Step-by-step explanation:
I assume our task is to find that point of time, when it reaches the highest point.
and the function is
h(t) = -16t² + 96t + 112
well, a maximum or minimum of a curve (function) is found as a zero solution of the first derivative of the function.
given the nature of the function, the extreme point has to be a maximum (the firecracker goes up and then down again).
h'(t) = -32t + 96
we are looking for the zero :
0 = -32t + 96
32t = 96
t = 3 seconds
so, after 3 seconds, the firecracker reaches its highest point, which is at
-16×3² + 96×3 + 112 = -16×9 + 96×3 + 112 =
= -144 + 288 + 112 = 256 ft
FYI - we know for x = 0 (the starting point) the height of the starting window was 112 ft.
PLEASE HELP ASAP!! Represent the following expressions as a power of the number a where a≠0.
(a^3)^-2
(a^-1 • a^-2)^-3
((a^2)^-2)^2
After using the property of power, the expressions as a power of the number a is [tex](a^3)^{-2} = a^{-6}[/tex] , [tex](a^{-1}\cdot a^{-2})^{-3} = a^{9}[/tex] and [tex]((a^2)^{-2})^2=a^{-8}[/tex] .
In the given question we have to solve the given expressions as a power of the number a where a≠0.
The first given expression is [tex](a^3)^{-2}[/tex].
Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].
Simplifying the expression.
[tex](a^3)^{-2} = a^{3*(-2)}[/tex]
[tex](a^3)^{-2} = a^{-6}[/tex]
The second expression is [tex](a^{-1}\cdot a^{-2})^{-3}[/tex]
Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].
[tex](a^{-1}\cdot a^{-2})^{-3} = a^{(-1)\times(-3)}\cdot a^{(-2)\times(-3)}[/tex]
[tex](a^{-1}\cdot a^{-2})^{-3} = a^{3}\cdot a^{6}[/tex]
Using the property of sum of power [tex]a^m\cdot a^n=a^{m+n}[/tex]
[tex](a^{-1}\cdot a^{-2})^{-3} = a^{(3+6)}[/tex]
[tex](a^{-1}\cdot a^{-2})^{-3} = a^{9}[/tex]
The third expression is [tex]((a^2)^{-2})^2[/tex].
Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].
[tex]((a^2)^{-2})^2=((a^2)^{(-2)\times2})[/tex]
[tex]((a^2)^{-2})^2=(a^2)^{-4}[/tex]
Again using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].
[tex]((a^2)^{-2})^2=a^{2\times(-4)}[/tex]
[tex]((a^2)^{-2})^2=a^{-8}[/tex]
To learn more about property of power link is here
brainly.com/question/28747844
#SPJ1
Which graph represents the polynomial function?
The graph which represents the polynomial function f(x) = x^3 - 2x^2 - 5x + 6 is in option A.
First, let us understand the polynomial function:
A polynomial function is one that uses only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on. For example, 9y + 6 is a polynomial with an exponent of 1.
We are given:
f(x) = x^3 - 2x^2 - 5x + 6
We know that, when the graph intersects the x-axis, it satisfies the equation that is f(x) = 0 at that point.
Let us check the points one by one;
Option A;
The graph intersects the x-axis at -2, 1, and 3 it should satisfy the equation f(x) = 0.
Let's put x = -2 in f(x), we will get;
f(-2) = -2^3 - 2(-2)^2 - 5(-2) + 6 = -8 - 8 + 10 + 6 = -16 + 16 = 0
f(-2) = 0.
Let's put x = 1 in f(x), we will get;
f(1) = 1^3 - 2(1)^2 - 5(1) + 6 = 1 - 2 - 5 + 6 = 7 - 7 = 0
f(1) = 0.
Let's put x = 3 in f(x), we will get;
f(3) = 3^3 - 2(3)^2 - 5(3) + 6 = 27 - 18 - 15 + 6 = 33 - 33 = 0
f(3) = 0.
So, the points -2, 1, and 3 satisfy the equation f(x).
