(a) The distance of P from O when it is instantaneously at rest is 40 metres. (b) The values of t are 5 and 1 second. (c) The average velocity = 2/2 = 1 m/s. (d) The total distance travelled in the first 6 seconds is -234 meters.
What is the velocity?Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.
a) To find the distance of P from O when it is instantaneously at rest, we need to find the value of s when t = 0.
s = t³ - 9t² + 15t + 40
s = 0 - 9(0)² + 15(0) + 40
s = 40
So the distance of P from O when it is instantaneously at rest is 40 metres.
b) To find the values of t when the acceleration has a magnitude of 9 ms, we need to find the roots of equation 3t² - 18t + 15 = 0.
We can solve this equation by factoring or using the quadratic formula.
3t² - 18t + 15 = 0
(t-5)(t-1) = 0
t = 5, 1
So the values of t are 5 and 1 seconds.
c) To find the average velocity of P during the first 2 seconds, we can use the formula for average velocity:
average velocity = (distance travelled)/(time taken)
We can find the distance travelled by finding the value of s at t = 2 and t = 0 and subtracting them.
s = t³ - 9t² + 15t + 40
s(2) = 8 - 36 + 30 + 40 = 42
s(0) = 0 - 9(0)² + 15(0) + 40 = 40
distance = 42 - 40 = 2 metres
time = 2 - 0 = 2 seconds
average velocity = 2/2 = 1 m/s
d) To find the total distance travelled in the first 6 seconds, we can find the value of s at t = 6 and t = 0 and subtract them.
s = t³ - 9t² + 15t + 40
s(6) = 216 - 540 + 90 + 40 = -194
s(0) = 0 - 9(0)^2 + 15(0) + 40 = 40
distance = -194 - 40 = -234 metres
So the total distance travelled in the first 6 seconds is -234 meters.
Note that distance travelled is negative, which means that the particle is moving in the opposite direction of O.
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Dan invests £1200 into his bank account.
He receives 5% per year compound interest.
How much will Dan have after 5 years?
Give your answer to the nearest penny where appropriate.
Answer:
£1500
Step-by-step explanation:
If Dan starts out with £1200 and he gets 5% per year compound interest you would multiply 1200×0.05 and get 60, this is the amount of money that was collected with interest every year. Now you need to multiply 60×5 and get 300. With the total interest over 5 years we need to add the interest and the original amount which would be 1200+300=1500.
Please help I’m desperate (any weird links will be reported please don’t do that)
Answer:
plug in x as 3
3(3)^2+5(3)
Simplify
27+15= 42
Two candidates ran for class president. The candidate that won received 70% of the 350 total votes. How many votes did the winning candidate receive?
Answer:
49 votes
Step-by-step explanation:
Because 70% of the 350 is 49
can you help me on this 7th grade problems
Answer:
1. 11x + 11. 2. 3x - 4.
Step-by-step explanation:
sorry if im wrong
The most penetrating type of radiation is the___.
Gamma ray
betta particle
Alpha particle
none of these
Answer:gamma
Step-by-step explanation:alpha and beta can be stopped more easily
Emily is blocking off several rooms in a hotel for guests coming to her wedding. The hotel can reserve small rooms that can hold 2 people, and large rooms that can hold 3 people. Emily booked a total of 15 rooms which can accommodate 36 guests altogether. Graphically solve a system of equations in order to determine the number of small rooms reserved,
Answer: 9.
Step-by-step explanation:
6 large rooms which will add up to 18
9 small rooms which will also add up to 18 totaling the 36 guests.
The no. of small and large rooms in the hotel are 9 and 6 respectively.
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
Given, Emily is blocking off several rooms in a hotel for guests coming to her wedding.
Let us assume that small rooms be x and large rooms to be y.
Emily booked a total of 15 rooms which is x + y = 15...(i).
which can accommodate 36 guests altogether which is 2x + 3y = 36...(ii)
Now if we multiply eqn(i) by 2 it'll be 2x + 2y = 30...(iii)
Now subtracting eqn(iii) from eqn(ii) we get y = 6.
substituting the value of y in eqn(iii) we get x = 9.
So, the number of small rooms is 9 and no. of large rooms is 6.
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Can someone please help me with math.
Answer:
C
Step-by-step explanation:
because d + Q = 19 is just counting the coins, not the monetary value
and .25q + .10d signs values per coin type.
It is equally probable that the pointer on the spinner shown will land on any one of eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again. Find the probability that the pointer will stop on an odd number or a number greater than 7
What is the probability
Answer:
5 / 8
Step-by-step explanation:
Total possible outcomes = (1, 2, 3, 4, 5, 6, 7, 8)
Odd outcomes = (1, 3, 5, 7)
Outcomes > 7 = 8
Required outcomes = (1, 3, 5, 7, 8)
Number of required outcomes = 5
P(pointer stops on odd or number > 7) = required outcome / Total possible outcomes
P(pointer stops on odd or number > 7) :
= 5 / 8
The Colonel spots a campfire at a bearing N 71 ∘ E from his current position. Sarge, who is positioned 235 feet due east of the Colonel reckons the bearing to the fire to be N 45 ∘ W from his current position. Determine the distance from the campfire to each man, rounded to the nearest foot.
Answer:
[tex]X=85.123m[/tex]
[tex]Y=184.88m[/tex]
Step-by-step explanation:
From the question we are told that:
Campfire Bearing from Colonel[tex]x=N 71 \textdegree E[/tex]
Distance b/w Colonel and Sarge [tex]Z=235feet[/tex]
Campfire Bearing from Sarge [tex]y=N 45 \textdegree E[/tex]
Generally the angles x' and y' are solved
[tex]x'=90 \textdegree-71 \textdegree[/tex]
[tex]x'=19 \textdegree[/tex]
[tex]y'=90 \textdegree-45 \textdegree[/tex]
[tex]y'=45 \textdegree[/tex]
Generally the angle z' is solved
Sum of angles of a triangle is 180
Therefore
[tex]z'=180 \textdegree-(19+45) \textdegree[/tex]
[tex]z'=116 \textdegree[/tex]
Generally the sine rule equation for for all distances is mathematically given by
[tex]\frac{Z}{sinz'}=\frac{X}{sinx'}=\frac{Y}{siny}[/tex]
Generally the the distance b/w the Colonel and the campfire X is mathematically given as
[tex]\frac{235}{sin116}=\frac{X}{sinx'}[/tex]
[tex]\frac{235}{sin116}=\frac{X}{sin19}[/tex]
[tex]X=85.123m[/tex]
Generally the the distance b/w Sarge and the campfire X is mathematically given as
[tex]\frac{235}{sin116}=\frac{Y}{siny}[/tex]
[tex]\frac{235}{sin116}=\frac{Y}{sin45}[/tex]
[tex]Y=184.88m[/tex]
Jessie has successfully made 35 of her last 50 free throw attempts. Based on this information, what is the BEST calculation of the probability that she will make her next free throw?
Answer:
C. 70%
Step-by-step explanation:
35 / 50 = 70/100 = 70%
So she will be 70% accurate in the next shot.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Find the measure of the missing angles.
Answer:
hjrkfkfkfof
Step-by-step explanation:
jfkfbfhrhrnrjdur rier
C=160 degrees because it is the same angle as the known angle, 160+160=320
leaving 40 degrees unknown,
2 angles left that are the same angle meaning that b=20 degrees
Given circle B below, find the value of x.
A 27
B 44
C 71
D 142
Answer:
B. 44°
Step-by-step explanation:
Central angle = 3x + 10°
Inscribed angle = 2x - 17°
Now
Central angle = 2 * inscribed angle
( Central angle is double of the inscribed angle standing on same arc)
3x + 10° = 2 ( 2x - 17°)
3x + 10° = 4x - 34°
4x - 3x = 34 ° + 10°
x = 44°
Hope it will help :)❤
ASAP- Solve the system of equations and choose the correct answer from the list of
options. (4 points)
x - y = 7
y = 3x + 12
01 (3
O2)
2) (3)
03 ()
04 (2)
Carole worked her 40 regular hours last week plus 5 overtime hours at the
time-and-a-half rate. Her gross pay was $926.25. What is her regular hourly rate?
show work ?
Rewrite the 5 overtime hours as regular hours:
5 hours x 1.5 = 7.5
40 + 7.5 = 47.5
Divide total pay by hours:
926.25/47.5 = 19.50
The hourly rate is $19.50
Write the standard form of the equation of the circles that passes through (0, 3) with its center at (0,0)
Answer:
[tex]x^2+y^2=9[/tex]
Step-by-step explanation:
Equation of a circle (when centred at the origin):
[tex]x^2+y^2=r^2[/tex] where r is the radius of the circle
Plug in the point (0,3) to solve for the radius squared
[tex]0^2+3^2=r^2\\9=r^2[/tex]
Plug r² back into the original equation
[tex]x^2+y^2=9[/tex]
I hope this helps!
Leo is constructing a tangent line from point Q to circle P. What is his next step?
Mark the point of intersection S of the segment created from the arcs and circle R, and construct line RS.
Mark the point of intersection S of circles R and P, and construct line QS.
Construct arcs from point Q that are greater than half the length of segment PQ.
Construct a circle from point P that has a radius of P and the intersection of circles P and R.
Answer:
hello your question has a missing diagram attached below is the missing diagram
answer :
Mark the point of intersection S of circles R and P, and construct line QS ( option 2 )
Step-by-step explanation:
when constructing a tangent line from one point ( lets say Q as seen in the question ) to a circle P. The next step should be to mark a point of intersection between the given circles and then construct a line through it
Answer:
Mark the point of intersection S of circles R and P, and construct line QS.
Step-by-step explanation:
This is correct because after you create circle R that intersects circle p, you're supposed to mark the intersection points. If your in FLVS, it would be in lesson 7.04. I also got this right on my test. Good luck!
Please explain the answer and real answers only. Find the y=mx+b
Answer:
-2
Step-by-step explanation:
Given equation
x - 2y = 4
2y = x - 4
y = ( x - 4 ) / 2
y = x/2 - 4 /2
y = x/2 - 2
Comparing with y = mx + b
y-intercept (b) = - 2
Hope it will help :)❤
Question 1
1 pts
What is the value of x in the equation shown below?
2(x + 8) - 4x = 10x + 4
RENA
Answer: 1
Step-by-step explanation:
Could someone please help me...... this is hopeless.....
Answer:
[tex]m=-\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{9-10}{6-4}[/tex]
Y=-5x + 30
x=10
What is the solution to the system of equations? (-20. 10)
(10, -20)
(10, 4)
(4, 10)
Answer: B. (10, –20)
Step-by-step explanation:
Fill in the blank to make the sentence correct.
A______numerical factor of a multiplication expression like 4x.
coefficient
power
expression
variable
Tyrone is making 52 cookies for a party. Some will be a pecan cookies and some will be honey ginger. The ratio pecans a honey ginger is 76. How many of each kind of cookie will he make
Complete Question
Tyrone is making 52 cookies for a party. Some will be a pecan cookies and some will be honey ginger. The ratio of pecans to a honey ginger is 7:6. How many of each kind of cookie will he make
Answer:
28 pecan cookies and 24 Honey ginger cookies
Step-by-step explanation:
From the above question
Pecans : Honey ginger = 7:6
Sum of Proportion = 7 + 16 = 13
Total number of cookies = 52
Number of pecans
= 7/13 × 52 = 28 pecans cookies
Number of Honey ginger
= 6/13 × 52 = 24 Honey ginger cookies
Therefore, we have:
28 pecan cookies and 24 Honey ginger cookies
Which exponential equation is equivalent to this logarithmic equation?
log x = 4
Answer:
B
Step-by-step explanation:
Use the definition of a logarithm, log b ( x ) = y ⟹ b y = x , to convert from the logarithmic form to the exponential form. 10^ 4 = x
The exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by: Option B: 10^4 = x
What is logarithm ?When you raise a number with an exponent, there comes a result.
Lets say you get [tex]a^b = c[/tex]
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
Log with base e = 2.71828... is written as [tex]\ln(x)[/tex] simply.
Log with base 10 is written as [tex]\log(x)[/tex] simply.
The given logarithmic equation is;
[tex]\log x = 4[/tex]
Since, log with base 10 is written as [tex]\log(x)[/tex] simply, therefore, we have:
[tex]\log_{10} x = 4[/tex]
Using the definition of logarithm, we get;
[tex]x = 10^4[/tex]
Equivalently, [tex]10^4 = x[/tex] (option B).
Thus, the exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by: Option B: 10^4 = x
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Thomas is going to deposit $840 in an account that earns 7.5% interest compounded annually. His wife Sheril will deposit $1,250 in an account that earns 6.9% simple interest each year. They deposit the money on the same dayand make no additional deposits or withdrawals for the accounts. What statement is true concerning Thomas' and Sheril's account balance after 5 years?
a
Thomas' account will have about $475.32 less than Sheril's account.
b
Sheril's account will have about $475.32 less than Thomas' account.
c
Thomas' account will have about $431.25 less than Sheril's account.
d
Sheril's account will have about $431.25 less than Thomas' account.
Answer:
A
Step-by-step explanation:
I am to determine the future value of Thomas' deposit with annual compounding
The formula for calculating future value:
FV = P (1 + r)^n
FV = Future value
P = Present value
R = interest rate
N = number of years
840 x (1.075)^5 = 1205.93
I am to determine the future value of Sherill's deposit in 5 years using simple interest
The amount that would be in the account = amount deposited + interest earned on deposit
interest earned on deposit can be determined by determining the simple interest
Simple interest = amount deposited x time x interest rate
1250 x 0.069 x 5 = 431.25
Amount that would be in her account after 5 years = 1250 + 431.25 = 1681.25
Sheril's money is higher by - 1681.25 - 1205.93 = 475.32
Find the area of the polygon.
2.cm
3 cm
2 cm
Someone please help me ! Im behind on school work and Im trying to improve my grades! <3
please help me tysm !!
Beth has to do 20 math problems tonight. She has completed 20%. How many problems has she completed?
Answer:
She has completed 4 problems
Step-by-step explanation:
Take the total number of problems and multiply by the percent completed
20 * 20%
20 * .20
4
She has completed 4 problems
Answer:
4
Step-by-step explanation:
please help!!!!!!!!....
Answer:
Area:12.5663706 Circumference: 12.5663706
Step-by-step explanation:
Plzzzzzzzzz helpppppppppoopoooo
Answer:
a. x = 180 - (j + k)
b.
j + k = (5x - 2) + (2x - 2) = 7x - 4
l = x
x = 180 - (7x - 4)
x = 180 - 7x + 4
8x = 184
x = 184/8
x = 23
l = 23°
j = 5x - 2
j = 5 × 23 - 2
j = 115 - 2
j = 113°
k = 2x - 2
k = 2 × 23 - 2
k = 46 - 2
k = 44°
or k = 180 - (23 + 113) = 180 - 136 = 44°