between the two numbers:
x = (1 / 2) · (- 1 / 3) + (1 / 2) · (- 1 / 2) Given
x = - 1 / 6 - 1 / 4 Multiplication of rational numbers
x = - 4 / 24 - 6 / 24 Modulative, commutative and associative properties / Existence of multiplicative inverse
x = - 10 / 24 Addition of fraction with same denominator
x = - 5 / 12 Simplification / Result
The real number - 5 / 12 is between the rational numbers - 1 / 3 and - 1 / 2.
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Jane needs $20 to buy her radio.She has saved $15.What precent of the cost of the radio has she saved?
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Let's begin by listing out the information given to us:
Cost of Radio (c) = $20
Jane's saving (s) = $15
% of radio cost saved = (Jane's saving / Cost of Radio) * 100%
[tex]\begin{gathered} x=\frac{s}{c}\cdot100 \\ x=\frac{15}{20}\cdot100=75 \\ x=75 \end{gathered}[/tex]Jane has saved 75% of the radio cost
5) 40,20,10,5, _,_,_a) Explain and Complete the sequence.B) write an explicit and recursive formula for the sequence
Answers
We have the sequence: 40, 20, 10, 5,...
Each term is half the previous term, so it is a geometrical sequence with common ratio r = 0.5.
We can not complete the sequence, as it becomes infinitely smaller and does not have a last term.
But we can write the three next terms to complete the blank spaces: 2.5, 1.25, 0.625.
We can start by writing the recursive formula. We know that each term is half the value of the previous term, so we wil have:
[tex]a_n=0.5\cdot a_{n-1}[/tex]From this recursive formula, we can deduce the explicit formula (in terms of n) as:
[tex]\begin{gathered} a_1=40 \\ a_2=0.5\cdot40=20 \\ a_3=0.5\cdot20=0.5\cdot(0.5\cdot40)=0.5^2\cdot40=10 \\ a_4=0.5\cdot10=0.5\cdot(0.5^2\cdot40)=0.5^3\cdot40 \\ \Rightarrow a_n=40\cdot0.5^{n-1} \end{gathered}[/tex]Answer:
a) Geometric sequence with r = 0.5.
The sequence first terms are: 40, 20, 10, 5, 2.5, 1.25, 0.625.
b) The recursive formula is a(n) = 0.5*a(n-1).
The explicit formula is a(n) = 40*0.5^(n-1).
The solution process is shown for any equation. Justify each step in the process with the appropriate property. Select the correct answer from each drop down menu.
Answers
Answer:
Explanation:
Here, we want to get the values in the segments
a) Here we would have to open up the brackets
Now, to do this, we are going to use the distributive property
By using the distributive property, we will be able to open up the brackets
Doing this, we can get the values in the brackets
So the answer here is distributive property
b) Here, we have
14 = -y after combining the like terms
The correct answer here is the subtraction property of equality
We simply subtract 3y from both sides of the equation to arrive at this answer
c) -14 = y
We have the multiplication property of equality
The reason for this is that we multiplied both sides by -1 to arrive at this answer
d) y = -14
This is the symmetric property of equality
We have this here because if two values are equal on both sides, we can switch each to the opposite sides and still retain the same equality values
Cai says you can divide both quantities in a ratio by the same non-zero number to find an equivalent ratio. Explain why cai is correct.
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In this case, Cai is right.
Basically, Cai is right because a ratio is a fraction. So, if you divide the numerator and denomirator by the same number, the fraction won't be changed, in that case you would get an equivalent fraction.
For example, if we have 4/6, and we divide both numbers by 2, we get 2/3, these operations are valid because you are dividing both numbers by the same (2).
what property justifies the statement? if a=b and b=5,then a=5. A. addition property of equality. B. reflexive property.C transitive property. D. symmetric property.
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a=b
b=5
a=5
Symmetric propery of equality. (D)
It states that if quantity a equals quantity b, then a equals b.
Question Evaluate. 7⋅5+42−23÷4 Responses 49 49 41 41 34 34 9 9
Answers
Answer: 71.25
This is not of of the options, but is the right answer.
