Answer:
7.96 s
Step-by-step explanation:
Given the following :
h = 3t³
After t seconds, that is, t = 2
h = 3(2)³ = 3 × 8 = 24 m
Rate of change, Velocity = dh/dt
dh/dt = 3*3t^(3 - 1) = 3*3t² = 9t²
At t = 2 s ; initial velocity = 9(2)² = 9 × 4 = 36 m/s
From the 3rd equation of motion:
v² = u² + 2gh
Where g = acceleration due to gravity 9.8m/s
upward motion, g = - ve
Displacement = - 24
v² = 36² + 2(-9.8)(-24)
v² = 1296 + 470.4
v² = 1766.4
v = sqrt(1766.4)
= 42.03 m/s
Since final velocity is in downward direction : take it as negative.
Recall, :
Velocity = Displacement / time
Displacement = Velocity × time
Average Velocity = (Initial + final velocity) / 2
Displacement = - 24 m
-24 = [(36 + (-42.03)) /2] × t
-48 = - 6.03t
t = 48 / 6.03
t = 7.96s
The sum of ten and the quotient of a number 2 and 6.
Answer:
10+(n/2)=6
Step-by-step explanation:
Let the number be n
Quotient of n and 2 is (n/2)
Sum of this and 10 is
10+(n/2)=6
Help me find this asap
Answer:
DQ = [tex]\frac{5}{(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}-\sqrt{x+h})}[/tex]
Step-by-step explanation:
Given function is f(x) = [tex]\frac{5}{2-\sqrt{x}}[/tex]
f(x + h) = [tex]\frac{5}{2-\sqrt{x+h} }[/tex]
Therefore, indicated difference quotient will be,
DQ = [tex]\frac{f(x+h)-f(x)}{h}[/tex]
Now we substitute the values in the difference quotient,
DQ = [tex]\frac{\frac{5}{2-\sqrt{x+h} }-\frac{5}{2-\sqrt{x}}}{h}[/tex]
= [tex]\frac{5(2-\sqrt{x})-5(2-\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]
= [tex]\frac{10-5\sqrt{x}-10+5\sqrt{x+h}}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]
= [tex]\frac{-5\sqrt{x}+5\sqrt{x+h}}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]
= [tex]\frac{5(-\sqrt{x}+\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})}[/tex]
= [tex]\frac{5(-\sqrt{x}+\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]
= [tex]\frac{5[(x+h)-x]}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]
= [tex]\frac{5h}{h(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]
= [tex]\frac{5}{(2-\sqrt{x})(2-\sqrt{x+h})(\sqrt{x}+\sqrt{x+h})}[/tex]
Find the equation of the line in slope-intercept form that passes through the following point with the given slope. Simplify your answer.
Point (9,−11); Slope=−8
Answer:
Step-by-step explanation:
y + 11 = -8(x - 9)
y + 11 = -8x + 72
y = -8x + 61
The equation of the line in slope-intercept form having the given point and slope is: y = -8x + 61.
How to Find the Equation of a Line in Slope-intercept Form?Slope-intercept formis expressed as y = mx + b.
Given the following:
A point = (9, -11) = (a, b)
Slope = -8 = m
Substitute m = -8 and (a, b) = (9, - 11) into y - b = m(x - a)
y - (-11) = -8(x - 9)
Rewrite in slope-intercept form
y + 11 = -8x + 72
y = -8x + 72 - 11
y = -8x + 61
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Using the slope formula, find the slope of the line through the given points.
(2,6) and (6,2)
Answer:
m=(y2-y1)/(x2-x1)
=(2-6)/(6-2)
=-4/4
=-1
Step-by-step explanation:
SOLVING EQUATIONS
1) Solve 3x - 5 = -26
SOLVING QUADRATIC EQUATIONS
Answer:
x = -7
Step-by-step explanation:
This isn't a quadratic.
Step 1: Write out equation
3x - 5 = -26
Step 2: Add 5 to both sides
3x = -21
Step 3: Divide both sides by 3
x = -7
Step-by-step explanation:
[tex]\sf \bf We \: have,[/tex]
[tex]\sf 3x - 5 = -26[/tex]
[tex]\sf : \implies \bf 3x - 5 \green{+5}= -26\green{+5}[/tex]
[tex]\sf : \implies \bf 3x =-21[/tex]
[tex]\sf : \implies \bf 3x× \green{\dfrac{1}{3}}=-21× \green{\dfrac{1}{3}}[/tex]
[tex]\sf : \implies \bf \underline{\boxed{\sf \bf x = -7}}[/tex]
An elm tree is 3 times as tall as an apple tree. The apple tree is 10 feet tall. How tall is the elm tree?
Answer:
LET ME GUESS hmmmm... OH WAIT 30
Step-by-step explanation:
Answer:
30 ft
Step-by-step explanation:
The elm tree is 3 times as tall as the apple tree.
