Answer:
The position at time t is [tex]s(t) = 8t^2 - 14t -8[/tex]
Step-by-step explanation:
From the question we are told that
The acceleration is [tex]a = 16[/tex]
The velocity at t = 0 is [tex]v(0) = -14[/tex]
The position at time t = 0 is [tex]s(0) = -8[/tex]
Generally acceleration is mathematically represented as
[tex]a(t) = \frac{d v}{dt }[/tex]
=> [tex]\frac{dv}{dt} = 16[/tex]
=> [tex]dv = 16 dt[/tex]
integrating both sides we have
[tex]\int\limits dv = \int\limits16 dt[/tex]
=> [tex]v(t) = 16 t + c[/tex]
Now at t = 0
[tex]v(0) = 16 * 0 +c = -14[/tex]
=> [tex]c = -14[/tex]
So
[tex]v(t) = 16 t -14[/tex]
Generally the position of the body is mathematically represented as
[tex]s(t) = \int\limits v(t)dt[/tex]
So
[tex]s(t) = \int\limits 16t - 14 dt[/tex]
So
[tex]s(t) = 16 \frac{t^2}{2} - 14t + C[/tex]
Now at t = 0
[tex]s(0) = 16 \frac{0^2}{2} - 14(0) + C = -8[/tex]
=> [tex]C = -8[/tex]
So
[tex]s(t) = 8t^2 - 14t -8[/tex]
Rate of change of velocity with respect to time is known as acceleration.
Rate of change of displacement with respect to time is known as velocity.
Body position at time t is given by, [tex]s(t)=8t^{2}-14t-8[/tex]
Data given are, a=16, v(0) = -14, s(0) = -8
Since, [tex]\frac{dv}{dt}=a\\\\\frac{dv}{dt}=16\\\\dv=16dt[/tex]
Integrating both side
We get, [tex]v=16t + C[/tex]
Substituting v(0)=-14 in above equation
We get, C = -14
So, [tex]v=16t-14[/tex]
Since, Rate of change of displacement with respect to time is known as velocity.
[tex]v=\frac{ds}{dt}\\\\ds=vdt\\\\ds=(16t-14)dt[/tex]
Taking integration on both side
We get, [tex]s=16\frac{t^{2} }{2}-14t+c[/tex]
Substituting s(0)= - 8 in above equation
We get, [tex]c=-8[/tex]
So, [tex]s=16\frac{t^{2} }{2}-14t-8\\\\s(t)=8t^{2} -14t-8\\[/tex]
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Calculate the volume of the cube ____ cm³
Answer:
48
Step-by-step explanation:
volume=width×length×hight
2×4×6
48
A group of 4 children and 8 adults are going to the zoo. Each child tickets cost $10, and each adult tickets cost $15. How much will the group spend on tickets to the zoo?
Answer:
160
Step-by-step explanation:
4 times 10 is 40
8 times 15 is 120
add 40 plus 120 and get 160
Step-by-step explanation:
4×10+8×15
=40+120
=$160
If A, B, and C are the vertices of a triangle, find AB + BC + CA.
Answer:
0Step-by-step explanation:
When drawing a triangle, note that the vectors can be drawn either in a clockwise or anticlockwise direction. For a triangle with vertices A, B and C, te vectors are AB, BC and CA
In vector notation CA = - AC (length CA is equal to AC but acting in opposite direction to AC)
and AB+BC = AC
To evaluate AB + BC + CA, we will substitute the vector expression above into the given expression and simplify as shown;
= (AB + BC) + CA
= AC + (-AC)
open the parenthesis
= AC-AC
= 0
Hence the sum of the vector expression AB + BC + CA is a zero vector
On Monday Ken spent half of his money on a new game. The next day he earned $12 mowing lawns. He now has #32. How much money did ken have before he bought the game?
Answer:
Step-by-step explanation:
ken has 64 dollars
What is the volume of a sphere with a radius of 3 inches? 12π cubic inches 24π cubic inches 36π cubic inches 48π cubic inches
Answer:
The answer is
36π cubic inchesStep-by-step explanation:
Volume of a sphere is given by
[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]where r is the radius
From the question
r = 3 inches
Substitute the value into the above formula and solve for the volume
That's
[tex]V = \frac{4}{3}( {3})^{3} \pi \\ = \frac{4}{3} \times 27\pi \\ = 4 \times 9\pi[/tex]We have the final answer as
36π cubic inchesHope this helps you
People wait for sales to_______
1. buy the most goods
2. get the best price for a good
2. get the best price for a good
A ranger in a lookout tower spots two fires on the campground below. Fire A is 75 meters east
and 40 meters south of the tower. Fire B is 37 meters west and 64 meters south of the tower.
If there is a fire hydrant located three-fourths of the way from Fire A to Fire B, find the location
of the fire hydrant relative to the tower.
Answer:
the fire hydrant is 9 meters west and 58 m south of the tower
Step-by-step explanation:
Fire A and Fire B can be represented as a point in the Cartesian coordinate with the tower as the origin. Fire A is 75 meters east and 40 meters south of the tower, It can be represented as (75, -40). Fire B is 37 meters west and 64 meters south of the tower, It can be represented as (-37, -64).
If a point O(x, y) divides a line segment AB in the ratio n:m, with A([tex]x_1,y_1[/tex]) and B([tex]x_2,y_2[/tex]), the point O(x, y) is at:
[tex]x=\frac{n}{n+m}(x_2-x_1)+x_1\\ \\y=\frac{n}{n+m}(y_2-y_1)+y_1[/tex]
The fire hydrant (x, y) divides Fire A(75, -40) and fire B(-37, -64) in the ratio 3:1(three fourth), hence:
[tex]x=\frac{n}{n+m}(x_2-x_1)+x_1=\frac{3}{4}(-37-75) +75=\frac{3}{4}(-112)+75=-84+75\\x=-9 \\ \\y=\frac{n}{n+m}(y_2-y_1)+y_1=\frac{3}{4}(-64-(-40))+(-40)= \frac{3}{4}(-18)-40=-18-40\\y=-58[/tex]
The fire hydrant is at (-9, -58). That is the fire hydrant is 9 meters west and 58 m south of the tower
The location of the hydrant relative to the tower is [tex]\left(-9, -58 \right)[/tex] meters.
How to locate the coordinates of the hydrant relative to the towerIn this question we should use the vectorial formula for a line segment to determine the coordinates of the hydrant relative to the tower ([tex]\vec C[/tex]), in meters:
[tex]\vec C = \vec A + r\cdot (\vec B - \vec A)[/tex] (1)
Where:
[tex]\vec A[/tex] - Coordinates of the fire A relative to the tower, in meters. [tex]\vec B[/tex] - Coordinates of the fire B relative to the tower, in meters. [tex]r[/tex] - Distance ratio.Now we determine the location of the hydrant: ([tex]\vec A = (75, -40)\,[m][/tex], [tex]\vec B = (-37, -64)\,[m][/tex], [tex]r = \frac{3}{4}[/tex])
[tex]\vec C = (75,-40) + \frac{3}{4}\cdot [(-37,-64)-(75,-40)][/tex]
[tex]\vec C = (75,-40) + \frac{3}{4} \cdot (-112,-24)[/tex]
[tex]\vec C = (75,-40) + \left(-84, -18\right)[/tex]
[tex]\vec C = \left(-9, -58 \right)\,[m][/tex]
The location of the hydrant relative to the tower is [tex]\left(-9, -58 \right)[/tex] meters. [tex]\blacksquare[/tex]
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-x+7= -6x-13 how do you solve it
Answer:
-4=x
Step-by-step explanation:
Okay, let's do this step-by-step for the best results!
We need to make sure that common variables can be put together first. If you did not know this, look at PEMDAS.
-x+7=-6x-13
We need to add -x and -6x together. If we do that then you would get,
7=-5x-13
Let's add 13 to 7 now.
20=-5x
Lets divide -5 with 20.
-4=x
I hope this helped!
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = - 4}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ - x + 7 = - 6x - 13}[/tex]
Move 6x to left hand side and change it's sign
[tex] \dashrightarrow{ \sf{ - x + 6x + 7 = - 13}}[/tex]
Move 7 to right hand side and change it's sign
[tex] \dashrightarrow{ \sf{ - x + 6x = - 13 - 7}}[/tex]
Collect like terms
[tex] \dashrightarrow{ \sf{ 5x = - 13 - 7}}[/tex]
Calculate
[tex] \dashrightarrow{ \sf{5x = - 20}}[/tex]
Divide both sides by 5
[tex] \dashrightarrow{ \sf{ \frac{5x}{5} = \frac{ - 20}{5} }}[/tex]
Calculate
[tex] \dashrightarrow{ \sf{x = - 4}}[/tex]
Hope I helped!
Best regards! :D
I need help 2x+y=7 to solve for y
Answer:
X=7-y over 2
Step-by-step explanation:
Subtract yy from both sides.
2x=7-y2x=7−y
2 Divide both sides by 22.
x=\frac{7-y}{2}x=
2
7−y
The equation solved for y is y=7-2x.
The given equation is 2x+y=7.
We need to solve the given equation for y.
How to solve an equation?Solving equations is computing the value of the unknown variable still balancing the equation on both sides. An equation is a condition on a variable such that two expressions in the variable have equal value. The value of the variable for which the equation is satisfied is said to be the solution of the equation. An equation remains the same if the LHS and the RHS are interchanged.