Step-by-step explanation:
7 x 5 + 42 - 23 / 4 =
Step 1: Make parentheses
(( 7 x 5 ) + 42) - ( 23 / 4) =
Step 2: Solve parentheses ( Multiplication and division first )
(35 + 42) - 5.75 =
Step 3: Solve parentheses ( Addition )
77 - 5.75 =
Step 4: Subtract
= 71.25
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The total payroll for a baseball team is 2.44 × 109 dollars, and the total payroll for a football team is 2.9 × 1011 dollars. How many more dollars is the football team's total payroll than the baseball team's total payroll?
0.46 × 109 dollars
2.8756 × 109 dollars
4.6 × 1011 dollars
2.8756 × 1011 dollars
Answers
Answer: I belive it would be 4.6 x 10^11 dollars. I hope this helps you :)
Step-by-step explanation:
Answer:it would be 4.6x10^11
Step-by-step explanation:
Please help me with this sample question.Find f(0)Find f(1)Find f(2)
Answers
In order to find the values of f(0), f(1) and f(2), we just need to find in the graph for the value of the function (that is, the value of y) for the values of x equal to 0, 1 and 2 respectively.
Looking at the graph, for x = 0 we have y = -7, therefore f(0) = -7
For x = 1 we have y = -2, therefore f(1) = -2
For x = 2 we have y = -5, therefore f(2) = -5
The graph of y = 2x2 - 4x + 2 opens downward.true or false
Answers
The equation for the graph is :
[tex]y=2x^2-4x+2[/tex]You can graph the equation on a graph tool and view the graph as below:
From the graph, you can see that it opens upwards, so the statement is False.
Correct answer is that the graph opens upwards.
Answer choice : False
d1 = 16 m; d2 = 14 m what's the rhombus?
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Step 1 : To determine the area of the rhombus
[tex]\begin{gathered} d_1=16m,d_2\text{ = 14m } \\ Area\text{ = }\frac{1}{2}\text{ }\times d_1\text{ }\times d_2 \\ Area\text{ = }\frac{1}{2}\text{ }\times\text{ 16 }\times\text{ 14} \\ Area\text{ = }\frac{224}{2} \\ Area=112m^2 \end{gathered}[/tex]Therefore the area of the rhombus = 112m²
find the area of the semicircle round to the nearest tenth use 3.14 for pi do not include units with your answer 12 in
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226.08
1) Since the area of the semicircle is half the circle area, then we can write:
[tex]S=\frac{1}{2}\cdot\pi\cdot r^2[/tex]2) So we can plug into that the size of that radius:
[tex]\begin{gathered} S=\frac{1}{2}\cdot\pi\cdot(12)^2 \\ S=\frac{1}{2}\cdot\pi\cdot144 \\ S=72\pi\Rightarrow S=72\times3.14\Rightarrow S=226.08 \end{gathered}[/tex]3) Hence, the area of that semicircle is 226.08 in²
A grocery store sells bags of oranges in two different sizes.The 3-pound bags of oranges cost $4. The 8-pound bags of oranges cost $9. Which oranges cost less per pound? Explain your reasoning
Answers
The per pound cost of the bag of oranges which price is $9 for 8-pounds is less .
In the question ,
it is given that a grocery store sells bags of oranges in two different sizes .
in first bag where 3 pound bags of oranges cost $4 .
So, 1 pound bag of orange will cost = 4/3 = $1.333 .
in the second bag where 8 pounds bags of oranges cost $9 .
So, 1 pound bag of orange will cost 9/8 = $1.125 .
we can see that $1.125 < $1.333 .
hence , the second bag of oranges costs less .
Therefore , the per pound cost of the bag of oranges which price is $9 for 8-pounds is less .
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The volume of the right cone below is 36π units ^3. Find the value of x
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The formula to find the volume of a cone is:
[tex]\begin{gathered} V=\frac{1}{3}\pi r{}{}^2h \\ \text{ Where} \\ V\text{ is the volume} \\ r\text{ is the radius} \\ h\text{ is the heigth} \end{gathered}[/tex]Then, we replace the know values in the above formula and solve for h.
