Step-by-step explanation:
The answer is dhdt=325πmmin.
With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:
V=πr2h
There is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:
V=π(5m)2h
Since the rate in this problem is time related, we need to implicitly differentiate wrt (with respect to) time:
dVdt=(25m2)πdhdt
In the problem, we are given 3m3min which is dVdt. So we substitute this in:
dhdt=3m3min(25m2)π=325πmmin
Can someone explain this to me
Angle ADB is a right angle --- Given
Angle ADB is 90 degrees --- Definition of a Right Angle
Angle CDB is 90 degrees --- Definition of Supplementary Angles
Angle ADB = Angle CDB --- Definition of Congruent Angles
Proofs can be tricky! What helps me is thinking through them step by step and how I would prove I did something. While I'm not entirely sure what options you have for this proof, I've given my best guess.
Hope this helps!! :)
Hello I really need help 30 points
Answer:
C
Step-by-step explanation:
The vertical line test determines that more than 1 point falls on the vertical line making the graph NOT a function
Write the following as an inequality.
w is less than 8 and greater than or equal to -3
Omar wants to open an account for his grandchildren that he hopes will have
$80,000 in it after 20 years. How much must he deposit now into an account
that yields 1.75% interest, compounded monthly, so he can be assured of
reaching his goal?
Using compound interest, it is found that he must deposit $56,389.
Compound interest:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year. t is the time in years for which the money is invested or borrowed.In this problem:
Hopes to have $80,000 in 20 years, thus [tex]t = 20, A(t) = 80000[/tex].Interest rate of 1.75%, thus [tex]r = 0.0175[/tex].Compounding monthly, thus [tex]n = 12[/tex]The investment is of P, for which we have to solve.Then:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]80000 = P(1 + \frac{0.0175}{12})^{12(20)}[/tex]
[tex]P = \frac{80000}{(1 + \frac{0.0175}{12})^{12(20)}}[/tex]
[tex]P = 56389[/tex]
He must deposit $56,389.
A similar problem is given at https://brainly.com/question/25263233
A fitness trainer decided to track the combined weight loss of
several new customers. She recorded the combined weight loss
each month and kept track for 6 months. Identify the best
mathematical model with its corresponding R2 value and tell
whether it is a good model.
Month
1
2
3
4
5
6
Weight loss
175
120
95
63
44
30
4.
exponential model, 0.996
Yes, 0.996 is very close to 1.
quadratic model, 0.994
Yes, 0.994 is very close to 1.
quadratic model, 0.994
No, 0.994 is too high an R2 value.
exponential model, 0.996
No, 0.966 is too high an R2 value.
Now, the R² value comes out as 0.996 and it is an exponential model and it is close to 1. Hence, option A is correct.
What is an exponential model?
Quantity rises over time through a process called exponential growth. It happens when the derivative, or instantaneous rate of change, of a quantity with respect to time is proportionate to the original quantity. A quantity that is growing exponentially is referred to as an exponential function of time, meaning that the exponent is the variable that represents time (in contrast to other types of growth, such as quadratic growth).
The amount declines over time and is said to be experiencing exponential decay if the constant of proportionality is negative. It is also known as geometric growth or geometric decay when the discrete domain of definition has equal intervals since the function values form a geometric progression.
Given that a fitness trainer is tracking the combined weight loss of several new customers.
She is recording for 6 months.
Now, we have to find the best mathematical model with the corresponding R² value
Given, the combined weight loss are - 175, 120, 95, 63, 44 and 30.
The formula for coefficient of determination R² = (x-x')(y-y')/√∑(x-x')²(y-y')²
≈ 0.996
Now, the R² value comes out as 0.996 and it is an exponential model and it is close to 1. Hence, option A is correct.
To know more about exponential model:
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if someone writes "/" does it mean Division or a Fraction Line
help plz i will give brainliest
Answer:
12
(If needed explanation ask in the comments! ty)
Hope This Helps! •v•
3/7x2/3.....................
Answer:
3/7 times 2/3 is 2/7
Step-by-step explanation:
I used a calculator ! Please let me know if i am incorrect.
Answer:
0.28571428571
basically 0.28
Step-by-step explanation:
gooogle calculator
helppppppppppppppppppppppppppppppppp
Answer:
You want to find how much it cost for 1kg of potatoes, which in this case is .45 cents. After that you want to multiply the price of 1kg by 50, to get your cost for 50 kg of potatoes, which would be $22.50 I hope this helps! :)
Answer:
$22.50
Step-by-step explanation:
If one. again is 10k and it costs 4.50, then you would do 4.50 multiplied by 5 because each 10k is 4.50 and thier is 50 in total so 5 bags of 4.50 meaning 4.5x5 which would get you $22.50
Convert the mixed numbers to improper fractions:1. 5 6/72. 8 3/9
Factor Completely. (and please show work)
-10x^2 + 3x + 4
Step-by-step explanation:
=>-10x²+3x+4
=>-10x²-5x+8x+4
=>-5x(2x+1)+4(2x+1)
=>(2x+1)(4-5x)
hope this helps you.
I need help please!!!
Answer:
yes (the given angles are co-interior {130+50=180} )yes( corresponding angles are equal) .....yes (exterior alternate angles are equal)yes ( vertically opposite angles are equal)7) 3x=45( corresponding angles formed on parallel lines)
x=45/3
x=15
8)120=2x+10(corresponding angles formed on parallel lines)
or,120-10=2x
or,110/2=x
or,x=55
A retiree has $200,000 to invest and needs to make $13,000 with her investments. If she can invest in government bonds at 6% or investment-grade bonds at 8%, how much should she invest in each?
Answer:
$50,000 at 8%; $150,000 at 6%
Step-by-step explanation:
$50,000 x .08 = $4000
$150,000 x .06 = $9000
$4000 + $9000 = $13,000
Find the GCF for the pair of numbers. 9,4
The GCF of numbers is the greatest common factor of the numbers.
The numbers are given as: 4 and 9.
Factorize both:
[tex]\mathbf{4 = 1 \times 2 \times 2}[/tex]
[tex]\mathbf{9 = 1 \times 3 \times 3}[/tex]
The common factor between both is 1.
So, we have:
[tex]\mathbf{GCF = 1 }[/tex]
Hence, the GCF of 4 and 9 is 1
Read more about GCFs at:
https://brainly.com/question/20061154
fifteen is the same a one-fifth a number
15 = 1/5+x or 15 = 1/5x
Answer:
74/5
Step-by-step explanation:
15x5 =75 5ths. 1/5 + 74/5 = 75/5
Someobe pleaseeee help I need it
Answer:
its 35
Step-by-step explanation:
Susan is an interior floor designer. When designing a new floor, she uses a coordinate grid to
represent the room. The client wants a rectangular tile insert in the floor of the room. The
coordinates for 3 of the corners of the insert are A (-7,-4), B (1,6), and C (6,2).
YA
A rectangle has 4 coordinates.
The coordinate of the last vertex is (-2,-8)
The points are given as:
[tex]\mathbf{A = (-7,-4)}[/tex]
[tex]\mathbf{B = (1,6)}[/tex]
[tex]\mathbf{C = (6,2)}[/tex]
Calculate distance AB
[tex]\mathbf{AB = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]
So, we have:
[tex]\mathbf{AB = \sqrt{(-7 - 1)^2 + (-4 - 6)^2}}[/tex]
Calculate distance CD
[tex]\mathbf{CD = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}[/tex]
So, we have:
[tex]\mathbf{CD = \sqrt{(x - 6)^2 + (y - 2 )^2}}[/tex]
Equate AB and CD
[tex]\mathbf{ \sqrt{(x - 6)^2 + (y - 2)^2} = \sqrt{(-7 - 1)^2 + (-4 - 6)^2}}\\[/tex]
Cancel out the squares
[tex]\mathbf{ (x - 6)^2 + (y - 2)^2 = (-7 - 1)^2 + (-4 - 6)^2}[/tex]
By comparison
[tex]\mathbf{x -6 = -7-1}[/tex]
[tex]\mathbf{y-2 = -4-6}[/tex]
So, we have:
[tex]\mathbf{ x = 6-7-1 }[/tex]
[tex]\mathbf{ x = -2}[/tex]
[tex]\mathbf{y = 2-4-6 }[/tex]
[tex]\mathbf{y = -8}[/tex]
Hence, the coordinate of the last vertex is (-2,-8)
Read more about coordinates at:
https://brainly.com/question/2254540
Can some please write my knowns and unknowns for this question
Answer:
Knowns:
initial velocity (v₀) = 0
final velocity (v₁) = 100 km/h
acceleration (a) = 9.00 m/s²
Unknowns: how long the acceleration took (Δt) = ?
Step-by-step explanation:
Use one of the kinematics equations to find what you're looking for.
This equation with a little algebra should help
v₁ = v₀ + aΔt
On a graph, points form a curved line.
Using the scatterplot, determine the association.
Answer:
Nonlinear association, B
Step-by-step explanation:
Answer:
strong
Step-by-step explanation:
Can someone pls help me
Ill give Brainly
NO BOTS OR ILL REPORT YOU
solve the matrix equation
Answer:
c
Step-by-step explanation:
I don't understand this question can someone help me with this please, please explain!! and thank you for the help!! If u dont know try your best :D
Answer:
3.5 hours
Step-by-step explanation:
You are trying to isolate X (get X by it self) to do that you need to divided both sides of the equation by 60 resulting in X=3.5
Divide both sides by 60 to isolate x
x=3.5 hours
Hope this helps you! :)
[tex]GraceRosalia[/tex]
please help me solve for the slope of the graph
Answer:
4/5
Step-by-step explanation:
Take two points on the lines. From here, we can get (5, 2) and (10, 6). Slope formula involves taking RISE/RUN, which is where you take y-y/x-x. Stay consistent on how you order the numbers. I like positive numbers, so we'll do (6-2)/(10-5). That gives us 4/5, which is your slope.
What is the slope of the line on the graph?
Enter your answer in the box.
Answer: The slope of the line is 6.
You can use the distance formula to find the slope (Y2-Y1/X2-X1). You can plug in any two points seen on the graph into the formula. I will use (0,-1) and (1,5). When I plug in the values, 5-(-1)/1-0=6/1=6. So the slope of the line is 6.
:)
Can anyone help me with this?
Answer:
x = 42 degrees
y = 37 degrees
Step-by-step explanation:
Those are right angle triangles. So you know the right angles are 90 degrees, and each triangle gives you the measurement of another angle.
So, take the triangle in the top left (x):
180 - 90 - 48 = x
Same with the other triangle (y)
180 - 90 - 53 = y
8th grade math!!! Help ILL BRAINLIST
The picture I took is what I need help with.
Answer:
4th option
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, 0 ) and (x₂, y₂ ) = (0, - 9) ← 2 points on the line
m = [tex]\frac{-9-0}{0-(-6)}[/tex] = [tex]\frac{-9}{0+6}[/tex] = [tex]\frac{-9}{6}[/tex] = - [tex]\frac{3}{2}[/tex]
The line crosses the y- axis at (0, - 9 ) ⇒ c = - 9
y = - [tex]\frac{3}{2}[/tex] x - 9 ← in slope- intercept form
Multiply through by 2 to clear the fraction
2y = - 3x - 18 ( add 3x to both sides )
3x + 2y = - 18 ← in standard form
2. A line passes through the points (4,7) and
(8, 6). The line also passes through the point
(a, 3.5) for what value of a?
Answer:
a = 18
Step-by-step explanation:
Slope = (7-6)/(4-8) = -1/4
y-intercept = 7 - (-1/4)(4) = 8
Equation of the line: y = - 1/4x + 8
(Substitute y for 3.5. When y is 3.5, what is x)
3.5 = - 1/4x + 8
3.5 - 8 = - 1/4x
(-4.5) / (- 1/4) = x
x = 18
Match the inequality to the graph of the solution C - 6 < 4
Answer:
A
Step-by-step explanation:
C - 6 < 4
+6 +6
C < 10
Open circle at 10 and shade to the left.
How many gallons of pure water should be added to 10 gallons of a solution containing 15% juice so that
the remaining solution contains 5% juice?
Fill in the table:
What is the amount of juice in the original solution? a =
What is the original amount of solution in gallons? b =
How much juice is added? c =
How much total solution is added? d =
Original
Added
New
Amount of juico
a
Total solution
Answer:
A = 1.5, B = 10, C = 0, D = 20
Step-by-step explanation:
A = 10 * 15% = 1.5
b = 10
c = 0
(10 + x) * 5% = 1.5
0.5 + 0.05x = 1.5
0.05x = 1
x = 20
(assume 'x' is added solution)
d = 20
Answer: A. 1.5 B. 10 C. 0 D. X