Answer:
Maximum height = 500 feet
Land after = 20 seconds
Step-by-step explanation:
Let us follow the movement of the ball as it is thrown upwards. We notice that we get to a point, where the change in the height of the ball with respect to time becomes = 0. This means that the ball is at its maximum position.
Hence, mathematically, at maximum height, [tex]dh/dt = 0[/tex]
Recall,
[tex]h = 100t - 5t^2[/tex]
[tex]dh/dt=100-10t[/tex]
From our problem, we can also deduce that at the maximum height, the velocity of the ball is = 0. i.e [tex]dh/dt = 0[/tex]
hence,
[tex]0 = 100-10t\\t =10 seconds[/tex]
The time the ball takes to reach a maximum height is 10 seconds.
The next step will be to substitute this time value into the equation for the height.
[tex]h = 100(10) -5(10)^2=500 feet[/tex]
The maximum height is 500 feet
The object will land after t X 2 seconds = 10 X 2 = 20 seconds. This is because it will have to go up and come back down. This should take twice the time.
f ( x ) = - x^3 + 3x^2 + 4x - 5
answear ?
Answer:
There are no like terms.
Step-by-step explanation:
convert 1.97 kJ to calories
Answer:
0.4708413 is the answer
translate the sentence into an equation
Eight times the sum of a number and 6 is 9.
use the variable w for the unknown number
Answer:
8(w+6)=9
You must add parentheses to show the order in which you will complete the problem. Because it says “eight times the sum of a number and 6” you have to find the sum first, then multiply 8.
help meee if answer correctly I will follow you and make you brilliant
Answer:
a = 2; b = -1; and c = 3
Step-by-step explanation:
Please see attached image for the step by step answer
can someone please help me with this question?
Answer:
1/2
Step-by-step explanation:
you are going from 20 to 10, meaning you have to multiply by a 1/2. This means that the scale factor is 1/2! Brainly pls!
SOMEONE PLEASE HELP
help
Answer:
K1. 25 K2. 25 K3. 22.5 K4. 22
Step-by-step explanation:
im kinda confused what its asking
Completely factor this quadratic expression: 4x2 + 12x − 72.
Answer:
4(x-3)(x+6)
Step-by-step explanation:
Answer:
Have a great rest of your day :)
Step-by-step explanation:
There are six wires which need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attached in any order, and the production manager wishes to determine which order would be fastest for the robot to use. Use the multiplication rule of counting to determine the number of possible sequences of assembly that must be tested. (Hint: There are six choices for the first wire, five for the second wire, four for the third wire, etc.)
Answer:
[tex]S=720[/tex]
Step-by-step explanation:
From the question we are told that
Six wire are attached to a circuit board
Generally using multiplication rule
Let number of possible sequence be given as S
Mathematically
[tex]S=6! =6*5*4*3*2*1=720[/tex]
Therefore
Number of possible sequence [tex]S=720[/tex]
Solve and check: x + 10 + 4x + 90 = 180
Answer:
40
Step-by-step explanation:
If a system of two linear equations has no solutions, which of the following statements describes the graph of the two corresponding lines in the xy-plane?
a. The lines are coinciding
b. The lines intersect at only one point
c. The lines are parallel
d. The lines are perpendicular
Explain why you picked your answer:
From the linear equation, the option that describes the graph of the two corresponding lines is C. The lines are parallel.
Based on the complete information, it should be noted that the lines are not coinciding and they don't intersect at only one point.
Rather, it can be deduced that the graph of the two corresponding lines in the xy-plane are parallel.
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Which value from the set (5,7,9,11,13) make inequality w-4<8 true?
Answer:
5,7,9,11
Step-by-step explanation:
Compute the multifactor productivity measure for each of the weeks shown for production of chocolate bars. What do the productivity figures suggest? Assume 40-hour weeks and an hourly wage of $12. Overhead is 1.5 times weekly labor cost. Material cost is $6 per pound.Week Output (units) Workers Material (lbs)1 30,000 6 4502 33,600 7 4703 32,200 7 4604 35,400 8 480
Answer:
Week 1 =3.03
Week 2 =2.99
Week 3=2.9
Week 4=2.83
Step-by-step explanation:
Computation for the multifactor productivity measure for each of the weeks shown for production of chocolate bars.