[tex]\begin{gathered} V=36\pi \\ r=\frac{\text{ diameter}}{2}=\frac{6}{2}=3 \\ h=x \end{gathered}[/tex][tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ 36\pi=\frac{1}{3}\pi(3)^2x \\ 36\pi=\frac{9\pi x}{3} \\ 36\pi=3\pi x \\ \text{ Divide by }3\pi\text{ from both sides} \\ \frac{36\pi}{3\pi}=\frac{3\pi x}{3\pi} \\ 12=x \end{gathered}[/tex]AnswerThe value of x is 12 units.
Based on what you've read, decide which of the four basic operations you need to use. Then, solve the problems.
On a trip to Florida, Santina drove 203 miles and Carole drove 189 miles. How many more miles did Santina drive than Carole?
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The basic operation use for the problem is subtraction.
The number of miles Santina drove than Carole is 14 miles.
How to solve problems with basic operations?Basic operations are the building blocks and rules of math.
The basic operations are addition, subtraction, multiplication, and division.
On a trip to Florida. Santina drove 203 miles and Carole drove 189 miles.
The distance in miles Santina drive than Carole is the difference between there distance travelled.
Therefore, the basic operation applied in this problem is subtraction.
Hence, let's solve it as follows:
miles Santina drove than Carole = 203 - 189 = 14 miles
Therefore, Santina drove 14 more miles.
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The basic operation used for the problem will be; subtraction. Santina drove 14 more miles than Carole.
How to solve problems with basic operations?Basic operations are the building blocks and rules of math. The basic operations are addition, subtraction, multiplication, and division.
On a trip to Florida. it is given that Santina drove 203 miles and Carole drove 189 miles.
The distance Santina drives is miles than Carole, which is the difference between their distance traveled.
Thus, the basic operation applied in this problem will be; subtraction.
Hence, let's simplify it as follows:
The miles, Santina drove = 203 - 189 = 14 miles
Therefore, Santina drove 14 more miles than Carole.
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the table shows the number of incorrect answers given by nine students on a standardized test which of the following measures would make the number of missed questions appear as a small as possible
Answers
Let's take them one after the other
To calculate the mean:
Mean = 4 +20+ 5 +10+ 21+ 18 +10+ 11+ 16 / 9
Mean= 115/9= 12.7
To calculate the median;
Median: position (n+1)/2=(9+1)/2=5
This implies it is the fiifth value after ordering them from least to gratest
4, 5, 10, 10, 11, 16, 18, 20, 21
The fifth observation is 11, that's the median
Calculate the range;
Range = highest - lowest = 21 - 4 = 17
Mode = bi modal = 10
The answer is the Mode which is 10
The correct option is the last option : Mode
On the last day of his summer tennis camp, Zach helps his instructor sort through a basket of tennis balls to throw out the old ones. Zach ends up throwing away 13 of the balls. He returns the remaining 42 balls to the basket. Which equation can you use to find the total number of tennis balls t Zach checks?
Answers
The equation that represents the total tennis balls is t = 13 + 42 and the value is 55
How to determine the equation that represents the total tennis balls?From the question, the given parameters are
Total number of tennis ball = tNumber of tennis ball thrown away = 13Number of tennis ball returned = 42The total number of tennis ball is the sum of the number of tennis ball thrown away and the number of tennis ball returned
Mathematically, this is represented as
Total number of tennis ball = Number of tennis ball thrown away + Number of tennis ball returned
Substitute the known values in the above equation
So, we have the following equation
t = 13 + 42
Evaluate the sum
t = 55
Hence, the equation of the tennis ball is t = 13 + 42
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if x=2, then x^2=4, what is the inverse or give a counterexample
Answers
Step-by-step explanation:
if x = 2, then x^2 = 4, the inverse would thus be: if x^2 = 4, then x = 2.
This is partially true though since multiple values would satisfy the equation x^2 = 4, or rather 2 values. negative two and positive two. So x=2 is one solution, but just because x^2 = 4, that doesn't necessarily imply that x=2.
Sales tax in South Carolina is 5%. Mr. Smith bought a new car there for $18,700. What did he pay in sales tax?
