Answer:
The definite integral expressing the total quantity of oil, 'V', which leaks out of the tanker in the first hour is given as follows;
[tex]V = \int\limits^{60}_0 {A \cdot e^{(-k \cdot t)}} \, dt[/tex]
Step-by-step explanation:
From the question, we have;
The rate at which oil leaks out of the tanker, r = f(t)
The unit of the oil leak = Liters per minute
The unit of t = Minutes
[tex]If \ f(t) = A \cdot e^{(-k \cdot t )}[/tex]
Therefore, we have;
The definite integral expressing the total quantity, 'V', of oil which leaks out of the tanker in the first hour is given as follows;
[tex]V = \int\limits^{60}_0 {A \cdot e^{(-k \cdot t)}} \, dt[/tex]
Therefore, we have;
[tex]\int\limits^{60}_0 {A \cdot e^{(-k \cdot t)}} \, dt = \dfrac{A \cdot e ^{60 \cdot k} - A}{k \cdot e ^{60 \cdot k} }[/tex]
9. The height of a ball thrown into the air is a quadratic function
of time. The ball is thrown from a height of 6 ft above the
ground. After 1 second, the ball reaches its maximum height of
22 ft above the ground. Write the equation of the function in
vertex form.
Answer:f(x)=-16(x-1)^2+22
Step-by-step explanation:
The equation for the trajectory of ball in the air is h(t) = -16t² + 32t + 6.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = lim h --> 0 (f(x + h) - f(x)) /(x + h - x).
It can also be said as the slope of the tangent for the function at a given point.
Given that,
The maximum height reached by the ball after 1 sec is 22 ft above ground.
And, the height at which it is thrown is 6 ft above the ground.
Which implies at 0 sec the height is 6 ft.
The quadratic function for the height can be written as,
h(t) = at² + bt + c
Substitute t = 0 to gat,
f(0) = a × 0² + b × 0 + c
=> c = 6
Now, for maximum height,
h'(t) = 0
=> 2at + b = 0
At maximum height t = 1
Then, the above expression becomes,
2a × 1 + b = 0
=> a = -b/2
Substitute t = 1 in h(t) = at² + bt + c to get,
22 = a + b + c
=> 22 = -b/2 + b + 6
=> b/2 = 16
=> b = 32
Then, a = -b/2
= -32/2
=-16
Thus substituting the corresponding values the equation can be written as h(t) = -16t² + 32t + 6.
Hence, the required equation for the path of the ball in the air is h(t) = -16t² + 32t + 6.
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Steve types at a rate of 45 words per minute. He writes an equation relating the number of words he can type, w, to the number of minutes he spends typing, m.
w = 45m
Xena doesn’t know the number of words per minute that she can type. But she recorded the time it took her to type different numbers of words in this table.
Minutes Words
2 100
4 200
8 400
If we graphed both of these proportional relationships, the graph representing _____
typing would be steeper than the graph representing ______typing. So, _______
types more words per minute.
Factor `y=2x^2+11x+5`
Answer:
(2x + 1)(x + 5).
Step-by-step explanation:
`y=2x^2+11x+5`
2 * 5 = 10
1 * 10 = 10 and 1 + 10 = 11 so we write:
y = 2^2 + 10x + x + 5
y = 2x(x + 5) + 1(x + 5)
= (2x + 1)(x + 5).
Matthew is half as old as Alan. If the sum of their ages is 54, find their ages.
Answer:
26
Step-by-step explanation:
What is the value of
N?
1/2
3/2
3/3
3
c is the answer
Answer:
Step-by-step explanation:
Which four numbers will complete this addition puzzle?
Answer:
top 8, middle 7, 16, bottom 13
Please please help me!!!!
Answer:
Q = (9, 4 )
Step-by-step explanation:
Use the midpoint formula and equate to the coordinates of the midpoint.