The elm tree is 3 times as tall as 10 ft.
3 * 10 ft = 30 ft
A toy company uses the linear model y=-2x+380 to predict the decline in sales of a toy after it has been on the market more than one year. If x is the number of months after the first year and y is the number of toys sold in hundreds during that month how many toys will be sold 11 months after the first year
Answer:
358 toys sold 11 months after the first year.
Step-by-step explanation:
y = - 2x + 380
x is number of months after release in this case x = 11
y is number of toy sold in the hundreds.
y = - 2 ( 11 ) + 380
y = - 22 + 380
y = 358
Number of toys sold 11 months after the first year = 358
What is linear equation?A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.
Given,
Linear equation
y = - 2x + 380
x is number of months after release
y is number of toy sold in the hundreds.
No. of months, x = 11
Putting value of x in above equation
y = - 2 ( 11 ) + 380
y = - 22 + 380
y = 358
Hence, 358 toys sold 11 months after the first year.
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If Mikayla rides for 2 hours on a bicycle, what is her rate if she rides for 22 miles?
Define intersecting lines
Answer:
lines that meet at a point
The temperature is _____ °C
Answer:
25 0r 26 F
Step-by-step explanation:
around .5 - 1 C
Which planet is an inner planet, and which one is an outer planet? Explain your answer.
The correct answers are Planet A 16 hours - Inner planet and planet B 1,408 hours - Outer planet.
What is a planet?Large, circular celestial objects that are neither stars nor their remnants are known as planets. The inner planets are the ones that are much closer to the sun, thus they have much smaller orbits around it and it takes them much less time to circle around it. Also, these planets are much smaller, which enables them to spin around their axis much quicker too, so one day passes much quicker.
The outer planets are the total opposite. They are much further from the sun, so for them to be able to make a single circle around the sun it takes much more time, and also because they are much bigger, it takes them much more time to spin around their own axis, thus making one day much longer than the days of the inner planets.
The complete question is given below as:-
Which planet is an inner planet, and which one is an outer planet? Explain your answer. Planet A 16 hours planet B 1,408 hours
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Evaluate 10bc-b+c, when b = 3 and c= 2.
I need help ASAP!!!!!!!
Write an equation of the line passing through the points (3,7) and (-1,-13)
Answer:
Step-by-step explanation:
(-13 - 7)/(-1 + 3) = -20/2 = -10
y - 7 = -10(x - 3)
y - 7 = -10x + 30
y = - 10x + 37
Find a vector equation for the line through the point P = (4, 2, 4) and parallel to the vector v = < -2, -5, -3 > . Assume r(0) = 4i + 2j + 4k and that v is the direction vector of the line. R(t) = Rewrite this in terms of the corresponding parametric equations for the line. x = ______y = ______z = ______
Answer:
The parametric equations are
x = - 2 t + 4 , y = - 5 t + 2 , z = - 3 t + 4
Step-by-step explanation:
Step(i):-
Given point P = ( 4,2,4)
Given vector is -2 i - 5 j - 3 k
The vector equation of a line through the point a⁻ and parallel to b⁻ is
r⁻ = a⁻ + t b⁻
Given r⁻ = 4 i + 2 j + 4 k
r⁻ = 4 i + 2 j + 4 k + t (-2 i - 5 j - 3 k)
Step(ii):-
The Cartesian form
[tex]\frac{x-a_{1} }{b_{1} } = \frac{y-a_{2} }{b_{2} } = \frac{z-a_{3} }{b_{3} } = t[/tex]
[tex]\frac{x-4 }{-2 } = \frac{y-2 }{-5 } = \frac{z-4 }{-3 } = t[/tex]
[tex]\frac{x-4 }{-2 } = t[/tex]
⇒ x - 4 = -2 t
⇒ x = - 2 t + 4
[tex]\frac{y-2 }{-5 } = t[/tex]
⇒ y - 2 = - 5 t
⇒ y = - 5 t + 2
[tex]\frac{z-4 }{-3 } = t[/tex]
z - 4 = -3 t
z = - 3 t + 4
Conclusion:-
The parametric equations are
x = - 2 t + 4 , y = - 5 t + 2 , z = - 3 t + 4
what is the answer to 1.58x1.78=
Simplify the expression: 42x3y6 6xy6 A) 7x2y12 B) 7x2y C) 36x2y12 D) 7x2
Answer:
D
Step-by-step explanation:
So first you simplify
Step 1: (2•3•7x3y6) (2•3xy6)
Step 2: you divide x3 by x1 = x (3-1) = x2
step 3: You cancel out y6 as it appears on both sides of the fraction line.
step 4: cancel out 2 as it appears on both sides.
step 5: cancel out 3 as it appears on both sides.
step 6: final result 7x2
What percent of 150 is 900
Answer:
600 %
Step-by-step explanation:
x · 150 ÷ 100 = 900
150x = 90000
x = 600
Find the counterexample to show that the statement is incorrect. The difference of any two counting numbers will be a counting number Choose the correct answer below. A. 3-5= -2, which is not a counting number. B. 7-4 = 3, which is not a counting number. C. 10-2 = 8, which is counting number D. There is no counterexample. The statement is correct.