Answers
Answer: $935
Step-by-step explanation:
Mr. Smith paid $935 in sales tax
Which of the following is a correct interpretation of the expression -8 + (-8)?
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The solution is:
*The expression describes the number that is 8 to the left of -8 on the number line. [Option A].
What’s the last number in row 8 for the new number triangle I made
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We have the sequence, shown as a number triangle, where in each step we add 5 (that is the constant difference).
We can write:
1
6 11
16 21 26
31 36 41 46
51 56 61 66 71
76 81 86 91 96 101
106 111 116 121 126 131 136
141 146 151 156 161 166 171 176
Answer: The last number in row 8 is 176.
Answer:
thr last number in row eight is 176
the number of regular telephones in use is how many times the number of cellular phones? 45% regular phones15% cellular phones6% others34% Cordless phones
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Solution
For this case we have the following info:
45% regular phones
15% cellular phones
6% others
34% Cordless phones
We know that the total regular of phones is 45% and the total of cellular phones are 15% then we can find the ratio like this:
45/15 = 3
Endpoint 19,-10) Midpoint (4,8).What is the other endpoint
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Let the first end point be x1 y1 and the second x2 y2 the midpoint would be
x1 + x2 / 2 y1 + y2 / 2
Hence
(19 + x2)/2 = 4
19 + x2 = 8
x2 = 8 -19
x2 = -11
(-10 + y2)/2 =8
- 10 + y2 = 8
y2 = 8 + 10
= 18
The other end point is (-11, 18)
Solve for x.2x + 3 ≤ x + 5
Answers
Answer:
x ≤ 2
Explanation:
Given the inequality:
[tex]2x+3\le x+5[/tex]First, we subtract x from both sides.
[tex]\begin{gathered} 2x-x+3\le x-x+5 \\ x+3\le5 \end{gathered}[/tex]Next, we subtract 3 from both sides.
[tex]\begin{gathered} x+3-3\leqslant5-3 \\ x\leqslant2 \end{gathered}[/tex]You want to put a 4 inch thick layer of topsoil for a new 23 ft by 31 ft garden. The dirt store sells by the cubicyards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Answers
Remember that
1 ft=12 in
1 yd =36 in
so
The garden is 23 ft by 31 ft
Convert to inches
23 ft=23*12=276 in
31 ft=31*12=372 in
Find out the volume
V=(276)*(372)*(4)
V=410,688 in3
Convert to cubic yards
410,688 in3=410,688*(1/36)^3=8.80 cubic yards
Remember that
The store only sells in increments of 1/4 cubic yards
so
The volume is 9 cubic yardsAdd the complex numbers 3 + 11i and -3 - 11i.6 + 0i0 + 0i0 + 22i- 9 + 121i
Answers
SOLUTION
The given complex unbers are:
[tex]3+11i,-3-11i[/tex]Add the complex numbers:
[tex]3+11i+(-3-11i)[/tex]Simplify the expression:
[tex]\begin{gathered} 3+11i-3-11i \\ =3-3+11i-11i \\ =0+0i \end{gathered}[/tex]Therefore the required answer is: 0+0i
2. Graph the following inequality on the axes provided below: 6x + 2y = 8 -10 8 6 4 2 -101-8-6 1-4-2 -2 2 4_LG_L 8 10 -4 -6 -8 -10 True or False: (1,1) is a solution to the inequality. Explain using evidence from your graph.
Answers
We are given the following inequality
[tex]6x+2y<8[/tex]Let us first convert the inequality into slope-intercept form
[tex]\begin{gathered} 6x+2y<8 \\ 2y<-6x+8 \\ y<-\frac{6x}{2}+\frac{8}{2} \\ y<-3x+4 \end{gathered}[/tex]Comparing this inequality with the standard slope-intercept form we see that
Slope = -3 and y-intercept = 4
So the graph of the inequality is
The area left to the red line represents the solution of the inequality.
Now we need to check if the point (1, 1) lies left to the red line.
We can clearly see that point (1, 1) is just left to the red line hence it is a solution.
Therefore, it is true.