Step-by-step explanation:
What was Matthew's score?
Show that the velocity of the particle at time t is given by v(t)=70t(3t2+8)2 .
Question:
A particle moves along the x-axis so that its position at time t>0 is given by [tex]x(t)=\frac{t^2 -9}{3t^2 +8}[/tex]
Show that the velocity of the particle at time t is given by [tex]v(t) = \frac{70t}{(3t^2 + 8)^2}[/tex]
Answer:
[tex]v(t) = \frac{70t}{(3t^2 + 8)^2}[/tex]
Step-by-step explanation:
Given
[tex]x(t)=\frac{t^2 -9}{3t^2 +8}[/tex]
Required
Show that:
[tex]v(t) = \frac{70t}{(3t^2 +8)^2}[/tex]
To calculate v(t), we use:
[tex]v(t) = x'(t)[/tex]
So, we have:
[tex]x(t)=\frac{t^2 -9}{3t^2 +8}[/tex]
Apply quotient rule
[tex]x'(t) = \frac{vu' - uv'}{v^2}[/tex]
Where
[tex]u =t^2 - 9[/tex]
[tex]v=3t^2 + 8[/tex]
So:
[tex]u =t^2 - 9[/tex]
[tex]u' = 2t[/tex]
[tex]v=3t^2 + 8[/tex]
[tex]v' = 6t[/tex]
So, we have:
[tex]x'(t) = \frac{vu' - uv'}{v^2}[/tex]
[tex]x'(t) = \frac{(3t^2 + 8) * 2t - (t^2 - 9) * 6t}{(3t^2 + 8)^2}[/tex]
Expand the numerator
[tex]x'(t) = \frac{6t^3 + 16t - 6t^3 + 54t}{(3t^2 + 8)^2}[/tex]
Collect like terms
[tex]x'(t) = \frac{6t^3 - 6t^3+ 16t + 54t}{(3t^2 + 8)^2}[/tex]
[tex]x'(t) = \frac{70t}{(3t^2 + 8)^2}[/tex]
Recall that:
[tex]v(t) = x'(t)[/tex]
[tex]v(t) = \frac{70t}{(3t^2 + 8)^2}[/tex]
Proved
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
I have a 30% off Kohl’s coupon!!! I find a pair of jeans for $29. What would my cost be with the 30% off?
Answer:
$20.30 plus tax
Step-by-step explanation:
You multiply 28 x .30 and that is your discount.
Answer:
$20.30
Step-by-step explanation:
Find the coordinates of the midpoint M of the segment with the given endpoints. Then find the distance between the two points. Round the distance to the nearest tenth. P(−4, 1) and Q(0, 7) The midpoint is at M( , ). Question 2 The distance between the two points is about units.
Answer:
Midpoint (-2,4)
distance nearest tenth = 8.9
The approximate distance = 9
Step-by-step explanation:
Formulas
PQ midpoint = (x2 + x1)/2, (y2 + y1)/2
distance d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )
Givens
x2 = -4
x1 = 0
y2 = 1
y1 = 7
Solution
M(PQ) = (-4+0)/2, (1 + 7)/2
M(PQ) = -2, 4
The midpoint is -2,4
The distance = sqrt( (4 - 0)^2 + (1 + 7)^2 )
The distance = sqrt(16 + 64)
The distance = sqrt(80)
The distance = 4√5 exactly
The distance = 8.94
The distance = 8.9 To the nearest tenth
Question 2
The distance is rounded to the nearest whole number which is 9.
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
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]
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)
please help!!!!!!!!....
Answer:
Area:12.5663706 Circumference: 12.5663706
Step-by-step explanation:
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!
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
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
Fill in the blank to make the sentence correct.
A______numerical factor of a multiplication expression like 4x.
coefficient
power
expression
variable
can you help me on this 7th grade problems
Answer:
1. 11x + 11. 2. 3x - 4.
Step-by-step explanation:
sorry if im wrong
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:
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:
guys please help me with this question, I’d appreciate it a lot
Answer:
540
Step-by-step explanation:
area of trapezium is b×h
Answer:
540 Sq m
Step-by-step explanation:
Area of parallelogram EFGH
= base * height
= 30 * 18
= 540 Sq m
please help me tysm !!
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
Which is a linear equation
a. Y=2-3x^2
b. Y=15-2x
c. Y=7x^2
d. Y=4x^3
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:
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.
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.
learn more about linear equations here :
https://brainly.com/question/13738061
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-2 (4d-1)=26 how to solve plz
Answer:
-3 = D
Step-by-step explanation:
A really smart freind of mine says this is the answer.
how to solve for x
7/4x - 3 = 2 + 9/2x
Answer:
x = -20/11
Step-by-step explanation:
and how -(11 x)/4 - 5 = 0
1/4 (7 x - 12) = 1/2 (9 x + 4)
hope this helps
Answer:
X = 11/20
Step-by-step explanation:
7/4x-3=2+9/2x
We move all terms to the left:
7/4x-3-(2+9/2x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
7/4x-(9/2x+2)-3=0
We get rid of parentheses
7/4x-9/2x-2-3=0
We calculate fractions
14x/8x^2+(-36x)/8x^2-2-3=0
We add all the numbers together, and all the variables
14x/8x^2+(-36x)/8x^2-5=0
We multiply all the terms by the denominator
14x+(-36x)-5*8x^2=0
Wy multiply elements
-40x^2+14x+(-36x)=0
We get rid of parentheses
-40x^2+14x-36x=0
We add all the numbers together, and all the variables
-40x^2-22x=0
a = -40; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-40)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
x1=−b−Δ√2ax2=−b+Δ√2a
Δ−−√=484−−−√=22
x1=−b−Δ√2a=−(−22)−222∗−40=0−80=0
x2=−b+Δ√2a=−(−22)+222∗−40=44−80=−11/20
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 :)❤
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]
HELP PLEASE, NO FILES OR LINKS PLEASE
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
Someone please help me ! Im behind on school work and Im trying to improve my grades! <3
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
Learn more about logarithm here:
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