Using this formula
Week Multifactor productivity measure = (Output / Total Cost)
Where:
Output represent Quantity produced
Total cost represent Labor cost + Material cost + Overhead
Let plug in the formula
Week 1= 30,000/(40*12*6)+[(40*12*6)1.5]+(450*6)
Week 1 =30,000/(2,880)+(2,880*1.5)+2,700
Week 1 =30,000/(2,880+4,320+2,700)
Week 1=30,000/9,900
Week 1 =3.03
Week 2= 33,600/(40*12*7)+[(40*12*7)1.5]+(470*6)
Week 2 =33,600/(3,360)+(3,360*1.5)+2,820
Week 2=33,600/(3,360+5,040+2,820)
Week 2=33,600/11,220
Week 2 =2.99
Week 3= 32,200/(40*12*7)+[(40*12*7)1.5]+(460*6)
Week 3 =32,200/(3,360)+(3,360*1.5)+2,760
Week 3=32,200/(3,360+5,040+2,760)
Week 3=32,200/11,160
Week 3=2.9
Week 4= 35,400/(40*12*8)+[(40*12*8)1.5]+(480*6)
Week 4 =35,400/(3,840)+(3,840*1.5)+2,880
Week 4=35,400/(3,840+5,760+2,880)
Week 4=35,400/12,480
Week 4=2.83
Therefore the multifactor productivity measure for each of the weeks shown for production of chocolate bars is :
Week 1 =3.03
Week 2 =2.99
Week 3=2.9
Week 4=2.83
If y =- 5x + 3, find the value of x when y = 13.
Answer:
x=2
Step-by-step explanation:
You would first subsitute the y with 13. The you would subtract 3 from 3 and 13. Then you would have 10=5x. Then you would divide 5 by 5 and 10. You will get x = 2
:)
What equation is the rule for the function illustrated by the table of values?
Answer:
The equation which determined the rule for the function is:
y = 3x+2Thus, option B is true.
Step-by-step explanation:
We know the slope-intercept form of line function is
y = mx+b
where m is the slope and b is the y-intercept
Given the table
x -2 -1 0 1 2
y -4 -1 2 5 8
Finding the slope between the points (-2, -4) and (-1, -1)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-2,\:-4\right),\:\left(x_2,\:y_2\right)=\left(-1,\:-1\right)[/tex]
[tex]m=\frac{-1-\left(-4\right)}{-1-\left(-2\right)}[/tex]
[tex]m=3[/tex]
Thus, the slope of the function = m = 3
We know that the y-intercept can be determined by setting x = 0 and determining the corresponding y-value.
It is clear,
at x=0, y = 2
Thus, the y-intercept 'b' = 2
now substituting m = 3 and b =2 in the slope-intercept form
y = mx+b
y = 3x + 2
Therefore, the equation which determined the rule for the function is:
y = 3x+2Thus, option B is true.
helpppppppppppppppppp
Answer:
0
Step-by-step explanation:
(2m)/(2m+3)-(2m)/(2m-3)=1
Simplifying the left hand first
(2m)/(2m+3)-(2m)/(2m-3) = {2m(2m-3) - 2m(2m+3)}/(4m²-9)
(4m²-6m-4m²-6m)/(4m²-9) = (-12m) / (4m²-9)
Now this equates to 1
(-12m) / (4m²-9) = 1
-12m = 4m²-9
4m²+ 12m -9 =0 ⇒⇒⇒ This is a quadratic equation that has 2 real solutions.
4m²+ 12m -9 =0
m² + 3m + (3/2)²= 9/4 + 9/4
(m + 3/2)² = 18/4
m = √18/2 - 3/2 or m = -√18/2 - 3/ = 0.621 = -3.621
So we can say that the equation has NO extraneous solutions.
