Answer:
dx/dt = 4c - 4x/15
Step-by-step explanation:
a. Find a formula for the rate of change in the amount of salt, dx/dtdx/dt, in terms of the amount of salt in the solution
Let c be the concentration of the incoming brine in grams per liter. Since it flows in at a rate of 4 liters per minute, the mass flow in is thus 4m.
Let x be the mass of salt present at time, t. The concentration of salt present at time, t is thus mass of salt/volume of tank = x/15. Since the well mixed solution is drained at 4 liters per minute, the mass flow out is thus 4x/15.
The net rate of change of amount of salt dx/dt = mass flow in - mass flow out
dx/dt = 4c - 4x/15
1.62 was multiplied by a power of ten to get 16.2. What power of ten was it
multiplied by?
10
100
1,000
Answer:
10
Step-by-step explanation:
Every time you multiply by 10 you move the decimal point one digit to the right. So if you multiply 1.62 by 10 you move the decimal point one digit to the right so it becomes 16.2.
So the answer is 10
Answer:
The answer is 10
Step-by-step explanation:
Every time you multiply by a power of 10 that does not have a negative exponent, the decimal point moves to the right.
How many times, you might wonder. It all just depends on how many zeroes there are. If there's one 0, (10) then the decimal point just moves one over, if were multiplying by 100 then 2 places over, 1000 three places over, and so on.
1.62 * 10 = 16.2, since the decimal point moved one to the right.
10 is therefore the answer, but if you wanted to you could check the other answers as well.
1.62 * 100 = 162
1.62 * 1000 = 1620
Therefore, the answer is 10. Please mark brainliest if possible. Have a nice day.
Without using a calculator, compute the sine, cosine, and tangent of
330∘ by using the reference angle.
Answer:
sin(330)=-0.5
cos(330)=0.86
tan(330)=-0.57
At : a.m. the angle of elevation of the sun for one city is . If the height of a monument is approximately , what is the length of the shadow it will cast at that time? Round to the nearest foot.
This question is incomplete, the complete question;
At 11:30 a.m. the angle of elevation of the sun for one city is 55.7°. If the height of a monument is approximately 555 ft, what is the length of the shadow it will cast at that time? Round to the nearest foot.
Answer:
the length of the shadow will be 379 ft
Step-by-step explanation:
Given the data in the question and as represented in the diagram below;
height of monument = 555 ft
angle of elevation = 55.7°
From the image below, this makes a right angled triangle
we know that the some of the interior angles of a triangle is 180
so
∠ABC + ∠BCA + ∠CAB = 180°
90° + 55.7° + ∠CAB = 180°
∠CAB = 180° - 145.7°
∠CAB = 34.3°
Now, using sine rule;
BC / sinA = AB / sinC
so we substitute
BC / sin( 34.3°) = 555 / sin( 55.7° )
BC / 0.563526 = 555 / 0.826098
we cross multiply
BC × 0.826098 = 0.563526 × 555
BC × 0.826098 = 312.75693
BC = 312.75693 / 0.826098
BC = 378.595 ≈ 379 ft
Therefore, the length of the shadow will be 379 ft
Find the volume of the following shapes. Round to tenths and don’t forget the units. Show your work!
please help thx
Answer:
Step-by-step explanation:
1). Figure (1) comprises two cuboids, one small cuboid placed on the big cuboid at the bottom.
Volume of the figure = Volume of the cuboid on the top + Volume of the cuboid at the bottom
Volume of the cuboid on the top = Length × Width × Height
= 4 × 6 × 5
= 120 mm³
Volume of the cuboid at the bottom = Length × Width × Height
= 9 × 6 × 4
= 216 mm³
Volume of the figure = 120 + 216
= 336 mm³
2). Figure shown in the picture has two parts,
Cone placed on the top of a cylinder.
Volume of the given figure = Volume of cone + Volume of cylinder
= [tex]\frac{1}{3}\pi r^{2}h+\pi r^{2}h'[/tex]
= [tex]\frac{1}{3}\pi (\frac{3}{2})^{2}(3)+\pi (\frac{3}{2})^{2}(8.1)[/tex]
= [tex]\frac{9}{4}\pi +18.225\pi[/tex]
= [tex](2.25+18.225)\pi[/tex]
= [tex]20.475\pi[/tex]
= 64.3 ft³
Therefore, volume of the given figure = 64.3 ft³.
The outer diameter of a spherical shell is 36 pie cm³and its inner diameter is 9 cm. Find the volume of the metal contained the shell.
please help will give brainliest
Answer:
may be 11.460
sorry to say this but I'm not sure bout my answer
(ー_ー✿)
Which represents a quadratic function?
f(x) = -8X^3 – 16x^2 - 4x
f(x) = 3/4+ x^2 - 5
f(x) = 4/x^2-2/x+1
f(x) = 0x^2 - 9x + 7
Answer:
f(x) = 3/4x^2 + 2x -5
quadratic function formula is ax^2+b^2+c
5. Simplify: 2(4X+3)-(7X+6)
6. Find the perimeter of the metallic sheet
below
n
6
3n
3n
5
7. Write an expression for the sum of on-
sixth of m and one-seventh of n, minus 7
8. Simplify 5-³ x 5⁴ x 2²
9. Find the L.C.M of 2x3², 2x3x7 and 2x3²x5
10. What is the place value of 4 in the number
2043507?
11. Find the G.C.F OF 18,42 and 90
Answer:
hshdjdjdjffhdiosekskskdkcjfiririrotr8tti5tittttit4i5i6i6832wy
PLS HELP ME!!!! use the properties of exponents to simplify the expression
Answer:
According to Indices
(a⁴)²... The exponents will multiply each other to give (a⁶)
Using this here
The two Index would Multiply to give
½ x ⅔ = ⅓
= (27)⅓
Any Number to the Index of ½ simply means its Square root
so also...
Any Number to the index of ⅓ means its cube root...
Cube root of 27 = 3.
So
Option B is your answer.
ASAP there are three marbles in a bag. One is red and two are black. What is the probability of picking a black marble first, putting it back in the bag and then picking a black marble? Use the following probability to find the answer.
Answer:
[tex] \frac{4}{9} [/tex]
Step-by-step explanation:
[tex]p = \frac{favorable \: outcomes}{total \: outcomes} = \frac{4}{9} [/tex]
=============================================================
Explanation:
The probability you get a black marble on the first selection is 2/3 since we have 2 black marbles out of 2+1 = 3 total.
We put the marble back and then we have 2/3 as the probability of selecting another black marble on the second try. Nothing has changed because we put the marble back. That means the events are independent.
So we get (2/3)*(2/3) = 4/9 as the probability of selecting 2 black marbles in a row (with replacement).
A box has two balls, one white and one red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Find the probability of the following events:
a. Let F = the event of getting the white ball twice.
b. Let G = the event of getting two balls of different colors.
c. Let H = the event of getting white on the first pick.
d. Are F and G mutually exclusive?
e. Are G and H mutually exclusive?
Answer:
See explanation
Step-by-step explanation:
Given
Represent the balls with the first letters
[tex]W =1[/tex]
[tex]R =1[/tex]
Solving (a): P(F) --- White balls twice
The event of F is:
[tex]F = \{(W,W)\}[/tex]
So:
[tex]P(F) = P(W) * P(W)[/tex]
[tex]P(F) = \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]
[tex]P(F) = \frac{1}{2} * \frac{1}{2}[/tex]
[tex]P(F) = \frac{1}{4}[/tex]
Solving (b): P(G) --- two different colors
The event of G is:
[tex]G = \{(W,R),(R,W)\}[/tex]
So:
[tex]P(G) = P(W) * P(R) + P(R) * P(W)[/tex]
[tex]P(G) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(R)}{n} * \frac{n(W)}{n}[/tex]
[tex]P(G) = \frac{1}{2} * \frac{1}{2} + \frac{1}{2} * \frac{1}{2}[/tex]
[tex]P(G) = \frac{1}{4} + \frac{1}{4}[/tex]
[tex]P(G) = \frac{1}{2}[/tex]
Solving (c): P(H) --- White picked first
The event of H is:
[tex]H = \{(W,R),(W,W)\}[/tex]
So:
[tex]P(H) = P(W) * P(R) + P(W) * P(W)[/tex]
[tex]P(H) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]
[tex]P(H) = \frac{1}{2} * \frac{1}{2} + \frac{1}{2} * \frac{1}{2}[/tex]
[tex]P(H) = \frac{1}{4} + \frac{1}{4}[/tex]
[tex]P(H) = \frac{1}{2}[/tex]
Solving (d): F and G, mutually exclusive?
We have:
[tex]F = \{(W,W)\}[/tex]
[tex]G = \{(W,R),(R,W)\}[/tex]
Check for common elements
[tex]n(F\ n\ G) = 0[/tex]
Hence, F and G are mutually exclusive
Solving (e): G and G, mutually exclusive?
We have:
[tex]G = \{(W,R),(R,W)\}[/tex]
[tex]H = \{(W,R),(W,W)\}[/tex]
Check for common elements
[tex]n(G\ n\ H) = 1[/tex]
Hence, F and G are not mutually exclusive
for f(x)=4x+1 and g(x)=x^2-5, find (f-g) (x) need help guys!
Answer:
-x^2 +4x +6
Step-by-step explanation:
f(x)=4x+1
g(x)=x^2-5
(f-g)(x) = 4x+1 - (x^2-5)
Distribute the minus sign
= 4x+1 - x^2 +5
= -x^2 +4x +6
HELP MEEEEEEEEEEEEEEEEEEEEEWEW
log (3x+5)=log (2x-7)
Answer:
x=-12 (BUT IS EXTRENUS)
Step-by-step explanation:
If u dont know what extraneous is, dont worry about it...
How to learn tables 11 to 15
For 12 years old easyliy please tell guys
Answer:
For eleven, it had the same two numbers. For twelve, it continues up by even numbers. For thirteen, it's the same as twelve but by odd numbers. For fourteen, it's a little difficult but they have a pattern for every five multiples of fourteen. For fifteen, the numbers add by five but also counting up.
Step-by-step explanation:
Examples for the table of eleven would be: 11 × 3 = 33 or 11 × 6 = 66.
Table twelve would be (as examples): 12 × 2 = 24 and 12 × 3 = 36.
Table thirteen have numbers/answers like: 13 × 7 = 91 and 13 × 8 = 104.
Table fourteen as examples: 14 × 3 = 42 or 14 × 4 = 56.
Table fifteen would be like: 15 × 6 = 90 and 15 × 7 = 105.
Raymond is designing a ceramic pot on a coordinate system where each unit corresponds to 1 millimeter. The neck of the
pot has edges with the shape of a hyperbola, where the asymptotes y = 2.75x and y = -2.75x are followed. If the closest
that any part of the neck edges comes to the center of the neck is 32 millimeters, write an equation for the hyperbola used
to model the edges.
9514 1404 393
Answer:
x^2/1024 -y^2/7744 = 1
Step-by-step explanation:
The parent hyperbola relation is ...
x^2 -y^2 = 1
This has asymptotes of y = ±x and x-intercepts of ±1.
For the given hyperbola, we want to scale x by a factor of 32, and y by a factor that is 2.75 times that, or 88. Then the equation could be written as ...
(x/32)^2 -(y/88)^2 = 1
More conventionally, the denominator is shown at full value:
x^2/1024 -y^2/7744 = 1
A cone has a volume of 94.2 cubic millimeters and a radius of 3 millimeters. What is its
height?
Answer:
the answer is 97.2
Step-by-step explanation:
Just add 94.2+3
Who can answer this? I’ll mark brainliest!!
Answer:
y = 0.48(x - 0.5)² - 3
y = 0.48(x² - x - 6)
Step-by-step explanation:
From the graph the zeros are
x = {-2, 3}
The x coordinate of the vertex is the midpoint of the roots
x = (-2 + 3) / 2
x = 0.5
The y coordinate of the vertex is
y = -3
vertex = (0.5, -3)
--------------------------------------
Merhod I - vertex
Vertex form is
y = a(x - h)² + k
plug in the vertex
y = a(x - 0.5)² - 3
to find a plug in either root
using x = 3
0 = a(3 - 0.5)² - 3
0 = a(2.5)² - 3
0 = 6.25a - 3
3 = 6.25a
a = 3/6.25
a = 0.48
y = 0.48(x - 0.5)² - 3
-----------------------------
Method II - roots
y = a(x + 2)(x - 3)
-3 = a(0.5 + 2)(0.5 - 3)
-3 = a(2.5)(-2.5)
-3 = -6.25a
3/6.25 = a
0.48 = a
y = 0.48(x + 2)(x - 3)
Expand
y = 0.48(x² - x - 6)
Use the formula below to find the relative pressure inside the can in psi
Answer:
b
Step-by-step explanation:
you have to have psi to have p-e-n-i-s sand you get a jack hammer
In a binomial experiment :________
a. the probability does not change from trial to trial
b. the probability does change from trial to trial
c. the probability could change from trial to trial, depending on the situation under consideration
d. None of these alternatives is correct.
Answer:
Hence the correct option is Option (a).
Step-by-step explanation:
Option (a) is correct.
The probability does not change from trial to trial.
p = Probability of sucess.
B is the midpoint of segment AC trying to find AB using the definition of midpoint.
Answer:
12
Step-by-step explanation:
A midpoint of a line means that each segment connecting from the midpoint to an end is equal. For this problem, this means that AB = BC, as B is the midpoint, and A and B are the ends. Therefore, we can say that:
AB = BC
2x + 6 = 5x - 3
add 3 to both sides
2x + 9 = 5x
subtract 2x from both sides
9 = 3x
divide both sides by 3
3 = x
Plugging 3=x into AB, this means that 2(3) + 6 = AB = 12
Consider the expression 63+81 how can you use the distributive property and the gcf to find an equivalent expression?explain how you can check your answer
Step-by-step explanation:
63+81
gcf = 9
63÷9=7, 81÷9=9
so, 63+81 = (9×7)+(9×9)
= 9×(7+9)
63+81 = 144
9x(7+9) = 9×16 = 144
What is the monthly payment on a 15-year loan of $57,900 if the annual interest rate is 12%?
The cost of making 6 chairs is $410. The cost of making 22 chairs is $570.
What is the cost per chair?
What is the fixed cost (or startup cost) that you need to spend before making the first chair?
Write a linear equation that tells you the total cost, C. of making x chairs.
CE
What is the total cost of making 17 chairs? $
If your total cost is $820, how many chairs did you make?
Answer:
if it cost 410 dollars to make 6 chairs we can divide 410 by 6 which is 68.3333333333 or 68 1/3
now for the other set of chairs we can divide 570 by 22 which is
25.9090909091 or 25.9
and for the rest it doesn't make any sense to me sorry
geumath malah 17.pdf
1/21
* 16 The diagram shows a swimming pool in the shape of a prism.
10 m
Sm
Diagram NOT
accurately drawn
וו 1
2 m
4m
DO NOT WRITE IN THIS AREA
2 m
The swimming pool is empty.
Water from 3 water tankers is going to be put into the pool.
There are 20000 litres of water in each water tanker.
Sam thinks that the surface of the water in the pool will be 10 cm below the top of the pool.
Is Sam correct?
You must show how you get your answer.
(lm - 1000 litres)
TE IN THIS AREA
Answer:
He is wrong.
In my answer I found the complete volume of the pool and then what the volume would be 10 cm empty. You probably only need to find the 10 cm emptied to answer, just a heads up. if you have any questions though let me know.
Step-by-step explanation:
To most easily figure out the volume of the empty pool I think it is easiest to break it up into four parts..
First break off that skinny end bit so it will have 1 m in height, 4 m in length and 5m in width. Width is never going to shange because of how we are breaking this up, and the width is the distance from you into the paper, if that makes sense. Basically not up and down or left and right.
Next another rectangular prism from the right side with 2 height, 2m length and again 5m width.
Now you have a trapezoidal prism with one base of length 1m, another of base 2m and a height of length 4m.
To fond the volume of prisms you want to find the area of their bases then multiply it by their heights. In this instance height is going to be the width again, and the bases are th parts facing us on the picture.
For a rectangular prism area of the base is easy, just multiply length by height. a trapezoid is taking the two bases (b1 and b2) ading them together and dividing that sum by 2, THEN taking this new number and multiplying it by what would be the height of the trapezoid. the trapezoid has its bases as two heights, and its height then would be the horizontal length of the pool. Sorry if that is confusing. Here are the three volumes though.
Rectangular 1: 4*1*5 = 20 m^3
Rectangular 2" 2*2*5 = 20m^3
Trapezoidal: = ([1+2]/2)*4*5 = 30 m^3
So total it is 70 m^3
The question then says each cubic meter can contain 1,000 liters of water. 70 m^3 then is 70,000 liters
The question also says there are three barrels of 20,000 liters each, so combined that's 60,000 liters.
Finally it wants to know if Sam is right saying if you dump all of the 60,000 liters into the pool the surface of the water will not reach the top of the pool by 10 cm. 60,000 is less than 70,000, but we don't know how much lower it is in cm.
The trick here is to know that we are lowering a specific dimension of each prism to a certain amount to be lower by 10cm
In the 4x1x5 rectangular prism the 1m side is lowering.
In the 2x2x5 rectangular prism the 2m side representing the vertical length is getting some amount taken away.
int he trapezoidal prism both of the "bases" are getting an amount taken.
So the trick here is to set up the math again, except this time with 10 cm less being subtracted from each part, then solving t and see if it gets us the 60,000 liters or 60 m^3. Since we are measurng in meters, 10 cm less is the same a subtracting .1, or if you prefer subtracting a decimeter.
4*1*5 becomes 4(.9)5 = 18
2*2*5 becomes 2(1.9)5 = 19
Trapezoidal: = ([1+2]/2)*4*5 becomes ([(.9)+(1.9)]/2)*4*5 = 28
Adding this all together gets us 65 or 65,000 liters. This means that if the pool is filled 10 cm from the top the volume would be 65,000 liters, still more than if the three tankers are emptied completely into it.
You could have probably just done the second part, where we sbtracted 10 cm from each of the dimensions, but I am going to leave it all since I wrote it.
9514 1404 393
Answer:
Sam is not correct.
Step-by-step explanation:
As shown in the attachment, the "base" (front face) of this prism can be divided into a rectangle and a trapezoid. The relevant area formulas are ...
A = LW . . . . area of a rectangle of length L and width W
A = 1/2(b1 +b2)h . . . . area with parallel bases b1 and b2 and height h
__
The rectangle portion of the "base" of the pool has area ...
A = (10 m)(1 m) = 10 m²
The trapezoid portion of the "base" of the pool has area ...
A = 1/2(6 m +2 m)(1 m) = 4 m²
Then the "base" area is ...
B = 10 m² +4 m² = 14 m²
__
The volume of the prism is given by ...
V = Bh . . . . where B is the base area and h is the distance between bases
V = (14 m²)(5 m) = 70 m³
We are told that 1 m³ = 1000 L and that 3 tankers of 20,000 L each are emptied into the pool. That leaves an unfilled volume of ...
70 m³ -3×(20 m³) = 10 m³ . . . . unfilled volume
__
The surface area of the pool is ...
A = LW = (10 m)(5 m) = 50 m²
So the unfilled volume has a height of ...
V = Bh
10 m³ = (50 m²)h
h = (10/50) m = 20/100 m = 20 cm . . . . . the height of the unfilled space
The water in the pool will be 20 cm below the top, not 10 cm. Sam is not correct.
The radius of a circle is 12.4 cm. Find the circumference to the nearest tenth.
Moving to another question will save this response.
1 points
Save Answer
Question 12
Mr Espent 65% of his salary on household expenses, and 15% of the remainder on travelling expenses and was finally left with R9 500. How much was his salary?
Answer:
rs.1680.67
Step-by-step explanation:
His salary = x
remaining % = 100 - 65 = 35%
= 100 - 15 = 85%
x × 35/100 × 85/100 = 500
x = 1680.67
The question is one the picture
Answer:
y=-1/2x+4
Step-by-step explanation:
The line is going down, which means it's negative. You then do rise over run, go up by 1 and go to the left by 2. To find the y intercept, it's 4 since the coordinate is (0,4).
Only higher experienced need answer theorems all 5 questions. Thank you 200points if repeating the last question.
Answer:
first one : inscribed angles create arc twice their degree
so, 115° created a 230 ° arc
360 - 230 = 130°
that means ∠EDG = 1/2 (130) or 65°
second : ∠ABD = 180 - 112 = 68
The arc created APD is 2 times ∠ABD or 136°, therefore ∠x = 136°.
Central Angles and arcs are equal
360° - 136° = 224°
224° is the arc created by ∠APD. Take 1/2 of 224° and you get 112°
Third: ∠ACB and ∠ AOB create the same arc.
since ∠ACB is 48°, the arc is 96° (twice the angle)
if the arc is 98° then the central angle ∠AOB = 98°
360°-98° = 262°
You need this because ∠APB is 1/2(262-98) or 82°
Fourth : Both inscribed angles create the same arc
so the angles are equal
∠DEG = 38°
Answer:
15° created a 230 ° arc
360 - 230 = 130°
that means ∠EDG = 1/2 (130) or 65°
second : ∠ABD = 180 - 112 = 68
The arc created APD is 2 times ∠ABD or 136°, therefore ∠x = 136°.
Central Angles and arcs are equal
360° - 136° = 224°
224° is the arc created by ∠APD. Take 1/2 of 224° and you get 112°
Third: ∠ACB and ∠ AOB create the same arc.
since ∠ACB is 48°, the arc is 96° (twice the angle)
if the arc is 98° then the central angle ∠AOB = 98°
360°-98° = 262°
You need this because ∠APB is 1/2(262-98) or 82°
Fourth : Both inscribed angles create the same arc
so the angles are equal
∠DEG = 38°
Step-by-step explanation:
Mrs.Montana has five students namely:rodley,cristina,christian,elsa and made .Count all the letters in each name.In which of the following sets the order of the names least to greatest.
ARodley,cristina,Christian,mae,elsa
Bcristina,Christian elsa mae rodley
c Mae elsa rodley cristina Christian
D Christian Cristina rodley mae elsa
Answer:
C
Step-by-step explanation:
Mae, Elsa, Rodley, Cristina, Christian
14.32 × 1.2,...........
Answer:
17.18400
Step-by-step explanation:
When rounded to the nearest whole number, it's 17.
Hope this helped :)