Answers
The object change direction when the first derivative change its sign,. So we need to find the first derivative and equate this result to zero.
The first derivative is given by
[tex]s(t)=7\frac{5}{2}t^{\frac{3}{2}}-\frac{7}{2}t^{\frac{5}{2}}[/tex]By equating this result to zero ,we have
[tex]7\frac{5}{2}t^{\frac{3}{2}}-\frac{7}{2}t^{\frac{5}{2}}=0[/tex]This implies that
[tex]\frac{7}{2}t^{\frac{3}{2}}(5-t^)=0[/tex]so, the first derivative change its sign when
[tex]\begin{gathered} t=0 \\ and \\ t=5 \end{gathered}[/tex]as we can note in the following graph:
because the graphs falls when t= 5seconds.
This means that the motion objects change direction at t=5 seconds.
Related Questions
Write an equation in slope-intercept form for the line described. Write the slope and y-intercept as improper fractions, if necessary.
passes through (-2, 2), perpendicular to y = -5x-8
Answers
The equation of the line is y = (1/5)x - 8/5, the slope of the line is 1/5 and the y intercept is -8/5
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
The perpendicular line equation is
y = -5x-8
The slope of the perpendicular line = -5
The slope of the main line = -(1/-5)
= 1/5
The line is passing through the point (-2,2)
y = mx + b
-2 = (1/5)(-2) + b
-2 = -2/5 +b
-2 +2/5 = b
b = -8/5
The equation of the line
y = (1/5)x - 8/5
Hence, the equation of the line is y = (1/5)x - 8/5, the slope of the line is 1/5 and the y intercept is -8/5
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What is the slope-intercept form of the equation of the line that passes through (2, -3) and (4, 3)?
A. y = - 3x + 6
B. y= 3x - 12
C. y= 1/3x - 9
D. y= 3x - 9
Answers
The equation of line is D. y = 3x - 9
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The m is a common symbol for slope.
The equation of a straight line is given by y=mx+c where m is the slope, c is the intercept, and x and y are variables.
Formula to be used :
[tex]m=\frac{y_{1}-y_{2} }{x_{1} -x_{2} }[/tex] where( y1,x1) and (y2 ,x2) are the coordinates of the points passing through the line.
Calculating Slope, [tex]m=\frac{3-(-3)}{4-2} =\frac{6}{2} =3[/tex]
Now, writing the equation of line is
[tex]y -y_{1} =m(x-x_{1} )\\y -3 =3(x-4)\\y-3 =3x - 12\\y =3x -12+3\\y =3x -9[/tex]
Thus, the slope-intercept form of the equation is y =3x -9.
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What’s the correct answer answer asap for brainlist
Answers
Answer:
C
Step-by-step explanation:
Answer:
are made of cells
Step-by-step explanation:
Valerie picked a card from a standard deck at random, recorded the suit, then put the card back in the deck and shuffled. If Valerie repeated this 60 times, how many times should she expect to pick a heart?
Answers
Probability is calculated as follows:
[tex]p=\frac{\text{ }number\text{ of favorable outcomes}}{\text{ total number of possible outcomes}}[/tex]In a standard deck of cards, there are 13 hearts and a total of 52 cards. Then, the probability of picking a heart is:
[tex]p=\frac{13}{52}=\frac{1}{4}[/tex]To find how many times she should expect to pick a heart, we have to multiply the number of times the event is repeated (60) by the probability of picking a heart, that is,
[tex]\frac{1}{4}\cdot60=15[/tex]She should expect to pick a heart 15 times
A scale drawing for an apartment is shown below. In the drawing, 2 cm represents5m. Assuming the bed room is rectangular, find the area of the real bedroom.
Answers
The drawn bedroom ookis like this
as this is drawn to scale, to find the area of the real bedroom we should find the lengths of the real bedroom first. We are told that every 2cm represent 5m. So, we will define our scaling factor as
[tex]\frac{5m}{2cm}[/tex]as every 2 cm represent 5m. Now, to calculate the real lengths, we simply take the scaled lengths and multiply it by the scaling factor. So we have s
[tex]2cm\cdot\frac{5m}{2cm}=5m[/tex][tex]4cm\cdot\frac{5m}{2cm}=2\cdot5m=10m[/tex]so the real bedroom looks like this
which is a rectangl of height 210m and base 5m. Recalling tha the area of a rectangle is the product of it s height and its base, we have that the area of this rectangle would be
[tex]A=10m\cdot5m=50m^2[/tex]Find the area of a triangle with a triangle with a base of 18 meters and a height of 20 meters.
Answers
The area of a triangle is given by:
[tex]A=\frac{bh}{2}[/tex]Where:
b = base = 18 m
h = height = 20 m
Then, substitute the values:
[tex]A=\frac{18\times20}{2}=\frac{360}{2}=180m^2[/tex]Answer: 180 m^2
What is the converse of the conditional statement?x is even, then x + 1 is odd.O fx is not even, then x + 1 is not odd.Ox+1 is odd, then x is even.O fx+1 is not odd, then x is not even.Ofx is even, then x + 1 is not odd.
Answers
Given:
Conditional statement x is even, then x + 1 is odd.
Required:
What is the converse of the conditional statement?
Explanation:
The converse statement of a conditional statement "If p then q" is given by "If q then p".
Then, the converse statement of the given conditional statement will be :
If x is odd then x+1 is even.
Answer:
If x is odd then x+1 is even.
The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest:16 ; 17 ; 19 ; 20 ; 20 ; 21 ; 23 ; 24 ; 25 ; 25 ; 25 ; 26 ; 26 ; 26 ; 27 ; 27 ; 28 ; 29 ; 29 ; 32 ; 33 ; 33 ; 34 ; 35 ; 37 ; 39 ; 43
Answers
Given:
Data is given as below
16 ; 17 ; 19 ; 20 ; 20 ; 21 ; 23 ; 24 ; 25 ; 25 ; 25 ; 26 ; 26 ; 26 ; 27 ; 27 ; 28 ; 29 ; 29 ; 32 ; 33 ; 33 ; 34 ; 35 ; 37 ; 39 ; 43
Find:
we have to find Mean, Median and Mode of the given data.
Explanation:
(a) Mean is 27.37
(b) Median is 26
(c) Mode is 25 ; 26
perform the indicated operation 2 1/6+7 3/6
Answers
The solution to the indicated operation will be 9 and 2/3.
We have to find the sum of 2 and 1/6 and 7 and 3/6.
We can write the mixed fractions as:-
2 and 1/6 = 13/6
7 and 3/6 = 45/6
Adding the improper fractions, we get,
(13+45)/6 = 58/6 = 29/3
We can this improper fraction write it as :-
9 and 2/3
Mixed fraction
It is a form of a fraction which is defined as the ones having a fraction and a whole number.
2 and (1/7), where 2 is a whole number and 1/7 is a fraction.
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5m x
= 20mn ???????????????
Answers
Answer:
the answer is 4n
Step-by-step explanation:
20/5 is equal to 4 so if u multiply 5m*4n=20mn
There are 1,150 souvenir paperweights that need to be packed in boxes. Each box will hold 12paperweights. How many boxes will be needed?boxes will be needed to hold all the souvenir paperweights.
Answers
Given data:
Total number of paperweights that needs to be packed in boxes = 1,150
Each box will hold paperweights = 12
Boxes will be needed to hold all the paperweights ,
Boxes = Total number of paperweights / Each box will hold paperweight
= 1,150 / 12
= 95.833
= 96
Thus, the boxes needed to hold all the souvenir paperweights is 96.
What is a biome?
A
B
C
What’s the correct answer answer asap for brainlist
Answers
Option A
Step-by-step explanation:A large naturally occurring community of flora and fauna occupying a major habitat, e.g. forest or tundra. A biome is a large area characterized by its vegetation, soil, climate, and wildlife.
The following table shows the breakdown of opinions for both faculty and students in a recent survey about the new reconstructing of the campus to include an honors college. find the probability that a randomly selected person is either a faculty member in favor of the change or a student who has an opinion either for or against. express your answer as a fraction.
Answers
Given:
The objective is to find the probability that a randomly selected person is either a faculty member in favor of the change or a student who has an opinion either for or against.
Explanation:
The required probability can be calculated as,
[tex]P(\text{AorB)}=P(A)+P(B)-P(AandB)\text{ . . . .(1)}[/tex]Here, P(A) represents the probability of faculty member in favor of the change, P(B) represents the probability of student who has an opinion either for or against.
The probability of faculty member in favor of the change can be calculated as, T
[tex]P(A)=\frac{7}{217}\text{ . . . .(2)}[/tex]The probability of student who has an opinion either for or against can be calculated as,
[tex]\begin{gathered} P(B)=\frac{69}{217}+\frac{75}{217} \\ P(B)=\frac{144}{217}\text{ . . . . . .(3)} \end{gathered}[/tex]Since, it is mutually exclusive events,
[tex]P(\text{AandB)}=0\text{ . . . . . . .(4)}[/tex]To find P(A or B):
On plugging the equations (2), (3) and (4) in equation (1),
[tex]\begin{gathered} P(\text{AorB)}=\frac{7}{217}+\frac{144}{217}+0 \\ =\frac{151}{217} \end{gathered}[/tex]Hence, the probability that a randomly selected person is either a faculty member in favor of the change or a student who has an opinion either for or against is 151/217.
Bisectors in Triangles
Find the value of x, then find FD and FB.
Angle BCD is 90. C
Answers
A "Bisector" in Geometry is a line that divides a line into two different or equal parts. It is used on line segments and angles.
The Value of X = angle BCF =90-45 =45.
What is meant by bisector?A "Bisector" in Geometry is a line that divides a line into two different or equal parts. It is used on line segments and angles.The perpendicular bisector theorem deals with congruent triangle segments, allowing for congruent diagonals from the vertices to the circumcenter. The angle bisector theorem, on the other hand, deals with congruent angles, resulting in equal distances from the incenter to the side of the triangle.A triangle angle bisector is a line segment that bisects one of the triangle's vertex angles and ends on the opposite side. A triangle's three angle bisectors meet at a single point known as the incenter.Angle BCD = 90
angle FCD = 45
The Value of X = angle BCF =90-45 =45.
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A rectangle has a length of x+2 and a width of x+4, what is the perimeter?
Answers
Answer:
4x + 12
Explanation:
The perimeter of a rectangle can be calculated as two times the length plus two times the width. So, the perimeter is:
Perimeter = 2(x + 2) + 2(x + 4)
Applying distributive property, we get:
Perimeter = 2*x + 2*2 + 2*x + 2*4
Perimeter = 2x + 4 + 2x + 8
perimeter = 4x + 12
Therefore, the perimeter is 4x + 12
The center of the circle below is at P. If the angle < APB measures 67°, and the radius is 13 cm., find the length of the arc AB in cm.. (round to the nearest tenth)
Answers
The length s of an arc enclosed by an angle θ (in degrees) in a circle with radius r is:
[tex]s=\frac{\theta}{360º}\times2\pi r[/tex]Replace θ=67º and r=13cm:
[tex]s=\frac{67º}{360º}\times2\pi(13cm)=15.2018...cm\approx15.2cm[/tex]Therefore, the correct choice is option C) 15.2cm.
A ball is thrown from a height of 70 meters with an initial downward velocity of 10 m/s. The bal's height h (In meters) after t seconds is given by the following.h = 70 - 10-512How long after the ball is thrown does it hit the ground?Round your answer(s) to the nearest hundredth.(If there is more than one answer, use the "or" button.)
Answers
Answer:
2.87secs
Explanation:
Given the expression for calculating the height reached by the ball expressed as;
[tex]h(t)=70-10t-5t^2[/tex]The ball will hit the ground when h(t) = 0.
Substituting into the expression given;
[tex]\begin{gathered} 0=70-10t-5t^2 \\ \text{Rearrange;} \\ 5t^2+10t-70=0 \\ \end{gathered}[/tex]Factorize the resulting equation and find the value of t
[tex]\begin{gathered} t\text{ = }\frac{-10\pm\sqrt[]{10^2-4(5)(-70)}}{2(5)} \\ t=\frac{-10\pm\sqrt[]{100+1400}}{10} \\ t=\frac{-10\pm\sqrt[]{1500}}{10} \\ t=\frac{-10\pm38.73}{10} \\ t=\frac{-10+38.73}{10} \\ t=\frac{28.73}{10} \\ t=2.87\sec s \end{gathered}[/tex]This means that it will take 2.87secs for the ball to hit the ground
Factor the common factor out of each expression.1) 5a+10 2) 16k+12
Answers
1) Examining the expressions, let's factorize them taking the LCM out of the parentheses
5a +10 The LCM 5,10 is 5
5(a +2)
16k +12 The LCM 16, 12 is 4
4(4k +3)
2) So the answers are 5(a +2) and 4(4k +3) notice that if we distribute those factors you'll get the initial form.
Samuel Morse determined that the percentage of t's being used in the English language in the 1800's was 12%. A random sample of 600 letters from a current newspaper contained 95 t's. Test the claim that the proportion of t's has changed in modern times, using the current newspaper data and a significance level of 0.05. Determine the z score and find the p value ?
Answers
H0 : p0 = 0.12
H1 : p0 ≠ 0.12
Sample size, n = 600 ; α = 0.05
Zstatistic < Zcritical ; reject H0
P = 95/600 = 0.16
Zstatistic = (p - p0) ÷ sqrt((p0(1 - p0)) /n)
Zstatistic = (0.16 - 0-12)/ sqrt((0.12(0.88))/600)
Zstatistic = 3.01
Zcritical at 0.05, = - 1.96
Zstatistic > Zcritical
robin invests $55 at 10% compounded annually for 3 years. How much will her investment be worth in 3 years?
Answers
the investment after 3 years will be worth $73.21
Explanation:Amount invested = Principal
P = $55
n = number of time scompounded = annually
n = 1
rate = r = 10% = 0.1
FV = future value after 3 years
Using compound interest formula:
[tex]FV\text{ = P(1 +}\frac{r}{n})^{nt}[/tex]substituting the values in the formula:
[tex]\begin{gathered} FV\text{ = }55(1\text{ + }\frac{0.1}{1})^{1\times3} \\ FV\text{ = }55(1\text{ + }0.1)^3 \\ FV\text{ = }55(1.1)^3 \\ FV\text{ = 55(}1.331) \\ FV\text{ = 73.205 approx i}mately\text{ to nearest cents is }73.21 \end{gathered}[/tex]Hence, the investment after 3 years will be worth $73.21
Your new job requires you to calculate the material costs for manufactured goods. One of goods you manufacture is a fabric sample in the shape of a circle. Given the formula A = r², find the area (A) of the fabric sample whose radius (r) is 8.4 x 100 ft. Round your answer to the nearest thousandth. (Use 3.14 for π)
Answers
Solution.
Given that the fabric sample is in a shape of a circle
[tex]Area\text{ of a circle =}\pi r^2[/tex][tex]Given\text{ that r=8.4 x 10}^0\text{ ft}[/tex][tex]\begin{gathered} Area\text{ of the circle = }\pi\text{ x \lparen8.4 x 10}^0\text{\rparen}^2 \\ Area=\text{ 3.14 x 8.4 x 8.4} \\ Area\text{ = 221.5584ft}^2 \\ Area\text{ of the fabric=221.558ft}^2(nearest\text{ thousandth\rparen} \end{gathered}[/tex]The answer is 221.558 ft^2
You accidentally dial one number on your phone's keypad. Find the probability that the number you dialed is greater than or equal to 0.
Answers
The probability of dialling one number of phones keypad and it being a number greater or equal to 0 is 100% as there is no smaller number than 0 in the keypad.
What is probability?Probability is defined as the ratio of favorable outcomes to all possible outcomes of an event. The proportion of positive outcomes, or x, for an experiment with 'n' outcomes can be expressed. The following formula can be used to determine the likelihood of an event.
Probability (Event) = Positive Outcomes/Total Outcomes = x/n
Let's say that we need to make a rain prediction. Both "Yes" and "No" are acceptable responses to this query. Both rain and no rain are possible outcomes. Probability can be used in this case. When throwing coins, rolling dice, or drawing a card from a deck of cards, the results are predicted using probability.
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The polynomial function f(x) has degree 4, a y-intercept of 20, roots of −5 and 4, and a multiplicity 2 root of −1.
Enter f(x)
Answers
The equation of the polynomial is P(x) = -(x - 1)²(x + 5)(x - 4)
How to determine the polynomial equation?The given parameters are
Degree of polynomial = 4y-intercept = 20Roots = -5 and 4Root 1, multiplicity 2The equation of the polynomial can be calculated as
P(x) = a * (x - zero)^ multiplicity
So, we have
P(x) = a * (x - 1)² * (x + 5) * (x - 4)
This gives
P(x) = a * (x - 1)²(x + 5)(x - 4)
From the question, we have
y-intercept = 20
This means that
P(0) = 20
So, we have
20 = a * (0 - 1)²(0 + 5)(0 - 4)
Evaluate products
20 = a * -20
Divide
a = -1
Substitute a = -1 in P(x) = a * (x - 1)²(x + 5)(x - 4)
P(x) = -(x - 1)²(x + 5)(x - 4)
Hence, the equation is P(x) = -(x - 1)²(x + 5)(x - 4)
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which choice shows how to simplify уб + y6A) y^6+6B) y^6×6C) y^6÷6
Answers
Using the above property,
[tex]y^6\cdot y^6=y^{6+6}[/tex].
Find the height
h of a cone
volume V = 32 cm³ and radius
r = 4 cm.
Pls help in simple instructions I don’t understand
Answers
volume V = 32 cm³ and radius r = 4 cm.The height is 6 cm tall.
The cone's height is determined using the cone height formula. Using cone height formulae, the cone's height is given as h = 3V/r 2.
What is the explanation:
Given,
Cone volume = V = 32 cm3
Cone radius = r = 4 cm
Cone height h=
Having said that,
Cone volume = [tex]\pi rx^{2} h/3[/tex]
Assigning values
[tex]32\pi =\pi (4)x^{2} h/3[/tex]
[tex]32\pi =16\pi h/3[/tex]
16 divided by both sides.
[tex]32\pi /16\pi =16\pi /16\pi *h/3[/tex]
[tex]2=h/3[/tex]
[tex]h/3=2[/tex]
Adding 3 to both sides
[tex]3*h/3=*3[/tex]
h=6
The heiht is 6 cm .
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It rained 2 out of the last 12 days in March. If this trend continues, how many rainy days would you expect in April?6759
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
It rained 2 out of the last 12 days in March. If this trend continues,
how many rainy days would you expect in April?
Step 2:
Recall that there are 30 days in the month of April, and for us to have a definite proportion, we need to do the following:
[tex]\frac{2}{12}=\frac{x}{30}[/tex]we cross-multiply and we have that:
[tex]\begin{gathered} 12\text{ x = 2(30)} \\ \text{Divide both sides by 12, we have that:} \\ \text{x=}\frac{60}{12} \\ \text{x = 5 days} \end{gathered}[/tex]CONCLUSION:
It is expected to rain for a given period of 5 days in the month of April.
You use a garden hose to fill a wading pool. If the water level rises 11 centimeters every 6 minutes and you record the data point of (18,y), what is the value of y?
Answers
Given:-
water level rises 11 centimeters every 6 minutes.
To find:-
The y value at the point (18,y).
Considor the time as x axis and the water level as y axis. so we get an graph as,
Now to find the value at the point (18,y). we extend the graph,
So the value of y is 33.
This is our required answer.
now construct line m such that it contains of line segment AE
Answers
Answer:
A line segment AE is part of a line that goes from A to E, so we can make a line m such that it contains line segment AE as follows
Line segment AE is the red part of the line that goes from A to E.
14b. State the domain of the function below. Use interval notationf(x) = 3Vx + 1 - 5
Answers
Given:
[tex]f(x)\text{ = 3 }\sqrt{x+1}\text{ - 5}[/tex]To state the domain of this using interval notation, means to find the values which x may assume for the function above.
We have:
Since there is a root, let's exclude any real number that leads to a negative number.
Here, let's solve for x by setting the radicand to be greater than or equal to zero.
x + 1 ≥ 0
x ≥ 0 -1
x ≥ -1
Therefore, the domain function using notation function will be:
(-1, ∞)
ANSWER:
(-1, ∞)
Find the value of ab when a = 2/7 and b = 2/5 The answer is (Simplify your answer.)
Answers
The expression ab means that a is multiplying b.
Substituting with a = 2/7 and b = 2/5 into the expression we get:
[tex]\frac{2}{7}\cdot\frac{2}{5}=\frac{2\cdot2}{7\cdot5}=\frac{4}{35}[/tex]