Thus, the graph which represents the polynomial function f(x) = x^3 - 2x^2 - 5x + 6 is in option A.
To learn more about the polynomial function visit:
https://brainly.com/question/12976257
#SPJ1
Franks’s annual salary is $80000. About 25% of her salary is deducted for taxes.
How much tax is deducted?
Explain.
Martin had 6 magazines. Then m more magazines came in the mail. Write an expression that shows how many magazines Martin has now.
Martin had 6 magazines. Then m more magazines came in the mail. Write an expression that shows how many magazines Martin has now.
Martin now has: 6 + m
five friends shared 8 1/3 pounds of apples equally. How many pund of apples do each of them get
Answer:
A fruit seller buys 712 fruits of which 3/4 are apples. The apples that he bought 1/3 were found to be rotten if he sold all the good apples at Rs.5 1/4 each.
Step-by-step explanation:
Represent the following expressions as a power of the number a where a ≠ 0.: (a^3)^-2
1/[tex]a^{6}[/tex] is the required number.
What is an expression?Numbers, symbols and operators (such as and times) grouped together that show the value of something.
Given an expression (a³)^-2
(a³)^-2 = [tex]a^{-6}[/tex] = 1/[tex]a^{6}[/tex]
Hence, 1/[tex]a^{6}[/tex] is the value of the expression (a³)^-2
For more references on expression, click;
https://brainly.com/question/14083225
#SPJ1
The formula for simple interest is I=Prt,I=Prt, where II is the interest earned, PP is the principal, rr is the interest rate and tt is the number of years. Solve the formula for PP in terms of r,r, II and t.t.
Answer:
[tex]P=\cfrac{I}{rt}[/tex]----------------------------
GivenI = PrtSolve for P[tex]I = Prt[/tex][tex]\cfrac{I}{rt} = \cfrac{Prt}{rt}[/tex][tex]\cfrac{I}{rt} =P[/tex][tex]P=\cfrac{I}{rt}[/tex]A fisherman catchs 12 fish in 5 days. How many fish does he get in
5 + x days?
( 60+12x )/5 fish fisherman will catch in 5+x days .
What is unitary method ?The unit method is a method of solving a problem by first obtaining the value of a single unit, then multiplying the value of the single unit to obtain the necessary value.
Assume you go to the market to buy six apples. The shopkeeper told you that he sells 10 apples for 100 rupees. In this case, the apple is the unit and the apple price is the value. Knowing the units and values is important when solving problems using unitary methods.
For simplicity, always write what you calculate on the right and what you know on the left. In the problem above, we know the amount of apples, but we don`t know the value of the apples. Note that the concept of ratio and ratio is used for problems related to this method.
Calculation5 days ------------> 12 fish
1 day --------------> 12/5 fish
5 + x days --------------> 12/5 x (5+x)
= ( 60+12x )/5 fish
learn more about unitary method here :
brainly.com/question/22056199
#SPJ13
The graph of the absolute value parent function, f(x) = |x), is stretched
horizontally by a factor of 3 to create the graph of g(x). What function is g(x)?
OA. g(x)= x+3|
OB. g(x) = 31x1
C. g(x) = 13x1
OD. g(x)= |||
Option A is the correct answer g(x) = |x+3| by using the relation with the parent function.
Explain absolute value function.
A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value.
The definition of the absolute value parent function, f(x)=| x |, is as follows:
f(x) = [tex]\left \{ {{x ~, ~ x > 0} \atop {0 ~ , ~x = 0}} \atop {-x ~, ~x < 0} \right.[/tex]
Given parent function is f(x) = |x|
g(x) is obtained by stretching the graph of f(x) by a factor of 3.
Use the function g(x)=f(x−h) to translate the absolute value function f(x)=| x | horizontally.
The graph of f(x) is moved h units to the right to obtain g(x) for h>0
The graph of f(x) is translated h units to the left to obtain g(x) when h>0
Therefore, g(x) = |x+3|
To learn more about the absolute value functions from the given link.
https://brainly.com/question/2473412
#SPJ1
A rectangular tank with a square base, an open top, and a volume of 37044 ft^3 is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.