Answer = 0
(I'm pretty sure it's correct)
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = y i + (z − y) j + x k S is the surface of the tetrahedron with vertices (0, 0, 0), (8, 0, 0), (0, 8, 0), and (0, 0, 8)
Answer:
[tex]\dfrac{-8^3}{6}[/tex]
Step-by-step explanation:
According to the divergence theorem;
The flux through the surface S is given by the formula:
[tex]\iint _S F.dS = \iiint_E \ div (F) \ dV[/tex]
where the vector field is:
F = [tex]\langle y,z-y,x \rangle[/tex]
Then the divergence of the vector field is:
[tex]div (F) = \bigtriangledown.F = \Bigg [ \dfrac{\partial (y)}{\partial x} + \dfrac{\partial (z-y)}{\partial (y)}+ \dfrac{\partial (x)}{\partial (z)} \Bigg ][/tex]
= 0 - 1 + 0
= -1
Thus, the flux through the surface of the tetrahedron is:
[tex]\iint_S . FdS = \iiint _E(-1) \ dV \\ \\ = - \iiint_E \ dV[/tex]
To determine the volume of the tetrahedron with vertices O(0,0,0), A(8,0,0), B (0,8,0) & C(0,0,6)
The equation of the plane P moving through the vertices A, B and C is:
[tex]P = \dfrac{x}{8}+ \dfrac{y}{8}+ \dfrac{z}{8} = 1[/tex]
x + y + z = 8
Range:
For z: 0 ≤ z ≤ 8 - x - y
For y: 0 ≤ y ≤ 8 - x
For x; 0 ≤ x ≤ 8
Thus;
[tex]\iiint_E \ dV = \int ^8_0 \int ^{8-x}_{0} \int ^{8-x-y}_{0}[/tex]
[tex]\int ^8_0 \int ^{8-x}_{0} [z] ^{8-x-y}_{0} \ dydx = \int ^8_0 \int ^{8-x}_{0} \ (8 -x-y) \ dy dx[/tex]
[tex]\int ^8_0 [ (8-x)^2 - \dfrac{(8-x)^2}{2} ] dx = \dfrac{1}{2} \int ^8_0 (8-x)^2 \ dx[/tex]
i.e.
[tex]= \dfrac{1}{2} [ \dfrac{(8-x)^3}{(-1)^3}]^8_0[/tex]
[tex]= \dfrac{-1}{6}[(8-8)^3-(0-8)^3][/tex]
[tex]= \dfrac{-8^3}{6}[/tex]
This question is based on the Gauss Divergence theorem. Therefore, the surface integral [tex]\int\limits {F.dS}[/tex] is -85.33.
Given:
F(x, y, z) = y i + (z − y) j + x k S in outward orientation.
Tetrahedron with vertices (0, 0, 0), (8, 0, 0), (0, 8, 0), and (0, 0, 8).
We have to evaluate the surface integral [tex]\int\limits {F.dS}[/tex] .
According to the Gauss divergence theorem ,
The flux through the surface S is given by the formula:
[tex]\int\int _s F.dS = \int \int \int_e div (F)\; dV[/tex]
Where the vector field is:
F = ( y, z-y, x )
Therefore, the divergence of the vector field is:
[tex]div(F) = \bigtriangledown .F = ( \dfrac{\partial( y)}{\partial (x)} + \dfrac{\partial(z-y)}{\partial(y)} + \dfrac{\partial(x)}{\partial(z)} )\\\\div(F) = \bigtriangledown .F = 0-1+0=-1[/tex]
Thus, the flux through the surface of the tetrahedron is:
[tex]\int\int _s F.dS = \int \int \int_e (-1)\; dV = -\int \int \int_e \; dV[/tex]
Now, determine the volume of the tetrahedron with vertices O(0,0,0), A(8,0,0), B (0,8,0) & C(0,0,6).
The equation of the plane P moving through the vertices A, B and C is:
[tex]P = \dfrac{x}{8} +\dfrac{y}{8} +\dfrac{z}{8} = 1[/tex]
x + y + z = 8
Range:
For z: 0 ≤ z ≤ 8 - x - y
For y: 0 ≤ y ≤ 8 - x
For x; 0 ≤ x ≤ 8
Thus,
[tex]\int\int\int_e dV = \int\limits^8_0\int\limits^{8-x} _ 0 \int\limits^{8-x-y}_0 \; dzdxdy\\= \int\limits^8_0\int\limits^{8-x} _ 0 [z]\limits^{8-x-y}_0 dx \\= \int\limits^8_0\int\limits^{8-x} _ 0 (8-x-y) dy dx\\= \int\limits^8_0 [ 8y-xy-\dfrac{y^{2} }{2} ]\limits^{8-x}_ 0 dx\\= \int\limits^8_0 ([ 8-x]^{2} - \dfrac{ [ 8-x]^{2}}{2} ) dx\\= \dfrac{1}{2} [\dfrac{(8-x)^{3} }{(-1)^{3} } ] \limits^8_0\\=\dfrac{-8^{3} }{6} \\\\= -85.33[/tex]
Therefore, the surface integral [tex]\int\limits {F.dS}[/tex] is -85.33.
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The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 2135 miles, with a variance of 145,924. If he is correct, what is the probability that the mean of a sample of 40 cars would differ from the population mean by less than 29 miles
Answer:
0.36878
Step-by-step explanation:
Given that:
Mean number of miles (m) = 2135 miles
Variance = 145924
Sample size (n) = 40
Standard deviation (s) = √variance = √145924 = 382
probability that the mean of a sample of 40 cars would differ from the population mean by less than 29 miles
P( 2135 - 29 < z < 2135 + 29)
Z = (x - m) / s /√n
Z = [(2106 - 2135) / 382 / √40] < z < [(2164 - 2135) / 382 / √40]
Z = (- 29 / 60.399503) < z < (29 / 60.399503)
Z = - 0.4801364 < z < 0.4801364
P(Z < - 0.48) = 0.31561
P(Z < - 0.48) = 0.68439
P(- 0.480 < z < 0.480) = 0.68439 - 0.31561 = 0.36878
= 0.36878
Answer: 0.3688
Step-by-step explanation:
If you are rounding to the nearest 4 decimal places the correct answer is 0.3688
93 + 12m = 3(4m – 1) + 96
Answer:
m=0
Step-by-step explanation:
We simplify the equation to the form, which is simple to understand
93+12m=3(4m-1)+96
Reorder the terms in parentheses
93+12m=+(+12m-3)+96
Remove unnecessary parentheses
+93+12m=+12m-3+96
We move all terms containing m to the left and all other terms to the right.
+12m-12m=-3+96-93
We simplify left and right side of the equation.
m=0
Hope this helps!
Brain-List?
Answer:
infinite solutions
Step-by-step explanation:
First, you do the property of distribution
93+12m=3(4m-1) +96
93+12m=12m-3+96
then you combine like terms
93+12m=12m+93
0=0 is the answer if you were to continue.
PLS HELP ! 100 POINTS!!!!! Select the correct answer. This graph represents a quadratic function. What is the value of a in the function’s equation?
Answer:
a = 3
Step-by-step explanation:
The vertex form of a quadratic is
y = a(x-h) ^2 +k where ( h,k) is the vertex
the vertex is (-2,2)
y = a(x- -2) ^2 +2
y = a(x+2) ^2 +2
Pick another point on the graph to determine a
(-1,5) and substitute into the equation
5 = a( -1+2) ^2 +2
5 = a(1)^2 +2
5 = a(1) +2
Subtract 2 from each side
5-2 = a+2-2
3 = a
Answer:
A=3
Step-by-step explanation:
I got it right on the test
Chuck has a gross pay of $815.70. By how much will Chuck’s gross pay be reduced if he has the following items withheld? federal tax of $56 Social Security tax that is 6.2% of his gross pay Medicare tax that is 1.45% of his gross pay state tax that is 19% of his federal tax a. $73.04 b. $129.04 c. $235.51 d. $273.38 Please select the best answer from the choices provided A B C D
Answer:
B $129.04
Step-by-step explanation:
Just took the exam on edgu
Answer:
B
Step-by-step explanation:
The width of a rectangular room is 3 feet shorter than it is long. If the perimeter of the room is 42 feet, what is the width of the room? Show work
Answer:
Should be 9 feet.
Step-by-step explanation:
Well I just set up the equation 2x + 2(x-3) = 42 Then solved x and subtracted x by 9.
Answer:
9 feetStep-by-step explanation:
Let width be w and length be l
Then we have equations below:
w = l - 32(w + l) = 42Substitute l = w + 3 in the second equation and solve for w:
w + l = 21w + w + 3 = 212w = 21 - 32w = 18w = 18/2w = 9 feetRotate 90 clockwise wxyz
Answer:
Rotate 90 clockwise wxyz
Step-by-step explanation:
Find the inverse:
-3x+7y=14
9514 1404 393
Answer:
-3y +7x = 14
Step-by-step explanation:
The inverse relation is found by swapping the x- and y-variables. The relation that is the inverse of ...
-3x +7y = 14 . . . . given relation
is
-3y +7x = 14 . . . . inverse relation
4,509/10,000 as a decimal number.
Step-by-step explanation:
When dividing by 10,000, shift the decimal place 4 places to the left.
4509 => 0.4509
4,509/10,000 = 0.4509.
4,509/10,000 as a decimal number is 0.4509.
What are decimal numbers?Decimals are used to write a number that is not whole.
Given a fraction, 4,509/10,000
Dividing by 10,000, shift the decimal place 4 places to the left.
Therefore, 4,509/10,000 = 0.4509.
Hence, 4,509/10,000 as a decimal number is 0.4509.
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expand and simplify 2(5x+4)+3(2x+1)
pls help me
Step-by-step explanation:
2(5x + 4) + 3(2x + 1)
= 10x + 8 + 6x + 3
= 16x + 11.
On which number line are -9 and its opposite shown?
Answer:
Step-by-step explanation:
The answer is c.
this is because the sections on the line are counting by 3 and 3 away from -12 is -9. it's opposite is shown on the right of this line as shown to the right.
Are 4x, 4y, and 4xy like terms?
In algebra, like terms are terms that have the same combination of variables raised to the same powers. Let's determine whether 4x, 4y, and 4xy are like terms.
The term 4x consists of the variable x raised to the power of 1, while the term 4y contains the variable y raised to the power of 1. Thus, both 4x and 4y have the same combination of variables raised to the same power. Therefore, they can be considered like terms. On the other hand, the term 4xy consists of both the variables x and y, each raised to the power of 1.
Although it includes both x and y, the arrangement of the variables is different from the previous terms. This means that 4xy is not a like term to either 4x or 4y. In conclusion, among the given terms, 4x and 4y are like terms, while 4xy is not. It is important to identify like terms in algebra to simplify expressions and combine similar terms for easier calculations.
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Find the missing y-coordinate that makes the two triangles congruent. Triangle ABC: A(8,4), B(2,6), C(5, 0) Triangle MNO: M(7,4), N(1,2), O(4, y)
Answer:
y = 8
Step-by-step explanation:
Two triangles are said to be congruent if all the three sides and three angles of both triangles are equal.
The distance between two points on the coordinate plane is given as:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\[/tex]
In triangle ABC:
[tex]|AB|=\sqrt{(2-8)^2+(6-4^2)}=\sqrt{40} =2\sqrt{10}\\\\|AC|=\sqrt{(5-8)^2+(0-4)^2}=5\\\\|BC|=\sqrt{(5-2)^2+(0-6)^2 }=\sqrt{45}[/tex]
In triangle MNO:
[tex]|MN|=\sqrt{(1-7)^2+(2-4^2)}=\sqrt{40} =2\sqrt{10}\\\\|MO|=\sqrt{(4-7)^2+(y-4)^2}\\\\|NO|=\sqrt{(4-1)^2+(y-2)^2 }[/tex]
Since triangle ABC and triangle MNO are congruent, hence:
|AB| = |MN| = 2√10, |AC| = |MO| = 5, |BC| = |NO| = √45
[tex]|AC|=|MO|=5\\\\\sqrt{(4-7)^2+(y-4)^2}=5\\\\(4-7)^2+(y-4)^2=25\\\\9 +(y-4)^2=25\\\\(y-4)^2=16\\\\square\ root\ of\ both\ sides:\\\\y-4=4\\\\y=4+4\\\\y=8[/tex]
Hence O = (4, 8)
3/8-1/3
I rly need help and FAST
Answer:
Step-by-step explanation:
1/24
⚠️PLEASE HELP!!⚠️
find the measures of the angles labeled in the figure below.
measure angle EFD
measure angle EHF
measure angle HFG
measure angle G
Answer:
Angle EFG= 90
Angle EHF= 130
Angle HFG=56
Angle G =74
Answer:
angle EFD = 90
angle HFG=56
angle EHF= 29
angle G=73
Step-by-step explanation:
angle EHF=180-51=29
In triangle FGH :
angle FHG = 51 (given)
angle HFG= 90-34= 56( angle EFG given 90)
angle HGF= 180-(51+56) (anglesome prop)
angle G=180-107=73