M = ([tex]\frac{x_{1}+x_{2} }{2}[/tex] ) , ([tex]\frac{y_{1}+y_{2} }{2}[/tex] )
let the coordinates of Q = (x, y ) , R = (- 7, 0 ) , then
[tex]\frac{x-7}{2}[/tex] = 1 ( multiply both sides by 2 )
x - 7 = 2 ( add 7 to both sides )
x = 9
and
[tex]\frac{y+0}{2}[/tex] = 2 ( multiply both sides by 2 )
y = 4
Thus Q = (9, 4 )
i need help please as soon as possible thanks
Step-by-step explanation:
12a-9a>-12+6
3a>-6/:3
a>-2
need help asap just need answer
Answer:
89m
Step-by-step explanation
area of the triangle 15
area of the rectangle 104
104-15=89m
Answer:
[tex]89[/tex] [tex]m^{2}[/tex]
Step-by-step explanation:
area of a triangle = [tex]\frac{bh}{2}[/tex]
so [tex]\frac{(5)(6)}{2}[/tex] = 15 [tex]m^{2}[/tex]
area of a rectangle = [tex]\\ bh[/tex]
so [tex]\\ 8[/tex]×[tex]\\ 13[/tex] [tex]\\ = 104[/tex] [tex]m^{2}[/tex]
so the area of the figure is
[tex]\\ 104[/tex] [tex]m^{2}[/tex] - 15 [tex]m^{2}[/tex] = [tex]89[/tex] [tex]m^{2}[/tex]
Have a conversation :>
yep c:
Answer:
Yep......a lot of notifications on my phone.....lol
thx for points!
Follow me! :)
Which value makes the equation 2x -4 = 16 true? *
Answer:
10 makes this equation true
Step-by-step explanation:
2x -4 = 16 /+4
2x= 20 /÷2
x= 10
Test
2(10) - 4 = 16
20 - 4 = 16 Correct
phoenix is a businessman who travels frequently he uses atms in many cities and does not write many checks he also uses direct deposit and has a savings account. Phoenix's bank is one of the four financial institutions described below which is most likely Phoenix's bank
Answer:
Bank 3
Step-by-step explanation:
No additional charges for automatic deposit and includes saving account.
Joshua is going to invest $680 and leave it in an account for 19 years. Assuming the interest is compounded continuously, what interest rate, to the nearest tenth of a percent, would be required in order for Joshua to end up with $1,680?
Answer:
4.8%
Step-by-step explanation:
Answer:4.8
Step-by-step explanation:
Trust
If x=3
Arrange the list in an increasing order.
Answer:
It is already in an increasing order
1. 4x - 8 Highest
2. 3x - 2
3. 2x + 1
4. 1x - 0 Lowest
Step-by-step explanation:
1. 56
2. 25
3. 9
4. 1
make a the subject of d=g+2ac
Answer:
Step-by-step explanation:
From what I understand, you are trying to solve for a.
So,
d=g+2ac
d-g=2ac
(d-g)/2c=a
So,
a = (d-g) / 2c
2. Cross out the equations that are NOT linear functions.
y = 3x+2
y = 3/x
y = -2
y=4
y = x2(square) + 5
Welcome to the concept of the maths.
Here, we can see, that Linear equation always have highest power or degree of its variable as '1' ,
thus here, y = 3/x has degree as -1 and y = x^2 +5 has degree 2 ,
hence,
The equations that are NOT linear are
2.) y = 3/x and 5.) y = x^2 + 5
Can someone please help me with math
8) is B
9) is also B ([tex]y=2x+3[/tex])
will the standard form of 8.5*10 to the power of -3 be more or less than 1 ? explain the effect the negative exponent has.
Answer:
The answer is 0.0085 So I'm guessing less than one.
can you help me plz NO LINKS
I need help with this
Answer:
a is the answer for this question
Determine the sine, cosine, and tangent of the angle
John bought 8 goats at 1040000.He sold these goats and made a profit of 15% on each goat.How much did he sell each goat?
Answer:
149500
Step-by-step explanation:
since there's 8 goats, each goat would be 1040000/8, which is 130000 per goat.
marketing at a 15% increase means the new percentage would be 115%, which could be represented by 1.15.
130000 * 1.15 = 149500 / goat
I need help with this question? 2(t+1) =10
Answer:
Distribute
Subtract two from both sides of the equation
Simplify
and that's your solution
which should be t=4
Step-by-step explanation:
A shoe store donated a percent of every sale to charity. a the total sales were $9,800 so the store donated $588. What percent of $9,800 was donated to charity?
Answer:
They donated 6%.
Step-by-step explanation:
The total sales were $9800.
The amount donated is $588.
We want to know what percent of 9800 is 588.
Let's make an equation.
what percent of 9800 is 588
x/100 • 9800 = 588
Divide by 9800.
x/100 = 0.06
Multiply by 100.
x = 6
They donated 6%.
Hope this helps!
If cos A= -4/5 and A is in the second quadrant, then cos 2A = ?
Answer:
i think its second pythagreom therom
Step-by-step explanation:
because
Please help i will mark brainliest!!!
Answer:
64 square units
Step-by-step explanation:
if you spilt up the polygon you can find the area of the square and triangle making up the square.
length * width = Area; 6 * 8 = 48 sq units for the square part
1/2 * base * height = Area; 1/2 * 4 * 8 = 16 sq units for the triangle part
then add the two areas together for the area of the entire polygon:
48 + 16 = 64 sq units
A box contains 5 red, 4 white and 6 blue balls. If three balls are drawn at random without replacement, determine the probability that none of the balls selected is red.
Answer:
The probability that none of the balls selected is red ²⁴/₉₁
Step-by-step explanation:
Given;
number of red balls, R = 5
number of white balls, W = 4
number of blue balls, B = 6
Total number of balls, = 5 + 4 + 6 = 15
Probability of selecting 3 none red balls = P(WWW) or P(BBB) or P(WWB) or P(WBW) or P(BWW) or P(BBW) or P(BWB) or P(WBB)
[tex]P = (\frac{4}{15} \times \frac{3}{14} \times \frac{2}{13} ) + (\frac{6}{15} \times \frac{5}{14} \times \frac{4}{13} ) + (\frac{4}{15} \times \frac{3}{14} \times \frac{6}{13} ) + (\frac{4}{15} \times \frac{6}{14} \times \frac{3}{13} ) + \\\\(\frac{6}{15} \times \frac{4}{14} \times \frac{3}{13} ) + (\frac{6}{15} \times \frac{5}{14} \times \frac{4}{13} ) + (\frac{6}{15} \times \frac{4}{14} \times \frac{5}{13} ) + (\frac{4}{15} \times \frac{6}{14} \times \frac{5}{13} )[/tex]
[tex]P = \frac{24}{2730} + \frac{120}{2730} + \frac{72}{2730} +\frac{72}{2730} + \frac{72}{2730} + \frac{120}{2730} + \frac{120}{2730} + \frac{120}{2730} \\\\P = \frac{720}{2730} \\\\P = \frac{24}{91} \\\\[/tex]
Therefore, the probability that none of the balls selected is red ²⁴/₉₁
Directions: Find the value of x.
Round angle measures to the nearest degree.
Given:
The figure of a right triangle.
To find:
The value of x.
Solution:
In a right angle triangle,
[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
In the given right triangle,
Hypotenuse = 15
Perpendicular = 12.5
Now,
[tex]\sin x^\circ=\dfrac{12.5}{15}[/tex]
[tex]\sin x^\circ=0.83333[/tex]
[tex]x^\circ=\sin^{-1}0.83333[/tex]
[tex]x^\circ =56.442345^\circ[/tex]
[tex]x\approx 56[/tex]
Therefore, the equation used to find x is [tex]\sin x^\circ=\dfrac{12.5}{15}[/tex] and the value of x is 56.
Find the lateral area of this cone.
Leave your answer in terms of pi.
3cm
4cm
The lateral area of the cone is 20π square centimeters.
Given that a cone with base radius of 4 cm and the height is 3 cm, we need to find the lateral area of the cone,
The lateral area of a cone can be calculated using the formula:
Lateral Area = π r l
where:
π is a mathematical constant approximately equal to 3.14159.
r is the radius of the base of the cone.
l is the slant height of the cone.
To find the slant height, we can use the Pythagorean theorem.
The slant height (l) is the hypotenuse of a right triangle formed by the height (h) and the radius (r) of the cone.
The formula is:
l = √(r² + h²)
Given that the base radius (r) is 4 cm and the height (h) is 3 cm, we can calculate the slant height (l):
l = √(4² + 3²)
= √(16 + 9)
= √(25)
= 5
Now we can substitute the values into the formula for the lateral area:
Lateral Area = π r l
= π × 4 × 5
= 20π
Therefore, the lateral area of the cone is 20π square centimeters.
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Find the Average
100-90-80-89-75-0
Explain how u got ur answer
Someone help I will give brainlist for whoever explains it
Answer:
72.3
Step-by-step explanation:
So, to find the average you need to add all the numbers together and divide it by the amount of numbers there are, if that makes sense.
so in your question: 100 + 90 + 80 + 89 + 75 + 0= 434
and there are 6 numbers that you had to add together, so you divide 434 by 6, which is 72.3 so that's the answer! It's quite easy once you understand how to do it :)