Answer:
A. 3-5= -2, which is not a counting number.
Step-by-step explanation:
Counting numbers are non negative numbers greater than 1 up to infinity. Counting numbers are also called natural numbers, and they do not include the negative numbers.
The statement states that "The difference of any two counting numbers will be a counting number"
From option A we can disprove that, since we can see that not all the difference between two counting numbers gives a counting number.
3 is a counting number
5 is a counting number
The difference between 3 and 5 gives -3, which is not a counting number.
This is a counterexample to the statement above.
Evaluate the given expression if x= -3 and y=6.
x+3y / 6+3y
Answer:
5/8
Step-by-step explanation:
The given expression is [tex]\dfrac{x+3y}{6+3y}[/tex]
We need to find of above expression when x = -3 and y = 6
Put x = -3 and y = 6 in given expression such that,
[tex]\dfrac{x+3y}{6+3y}=\dfrac{(-3)+3(6)}{6+3(6)}\\\\=\dfrac{-3+18}{6+18}\\\\=\dfrac{15}{24}\\\\=\dfrac{5}{8}[/tex]
So, the value of given expression is 5/8.
Business: Discount Pricing A store sells refurbished
iPhones that cost 12% less than the original price. If the new price of a refurbished iPhone is $572, what was the original price? How much is saved by purchasing the refurbished
The original price of the iPhone will be $650 thus the buyer saved $78 by buying the refurbished mobile.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
Let's say the original price of the mobile is x.
12% of x is 0.12x
The cost of refurbished mobile will be as x - 0.12x = 0.88x
0.88x = 572
x = $650
The amount saved = $650 - $572 = $78
Hence "The original price of the iPhone will be $650 thus the buyer saved $78 by buying the refurbished mobile".
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42 is 64% of what number
Answer:
the answer is 65.625, 42 is 64% of 65.625
How can you tell that 7. 630 and 7. 63 are equivalent decimals?
because if you add a zero onto something after the decimal point it doesn't increase or decrease the value of the number.
7.630 is literally just 7.63.
but if it was 76.3 and 760.3 it would be different.
Rewrite as a logarithmic equation.
*=8
Answer:
yes in the steps
Step-by-step explanation:
conclusive
1 point
#11: At MVP Fitness, the enrollment fee is $95 and it costs $40 per month.
At the Body Factory, the enrollment fee is only $25, but it costs $50 per
month. Write and solve an equation to find the number of months at which
the total cost charged by the two companies would be the same.
Your answer
Write 18% as a fraction
Hi there!
~
[tex]18[/tex]% [tex]= \frac{9}{50}[/tex]
Answer9/50:
Step-by-step explanation:
18/100
18÷2
100÷2
9/50
Suppose R is the solid bounded by the plane z=5x, the surface z=x2, and the planes y=0 and y=3. Write an iterated integral in the form below to find the volume of the solid R.
I have attached the complete question.
Answer:
See 2nd attachment
Step-by-step explanation:
We are told that R is the solid bounded by the plane z = 5x, the surface z = x², and the planes y = 0 and y = 3.
Thus, the region in the xz plane would be defined as;
0 ≤ x ≤ 3 and x² ≤ z ≤ 5x
For the iterated integral for the volume of the solid R, see 2nd attachment.
You want to share 1000 dollars between you and 5 friends,
Can you share the money evenly
What is the maximum amount that can be shared evenly
What is then the leftover as a fraction
Answer:
the answer is 200
Step-by-step explanation:it's because
you have to divide 1000 in to 5 and 1000 divided by 5 is 200
(3 + 5i) + (11 -7i) Write answer in standard form a +bi
Answer:
14-2i
Step-by-step explanation:
[tex]\left(3+5i\right)+\left(11-7i\right)\\\\Group\:the\:real\:part\:and\:the\:imaginary\:part\:of\:the\:complex\:number\\\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\\\=\left(3+11\right)+\left(5-7\right)i\\3+11=14\\5-7=-2\\\\=14-2i[/tex]
What is the image of (-5, -8) after a reflection over the y-axis?
Answer:
[tex](5,-8)[/tex]
Step-by-step explanation:
The rule for a reflection over the y-axis is
[tex](x,y) -> (-x,y)[/tex]
In this situation, we have to change the sign of x.
[tex](-5,-8) -> (5,-8)[/tex]
The mean absolute deviation is best described as:
The value obtained when averaging the distances between each data point in the data set and the mean.
The value obtained when you add all the values in the data set and divide by the number of values.
The difference between the means of two similar data sets.
An approximation of the center of a data set.
Answer: It’s the second one
Step-by-step explanation: