Answer:
1.-dh/dt = 5.31*10⁻⁵ m/seg
2.-dh/dt = 1.99*10⁻⁵ m/seg
3.-dh/dt = 1.59*10⁻⁴ m/seg
Step-by-step explanation:PREGUNTA INCOMPLETA NO SE INDICAN LAS FORMAS DE LOS TANQUES.
Asumiremos que los tres tanques son:
el primero cilindro recto de Vc = π*r²*h ( r es radio de la base y h la altura)
el segundo asumiremos que es eliptico recto de Ve = π*a*b*h aqui a y b son los ejes de la elipse y h la altura
El tercero es un cono invertido Vco = 1/3 *π*r²*h ( r es el radio de la base.
1.-Caso del cilindro
Vc = π*r²*h
Derivando en ambos miembros de la expresión tenemos:
dV(c) / dt = π*r²*dh/dt
Sustituyendo
1.5 Lts/seg = 3.14 * (3)²*dh/dt
1.5/1000 m³/seg = 28.26 m² dh/dt
1.5/ 28260 m = dh/dt
Despejando dh/dt
dh/dt = 1.5 / 28260 = 5.31*10⁻⁵ m/seg
dh/dt = 5.31*10⁻⁵ m/seg
2.-La elipse
Ve = π*a*b*h
Aplicando el mismo procedimiento tenemos:
DVe/dt = 1.5 Lts/seg = π* 6*4* dh/dt
1.5 /1000 = 75.36 *dh/dt
dh/dt = 1.5 / 75360 m/seg
dh/dt = 1.99*10⁻⁵ m/seg
3. El cono invertido
Vco = (1/3)*π*r²*h
DVco/dt = (1/3)*π*r²*dh/dt
1.5/1000 = 9.42 *dh/dt
dh/dt = 1.5/9420
dh/dt = 1.59*10⁻⁴ m/seg
A particle is projected with a velocity of [tex]29.4ms^-^1[/tex] . Find it's maximum range on a horizontal plane through the point of projection.
A.88.2m B.44.1m C.32.6m D.29.4m E.14.7m
A.88.2m
Answer:
Solution given:
initial velocity[u]=29.4m/s
g=9.8m/s²
maximum range=?
now
we have
[tex]\theta=90°[/tex]
maximum range =[tex]\frac{29.4²*sin90}{9.8}=88.2m[/tex]
The initial velocity is,
→ u = 29.4 m/s
General assumption,
→ g = 9.8m/s²
→ θ = 90°
Then the maximum range is,
→ (29.4² × sin90)/9.8
→ 88.2 m
Hence, option (A) is answer.
The sales tax rate for the state of Washington was 7.6%.
What is the state sales tax on a $5,300 car in WashingtoN
What is the final cost of the car, including tax?
Answer:
Sales tax: 402.80 Final cost: 5,702.80
Step-by-step explanation:
Sales price x sales tax rate = sales tax
5300 x .076 (7.6%) = 402.80
Sales price + tax = final cost
5300 + 402.80 = 5702.80
PLEASE SOMEONE HELP I need help ASAP!!!
Answer:
using the pythagoras theorem
Step-by-step explanation:
[tex] \sqrt{4 {}^{2} - ( \sqrt{7}) {}^{2} } = 3[/tex]
Can someone help with 11 & 13
[tex]11. \: we \: know \: that \\ \frac{sum \: of \: all \: quantities}{number \: of \: quantities} = mean \\ => \frac{7 + 11 + 13 + 6 + 8 + x}{6} = 8 \\ = > \frac{45 + x}{6} = 8 \\ = > 45 + x = 8 \: \times 6 \\ = > 45 + x = 48 \\ = > x = 48 - 45 \\ = > x = 2 \\ \\ 12. we \: know \: that \\ \frac{sum \: of \: all \: quantities}{number \: of \: quantities} = mean \\ => \frac{2 + 5 + 1.3 + 2.2 + x}{5} = 1.8 \\ = > \frac{10.5 + x}{5} = 1.8 \\ = > 10.5 + x = 5 \times 1.8 \\ = > 10.5 + x = 9 \\ = > x = 9 - 10.5 \\ = > x = - 1.5 \\ [/tex][/tex]
This is the answer.
Hope it helps!!
Find the value of x that makes A || B
HELPPPPP
Answer:
x = 90
Step-by-step explanation:
If lines A and B were parallel , then
∠ 1 and ∠ 4 are corresponding angles and congruent, so
3x - 160 = x + 20 ( subtract x from both sides )
2x - 160 = 20 ( add 160 to both sides )
2x = 180 ( divide both sides by 2 )
x = 90
What is the midpoint of the segment with endpoints(-4, -
2) and (2, 6)?
Answer:
(-1,2)
Step-by-step explanation:
hope you find this useful!
https://ncalculators.com/geometry/mid-points-calculator.htm
The rate (In mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function 110I 12 +1+ 9 where I is the light intensity (measured in thousands of foot-candles). For what light intensity is P a maximum?
Answer:
P is maximum at I = 2
Step-by-step explanation:
Here is the complete question
The rate (in mg carbon/m³/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function P = 100I/(I² + I + 4) where I is the light intensity (measured in thousands of foot candles). For what light intensity P is a maximum?
To find the value of I at which P is maximum, we differentiate P with respect to I and equate it to zero.
So, dP/dI = d[100I/(I² + I + 4)]/dI
= [(I² + I + 4)d(100I)/dI - 100Id(I² + I + 4)/dI]/(I² + I + 4)²
= [(I² + I + 4)100 - 100I(2I + 1)]/(I² + I + 4)²
= [100I² + 100I + 400 - 200I² - 100I]/(I² + I + 4)²
= [-100I² + 400]/(I² + I + 4)²
= -100[I² - 4]/(I² + I + 4)²
Since dP/dI = 0, -100[I² - 4]/(I² + I + 4)² = 0 ⇒ I² - 4 = 0 ⇒ I² = 4 ⇒ I = ±√4
I = ±2
Since I cannot be negative, we ignore the minus sign
To determine if this is a maximum point, we differentiate dP/dI. So,
d(dP/dI)/dI = d²P/dI² = d[-100[I² - 4]/(I² + I + 4)²]/dI
= [(I² + I + 4)²d(-100[I² - 4])/dI - (-100[I² - 4])d(I² + I + 4)²/dt]/[(I² + I + 4)²]²
= [(I² + I + 4)²(-200I) + 100[I² - 4]) × (2I + 1) × 2(I² + I + 4)]/(I² + I + 4)⁴
= [-200I(I² + I + 4)² + 200[I² - 4])(2I + 1)(I² + I + 4)]/(I² + I + 4)⁴
= [-200(I² + I + 4)[I(I² + I + 4) - [I² - 4])(2I + 1)]]/(I² + I + 4)⁴
= [-200(I² + I + 4)[I³ + I² + 4I - I² + 4])(2I + 1)]]/(I² + I + 4)⁴
= [-200(I² + I + 4)[I³ + 4I + 8])(2I + 1)]]/(I² + I + 4)⁴
Substituting I = 2 into d²P/dI², we have
= [-200(2² + 2 + 4)[2³ + 4(2) + 8])(2(2) + 1)]]/(2² + 2 + 4)⁴
= [-200(4 + 2 + 4)[8 + 8 + 8])(4 + 1)]]/(4 + 2 + 4)⁴
= [-200(10)[24](5)]]/(10)⁴
= -240000/10⁴
= -24
Since d²P/dI² = -24 < 0 at I = 2, this shows that it I = 2 is a maximum point.
So, P is maximum at I = 2
Sketch the graph of each of the following quadratic functions. (a) f(x) = x² - 4x - 5 for -2 ≤ x ≤ 6.
pls help me solve this
To sketch the graph we have to solve the function with each value of x to get the coordinates.
f(x) = x² − 4x − 5
−2 ≤ x ≤ 6
This inequality represents the domain for x. Therefore x is greater than equal to -2 but less than equal to 6.
The range of x is as follows:
x = -2, -1, 0, 1, 2, 3, 4, 5, 6
We already have the values for x therefore, we must substitute the values of x into the function f(x) = x² − 4x − 5 to find the y values.
Solutions:
For x = -2
f(x) = x² − 4x − 5
= -2² − 4(-2) - 5
= 4 + 8 - 5
= 7
Point = (-2,7)
For x = -1
f(x) = x² − 4x − 5
= -1² - 4(-1) - 5
= 1 + 4 - 5
= 0
Point = (-1,0)
For x = 0
f(x) = x² − 4x − 5
= 0² - 4(0) - 5
= 0 - 0 - 5
= -5
Point = (0,-5)
For x = 1
f(x) = x² − 4x − 5
= 1² - 4(1) - 5
= 1 - 4 - 5
= -8
Point = (1,-8)
For x = 2
f(x) = x² − 4x − 5
= 2² - 4(2) - 5
= 4 - 8 - 5
= -9
Point = (2,-9)
For = 3
f(x) = x² − 4x − 5
= 3² - 4(3) - 5
= 9 - 12 - 5
= -8
Point = (3,-8)
For x = 4
f(x) = x² − 4x − 5
= 4² - 4(4) - 5
= 16 - 16 - 5
= -5
Point = (4,-5)
For x = 5
f(x) = x² − 4x − 5
= 5² - 4(5) - 5
= 25 - 20 - 5
= 0
Point = (5,0)
For x = 6
f(x) = x² − 4x − 5
= 6² - 4(6) - 5
= 36 - 24 - 5
= 7
Point = (6,7)
Coordinates for graph = (-2,7) , (-1,0) , (0,-5) , (1,-8) , (2,-9) , (3,-8) , (4,-5) , (5,0) , (6,7)
These are the points to sketch the quadratic graph.
find the 9th and 15th terms of the following geometric sequence 2, -4, 8, -16
Step-by-step explanation:
given the geometric sequence 2, -4, 8, -16, ...
a1 = 2
r = -4/2 = -2
find : a9 and a15
solutions:
an = a1. r^(n-1)
=> a9 = 2. (-2)^(9-1)
= 2. (-2)^8
= 2. 2^8
= 2^9
= 512.
=> a15 = 2. (-2)^(15-1)
= 2. (-2)^14
= 2. 2^14
= 2^15
= 32,768
Step-by-step explanation:
Hey there!
The given geometric sequence is: 2, -4, 8, -16.
The;
a1 = 2
Common ratio (r) = T2/T1
= -4/2
= -2
Now;
Use general formula of geometric sequence;
[tex]tn = {a1.r}^{n - 1} [/tex]
Where, "a1" is first term, "n" is no.of terms and "r" is common ratio.
Then;
[tex]t9 = 2 \times { (- 2)}^{9 - 1} [/tex]
or, t9 = 2*256
Therefore, t9 = 512.
Again;
[tex]t15 = 2. { (- 2)}^{15 - 1} [/tex]
or, t15= 2*16384
Therefore, t15 = 32768.
Hope it helps!
Work out the area of the shaded shape.
Hi there!
[tex]\large\boxed{77m^2}}[/tex]
We can divide the figure into 3 rectangles.
Area of top rectangle:
5 × 5 = 25m²
Long rectangle:
14 × 3 = 42m²
Bottom rectangle:
2 × 5 = 10m²
Add up the areas:
10 + 42 + 25 = 77m²
. It is known that the glucose level in blood of diabetic persons follows a normal distribution model with mean 106 mg/100 ml and standard deviation 8 mg/100 ml. a. Calculate the probability of a random diabetic person having a glucose level less than 120 mg/100 ml. b. What percentage of persons have a glucose level between 90 and 120 mg/100 ml?
Answer:
a. 0.9599 = 95.99% probability of a random diabetic person having a glucose level less than 120 mg/100 ml.
b. 0.9371 = 93.71% of people have a glucose level between 90 and 120 mg/100 ml.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean 106 mg/100 ml and standard deviation 8 mg/100 ml
This means that [tex]\mu = 106, \sigma = 8[/tex]
a. Calculate the probability of a random diabetic person having a glucose level less than 120 mg/100 ml.
This is the p-value of Z when X = 120. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 106}{8}[/tex]
[tex]Z = 1.75[/tex]
[tex]Z = 1.75[/tex] has a p-value of 0.9599
0.9599 = 95.99% probability of a random diabetic person having a glucose level less than 120 mg/100 ml.
b. What percentage of persons have a glucose level between 90 and 120 mg/100 ml?
The proportion is the p-value of Z when X = 120 subtracted by the p-value of Z when X = 90. So
X = 120
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 106}{8}[/tex]
[tex]Z = 1.75[/tex]
[tex]Z = 1.75[/tex] has a p-value of 0.9599
X = 90
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 106}{8}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228
0.9599 - 0.0228 = 0.9371
0.9371 = 93.71% of people have a glucose level between 90 and 120 mg/100 ml.
You are given the exponential function g(x)=3^x. Which ootion below gives the formula for the new function h created by stretching g by a factor of 3 along the y-axis?
Answer:
h(x) = 3^(x + 1)
Step-by-step explanation:
The exponential function is;
g(x) = 3^(x)
Now, in transformation of exponential functions of say f(x) = b^(x), when the new function g(x) is created by stretching by a factor of say c along the y-axis, we have;
g(x) = c•b^(x)
In this question, we are told it is stretched by a factor of 3 along the y-axis.
Thus, new function h is;
h(x) = 3 × 3^(x)
Using law of indices, we have;
h(x) = 3^(x + 1)
Thanks for helping me two more problems
Answer:
A. Energy (weight)
Step-by-step explanation:
Mark me as brainiest
The Fun Committee is hosting the Annual City Festival. Jennifer is in charge of the committee and is planning a race to raise money for the Festival. The runners will earn money from donors for the number of miles they run. If the runners start at the park, run to City hall, and then run back to the park, how many total miles will each runner run? Show your work and leave your answer in simplest radical form if necessary.
Answer: [tex]6\sqrt{5}[/tex] miles
This is the same as writing 6*sqrt(5) miles
==========================================================
Work Shown:
P = park
C = city hall
Point P is at the location (10,11)
Point C is at the location (7,5)
Apply the distance formula to find the length of segment PC
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(10-7)^2 + (11-5)^2}\\\\d = \sqrt{(3)^2 + (6)^2}\\\\d = \sqrt{9 + 36}\\\\d = \sqrt{45}\\\\d = \sqrt{9*5}\\\\d = \sqrt{9}*\sqrt{5}\\\\d = 3\sqrt{5}\\\\d \approx 6.7082039\\\\[/tex]
The exact distance between the park (P) and city hall (C) is [tex]3\sqrt{5}[/tex] miles.
This doubles to [tex]2*3\sqrt{5} = 6\sqrt{5}[/tex] miles because the runners go from P to C, then back to P again. In other words, they run along segment PC twice. This is assuming there is a straight line road connecting the two locations.
Extra info:
[tex]6\sqrt{5} \approx 13.41641[/tex] so the runner travels a total distance of roughly 13.4 miles.
Which expression is equivalent to 3/2?
Answer: the answer is D. I took the test & got it right
Step-by-step explanation:
The expression is equivalent to 3/2 will be;
⇒ 3y/(2y - 6) + 9/(6 - 2y)
Option D is true.
What is an expression?
Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
Equivalent expression is 3/2.
Now,
Let the expression is;
⇒ 3y/(2y - 6) + 9/(6 - 2y)
Solve the expression as;
⇒ 3y/(2y - 6) - 9/(2y - 6)
⇒ (3y - 9) / (2y - 6)
⇒ 3 (y - 3) / 2 (y - 3)
⇒ 3/2
So, The expression is equivalent to 3/2 will be;
⇒ 3y/(2y - 6) + 9/(6 - 2y)
Option D is true.
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The number 6 is a solution to which of the following inequalities?
X - 13 > 7
6x < -12
6x > 32
21 + x < 28
Answer:
21 + x < 28
Step-by-step explanation:
27 is in fact greater than 28 if you where to input 6 into the x spot, this is the only one that's a true expression.
write 36,438 correct to 2 significant figure
(show how you did it)
Answer:
36,000
Step-by-step explanation:
Rounding Significant Figures Rules
Non-zero digits are always significant Zeros between non-zero digits are always significant Leading zeros are never significant Trailing zeros are only significant if the number contains a decimal pointRounding Rules
When rounding significant figures the standard rules of rounding numbers apply, except that non-significant digits to the left of the decimal are replaced with zeros.
Example: 356 rounded to 2 significant digits is 360
This calculator rounds down if the next digit is less than 5 and rounds up when the next digit is greater than or equal to 5.
In the table below 305.459 is rounded from 0 to 6 significant figures. For comparison the same number is rounded from 0 to 6 decimal places. You can see the difference between rounding for significant figures and rounding to decimal places.
cross out 3 digits in the number 51489704 so that the number remaining is divisible by 45
Answer:
1,152
Step-by-step explanation:
So here, we shall be removing random numbers
For ease, since the number is divisible by 45: it is advisable to end the selected number with zero
So we have it that;
we are crossing the first 4, 9 and 7
So, we are left with;
51,840
dividing this by 45 will give 1,152
If / is a midsegment of /, find x.
A.
2
B.
3
C.
6
D.
9
Please select the best answer from the choices provided
A
B
C
D
Answer:
It is d
Step-by-step explanation:
Help, I have a time limit for this
Answer:
I believe that it is the first one.
Step-by-step explanation:
Someone tell me where everyone is going right please !!
9514 1404 393
Explanation:
The problem statement tells you the meaning of t. It is minutes after Riko leaves. 0 ≤ t < 52.5 is the answer to the question regarding the interval Riko is behind Yuto. It means Riko is behind Yuto for 52.5 minutes after she leaves their house.
t will not be negative because time moves forward. Here, we're only counting time after Riko leaves the house. A negative value for t would refer to a time before Riko leaves the house, which is irrelevant in this problem.*
_____
* One might argue that Riko is behind Yuto for all values of time after Yuto leaves the house, which would be for -21 < t < 52.5. The concept of "behind Yuto" has no meaning except in that interval.
Answer:
again again again hello or merhaba(hello)
speed = path / time
so we can say this;
speed × time = path
note;
two speeds in different directions add up
and
two speeds in the same direction subtract
our speeds are in the same direction so we subtract
0.35 - 0.25 = 0.10 speed
and our path is 5.25 miles because there are 5.25 miles between Yuto and Rico
when will they be in the same place now?
Let's solve with the formul;speed × time = path
0.10 × time = 5.25 miles
in this equation we find the time 52.5 minutes
After 52.5 minutes they will be in the same place but before 52.5 minutes Riko will be behind Yuto
When Riko was behind Yuto;0≤ t ≤ 52,5 ( this is our equation of time)
now the second question?Why can't t be less than 0?because time cannot take a negative value, as soon as they start moving, time passes and this cannot take a negative value
GOOD LUCK :D
Step-by-step explanation:
greetings from Turkey (≧▽≦)
find the distance between the points (7,23) and (3,-3), rounded to the hundredths place
Answer:
26.31
Step-by-step explanation:
Use distance formula
d = [tex]\sqrt{(x_{2}-x_{1)^{2} + (y_{2}-y_ ^{1)^2} } }[/tex]
substitute in points and solve
d = [tex]\sqrt{(7-3)^2 + (23-(-3))^{2} }[/tex]
d = [tex]\sqrt{4^{2}+26^{2} }[/tex]
d = [tex]\sqrt{16 + 676}[/tex]
d = [tex]\sqrt{692}[/tex]
d = 26.30589288
d = 26.31 rounded
Find x
Help me please
I'll give you 13 points if it's correct
Can someone help me with this math homework please!
The ratio of two side lengths for the triangle is given. What is the value of “q” AB:BC is 3:4
Answer:
[tex]q=8.5[/tex]
Step-by-step explanation:
The ratio of the side lengths (AB) and (BC) is given. One is also given an expression for the side lengths of each of these sides. Set up a proportion to describe this scenario, then solve using cross products;
[tex]\frac{AB}{BC}=\frac{3}{4}[/tex]
Substitute,
[tex]\frac{60}{10q+15}=\frac{3}{4}[/tex]
Cross products,
[tex]\frac{60}{10q+15}=\frac{3}{4}[/tex]
[tex](60)(4)=(10q+15)(3)\\\\240=30q+45[/tex]
Inverse operations,
[tex]240=30q+45\\\\195=30q\\\\8.5=q[/tex]
There are 24 students in a class. Three new students join the class. Work out the percentage change in the number of students in the class.
Answer:
12.5% increase
Step-by-step explanation:
To find the percentage increase ( students joined)
Take the new number minus the original amount
There are 27 students in the class after 3 joined
27 - 24 = 3
Divide by the original amount
3/24 = 1/8 = .125 = 12.5%
Answer:
12.5%
Step-by-step explanation:
Intial number = 27
Final number = 24 + 3 = 27
Percentage change :-
% change = 3/24 × 100 % change = 100/8 % Change = 25/2 % change = 12.5 %Region A has a total of 81,218,576 acres. Estimate the number of acres owned by the government in Region A. Choose the correct estimate below.
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]Region\ A = 81218576[/tex]
Required
The acres owned by the government
The question is incomplete as the proportion (p) owned by the government is not given.
However, the formula to use is as follows:
[tex]Govt = p * Region\ A[/tex]
Assume the proportion is 28%, the equation becomes
[tex]Govt = 28\% * 81218576[/tex]
[tex]Govt = 22741201.28[/tex]
The acres owned by the government will be 22741201.28
Luego de su cumpleaños, Benjamín ha decidido donar la tercera parte del dinero que recibió de regalo de sus familiares a una fundación. Considerando las variables cantidad de dinero recibido por Benjamín y cantidad de dinero que donará Benjamín. a. ¿Cuál es la variable dependiente en esta situación.
Answer:
The dependent variable is the amount of money he received for birthday.
Step-by-step explanation:
After his birthday, Benjamin has decided to donate a third of the money he received as a gift from his relatives to a foundation. Considering the variables amount of money received by Benjamin and amount of money that Benjamin will donate. to. What is the dependent variable in this situation.
Here, the money he received for the birthday is x.
So, he donated x/3.
The variable is the money which he gets, so the dependent variable is amount of money he received for the birthday.
Someone help me with these math problems please !! (It is not obligatory to put the explanation so I save time and you will answer me more quickly please!
Answer:
Step-by-step explanation:
[tex]\frac{2}{3} * 5 = \frac{2}{3}\frac{3}{2} x \\[/tex]
x = 10/3
The diameter of a wheel on harrys bicycle is 0.65m calculate the circumference of the wheel give your answer correct to 2 decimal places
Answer:
Step-by-step explanation:
[tex]C =2\pi r[/tex] and since we have to state the answer to 2 decimal places, that means that we are using the number value for π. In specific, π = 3.1415 is good enough. The other thing we note is that the formula for circumference could also be written in terms of its diameter as opposed to its radius:
C = πd. Let's use that one since we are given the diameter of the tire, not the radius.
C = (3.1415)(.65) so
C = 2.04 m
The circumference of the wheel is C = 2.04 m.
What is area of the circle?Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2, (Pi r-squared) where r is the radius of the circle. The unit of area is the square unit, such as m2, cm2, etcGiven ,
d = 0.65 m
π = 3.14
Let's use that one since we are given the diameter of the tire, not the radius.
Use this formula , C = πd
C = (3.1415)(.65)
so, C = 2.04 m
Therefore, the circumference of the wheel is C = 2.04 m.
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