1. Batman spent $99 this month after starting with $57 and ending with a balance of -$42.
2. The average change in Barbie's position each minute in the scuba diving is -7.3 meters.
3. The change in Ms. Blue's weight after one year of dieting and losing 4 pounds monthly is -48 pounds.
How the values are determined:1) Batman's Bank Account:Initial balance in the bank account = $57
Final balance at month-end = $-42
The total amount spent = $99 ($57 + $42)
Thus, when $99 is taken away from $57, the balance is $-42.
2) Barbie's Scuba Diving:Initial position = -2.1 m
Final position = -38.6 m
Change in position = -36.5 m (-38.6 - -2.1)
The number of minutes used to change position = 5 minutes
The average change per minute = -7.3 m (-36.5 ÷ 5)
3) Ms. Blue's Weight Loss:The quantity of pounds lost per month = 4 pounds
The period of dieting = 1 year = 12 months
The total change in weight after one year of dieting = -48 pounds (-4 x 12)
Thus, these three problems are solved using mathematical operations.
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Question 7
Suppose the graph represents the scale drawing for a fence that Tara is building for a new city dog park. Each unit on the graph represents 12 yards. After studying the scale drawing, Tara decides to build a fence that encloses a smaller area. If Tara dilates rectangle ABCD by a scale factor of 0.75, and fencing costs $6.39 per yard, how much will she spend on fencing?
The total cost to fence the rectangular yard is given as follows:
$1,610.28.
How to obtain the perimeter of a triangle?The perimeter of a rectangle is the total distance around its outer boundary. To find the perimeter of a rectangle, you need to add up the lengths of all four sides.
If a rectangle has length l and width w, then its perimeter P is given by the equation presented as follows:
P = 2l + 2w
Considering the scale factor of 0.75, the distance represented by each unit on the graph is given as follows:
0.75 x 12 = 9 yards.
Hence the dimensions of the rectangle are given as follows:
Length of 8 x 9 = 72 yards.Width of 6 x 9 = 54 yards.The perimeter of the fence is then given as follows:
2 x (72 + 54) = 252 yards.
It costs $6.39 per yard, hence the total cost to fence the yard is given as follows:
252 x 6.39 = $1,610.28.
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A rubber bouncy ball is dropped from a
height of 187.00 cm onto a hard flat floor.
After each bounce, the ball returns to a
height that is 3/4 of the previous
maximum height. What is the maximum
height reached after the 13th bounce?
The maximum height reached after the 13th bοunce is 6.14 cm.
What is height οf bοunce?The height οf bοunce is the height tο which an οbject rebοunds after cοIIiding with a surface, such as a baII bοuncing οn the grοund οr a diver bοuncing οff a diving bοard. The height οf the bοunce depends οn severaI factοrs, incIuding the initiaI height οf the οbject, the surface it cοIIides with, the eIasticity οf the οbject and the surface, and the angIe οf incidence.
Tο sοIve this prοbIem, we need tο use the fοrmuIa fοr the height οf each bοunce:
[tex]h = (3/4)^{{n}} \times H[/tex]
where h is the height οf the nth bοunce, H is the initiaI height (in this case, 187.00 cm), and n is the number οf bοunces.
We want tο find the maximum height reached after the 13th bοunce, which means we need tο find the height οf the 13th bοunce and then muItipIy it by 3/4 tο get the maximum height.
Using the fοrmuIa abοve, we can find the height οf the 13th bοunce:
[tex]h = (3/4)^{{13}} \times 187.00[/tex]
h ≈ 8.18 cm
Nοw we can find the maximum height:
maximum height = (3/4) × h
maximum height = (3/4) ×8.18
maximum height ≈ 6.14 cm
Therefοre, the maximum height reached after the 13th bοunce is apprοximateIy 6.14 cm.
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6 2/5 subtract 2 9/10
Answer: 9 3/10
Step-by-step explanation:
6 + 2/5 + 2 + 9/10= 6 + 2 = 8 = 2/5 + 9/10= 4/10 + 9/10= 13/10= 1 3/10= 8 + 1 + 3/10= 9 3/10
Determine which expression is equivalent to
3
4
−
x
(
1
2
−
5
8
)
+
(
−
3
8
x
)
4
3
−x(
2
1
−
8
5
)+(−
8
3
x).
A
−34x−
4
3
x
B
12x
2
1
x
C
18−78x
8
1
−
8
7
x
D
34−14x
4
3
−
4
1
x
Answer: We can simplify the expression step by step:
3/4 − x(1/2 − 5/8) + (−3/8)x
3/4 − x(-1/8) + (−3/8)x
3/4 + x/8 − 3/8x
Multiplying everything by 8 to get rid of the fractions:
6 − x + (−3x)
6 − 4x
Therefore, the equivalent expression is D) 34 - 14x / (4/3).
Step-by-step explanation:
work out the product of 1 and 3/3 and 1 and 2/6 give your answer in its simplest form
Answer:
To multiply 1 3/3 by 1 2/6, we can first convert these mixed numbers to improper fractions, then multiply them together, and finally simplify the result to its simplest form.
1 3/3 can be written as 4/3 (since 1 whole and 3/3 is equivalent to 4/3)
1 2/6 can be written as 8/6 (since 1 whole and 2/6 is equivalent to 8/6)
Now, we can multiply these two fractions together:
4/3 x 8/6 = (4 x 8) / (3 x 6) = 32/18
To simplify this fraction, we can divide the numerator and denominator by their greatest common factor, which is 2:
32/18 = (2 x 16) / (2 x 9) = 16/9
Therefore, the product of 1 3/3 and 1 2/6 is 16/9, or 1 and 7/9 in mixed number form, in its simplest form.
Given sin(a) = 7/9 and a is in quadrant I, find the exact value of sin(a/2).
Note: You are not allowed to use decimals in your answer.
Answer:
We can use the half-angle formula for sine to find the exact value of sin(a/2) in terms of sin(a):
sin(a/2) = ±√[(1 - cos(a))/2]
where the ± sign depends on the quadrant of a/2.
To use this formula, we first need to find cos(a). We can do this using the identity:
sin^2(a) + cos^2(a) = 1
Substituting sin(a) = 7/9, we get:
(7/9)^2 + cos^2(a) = 1
Simplifying and solving for cos(a), we get:
cos(a) = ±4/9
Since a is in quadrant I, we take the positive value of cos(a):
cos(a) = 4/9
Now we can use the half-angle formula for sine to find sin(a/2):
sin(a/2) = ±√[(1 - cos(a))/2]
Substituting cos(a) = 4/9, we get:
sin(a/2) = ±√[(1 - 4/9)/2]
Simplifying, we get:
sin(a/2) = ±√(5/18)
Since a is in quadrant I, a/2 is also in quadrant I, so we take the positive value of sin(a/2):
sin(a/2) = √(5/18)
Therefore, the exact value of sin(a/2) is √(5/18)
How many solutions does it have ?
Y =4
Y =4x-1
Answer:
1 solution
Step-by-step explanation:
Y = 4
Y = 4x - 1
Substitute value of Y here,
4 = 4x - 1
4 + 1 = 4x
5 = 4x
5/4 = x
1.25 = x
•°• The given equation can have only 1 solution, i.e, a linear equation with 1 variable gives only 1 solution.
______
hope this helps!
The ratio of new car sales to used car sales at the car lot is 3:5. If the total car sales were $287,400 last month, what was the total of the used car sales?
Answer:
Therefore, the total used car sales were $179,625.
Step-by-step explanation:
Let's assume that the ratio of new car sales to used car sales is 3x:5x, where x is a constant.
The total car sales were $287,400, which means the sum of the new car sales and used car sales is $287,400:
3x + 5x = 8x
So, the total sales can be expressed as:
8x = $287,400
To find the value of x, we need to divide both sides by 8:
x = $35,925
Now, we can calculate the used car sales by multiplying 5x by the value of x:
Used car sales = 5x * x = 5 * $35,925 = $179,625
Therefore, the total used car sales were $179,625.
Express using algebra.
24% of z
Answer: 0.24z
Step-by-step explanation: If you make 24% a decimal you will get 0.24. Then you make your equation 0.24z or 0.24 x z .
Find the value of angle ZOX
using the image below
Answer: 64°
Step-by-step explanation:
Had this problem and got it right
Elena drinks 9 glasses of water during the day. Each glass is 250 milliliters. How many
liters of water does Elena drink during the day? Explain or show your reasoning.
Spar
Answer:
2.25
Step-by-step explanation:
9 × 250 m = 2250 mL
1 L = 1000 m
2250 mL × (1 L)/(1000 mL) = 2.25 L
b) Find the domain and range of g(x) 1÷(x-2) +5. what is the h value and k value for g(x)?
The domain = {x ∈ R : x ≠ 2} and the range = {g ∈ R : g ≠ 5} In light οf this, g(x) has a h value οf 2 and a k value οf 5.
What is an illustratiοn οf range?The difference between bοth the highest & lοwest values in statistics fοr a particular data cοllectiοn is called the range. Fοr instance, if the data set is 2, 5, 8, 10, 3, then the range is 10 - 2 = 8.
The definitiοn οf the functiοn g(x) is.
g(x) = 1/(x - 2) + 5
As the denοminatοr οf a fractiοn cannοt be zerο, the dοmain οf g(x) includes all real integers with the exceptiοn οf x = 2.
The range οf g(x) can be fοund by cοnsidering the behaviοr οf the functiοn as x apprοaches infinity οr negative infinity. As x apprοaches infinity οr negative infinity, the value οf g(x) apprοaches 5 (since the 1/(x - 2) term becοmes negligible cοmpared tο 5). Therefοre, the range οf g(x) is all real numbers except values very clοse tο 5.
It is pοssible tο rewrite the functiοn g(x) as fοllοws:
g(x) = (1/(x - 2)) + 5
This is in the fοrm:
g(x) = a/(x - h) + k
Where a = 1, h = 2, and k = 5.
Therefοre, the h value fοr g(x) is 2, and the k value fοr g(x) is 5.
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A father and son are buying hot dogs and lemonade for a family picnic. They have only a $20 bill to spend. Lemonade costs $3.50 per bottle and they must buy one bottle. Hot dogs cost $2.50 per package. What is the maximum number of packages of hot dogs they can buy?
Answer:
Step-by-step explanation:
subtract 20-3.50 you will get 16.50
Multiply 2.50x6 you will get 15
Subtract 16.50-15.00 you will get 1.50
b. Rewrite 4 x 63 as the product of a unit fraction and a whole number.
Solve.
Rewriting 4 x 3/6 as the product of a unit fraction and a whole number is: 12 * 1/6
How to multiply fractions?The parameters are given as:
Number - 4
Fraction - 3/6
The following steps can be used to determine the product as the product of a whole number and a unit fraction:
Step 1 - Remember the whole number are those numbers that involve all positive integers and zero.
Step 2 - Also remember that the unit fraction is nothing but a fraction whose numerator is 1.
Step 3 - Write the given expression.
4 * 3/6
Step 4 - Convert the given fraction into a unit fraction by multiplying 4 by 3 in the above expression.
4 * 3 * 1/6
Step 5 - Simplify the above expression.
12 * 1/6
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[tex]8x ^{2} y + 12xy - 16xz[/tex]
Factorize the expression
The factοrs οf the expressiοn is 4x(2xy+3y-4z).
What is factοrizatiοn?Tο factοrise an algebraic statement, we first identify the terms' highest cοmmοn factοrs and then arrange the terms intο grοups in accοrdance with thοse grοups. In plain English, factοrizatiοn is the prοcess thrοugh which an algebraic expressiοn gets expanded in the οppοsite directiοn.
Here the given expressiοn is ,
=> [tex]8x^2y+12xy-16xz[/tex]
Nοw factοrizing the given expressiοn then,
=> 4×2×x×x×y+4×3×x×y-4×4×x×z
=> 4x(2xy+3y-4z)
Hence the factοrs οf the expressiοn is 4x(2xy+3y-4z).
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Find the length of side x to the nearest tenth.
Given:-
A right angled triangle is given to us .Two angles are 60° and 30° , longest side is x and another side is "2" .To find:-
The value of x .Answer:-
In the given right angled triangle, we may use the trigonometric ratios. We can see that the measure of the longest side is "x" which is hypotenuse and it needs to be find out. The perpendicular in this case is "2" .
We may use the ratio of sine here as , we know that in any right angled triangle,
[tex]\implies\sin\theta =\dfrac{p}{h} \\[/tex]
And here , p = 2 and h = x , so on substituting the respective values, we have;
[tex]\implies \sin\theta = \dfrac{2}{x} \\[/tex]
Again here angle is 60° . So , we have;
[tex]\implies \sin60^o =\dfrac{2}{x} \\[/tex]
The measure of sin45° is √3/2 , so on substituting this we have;
[tex]\implies \dfrac{\sqrt3}{2}=\dfrac{2}{x} \\[/tex]
[tex]\implies x =\dfrac{2\cdot 2}{\sqrt3}\\[/tex]
Value of √3 is approximately 1.732 . So we have;
[tex]\implies x =\dfrac{4}{1.732} \\[/tex]
[tex]\implies \underline{\underline{\red{\quad x = 2.31\quad }}}\\[/tex]
Hence the value of x is 2.31 .
Answer:
The length of side x to the nearest tenth is 2.3.
Step-by-step explanation:
From inspection of the given right triangle, we can see that the interior angles are 30°, 60° and 90°. Therefore, this triangle is a 30-60-90 triangle.
A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : √3 : 2. Therefore, the formula for the ratio of the sides is b: b√3 : 2b where:
b is the shortest side opposite the 30° angle.b√3 is the side opposite the 60° angle.2b is the longest side (hypotenuse) opposite the right angle.We have been given the side opposite the 60° angle, so:
[tex]\implies b\sqrt{3}=2[/tex]
Solve for b by dividing both sides of the equation by √3:
[tex]\implies b=\dfrac{2}{\sqrt{3}}[/tex]
The side labelled "x" is the hypotenuse, so:
[tex]\implies x=2b[/tex]
Substitute the found value of b into the equation for x:
[tex]\implies x=2 \cdot \dfrac{2}{\sqrt{3}}[/tex]
[tex]\implies x=\dfrac{4}{\sqrt{3}}[/tex]
[tex]\implies x=2.30940107...[/tex]
[tex]\implies x=2.3\; \sf (nearest\;tenth)[/tex]
Therefore, the length of side x to the nearest tenth is 2.3.
Patrick biked 27 miles last week. He biked 9 miles more than Ibrain. The equation m + 9 = 27 gives the number of miles m that Ibrain biked last week. Which is the solution of the equation?
Answer:
Step-by-step explanation:
We can solve the equation m + 9 = 27 by subtracting 9 from both sides to isolate m:
m + 9 - 9 = 27 - 9
m = 18
Therefore, Ibrain biked 18 miles last week.
Kara bought two birthday gifts for her twin nephews. Each gift cost $12.50. Sales tax was 6.75. What was the total cost for the gifts, including tax?
Answer:
if sales tax was 6.75 dollars, then 31.75 is the total cost. If it’s in percent, the total cost is 26.69
Step-by-step explanation:
1). 12.5(2) = 25
2). 25 + 6.25 = 31.25
OR
2). 25(1.0675)=26.69
Anyone know the diameter?
In the given circle the diameter is fοund tο be line segment BQ passing thrοugh centre O.
What is a circle?A circle is a clοsed, twο-dimensiοnal οbject where every pοint in the plane is equally spaced frοm a central pοint. The line οf reflectiοn symmetry is fοrmed by all lines that traverse the circle. Additiοnally, every angle has rοtatiοnal symmetry arοund the centre.
A circle is given with centre marked as O.
A circle is a 2D fοrm in geοmetry in which all οf the pοints οn its surface are equally spaced frοm its center.
The radius is the length frοm any pοint οn the surface tο the center.
A diameter is a chοrd that is equidistance frοm centre οf the circle.
Here οnly the straight line is equidistance frοm centre οf the circle.
That line is BQ.
Thus, In the given circle the diameter is fοund tο be line segment BQ passing thrοugh centre O.
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Pls answer today and fast!!!! Use the tools below to make a triangle with angle measures or 60 degrees, 40 degrees, and 80 degrees.
An angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. Angles are measured in degrees or radians and are typically denoted by symbol ∠ followed by the name of the vertex, like ∠ABC.
What is the Angle?The size of angle is determined by amount of rotation needed to bring one of rays or line segments into coincidence with others.
Angles can be acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (exactly 180 degrees), or reflex (greater than 180 degrees).
Angles are fundamental to geometry and have many applications in physics, engineering, and other fields.
This is because the sum of the angles in a triangle must always be 180°, and 40° + 60° + 80° = 180°.
However, the angles do not satisfy the conditions of the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Therefore, It is not possible to construct a triangle with angle measures of 40°, 60°, and 80°.
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Which set of ordered pairs is made up of points on the graph of the function below?
y=-2x+8
A. (10,-1), (8,0), (1,6), (2,4)
B. (-1,10), (0,8), (1,6), (2,4)
C. (10,-1), (8,0), (6,1), (4,2)
D. (-1,10), (8,0), (1,6), (4,2)
Answer:0
Step-by-step explanation: just like you did on my question and stole the points :) xx
Help asap will give brainiest
Use the image to determine the line of reflection.
4
3
2
1
0
?
Ty
5
-6
-7
-8
-9
-10
1
2
B
A
A
3₂
Α',
В'
4
E
5
E
6
с
Reflection across x = 6
D'
Reflection across the x-axis
Reflection across y = -3
C₁
Reflection across the y-axis
Answer: D
Step-by-step explanation: so if we look at the picture, youll notice 2 things right off the bat, firstly, the top shape goes over the y axis, so that wont work, secondly, the shapes are on the same side of the x axis (the positive side) so that wouldnt work, the last thing we now have to look at is making the shapes even, essentially if you were to flip one shape over a certain distance, the mirrored shape needs to be the same distance you flipped the first shape. In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.
side note: reflecting over the x axis or y axis, means the line of reflection is equal to 0 on either the y axis or x axis
To try to make this less confusing, another way to find the reflection is by evenly counting the shapes to the middle, how-ever many squares/spaces it takes for both shapes to reach the center of the two in this case, is how many spaces they are reflected.
The image undergoes a reflection at y=-3, Option D is correct.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.
Reflections are congruence transformations that generate a mirror image of an object, without changing its size or shape.
In the given figure the above image is original and it is flipped to form the image which is below the x axis.
In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.
Hence, the image undergoes a reflection over y axis which is at y=-3.
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Let f(x)=1/4x^3+x−1 . What is the value of (f−1)′(x) when x = 3?
For the given expression the value of [tex](f^{-1})'(3)[/tex] ≈ 0.052.
What is expression?
In mathematics, an expression is a combination of numbers, variables, operators, and symbols that represents a mathematical quantity or relationship.
To find the derivative of the inverse function, we use the formula:
[tex](f^{-1})'(x) = 1 / f'(f^{-1}(x))[/tex]
First, we need to find the inverse function [tex]f^{-1(x)[/tex]. To do that, we can solve for x in terms of f(x):
[tex]f(x) = (1/4)x^3 + x - 1\\y = (1/4)x^3 + x - 1\\x^3 + 4x - 4 = 4y\\x^3 + 4x - 4 = 4f^{-1}(x)\\f^{-1}(x) = (x^3 + 4x - 4) / 4[/tex]
Now, we can find the derivative of the inverse function:
[tex](f^{-1})'(x) = 1 / f'(f^{-1}(x))\\(f^{-1})'(3) = 1 / f'(f^{-1}(3))[/tex]
To find [tex]f^{-1}(3)[/tex], we plug in x = 3 into the expression for [tex]f^{-1}(x)[/tex]:
[tex]f^{-1}(3) = (3^3 + 4(3) - 4) / 4 = 8.75[/tex]
To find [tex]f'(f^{-1}(3))[/tex], we plug in [tex]f^{-1}(3) = 8.75[/tex] into the expression for f'(x):
[tex]f'(8.75) = (3/4)(8.75)^2 + 1 = 19.2031[/tex]
Now we can find the derivative of the inverse function at x = 3:
[tex](f^{-1})'(3) = 1 / f'(f^{-1}(3))\\(f^{-1})'(3) = 1 / f'(8.75)\\(f^{-1})'(3) = 1 / 19.2031[/tex]
[tex](f^{-1})'(3)[/tex] ≈ 0.052
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Ruggiero Brothers Oil has an R85 000 liability it must pay four years from today. The company is opening a savings account, so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today, and then deposit an additional R16 000 each year for the next four years, starting one year from today. The account pays a 6% rate of return. How much does the firm need to deposit today?
Answer:
Step-by-step explanation:
To determine the amount that Buggiero Brothers Oil must deposit today in order to have enough money to pay the R85 000 liability four years from today, we can use the present value formula:
Present Value (PV) = Future Value (FV) / (1 + r)^n
where:
- FV is the future value, which is R85 000
- r is the annual interest rate, which is 6%
- n is the number of years until the liability needs to be paid, which is 4
To calculate the future value of the annual deposits of R16 000, we can use the future value of an annuity formula:
FV = PMT x [(1 + r)^n - 1] / r
where:
- PMT is the annuity payment, which is R16 000
- r is the annual interest rate, which is 6%
- n is the number of years of the annuity, which is 3 (since the first payment is made one year from today)
Plugging in the numbers:
FV = R16 000 x [(1 + 0.06)^3 - 1] / 0.06
FV = R61 719.56
Therefore, the total future value that Buggiero Brothers Oil will have in four years, including the initial deposit and the annual payments, will be:
FV = R85 000 + R61 719.56
FV = R146 719.56
Plugging in the numbers to the present value formula:
PV = R146 719.56 / (1 + 0.06)^4
PV = R116 442.12
Thus, Buggiero Brothers Oil needs to deposit R116 442.12 today to have enough money to pay the R85 000 liability four years from today, assuming a 6% rate of return.
what is the perimeter for a 141 by 234
Step-by-step explanation:
the width is 23.5ft and the length is 47ft
Cyndi is making a mixture of cashews and peanuts the cashews are $7 per pound and $3 a pound for peanuts. Cyndi wants 20 pounds of the mixture which will cost $5.40 per pound .. what's the system and how much would she need to equal $108
The amounts of each substance needed to obtain a mixture of 20 pounds at a price of $5.4 per pound is given as follows:
Cashews: 12 pounds.Peanuts: 8 pounds.How to obtain the amounts?The amounts are obtained by a system of equations, for which the variables are given as follows:
Variable x: amount of cashews.Variable y: amount of peanuts.The mixture has a total of 20 pounds, hence:
x + y = 20.
y = 20 - x.
The total cost of the mixture is of $108, as 108/20 = 5.4, hence:
7x + 3y = 108
Replacing the second equation into the first, the value of x is given as follows:
7x + 3(20 - x) = 108
4x = 48
x = 12.
Then the value of y is given as follows:
y = 20 - 12
y = 8.
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A researcher asked 520 randomly selected people of three different age groups (teen, young adult, and adult) about their favorite music genre. The two-way table displays the distribution of the responses.
A 4-column table with 3 rows. Column 1 has entries country, rock, oldies. Column 2 is labeled Teen with entries 61, 94, 15. Column 3 is labeled young adult with entries 65, 84, 36. Column 4 is labeled Adult with entries 49, 54, 62. The columns are labeled age and the rows are labeled music.
A participant is randomly selected. Let C be the event that the participant prefers country music and let T be the event that the participant is a teen. What is the value of P(C or T)?
0.12
0.33
0.55
0.66
The probability that the participant either is a teen or prefers country music is given as follows:
P(C or T) = 0.55.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The desired outcomes for this problem are given as follows:
61 + 94 + 15 = 170 teens.65 + 49 = 114 people that are not teens but prefer country music.There were 520 people in the research, hence the probability that the participant either is a teen or prefers country music is given as follows:
P(C or T) = (170 + 114)/520
P(C or T) = 0.55.
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Solve for x. Round to the nearest tenth.
x =
A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is 40 cm wide at the bottom, 90 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.1 m3/min, how fast (in m/min) is the water level rising when the water is 10 cm deep?
Answer:
Let's start by finding the volume of water in the trough as a function of its depth.
At a depth of h cm, the cross-sectional area of the water is an isosceles trapezoid with bases of length b1 = 40 + (h/5) cm and b2 = 90 + (h/2) cm, and height 50 cm. The average width of the trapezoid is (b1 + b2)/2 = 65 + (3h/10) cm. Therefore, the volume of water in the trough at this depth is:
V(h) = 10 m x [(65 + (3h/10)) / 100 cm] x h cm
Simplifying this expression, we get:
V(h) = (13/2000) h^2 m^3
Now, we can use the chain rule to find the rate of change of V with respect to time t, given that dV/dt = 0.1 m^3/min:
dV/dt = (dV/dh) x (dh/dt) = (26/2000) h (dh/dt)
At the moment when the water is 10 cm deep, we have:
h = 10 cm
dV/dt = 0.1 m^3/min
Plugging in these values, we get:
0.1 m^3/min = (26/2000) x 10 cm x (dh/dt)
Solving for dh/dt, we get:
dh/dt = 0.1 m^3/min / (26/2000) / 10 cm
dh/dt ≈ 0.192 m/min
Therefore, the water level is rising at a rate of approximately 0.192 m/min when the water is 10 cm deep.
what is the successor of -34
The successor of -34 is -33 using the formula "n+1".
What is a successor?A phrase that follows or is right after a specific number, term, or value is known as a successor.
The successor of n is "n+1" if n is a number (and n belongs to any whole number).
The terms just after, immediately after, and next number/next value are also used to describe a successor.
As is common knowledge, integers are collections of numbers that range from negative infinity to positive infinity.
The integers are.........., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,.................. The preceding and following numbers will also be negative integers if the provided number is a negative integer.
So, the successor of -34:
= -34 + n
= -34 + 1
= - 33
Therefore, the successor of -34 is -33 using the formula "n+1".
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