The dimensions of this rectangular tank that has the minimum surface area are 42 feet and 21 feet.
How to calculate the dimensions of the tank that has the minimum surface area?First of all, we would determine the surface area of this rectangular tank with a square base by using this formula:
h = V/s²
Where:
h represents the height of a rectangular tank.s represents the side of the square base.V represents the volume of a rectangular tank.For the surface area of this rectangular tank with a square base, we have:
Surface area, A = base area + 4(lateral area)
Surface area, A = s² + 4(s × h)
Surface area, A = s² + 4(s × V/s²)
Surface area, A = s² + 4V/s
Next, we would take the first derivative of the surface area as follows:
A' = 2s - 4V/s²
Substituting the given parameters into the formula, we have;
A' = 2s - 4(37044)/s²
For the minimum surface area dimension, the first derivative of the surface area would be equated to zero:
2s - 148,176/s² = 0
148,176/s² = 2s
148,176 = 2s³
s³ = 74,088
s = ∛74,088
s = 42 feet.
For the height, we have:
Height, h = V/s²
Height, h = 37044/42²
Height, h = 37044/1764
Height, h = 21 feet.
Read more on minimum surface area here: https://brainly.com/question/13789217
#SPJ1
Deshaun drove 469 miles in 7 hours.
At the same rate, how long would it take him to drive 335 miles?
We're assuming Deshaun is driving at a constant speed/at the same rate,
He drove 469 miles in 7 hours -> his speed = 469 : 7 = 67 (mph)
Therefore, it would take him 335 : 67 = 5 hours to drive 335 miles.
If I earn $11 /hr. I worked for 6 and a half hrs yesterday, How much did I earn?
He earned $71.5 if he earn $11 /hr. I worked for 6 and a half hrs yesterday.
Define hours.An hour (symbol: h; also abbreviated as hr) is a measure of time that is traditionally thought of as one-fourth of a day and that, according to science, lasts between 3,599 and 3,601 seconds, depending on how quickly the Earth rotates. There are 24 hours in a day and 60 minutes in an hour. 60 minutes is one of the 24 equally spaced out segments of a day.
Given,
Earns $11/hr
Worked for 6 hours and 30 minutes
Multiplying:
$11 × 6.5 hours
$ 71.5
He earned $71.5 if he earn $11 /hr. I worked for 6 and a half hrs yesterday.
To learn more about hours, visit:
https://brainly.com/question/13533620
#SPJ13
Pls help I’m failing
Answer:
{-9,-8,7,8,10}
-8 What is 9.15 x 10°° written in standard form?
The value of the number 9.15 x 10° written in standard form is equal to 9.15.
As given in the question,
Given number is equal to :
9.15 x 10°
Given number 9.15 x 10° is written in standard form.
The value of the given number 9.15 x 10° written in standard form is given by:
9.15 x 10°
Here 10° = 1
Using property of number: Any number raise to zero is always equal to 1.
9.15 x 1
Using Multiplicative identity , number multiply to 1 remain number itself.
= 9.15
Therefore, the value of the number 9.15 x 10° written in standard form is equal to 9.15.
The complete question is:
What is the value of 9.15 x 10° written in standard form?
Learn more about standard form here
brainly.com/question/17264364
#SPJ9
algebra help pleaseee
Answer:
3x^2-2x+3+1/x+2
Step-by-step explanation:
WHat is 5/1 x 4/5 This is a hard one
4
Step-by-step explanation:
[tex]{ \tt{ \frac{5}{1} \times \frac{4}{5}}} [/tex]
[tex]{ \tt{ \frac{5 \times 4}{5}}} [/tex]
[tex]{ \tt{ = \frac{20}{5}}} [/tex]
[tex] = { \green{ \boxed{ \pink{ \sf{4}}}}}[/tex]
In a set of eight consecutive integers, the smallest integer is more than $\frac35$ of the largest integer. What is the smallest possible value of the sum of the eight integers?
Answer:
116.
Step-by-step explanation:
Your welcome <3.
Answer:
116
Step-by-step explanation:
Notebook paper is about 0.003 in. thick. If you cut a sheet of paper in half, stack one piece on top of the other, cut those in half, stack all the pieces together, repeating this process 20 times, how high will the stack of paper be?
Answer:
765
Step-by-step explanation:
Graph the given equation by evaluating integer values of x from −2 to 2 and plotting the resulting points
y= _2x_1
The graph of the linear equation can be seen in the image at the end.
How to graph the equation?Here we have the linear equation:
y = -2x - 1
To graph this, we need to evaluate from x = -2 to x = 2, this means replacing the value of x by the correspondent number.
if x = -2, then:
y = -2*(-2) - 1 = 4 - 1 = 3
So we have the point (-2, 3)
if x = -1
y = -2*-1 - 1 = 2 - 1 = 1
We have the point (-1, 1)
If x = 0
y = -2*0 - 1 = -1
We have the point (0, -1)
If x = 1
y = -2*1 - 1 = -3
We have the point (1, -3)
If x = 2
y = -2*2 - 1 = -5
We have the point (2, -5)
Now we just need to graph these 5 points on a coordinate axis and then connect them with a line, the graph of the linear equation can be seen below.
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
Two sides are labeled 5,244 feet. The other two sides are labeled 1,495 feet. What is the perimeter to the nearest hundred?
Answer:
Step-by-step explanation:
42feet
Write the slope-intercept form for the equation of a line with slope m = -9 and y-intercept (0, 5).
The equation of this line is
The equation of the line is ,y= -9x+5.
What is an equation?A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions. For instance, an équation is defined as having one or more variables in French.Finding the variables' values that cause the equality to be true is the first step in solving an equation with variables. The variables for which the equation must be solved are also known as the unknowns, and the unknowns' values that fulfill the equality are known as the equation's solutions. Equations can be categorized as either identities or conditional equations.Acc to our question-,
We should use the slope-intercept formula to solve this problem.
The point-slope formula states:= [ y = mx + c]
Where m is the slope and c is the y-intercept for the point (0,y1)
Substituting the information provided we get the equation: y= -9x+5.
learn more about equations click here:
https://brainly.com/question/2972832
#SPJ13
Please help me thank you :))))
Answer: y= (2/3)x - 2
Step-by-step explanation:
The biggest way to remember equations like these is to know rise over run which means however many times it goes up until it intersects with both x and Y will be on the top of the fraction and however many times it goes to the right until it intersects with both x and y will be on the bottom of the fraction. So since it hits (0, -2) then intersects at (3,0) it will be 2/3x and the Y is where X equals zero so it would be -2. Hope that helps!
Answer:
y = [tex]\frac{2}{3}x - 2[/tex]
Step-by-step explanation:
Step 1:
Choose two points on the graph, (x1, y1) and (x2, y2), to find the slope.
Find the ratio between change in y-values and change in x-values.
m = (y2 - y1) / (x2 - x1)
Points I picked:
(x1, y1) = (0, -2)
(x2, y2) = (3, 0)
Then,
m = (0 - (-2)) / (3 - 0)
m = 2/3
Step 2 :
Find the y-intercept from the graph. That is the point at which the line intersects the y-axis.
The y-intercept is -2.
b = -2
Step 3 :
Use the slope (m) and y-intercept (b) to write the equation in slope-intercept form:
y = mx + b
Substitute m = 2/3 and b = -2
y = 2/3 x - 2
You deposit $500 into a savings account that earns interest annually. The function g(x) = 500(1.06)x can be used to find the amount of money in the savings account, g(x), after x years. What is the range of the function in the context of the problem?
ℝ
[500, ∞)
[0, 500]
[0, ∞)
Omar deposited d dollars into a savings account y years ago. ... following expressions could be used to determine the zeros of the function f (x) when f (x).
Step-by-step explanation:
he residence of a city voted on whether to raise property taxes the ratio of yes votes to no votes was 4 to 7 if there was a 5918 total votes how many yes votes were there
There is a total of 2152 yes votes
How to determine the number of yes votes?From the question, the statement is given as
The ratio of yes votes to no votes was 4 to 7
Mathematically, this can be represented as
Ratio = 4 : 7
Alternatively, we have
Yes : No = 4 : 7
Express the ratio as fraction
Yes = Yes/Yes + No
So, we have
Yes = 4/4 + 7
Evaluate the sum
Yes = 4/11
From the question, we have
Total votes = 5918
So, we have
Yes = 4/11 * 5918
Evaluate
Yes = 2152
Hence, the number of yes votes is 2152
Read more about ratios at
https://brainly.com/question/1781657
#SPJ1
What is the slope of line KH if H(-4, 2) and K(2, -2)? Remember to reduce!
The slope of a line KH if H(-4, 2) and K(2, -2) is -2/3.
What is a slope?A mathematical word used to define a line's direction and steepness is its slope or gradient.
If a line is rising from left to right, it is growing. The slope is positive, or m>0
If a line decreases from left to right, it is said to be diminishing. The slope is negative, indicating that m < 0
A line has zero slopes if it is horizontal. This function is constant.
The slope of a line is y - y₁ = m(x - x₁)
Slope m = (y₂ - y₁)/(x₂ - x₁)
m = (- 2 - 2)/(2 + 4)
m = - 4/6
m = - 2/3
To know more about slope, visit:
https://brainly.com/question/3605446
#SPJ13
We want 3 pizzas, each topped with 0, 1, 2, 3, 4, 5, or 6 of 6 available whole-pie toppings. How many different combinations of 3 such pizzas are possible if different pizzas need not have different toppings?
A new gaming chair costs $309.99. You have already saved $131.49 and earn $25.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
25.5w − 131.49 = 309.99; w = 17
25.5 + 131.49w = 309.99; w = 7
25.5w − 309.99 = 131.49; w = 17
25.5w + 131.49 = 309.99; w = 7
The linear equation we need to solve is:
$25.50*w = $309.99 - $131.49
And the solution is w = 7.
How to write and solve the equation?We know that the cost of the gaming chair is $309.99.
To buy this, you already have saved $131.49, and save another $25.50 per week, then the amount you have after w weeks is:
f(w) = $131.49 + $25.50*w
So the linear equation we need to solve is:
$131.49 + $25.50*w = $309.99
To solve this we need to isolate w.
$131.49 + $25.50*w = $309.99
$25.50*w = $309.99 - $131.49
w = ($309.99 - $131.49)/$25.50 = 7
So they can buy the chair after 7 weeks.
Learn more about linear equations:
https://brainly.com/question/13763238
#SPJ1
Which expression can be placed on the right side of the equals sign to form an equation?
2+3³ =
1. O 5³
2. 3 +4:3
3. 10-2-9
4. 52 +4
Expression which placed on the right side of equal sign is,
[tex]2+3^3 =2 +3\times 3\times 3[/tex]
[tex]2+3^3= 2+27[/tex]
[tex]2+3^3= 29[/tex]
What is expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
What do you mean by equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given, a expression 2 + [tex]3^3[/tex] = ?
what can be placed right side of the expression?
so, first we calculate the [tex]3^3[/tex] which means 3 x 3 x 3 = 27.
then , add 2 and 27 and the answer is 29.
but the answer is not present into the option.
Final answer will be 29 which placed right side of the equation 2 + [tex]3^3[/tex] = 29.
Know more about Expression click on the link:
https://brainly.com/question/1859113
#SPJ1
PLEASE HELP!!!! I WILL GIVE YOU BRAINLIST!! PLEASE ASAP :)
Which graph shows the image of ΔABC after a rotation about the origin?
Answer:
D.
Step-by-step explanation:
just click the rotate button until it matches one of the answers
Find the distance from the point (1,2) to the line-y= 1/2x-3. Round your answer to the nearest tenth.
Answer:
the graphical explanation please