Answer:[tex]z=a+bi=|z|(cos(θ)+isin(θ))tofindthtrigonometricform.√sin2(ga8A)+cos16(A)(cos(arctan(−1sin(ga8A)cos8(A)))+isin(arctan(−1sin(ga8A)cos8(A))))[/tex]
Step-by-step explanation:
t 0 2 4 6 8 10
P(t) 0 36 43 47 52 60
Kunyu's family has an above ground swimming pool in the shape of a cylinder, with a radius of 10 feet and a height of 5 feet. The pool contains 1000 cubic feet of water at time t=0. During the time interval 0≤t≤10 hours, water is pumped into the pool at the rate () cubic feet per hour. The table above gives values of () for selected values of . During the same time interval, water is leaking from the pool at the rate of () cubic feet per hour, where ()=18−0.04.
(Note: The volume V of a cylinder with radius r and height h is given by =2ℎ .)
Find the rate at which the volume of water in the pool is increasing at time t=6 hours. How fast is the water level in the pool rising at t=6 hours? Indicate units of measure in both answers.
Answer:
a. 24.12 ft³/hr b. 0.0768 ft/hr
Step-by-step explanation:
a. Find the rate at which the volume of water in the pool is increasing at time t=6 hours.
The net rate of change of volume of the cylinder dV/dt = volume flow rate in - volume flow rate out
Since volume flow rate in = P(t) and volume flow rate out = R(t),
dV/dt = P(t) - R(t)
[tex]\frac{dV}{dt} = P(t) - 18e^{0.04t}[/tex]
We need to find the rate of change of volume when t = 6.
From the table when t = 6, P(6) = 47 ft³/hr
Also, substituting t = 6 into R(t), we have R(6)
[tex]\frac{dV}{dt} = P(t) - 18e^{0.04t}[/tex]
[tex]\frac{dV}{dt} = 47 - 18e^{0.04X6}\\\frac{dV}{dt} = 47 - 18e^{0.24}\\\frac{dV}{dt} = 47 - 18 X 1.27125\\\frac{dV}{dt} = 47 - 22.882\\\frac{dV}{dt} = 24.118 ft^{3}/hr[/tex]
dV/dt ≅ 24.12 ft³/hr
So, the rate at which the water level in the pool is increasing at t = 6 hours is 24.12 ft³/hr
b. How fast is the water level in the pool rising at t=6 hours?
Since the a rate at which the water level is rising is dV/dt and the volume of the cylinder is V = πr²h where r = radius of cylinder = 10 ft and h = height of cylinder = 5 feet
dV/dt = d(πr²h)/dt = πr²dh/dt since the radius is constant and dh/dt is the rate at which the water level is rising.
So, dV/dt = πr²dh/dt
dh/dt = dV/dt ÷ πr²
Since dV/dt = 24.12 ft³/hr and r = 10 ft,
Substituting the values of the variables into the equation, we have that
dh/dt = dV/dt ÷ πr²
dh/dt = 24.12 ft³/hr ÷ π(10 ft)²
dh/dt = 24.12 ft³/hr ÷ 100π ft²
dh/dt = 0.2412 ft³/hr ÷ π ft²
dh/dt = 0.2412 ft³/hr
dh/dt = 0.0768 ft/hr
So, the arate at which the water level is rising at t = 6 hours is 0.0768 ft/hr
A log of wood weighs 120kg. After drying, it now weighs 80kg. Find the moisture content of the wood in percentage.
Answer: 33% is moisture content
Step-by-step explanation:
120kg - 80kg = 40kg
40 of 120 is %
Work:
40/120 = 0.33
0.33x100
= 33%
Which of the following is true because of the Associative Law of Addition?
A. 1000 + 2000 + 6 = 3006
B. (1000) + 2000 + 6 = 1000 + (2000) + 6
C. 1000 + 2000 + 6 = 2000 + 1000 + 6
D. 1000 + (2000 + 6) = (1000 + 2000) + 6
Answer:
d part is correct because in associative property the brackets and the numbers CAN be shifted
which decimal is equivalent to 6×100+7×10+4×1/10+8×1/1,000
The answer is 670.408, because 6x100=600, 7x10=70, 4x1/10 as a decimal is 0.4, 8x1/1,000 as a decimal is 0.008. Then, you add all of those [tex]600+70+0.4+0.008=670.408[/tex].
Find f(2) given f(x) = -3x^2 + 2x+11
Answer:
Answer:f(2)=-3(2)^2+2*2+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11 =3
hence, f(2)=3
The hypotenuse of a right triangle is two more than the length of one of its legs. Find the side lengths of the right triangle given the perimeter= 60 and it's area= 120
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Answer:
10 and 24
Step-by-step explanation:
We know that some of the Pythagorean triples that appear in math problems are (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17).
These have (perimeter, area) values of (12, 6), (30, 30), (56, 84), (40, 60).
For some scale factor n, we want (p·n, a·n²) = (60, 120). Of the triangles listed, we see that the (5, 12, 13) triangle scaled by n=2 will satisfy the problem requirements. (30·2, 30·2²) = (60, 120)
The side lengths are 10 and 24.
__
Check
For the side lengths we found, the perimeter is 10+24+26 = 60; the area is 1/2(10)(24) = 120. The hypotenuse is 2×13 = 26 = 24+2.
__
In the attached, one side is x, the other is y. The hypotenuse is (x+2). The square root equation comes from ...
x² +y² = (x+2)² ⇒ y² = (x² +4x +4) -x² ⇒ y² = 4x +4 = 4(x +1)
_____
Additional comment
The graph shows the solution of the various constraints. At least, the combination of constraints will give a quadratic equation in x. They can be combined in a way that gives a cubic equation in x. Either way, we prefer the graphical or "guess and check" approach (above) as being easier to do.
Using the third equation in the attachment to write an expression for y, we have ...
y = 58 -2x
Substituting that into the second equation gives ...
(x(58 -2x)/2 = 120
29x -x² = 120
x² -29x +120 = 0
(x -5)(x -24) = 0 . . . . x = 5 or 24.
The root x=5 is a legitimate solution to the pair of equations we chose to solve. The line y=58-2x intersects the hyperbola xy/2 = 120 in two places. However, (x, y) = (5, 48) does not satisfy the hypotenuse requirement that x+2 > y.
A rectangular window is 48 in long and 36 in wide. Lisa
would like to buy a screen for the window. The cost of
the screen is based on the number of square feet the
screen is. Use the facts to find the area of the window in
square feet.
Conversion facts for length
1 foot (ft) 12 inches (in)
1 yard (yd) = 3 feet (ft)
1 yard (yd) = 36 inches (in)
2
Х
$
?
[tex]\\ \sf\longmapsto Area=Length\times Breadth[/tex]
[tex]\\ \sf\longmapsto Area=48(36)[/tex]
[tex]\\ \sf\longmapsto Area=1728in^2[/tex]
[tex]\\ \sf\longmapsto Area=144ft^2[/tex]
[tex]\\ \sf\longmapsto Area=48yard^2[/tex]
If there are12 books on a rack,a person has to choose 5books.
In how many ways can he choose if one particular book is always selected?
Answer:
330
11 choose 4
[tex]=\frac{11!}{4!\left(11-4\right)!}\\= 330[/tex]
Step-by-step explanation:
Your help is very much appreciated I will mark brainliest:)
Answer:
B. Yes. By SSS~
Step-by-step explanation:
From the diagram given, we have the corresponding sides of both triangles as follows:
RQ/KL = 24/20 = 6/5
QP/LM = 18/15 = 6/5
RP/KM = 12/10 = 6/5
From the above, we can see that the ratio of the corresponding side lengths of both triangles are equal. This means that all three sides of one triangle are proportional to all corresponding sides of the other triangle.
The SSS similarity theorem states that if all sides of one triangle are proportional to all corresponding sides of another, then both triangles are similar to each other.
Therefore, ∆KLM ~ ∆RQP by SSS similarity.
What effect will replacing x with (x−4) have on the graph of the equation y=(x−3)2 y = ( x − 3 ) 2 ?
Answer:
y"= 2 wich is positive
Step-by-step explanation:
Step-by-step explanation:
Our equation is: y=(x-3)²
x should be replaced by x-4
y=(x-3)²
y=[(x-4)-3]²
y=(x-4-3)²
y=(x-7)²
The graph is still a parabola but with a different vertex
The vertex here is :
y= (x-7)²
y= x²-14x-49
y'= 2x-14
solve y'=0
2x-14=0
2x=14
x=7
You can easily find it without derivating by dividing -14 by -2
since: x²-14x-49
a=1 b= -14 c=-49
-b/2a = 14/2 = 7
the image of 7 is:
y=(7-7)² = 0
so the coordinates of the new vertex are (7,0) and it's a maximum
since y">0
y'= 2x-14
y"= 2 wich is positive
Find the length of side
x
x in simplest radical form with a rational denominator.
Thanks In advance.
Answer:
Sorry I dont really understand wish I could help:(
Step-by-step explanation:
Answer:
[tex]\sqrt{10}[/tex]
[tex]\sqrt{5 } ^{2} + \sqrt{5 } ^{2} = x^{2}[/tex]
[tex]x^{2} =10[/tex]
Step-by-step explanation:
Test scores are normally distributed with a mean of 68 and a standard deviation of 12. Find the z – score for a grade of 74. Round your answer to two numbers after the decimal.
Answer:
gang nem
Step-by-step explanation:
I really need help with this one
Write the ratio 4 L : 5.6 L as a fraction in the simplest form with whole numbers in the numerator and denominator
Answer:
Step-by-step explanation:
It's 5/7
You get that by having a calculator that does that. If you don't then the way to do it is multiply the numerator and denominator by 1.25
4 * 1.25 = 5
5.6 * 1.25 = 7
At a restaurant, the bill comes to $55. You decide to leave a 12
%
tip. How much did you leave for the tip?
Answer:
$6.60
Step-by-step explanation:
12% = 0.12
12% of $55 = 0.12 x 55
=6.6
So, $6.60
ANSWER PLS!! :DD
Which of the following is not a property of a regular pyramid?
A. lateral faces that are parallel
B. lateral faces that are congruent isosceles triangles
C. lateral edges that are congruent
D. volume of the pyramid is equal to one-third the product of the area of its base and its altitude
Answer:
a
Step-by-step explanation:
Lateral faces that are parallel is not a property of a regular pyramid. The correct option is A.
What is a regular pyramid?Any pyramid whose base is a regular polygon and whose lateral edges are all of the same lengths is said to be regular.
The properties of a regular pyramid are:-
Lateral faces that are congruent isosceles triangles. Lateral edges that are congruent and the volume of the pyramid is equal to one-third the product of the area of its base and its altitude.
Hence, option A is correct.
To know more about the regular pyramid follow
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I want to know how to solve this equation
Answer:
one property of log is that if the log expressions have the same base (in this case, 2), then you can multiply the added logs.
The answer would then be D
In parallelogram ABCD,AB^4+AD^2+AB^2*AD^2=AC^2*BD^2.If angle ABC=x,find the product of all possible values of x
Answer:
Hello,
Step-by-step explanation:
AB=DC=b, AD=BC=a
p=BD, q=AC
angle ABC=x
[tex]AB^4+AD^4+AB^2*AD^2=AC^2*BD^2\\\\b^4+a^4+b^2a^2=(a^2+b^2+2abcos(X))(a^2+b^2-2abcos(X)\\\\(a^2+b^2+2a^2b^2)-a^2b^2=((a^2+b^2)^2-4a^2b^2*cos^2(X))\\\\\\4a^2b^2cos^2(X)=a^2b^2\\\\\\cos^2(X)=\dfrac{1}{4} \\\\(cos(X)-\dfrac{1}{2} )(cos(X)+\dfrac{1}{2} )=0\\cos(x)=\frac{1}{2} \ or\ cos(X)=\dfrac{-1}{2} \\\\\\X=60^o =\dfrac{\pi}{3} rad \ or \ X=120^o=\dfrac{4\pi}{3} rad\\\\\\\\Product=\dfrac{\pi}{3}*\dfrac{4\pi}{3} =\boxed{\dfrac{4\pi^2}{9}}\\[/tex]
answer this now please :)
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Answer:
E. 384 cu ft
Step-by-step explanation:
The sum of length and width is half the perimeter, so the width is ...
(40/2) -12 = 8 . . . feet
The depth is half that, so is 8/2 = 4 feet.
The volume is ...
V = LWH = (12 ft)(8 ft)(4 ft) = 384 ft³
Use the diagram to answer the question below.
Name a point not on line AC
Answer:
It can be the point E or the point D
the ratio of sadia's age to her father's age is 3:6. The sum of their age is 96 .What is sadia's age?
Answer:
sadia is 32
Step-by-step explanation:
sadia : father : total
3 6 9
Divide 96 by 9
96/9 = 32/3
Multiply each by 32/3
sadia : father : total
3*32/3 6*32/3 9*32/3
32 64 96
Find x (round to the nearest tenth)
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Answer:
x = 8
Step-by-step explanation:
By AA similarity, ΔABD ~ ΔCDE. So, corresponding sides are proportional.
AB/BD = CD/DE
x/12 = 4/6
x = 12(4/6)
x = 8
Christian randomly selects students from his grade to rate a math test as easy, moderate, or difficult. Of the students he surveyed, 13 said the test was easy, 11 rated it as moderate, and 3 found it difficult. Assuming that all students took the same test, how many of the 162 total students in Christian’s grade would probably rate the test something other than easy?
A.
27
B.
78
C.
84
D.
126
Answer:
C.
84
Step-by-step explanation:
This question is solved using proportions.
From the sample:
11 + 3 = 14 out of 13 + 11 + 3 = 27 would rate the test something other than easy.
Out of 162:
Applying the rule of three:
14 - 27
x - 162
Applying cross multiplication:
[tex]27x = 14*162[/tex]
[tex]x = \frac{14*162}{27}[/tex]
[tex]x = 84[/tex]
Thus the correct answer is given by option C.
Answer:
I hope this helps
Step-by-step explanation:
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Chapter 11 part 3:
Of the three functions {f(x), g(x), h(x)} featured on the graph below (on the following page), rank the functions in order of greatest rate to least.
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Answer:
f, h, g
Step-by-step explanation:
You can look at the slope of the tangent lines to the graphs at any given x-value. At x=5, we see that g(x) is the flattest curve and f(x) is the steepest.
In order from greatest to least growth rate, the functions are ...
f(x), h(x), g(x)
The work of a student to solve a set of equations is shown:
Equation A: y = 15 − 2z
Equation B: 2y = 3 − 4z
Step 1: −2(y) = −2(15 − 2z) [Equation A is multiplied by −2.]
2y = 3 − 4z [Equation B]
Step 2: −2y = 15 − 2z [Equation A in Step 1 is simplified.]
2y = 3 − 4z [Equation B]
Step 3: 0 = 18 − 6z [Equations in Step 2 are added.]
Step 4: 6z = 18
Step 5: z = 3
In which step did the student first make an error?
Step1
Step 2
Step 3
Step 4
Step 2
−2y = 15 − 2z
should be
−2y = -30 + 4a
I need to know how to find the area and to simplify it
Area of parallelogram = b × h
Base = x + 7
Height = x + 3
ATQ
Area = (x + 7) ( x + 3)
x² + 3x + 7x + 21
x² + 10x + 21
Answered by Gauthmath must click thanks and mark brainliest
How tall is the table?
Answer:
too complex:<
Step-by-step explanation:
120cm+120cm=240cm (2 squirrels + 2 air spaces)
90cm+90cm=180cm (2 rats + 2 air spaces)
240cm-180cm=(2 squirrels + 2 air spaces) - (2 rats + 2 air spaces)
=2 squirrels + 2 air spaces - 2 rats - 2 air spaces
=2 squirrels - 2 rats
=60cm
1 squirrel - 1 rat = 60cm divided by 2
= 30cm
120cm + 90cm = squirrel + air space + rat + air space
= 210cm
I've no idea!! This qn is too challenging!!
But i hope the above workings might help you in a way or another:>
The table is 105cm tall.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let the table is x
Squirrel is y
Rat is z
From 1st diagram
x+y-z=120...(1)
From 2nd diagram
x+z-y=90...(2)
Add 1 and 2
x+y-z+x+z-y=120+90
2x=210
Divide both sides by 2
x=105
Hence, the table is 105cm tall.
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Find the first five terms to an=2an-1+3, a1=6
Answer:
a1=6 a2=15 a3=33 a4=69 a5=141
Step-by-step explanation:
an=2an-1+3
We should attempt n=2 to find the second term
a2=2a1+3= 2*6+3=15
n=3 to find the third term
a3=2a2+3= 2*15+3=33
n=4 to find the fourth term
a4=2a3+3=2*33+3=69
n=5 to find the fifth term
a5= 2a4+3=2*69+3= 141
(PLEASE HELP ITS URGENT)
What is the measure of angle x?
A) 60°
B) 30°
C) 45°
D) 90°
Answer:
B
Step-by-step explanation:
Reason...sum of angles in a triangle is equal to 180⁰
R+V+T=180⁰
60⁰+90⁰+x⁰=180⁰
150⁰+x⁰=180⁰
x⁰=180⁰-150⁰
:. x⁰=30⁰
===================================================
Explanation:
Ignore lines VS and SU. They're unnecessary clutter.
Triangle VRT is a right triangle with angles T = x, R = 60, V = 90
For any triangle, the angles must add to 180
T+R+V = 180
x+60+90 = 180
x+150 = 180
x = 180-150
x = 30
Or you could note that R+T = 90 Solves to T = 30 since triangle VRT is a right triangle. The rule with any right triangle is that the acute angles are always complementary (aka they add to 90 degrees).
How many roots does the equation (8/(x^2 - 16) )+ 1 = 1/(x -4) have?
Plz show ALL STEPS
Answer:
Step-by-step explanation:
