The instantaneous velocity of the ball after 4 seconds is -0.4 m/s
Step-by-step explanation:
If f(x) is the function which represents the distance that a particle moves after x seconds, with velocity v and acceleration a, then
v(x) = f'(x) ⇒ first derivativea(x) = f"(x) ⇒ second derivative∵ A ball is thrown vertically from the top of a building
∵ The height of the ball after t seconds can be given by the
function s(t)= -0.1(t -2)² + 10
- To find the function of the velocity differentiate s(t)
∵ s(t) = -0.1(t - 2)² + 10
- Solve the bracket
∵ (t - 2)² = t² - 4t + 4
∴ s(t) = -0.1(t² - 4t + 4) + 10
- Multiply the bracket by -0.1
∴ s(t) = -0.1t² + 0.4t - 0.4 + 10
- Add the like terms
∴ s(t) = -0.1 t² + 0.4t + 9.6
Now let us differentiate s(t)
∵ s'(t) = -0.1(2)t + 0.4(1)
∴ s'(t) = -0.2t + 0.4
- s'(t) is the function of velocity after time t seconds
∵ s'(t) = v(t)
∴ v(t) = -0.2t + 0.4
We need to find the instantaneous velocity of the ball after 4 seconds
Substitute t by 4
∴ v(4) = -0.2(4) + 0.4
∴ v(4) = -0.8 + 0.4
∴ v(4) = -0.4
∴ The v is -0.4 m/s ⇒ -ve means the velocity is downward
The instantaneous velocity of the ball after 4 seconds is -0.4 m/s
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Final answer:
To determine the estimated instantaneous velocity of the ball after 4 seconds, calculate the derivative of the height function s(t) and evaluate it at t = 4 seconds to find the velocity of -0.2 m/s.
Explanation:
The estimated instantaneous velocity of the ball after 4 seconds can be found by calculating the derivative of the height function s(t) with respect to time t, which gives the velocity function v(t) = -0.2(t - 2). Evaluating this at t = 4 seconds, we get a velocity of -0.2 m/s.
A principal of $4000 is invested at 8.75% interest, compounded annually. How many years will it take to accumulate $14,000 or more in the account?
Answer: 14.9 years, approximately 15years.
Step-by-step explanation:
Formular for finding the amount of a compound interest
A = P ( 1 + r/100 )n
From the question given,
A = $14,000; P = $4,000; n = ? (year)
Rate = 8.75%.
Substitute for these values in the above equation, we therefore have
14,000 = 4,000(1+ 8.75/100)n (is raised to the power of n)
Divide both side by 4,000
14,000/4,000 = 4,000(1+8.75/100)n/4,000.solving the one in bracket fractionally
3.5 = {(100 + 8.75)/100}n
3.5 = (108.75/100)n
3.5 = 1.0875n( raised to the power of n).In order to solve for 'n' to know the number of years, we take the logarithm of both side.
Log.3.5 = Log(1.0875)n
Going by the law of logarithm,
Log 3.5 = nLog1.0875
Checking your log table, log 3.5 =0.5441 and log1.0875 = 0.0364
Equating both and solve for n
0.5441 = 0.0364n
Divide through by the coefficient of n,
n = 0.5541/0.0364
n = 14.9 years
Approximately 15 years
Hence it will take $4,000 at 8.75% rate to amount to $14,000 a period of 14.9 years approximately 15years.
Write the equation of the line that passes through the point (3, -5) and is perpendicular to the line x = 4.
Answer:
Step-by-step explanation:
slope of line perpendicular to x=4 is 0
reqd. eq. of line is y=-5
Which answer is equal to i^39
Answer:
-i
Step-by-step explanation:
if sin square theta = 0.75, then cos =
Answer:
[tex]\cos\theta=\pm0.5[/tex]
Step-by-step explanation:
Given:
[tex]\sin^2\theta=0.75[/tex]
To find [tex]\cos\theta[/tex]
Using trigonometric relations for sums and differences of squares of the ratios.
We know:
[tex]\sin^2\theta+\cos^2\theta =1[/tex]
Plugging in [tex]\sin^2\theta=0.75[/tex] in the above relation.
[tex]0.75+\cos^2\theta =1[/tex]
Subtracting both sides by 0.75.
[tex]0.75+\cos^2\theta-0.75 =1-0.75[/tex]
[tex]\cos^2\theta =0.25[/tex]
Taking square root both sides.
[tex]\sqrt{\cos^2\theta} =\sqrt{0.25}[/tex]
∴ [tex]\cos\theta=\pm0.5[/tex] (Answer)
solve plzz!?!!?!?!?!?
Answer:
[tex]([7]x+[2])^2[/tex]
Step-by-step explanation:
Given:
[tex]49x^2+28x+4[/tex]
We need to factorize the given trinomial.
To solve the above expression we will Split the product of first term and third term to get the second term by either adding or subtracting.
So we get;
[tex]49x^2+14x+14x+4\\\\7x(7x+2)+2(7x+2)\\\\(7x+2)(7x+2)\\\\(7x+2)^2[/tex]
Hence Final Answer is:
[tex]([7]x+[2])^2[/tex]
Find the value of x.
124°
95°
92°
143
Answer:
92 are the value of x I think
Find the value of x and y
Answer:
y = 110°
x = 55°
Step-by-step explanation:
The line is a transversal.
∠Y = 110°, according to the rule of transversals.
Also, 2X = Y, since in a transversal the vertical angles are equal.
Vertical angles are the ones that are at the intersection of the parallel line and the transversal.
So, 2X = Y = 110°
⇒ X = 55°
Hence, X = 55° and Y = 110°.
what is 100000 less than 5 million
Answer: 4,900,000
Step-by-step explanation:
5 million - 100 thousand = 4.9 million
Type the correct answer in each box.
A circle is centered at the point (-7, -1)
The radius of the circle is
Answer:
Part 1) The radius is [tex]r=17\ units[/tex]
Part 2) The points (-15,14) and (-15,-16) lies on the circle
Step-by-step explanation:
The correct question is
A circle is centered at the point (-7, -1) and passes through the point (8, 7).
The radius of the circle is ____units.
The point (-15,
?) ) lies on this circle
step 1
Find the radius of the circle
we know that
The distance from the center to any point on the circumference is equal to the radius.
we have
[tex](-7,-1),(8,7)[/tex]
Find the distance
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute
[tex]r=\sqrt{(7+1)^{2}+(8+7)^{2}}\\r=\sqrt{(8)^{2}+(15)^{2}}\\r=\sqrt{289}\\r=17\ units[/tex]
step 2
The point (-15,y) lies on the circle
we know that
If a ordered pair lie on the circle, them the ordered pair must satisfy the equation of the circle
The equation of the circle is
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
The center is (-7,-1) an the radius is 17 units
substitute
[tex](x+7)^{2}+(y+1)^{2}=17^{2}\\(x+7)^{2}+(y+1)^{2}=289[/tex]
substitute the x-coordinate of the point and solve for the y-coordinate
For x=-15
[tex](-15+7)^{2}+(y+1)^{2}=289\\(-8)^{2}+(y+1)^{2}=289\\64+(y+1)^{2}=289\\(y+1)^{2}=289-64\\(y+1)^{2}=225[/tex]
square root both sides
[tex](y+1)=\pm15\\y=-1\pm15\\y=-1(+)15=14\\y=-1(-)15=-16[/tex]
therefore
The points (-15,14) and (-15,-16) lies on the circle
see the attached figure to better understand the problem
The question relates to the properties of a circle in a coordinate system, where the circumference and area can be calculated using the radius. The circumference of a circle is found using C = 2πr, and the area is A = πr². Without a given radius, these formulas are a guide for any calculations that may be done once the radius is known.
Explanation:The question asks about the properties of a circle given its center and radius, which fall under the topic of Geometry in Mathematics. No specific value for the radius is provided, so the answer should include an explanation of how one might calculate various properties of a circle, such as the circumference or area, given a radius.
Understanding the Circle
A circle with its center located at (-7, -1) means it is positioned on a coordinate system at that point. If a radius was provided, the circumference of the circle would be calculated using the formula C = 2πr and the area using A = πr², where 'r' represents the radius of the circle and 'π' (pi) is approximately 3.14159. For example, if r = 1.2 m, the area calculated to two significant figures would be A = 4.5 m².
For a circle to fit perfectly inside a square, its diameter should be equal to the side of the square; this implies that a = 2r. The area of the square is a² = 4r², and a circle inside this square would have an area of approximately three-quarters of the square, or near πr². The perimeter (circumference) of the circle is somewhat close to 6r as the perimeter should be 2πr.
A pet store sold 35 siamese cats. If the ratio of siamese cats to house cats sold was 7:3 what is the combined amount of cats sold
Answer:
50
Step-by-step explanation:
Answer:
50
Explanation:
Which ordered pair belongs to the solution set of the equation y = x2 - 2x + 1?
A. (510)
B. (-1,3)
c. (1,2)
D. (3,4)
The correct ordered pair for the given equation is D. (3,4).
To find the correct ordered pair, we substitute the x-value from each pair into the equation and check if the resulting y-value matches the one in the ordered pair.
Substituting x = 5 into the equation gives us 52 - 2(5) + 1 = 25 - 10 + 1 = 16, which does not match the y-value of 10 in the ordered pair (5,10), so A is not correct.
Substituting x = -1 gives us (-1)2 - 2(-1) + 1 = 1 + 2 + 1 = 4, which does not match the y-value of 3 in (-1,3), so B is not correct.
Substituting x = 1 gives us 12 - 2(1) + 1 = 1 - 2 + 1 = 0, which does not match the y-value of 2 in (1,2), so C is not correct.
Finally, substituting x = 3 into the equation gives us 32 - 2(3) + 1 = 9 - 6 + 1 = 4, which matches the y-value in the ordered pair (3,4), making D the correct answer.
Therefore, the correct ordered pair is D. (3,4).
Which of the following systems of linear equations has an infinite number of solutions?
Answer:
Here we do not have the options, but ill try to give an answer.
A system of equations is something of the shape:
A1*x + B1*y = C1
A2*x + B2*y = C2
Where this is a linear relationship, you could have a more complex system, but this will work for the example.
If you want to have a unique solution for a system of equations, you need to have the same number of linearly independent equations (this means that the equations are not repeated, like for example in x + y = 2, and 2x + 2y = 4, where the second equation is equal to two times the first one) than the number of variables, so if we have two variables X and Y, we need to have two linearly independent equations.
If we have less, suppose that you have two variables and only one equation, you will have:
A1*x + B1*y = C1
y = (C1 - A1*x)/B1
Here, for each value of x you have a different value of y, so you have infinite solutions.
So for an answer this you need to find the system where the number of linearly independent equations is smaller than the number of variables.
The florist makes the greatest number of identical
arrangements with the lilies and the daisies. Which
combination describes the arrangements?
6 arrangements with 10 lilies and 6 daisies
6 arrangements with 6 lilies and 10 daisies
12 arrangements with 10 lilies and 6 daisies
12 arrangements with 5 lilies and 3 daisies
Answer:
d
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
please solve this equation
Evaluate.
12.25 - 7 2/3 = 12 1/4 - 7 2/3 = 12 3/12 - 7 8/12 = 4 7/12
answer: B
Which scooter uses fewer gallons after 1,350 miles driven?
Ebony is cutting dough for pastries in her bakery. She needs all the pieces to be congruent triangles and has ensured that segment EF ≅ segment ON and ∠MON ≅ ∠GEF. What would Ebony need to compare in order to make sure the triangles are congruent by SAS?
Answer:
NM and FG
Step-by-step explanation:
To make sure the triangles are congruent by SAS, Ebony needs to compare the lengths of two sides and the measure of the included angle of the triangles.
Explanation:In order to make sure the triangles are congruent by SAS (Side-Angle-Side), Ebony would need to compare the lengths of two sides and the measure of the included angle of the triangles.
Specifically, Ebony would need to compare:
The lengths of segment EF and segment ONThe measure of ∠MON and ∠GEFIf the length of segment EF is equal to segment ON and the measure of ∠MON is equal to ∠GEF, then the triangles will be congruent by the SAS postulate.
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Sierra join a video rental club she paid an inutiatiin fee of 12.75 and it cost 0.75 per video that she rented write and equation show the total amount, t, Sierra pay to rent v videos.
Answer:
12.75 + 0.75v = t
Step-by-step explanation:
12.75 is the fee she has to pay to join so you would add that to the cost of videos she rented. Since 0.75 is the cost of one and you don't know how many she rented you would put a variable which in this case would be "v". So if she payed the fee and rented 2 videos it would be 12.75 + 0.75(2) = 14.25
The correct equation to represent the total amount Sierra pays to rent videos is:
[tex]\[ t = 0.75v + 12.75 \][/tex]
Where [tex]\( t \)[/tex] represents the total cost, [tex]\( v \)[/tex] represents the number of videos Sierra rents, [tex]\( 0.75 \)[/tex] is the cost per video, and [tex]\( 12.75 \)[/tex] is the initial fee Sierra paid to join the video rental club. The term [tex]\( 0.75v \)[/tex] calculates the total cost of renting [tex]\( v \)[/tex] videos, and adding [tex]\( 12.75 \)[/tex] accounts for the initial fee. This equation allows us to determine the total cost [tex]\( t \)[/tex] for any number of videos [tex]\( v \)[/tex] that Sierra rents.
Can u please help me I dont understand it
Answer:
11.43 kilometers
Step-by-step explanation:
Answer:
11.43 kilometers.
Step-by-step explanation:
All you have to do is add the two distances (AKA numbers, to make it even simpler). It doesn't matter what distance was traveled by train or bus! The point is that the distances traveled were both in kilometers! With that being said, all we have to do is add 7.22 + 4.21, and voila! We get 11.43!
Hope this answer helps! Please rate it and give me Brainliest! :D
Have a great day!
A person is standing 50 ft from a statue. The person looks up at an angle of elevation of 8 degrees when staring at the top of the statue. Then the person looks down at an angle of 14 degrees when staring at the base of the statue. How tall is the statue to the nearest tenth of a foot?
The height of the statue is 19.5 feet.
Why?
We can solve the problem using trigonometric formulas. In this case, we are going to use the trigonometric formula of the tangent.
We know that the person is standing 50ft from the statue, so, it will be the base of the two triangles formed by both angles (elevation and depression)
Using the trignometric formula, we have:
First triangle:
[tex]tg(\alpha )=\frac{h_{1}}{base} \\\\tg(8\°)=\frac{h_{1}}{50ft}\\\\0.14*50ft=h_1\\\\h_1=7ft[/tex]
Second triangle:
[tex]tg(\alpha )=\frac{h_{2}}{base} \\\\tg(14\°)=\frac{h_{1}}{50ft}\\\\0.25*50ft=h_1\\\\h_1=12.5ft[/tex]
Now, the total height of the statue will be:
[tex]TotalHeight=h_1+h_2=7ft+12.5ft\\\\TotalHeight=19.5ft[/tex]
Have a nice day!
In this question, we utilize trigonometry to calculate the height of the statue. By using the tangent of the given angles and the known distance from the observer to the statue, we can find the lines of sight when looking up and down. Subtracting these two measurements gives us the height of the statue, which we find to be 5.2ft.
Explanation:This question is about applying trigonometry to find the height of an object, in this case, a statue. First, we need to find the height of the line of sight when the person looks up and when they look down. The height for the line of sight when looking up can be found using the formula for the tangent of an angle: tan(θ) = opposite side/adjacent side. Applying this formula, we find that the height of this line of sight is tan(8°) * 50ft = 7.1 ft. Similarly, when looking down, the height is tan(14°) * 50ft = 12.3 ft.
The height of the statue is the difference between these two heights. Therefore, we find: 12.3ft - 7.1ft = 5.2ft
This is a simple application of the concept of the tangent of an angle in a right triangle, a basic part of trigonometry.
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Which correlation coefficient best matches the graph?
A) r = 0.91
B) r = 0.34
C) r = -0.83
D) r = -0.25
(PLEASE give right awnser. It's 11pm and Im so tired and want to get this over with. I still have other homework too :/)
Answer:
The answer is C, r = -0.83
Step-by-step explanation:
The graph has a negative slope, and the correlation between the points isn't super spread out. Therefore, the answer must be C because A and B are for positive slopes and D would be used for a graph with less correlation.
The correlation coefficient best matches the graph. The answer is C,
r = -0.83.
We have given that,
A) r = 0.91
B) r = 0.34
C) r = -0.83
D) r = -0.25
We have to determine the best matches graph.
What is the meaning of the correlation coefficient?The correlation coefficient is the specific measure that quantifies the strength of the linear relationship between two variables in a correlation analysis.
The graph has a negative slope, and the correlation between the points isn't super spread out.
Therefore, the answer must be C because A and B are for positive slopes and D would be used for a graph with less correlation.
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Answer of this question
Answer:
y = tan(x +π/2)
Step-by-step explanation:
It can be helpful to start with a simple sketch of the function you have and of the tangent function. Then, you can see the relationship.
The tangent function is always rising, has vertical asymptotes at -π/2 and π/2, and has a zero crossing at x=0.
The function we want is always rising, has vertical asymptotes at x=0 and x=±π, and a zero crossing at x=-π/2.
We can create the function we want by shifting the tangent function to the left by π/2. The formula that does that is ...
y = tan(x +π/2)
While in Europe, if you drive 117 km per day, how much money would you spend on gas in one week if gas costs 1.10 euros per liter and your car's gas mileage is 42.0 mi/gal ? Assume that 1euro = 1.26dollars.
You would spend $63.58 on gas per week.
Step-by-step explanation:
Given,
Distance per day = 117 km
Distance in a week = 117*7 = 819 km
1 km = 0.6214 mile
819 km = 819*0.6214 = 508.93 miles
Car's mileage = 42.0 mi/gallons
Let,
x be the gallons for 508.93 miles
x gallons = [tex]\frac{508.93}{42}=12.12[/tex]
Therefore,
12.12 gallons of gas is needed for one week.
1 US gallon = 3.785 liters
12.12 gallons = 12.12*3.785
12.12 gallons = 45.87 liters
Cost of gas per liter = 1.10 euro
Cost of 45.87 liters = 1.10*45.87 = 50.457 euros
1 euro = $1.26
50.457 euros = 1.26*50.457 = $63.58
You would spend $63.58 on gas per week.
Keywords: multiplication, division
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A large cheese pizza costs $11.99 a medium cheese pizza costs $8.99 how much do 2 large and 3 medium pizzas cost? (Estimate to)
Answer:
$50.95
Step-by-step explanation:
2(11.99)+3(8.99)=50.95
Drag each equation to show if it could be a correct first step to solving the equation
4(1 + x) = 20.
Answer:
4+4x=20
4x=20-4
4x=16
x=16/4
x=16
AnswerAnswerAnswerAnswerAnswerAnswerAnswer
PLEASE ITS SUPER SUPER URGENT
3/5 divided by 1/3
Answer: 3/5 * 3/1 is 9/5 I think
Step-by-step explanation: Go to a calculator and type it but I think it’s KCF so yeah
Answer:
9/5 or 1.8
Step-by-step explanation:
3/5 * 3/1 = 9/5 or 9 divided by 5 gets 1.8
Select two options that correctly describe the graph.
A. discrete
B. continuous
C. linear
D. nonlinear
Answer:
[see pdf]
Step-by-step explanation:
The graph makes a straight line, not a curve, so it is linear.
However, the graph has only points, not a full line, so it's also discrete.
(also yes I meant of instead of on in the pdf)
Answer:
A. discrete, C. linear
Step-by-step explanation:
By analysing the graph, it is evident that model is discrete since there is only information of certain points and shows a linear behavior, as there is a constant rate between dependent and independent variable. So, the right choices are A and C.
see i don't mind giving my points away..Can anyone help me solve this though for a brainlest and extra points?
Answer:
a=[tex]17\sqrt{2}[/tex]
Step-by-step explanation:
As we have 2 of the angles, we can find the third. The measure of the third angle is 45 degrees.
As this is the same measure as the other, that means that the side length will be the same.
Now was have two side lengths of 17 in a right triangle, so we can use the Pythagorean theorem to find a.
Recall that the pythagorean theorem states: [tex]a^2+b^2=c^2[/tex]
In this case, a is 17, b is 17, and c is a
Knowing this, we can input our value into this formula and solve for a.
[tex]17^2+17^2=a^2\\\\289+289=a^2\\\\a=\sqrt{578} \\\\a=17\sqrt{2}[/tex]
Answer:
17sqrt2
Step-by-step explanation:
45 45 90 triangles side: hypotenuse a:a*sqrt2
17*sqrt2=17sqrt2
HELP I WILL MARK YOU AS A BRAINLIEST!!
Nick bought raffle tickets to try to win a
prize. He paid $3.00 for 12 tickets.
What is the cost per raffle ticket?
Answer:
$0.25 per ticket
Step-by-step explanation:
$3 for 12 tickets so divided the number of tickets by amount of money spent to find price per ticket.
3/12 = $0.25 per ticket
Answer:
0.25
Step-by-step explanation:
beacuse it is 0.25 because 0.25 times 12 = $3.00
What is the value of x in the diagram below?
Answer:
were is the diagram
Step-by-step explanation:
A rectangle has a heigh if 4x^3 and a width of x^3+3x^2+2x
Answer:
Area = [tex]4x^6+12x^5+8x^4[/tex]
Step-by-step explanation:
The Complete Question:
A rectangle has height [tex]4x^3[/tex] and width [tex]x^3+3x^2+2x[/tex]. What is the area of the rectangle in terms of x?
Solution:
The formula for the area of a rectangle is:
Area = Height * Width
Both the expressions for height and width is given, so we just need to multiply both the expressions to get an expression, in x, for the area of the rectangle. The algebra is shown below:
[tex]A=(4x^3)(x^3+3x^2+2x)\\A=4x^6+12x^5+8x^4[/tex]
This is the area of the rectangle.