Now, solving the equation for y, we get y=7-2x.
Put x=1, 2, 3, 4,....in the equation and find the y value.
So, put x=1 in equation y=7-2(1)=5.
Put x=2, we get
y=7-2(2)=3
Verification: Put the ordered pair (1, 5) in the equation and verify.
That is, 5=7-2(1)
⇒5=5
Therefore, the equation solved for y is y=7-2x.
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What is the inverse of g(x)= 1/x-1 and is it a function? 1/x Yes 1/x +1 Yes 1/x - 1 No 1/y-1 No
Answer:
Step-by-step explanation:
hello,
[tex]g(x)=\dfrac{1}{x-1}\\\\x=g(g^{-1}(x))=\dfrac{1}{g^{-1}(x)-1} \\ \\g^{-1}(x)-1=\dfrac{1}{x}\\ \\g^{-1}(x)=\dfrac{1}{x}+1=\dfrac{1+x}{x}[/tex]
And this is a function defined for x different from 0.
Thanks
Is the square root of 900 rational
Answer:
Yes it is rational
Step-by-step explanation:
The square root of 900 is a rational number if 900 is a perfect square. It is an irrational number if it is not a perfect square. Since 900 is a perfect square, it is rational number.
Sample A weighed 2.96 pounds, sample B weighed 3.8 pounds, and sample C weighed 4.417 pounds. How much more does sample C weigh than sample A? Betty collected another sample. Sample D weighed 0.67 pounds more than sample A. How much more does sample B weigh than sample D? 0.17 0.17 3.63 3.63 0.787 0.787 1.26
Answer:
4.417 - 2.96 = 1.457
3.8-3.63=0.17
Sample C weighs 1.457 more pounds than Sample A.
Sample B weights 0.17 more pounds than Sample D.
in a given year, residents of a country spent approximately $54.7 billion on their pets. Of this amount, $17.6 billion wa for veterinarian bills. What percent of the total was spent on veterinary care?
Answer:
32.176 %
Step-by-step explanation:
(100% / 54.7) x 17.6 = about 32.176 percent
Do the equation yourself for a more precise answer!
Please and Thank youu
Answer:
5
Step-by-step explanation:
y = 2x - 3
{ x = 4 }
y = 2(4)-3= 8 - 3 = 5
Canada has a population of 1/10 as large as the United States and Canada population is about 32 million about how many people live in United States explain how many zeros in your answer
Answer:
Step-by-step explanation: If Canada(C) is 32,000,000 and America is A and C x 10 = A then 32,000,000 x 10 = A
And to multiply any whole number by 10 you just add a zero to the end so
320,000,000 is the answer which is pronounced "Three hundred twenty million" And there is 7 zeros in the answer
hope this helps mark me brainliest
Which of the following is equal to 7.5 × 4? A. (7 × 4) + (0.5 × 7) B. (7 × 4) + (0.5 × 4) C. (7 + 4) × (0.5 + 4) D. (7 × 4) × (0.5 × 4)
Answer:
012
3
4
5
61
8
9
10 11 12
13 14
OA. 3
OB. 4
C. 5
D. 7
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You buy a new wheel for your bicycle. Thaw diameter of the bicycle wheel is 22 inches.What is the radius of the bicycle wheel?What is the circumference of the bicycle wheel?What is the area of the bicycle wheel?
Answer:
R = 11
C ≈ 69.12
A ≈ 380.13
Step-by-step explanation:
R = d ÷ 2
C = 2πr
A = 2πr²
convert 2 2/3 into an improper fraction
Answer: 8/3
Step-by-step explanation:
Visna had 5 comic books. His brother gave him 4 more comic books. Visna bought some more comic books at the store. Now he has 15 comic books. How many comic books did Visna buy at the store?
Answer:6
Step-by-step explanation:
5+4+× = 15
9+x=15
15-9=x
X=6
what is (+21) ÷ (+7) =
Answer:
3
Step-by-step explanation:
Dimensional analysis. An adult mosquito's lifespan is about 16 days. How many minutes is that?
Answer:
23040 minutes.
Step-by-step explanation:
Its 23040 minutes long because there are 60 minutes in an hour, an 24 hours in a day and 60 times 24 is 1440. Then you multiply 1440 by 16 which equals 23040.
Which is the decimal expansion of 7/22?
0.318
0.318
0.318
0.318
Answer: B
Step-by-step explanation: Cuz I got a calculator
Hope this helps
The decimal expansion of 7/22 is 0.3181818..., which means that the answer is [tex]0.3\overline{18}[/tex]
Option B is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example: so
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find the decimal expansion of 7/22, we need to perform a long division:
0.3181818...
-----------------
22 | 7.0000000
6.6
-----
3.4
3.3
---
10
8
--
20
18
---
20
18
--
200
198
---
20
22
--
-2
Now,
0.3181818 can be written as [tex]0.3\overline{18}[/tex]
Therefore,
The decimal expansion of 7/22 is 0.3181818..., which means that the answer is 0.3181818...
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what is 12x8 please tell me i need to know :) ")
Answer:
96
Step-by-step explanation:
10 x 8 = 80
2 x 8 = 16
so 80 + 16 = 96 :)
The equivalent value of the equation is A = 96
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be p = 12
Let the second number be q = 8
Now , A = pq
On simplifying the equation , we get
A = 12 x 8
So , the left hand side of the equation is equated to the right hand side by the value of 12 x 8
On multiplying 12 times 8 , we get
A = 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8
A = 96
Therefore , the value of A = 96
Hence , the expression is A = 96
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Which is the best description for the graph below? A graph decreases from (0, 3) to (9, 0). The graph increases everywhere. The graph decreases everywhere. The graph remains constant. The graph increases, then decreases.
Answer:
the graph decreases everywhere
Step-by-step explanation:
the left side of the line is higher than the right side which means its a negative slope so it is decreasing
Answer:B
Step-by-step explanation:
1+6v+4=47
Be quick please :D
Answer:
1+ 6v + 4 = 47
collect like terms
5 + 6v = 47
Subtract the 5 from both sides
6v = 42
divide 6 from both sides
v = 7
Given that x = −2 and y = 5, what is the value of 3x+4y−2
Answer:
12
Step-by-step explanation:
Note:
x = -2 ; y = 5
Plug in -2 for x and 5 for y.
3(-2) + 4(5) - 2
Remember to follow PEMDAS. First solve for multiplication, then combine:
3 * -2 = -6
4 * 5 = 20
-6 + 20 - 2
Combine like terms:
20 - 6 - 2 = 12
12 is your value.
~
Answer:
12
Step-by-step explanation:
When answering these types of problems make sure you simplify the expression before substituting
In this case it is not necessasry so substitute x for -2 and y for -5. The expression is now ...
3(-2) + 4(5) - 2
Now just add like term
-6 + 20 -2
12
What are the six trigonometric functions and how are their values determined using the three sides of a right triangle?
Explanation:
Six trigonometric functions are ratio of sides with their angle in right angled triangle.
Six trigonometric functions are:
Sinθ = Perpendicular / Hypotenuse
Cosθ = Base / Hypotenuse
Tanθ = Perpendicular / Base
Cotθ = Base / Perpendicular
Secθ = Hypotenuse / Base
Cosecθ = Hypotenuse / Perpendicular
Maya runs 7 miles in 80 minutes. At the same rate, how many miles would she run in 64 minutes?
Answer:
5.6 miles.
Step-by-step explanation:
7/80=x/64 is our equation
Cross multiply to solve for x
x=7*64/80
x=5.6mi
Hope this helps ^-^
Answer:
5.6 miles
Step-by-step explanation:
Let's set up a proportion using the following setup.
[tex]\frac{miles }{minutes}=\frac{miles }{minutes}[/tex]
We know Maya can run 7 miles in 80 minutes.
[tex]\frac{7miles }{80minutes}=\frac{miles }{minutes}[/tex]
We don't know how many miles she can run in 64 minutes. Let's say she can run x miles in 64 minutes.
[tex]\frac{7miles }{80minutes}=\frac{x miles }{64 minutes}[/tex]
[tex]\frac{7}{80}=\frac{x}{64}[/tex]
We want to solve for x (miles in 64 minutes). Therefore, we must isolate x on one side of the equation.
x is being divided by 64. The inverse of division is multiplication. Multiply both sides of the equation by 64.
[tex]64*\frac{7}{80}=\frac{x}{64}*64[/tex]
[tex]64*\frac{7}{80}=x[/tex]
[tex]64*0.0875=x[/tex]
[tex]5.6=x[/tex]
[tex]x= 5.6 miles[/tex]
Maya can run 5.6 miles in 64 minutes.
Roxannee is buying suppliers for a catering job. She bought a piece of salmon for $31.28. If the cost of the salmon was $9.20 per pund, how many pounds did she buy? (Show your work)
Answer:
she bought 3.4 pounds
Step-by-step explanation:
The expression 36 ÷ 6 · 2 + 1 is equal to _____. 4 18 2 13
Answer:
13
Step-by-step explanation:
We have to use the BODMAS ( Bracket Of Division Multiplication Addition Subtraction) rule here
So first divide
36 ÷ 6 * 2 + 1
6 * 2 + 1
Now multiply
6 * 2 + 1
12 + 1
Now add
12 + 1 = 13
Answer:
13
Step-by-step explanation: