When the radius of the snowball is 4 and shrinks at a rate of 2 inches per hour then the rate of change of the surface area s is equal to 64π in²/hr
As the radius r is shrinking at the rate of two inches per hour, it can be represented as;
dr/dt = -2 in / hr
Here, the negative sign represents the shrinking of the snowball with time t.
The surface area of a sphere can be represented by the formula;
S = 4πr²
Now we differentiate S with respect to t by keeping radius (r) as a variable as follows;
dS/dt = d/dt (4πr²)
dS/dt = 4π (d/dt) (r²)
dS/dt = 4π × 2r (dr/dt)
Putting the value of r = 4 and calculated value of dr/dt = -2 in the equation as follows;
dS/dt = 4π × 2(4)(-2)
dS/dt = -64π
Therefore, the rate of change of surface area s is calculated to be 64π in²/hr.
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If x=-9 and y=3
evaluate the following expression:
2(y-3xy)
Answer:
168
Step-by-step explanation:
= 2[3-{3(-9)(3)}]
= 2[3-{-81}]
= 2(84)
= 168
Hope it helps!!
BTW it was very easy...
Question 3: Kylie needs to spend at least 5 hours each week practicing the piano. She has already practiced 2 and 3/4 hours this week. She wants to split the remaining practice time evenly between the last 3 days of the week. Write an inequality to determine the minimum number of hours she needs to practice on each of the 3 days.
Using proportions with mixed numbers, the inequality to determine the minimum number of hours she needs to practice on each of the 3 days is: m ≥ 3/4.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication or division.
One example is the mean of a data-set, as the mean is given by the sum of all observations in the data-set divided by the number of values.
For this problem, we have that:
She has already practiced 2.75 hours, as the decimal part is of 3/4 = 0.75, hence 2 and 3/4 = 2 + 0.75 = 2.75.She needs to practice 5 hours.Hence the minimum number of hours that she still needs to practice is:
5 - 2.75 = 2.25 hours.
The amount is split evenly amount the 3 days, hence the lower bound of the inequality is:
2.25/3 = 0.75 = 3/4.
Hence the amount is given by:
m ≥ 3/4.
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A student ran the Turkey Trot 5K (5 kilometers) race on Thanksgiving Day. Using the ratio 1 mile : 1.61 kilometers, which set-up would correctly convert 5 kilometers to miles
The conversion of 5 kiiometers to miles is 3.11 miles
How to convert the distance from kilometers to milesThe given parameters are
Distance covered by the students = 5 kilometers
The ratio of the distance is given as
1 mile : 1.61 kilometers
Multiply both sides of the ratio by 5
So, we have the following ratio expression
5 * 1 mile : 1.61 kilometers * 5
Evaluate the product in the above expression
So, we have the following ratio expression
5 miles : 8.05 kilometers
Divide both sides of the ratio by 1.61
So, we have the following ratio expression
5/1.61 miles : 8.05/1.61 kilometers
Evaluate the quotient in the above expression
So, we have the following ratio expression
3.11 miles : 5 kilometers
Rewrite as
5 kilometers : 3.11 miles
This means that
5 kilometers = 3.11 miles
Substitute 5 kilometers = 3.11 miles in Distance covered by the students = 5 kilometers
So, we have
Distance covered by the students = 3.11 miles
Hence, the distance covered by the students is 3.11 miles
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Please help me !!!!!!!
If one student is chosen at random, the probability that the student was a female and got 'A' is 0.38
What is probability?Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is expressed. To forecast the likelihood of events, probability has been introduced in mathematics.
The likelihood that something will occur is essentially what is meant by probability. This is the fundamental theory of probability, which is also used to calculate the probability distribution, and it is from it that you will learn the likelihood of various outcomes in a random experiment.
The total number of outcomes that can occur should be known before calculating the likelihood that a specific event will occur.
Total numbers of students = 53
Total numbers of females = 34
Total numbers of females of A grades = 20
So probability = 20/53
= 0.38
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-24+12d=2(d-3)+22
D=
During an local election the ratio of teens to adults who voted was 10:9 If 1,387 people
voted how many were teens?
730 teens voted.
What is ratio?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).
A ratio is the relationship or comparison between two numbers belonging to the same unit in order to determine how much larger one number is than the other. For instance, if a test result is 7 out of 10, the ratio of the number of points earned to the total number of points is 7:10.
Given Data
Teens to adult ratio 10:9
Total people votes = 1387
Ratio of teen vote:
= 1387 × [tex]\frac{10}{19}[/tex]
= 73(10)
= 730
730 teens votes.
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f(x)=(1/7)(7x) what is f(3)
The value obtained for f(3) after substituting x = 3 in the function f(x) is 0.0067.
What exactly is a function?A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.
What are the Function Formulas?The list of function formulas is divided into two categories: formulas for performing numerous arithmetic operations across functions and formulas for performing combined operations involving two or more functions.
The given function is f(x) = (1/7)/(7x)
We need to find the value of f(3) so we will substitute x = 3 in the given function as follows:
f(3) = (1/7)/(7×3)
∴ f(3) = (1/7)/21
∴ f(3) = 0.142/21
∴ f(3) = 0.0067
Therefore, after substituting x = 3 in the function f(x), the value obtained for f(3) is 0.0067.
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The price of a sweater was changed from $20 to $12. This is a(n) of %?
Answer:
If the proton proton chain produces gamma ray photons, why are the majority of photons we observe from the sun at visible wavelengths?
Step-by-step explanation:
Answer:If the proton proton chain produces gamma ray photons, why are the majority of photons we observe from the sun at visible wavelengths?
Step-by-step explanation:
Step-by-step explanation:
how do i identify the slope and y-intercept
y=-6x-8
Answer:
the formula of a line is y=mx+c
mx is the gradient/slope and c is the y intercept
so the slope here is -6
the y intercept is -8
hope it helps, mark as brainliest if correct.
the shapes below are mathematically similar 10,14,28,x
WE CAN USE THE SIMILARITY THEOREM WHEREIN
[tex] \frac{14}{28} = \frac{10}{x} \\ [/tex]
THE PROPORTIONS OF SIDES OF THE SIMILAR SHAPES A RE EQUAL.
NOW TO SIMPLIFY WE CAN DO CROSS MULTIPLICATION.
[tex]14(x) = 28(10) \\ 14x = 280 \\ \frac{14x}{14} = \frac{280}{14} \\ x = 20 [/tex]
x is therefore 20cmthe probability of picking a blue marble out of a bag of 50 marbles is 3/25. how many marbles in the bag are not blue?
Answer:
Okay so the probability is 3 outa 25 half the amount in the bag just add 3 and 3 together (cause 25 is half of 50) you get 6 subtract that from 50 you get 44.
If you can buy one can of pineapple chunks for $2, then how many can you buy with $10?
(WITH A GRAPH PLEASE)
Answer:
you can buy 5 cans
Step-by-step explanation:
$2 per can
have $10
10 divided by 2
5
Adriel buys 20 bottles of grapefruit juice at the corner store for a total cost of $7.80.
If each bottle costs the same amount, how much is 6 bottles of juice?
The cost of 6 bottles of juice is $2.34 if the each bottle costs the same.
According to the question,
We have the following information:
Adriel buys 20 bottles of grapefruit juice at the corner store for a total cost of $7.80.
Cost of 20 bottles of juice = $7.80
Now, from here we can find the cost of 1 bottle of juice by dividing the total cost by the number of bottles purchased.
Cost of 1 bottle of juice = $(7.80/20)
Cost of 1 bottle of juice = $0.39
Now, we can easily find the cost of 6 bottles of juice by multiplying the cost of 1 bottle of juice by 6.
Cost of 6 bottles of juice = $(0.39*6)
Cost of 6 bottles of juice = $2.24
Hence, the cost of 6 bottles of juice is $2.24.
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Convert 0.000 000 005 78 to scientific notation
Answer: 5.78 × 10 to the negative ninth power
Step-by-step explanation:
is (6,-2) and (8,-3); (15,9) and (13,8) parallel
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the lines above
[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{6}}} \implies \cfrac{-3 +2}{2}\implies \boxed{-\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{x_1}{15}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{13}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{13}-\underset{x_1}{15}}} \implies \cfrac{-1}{-2}\implies \boxed{\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \textit{different slopes, \underline{not parallel}}~\hfill[/tex]
Write the equation of the line that passes through the points (−9,−4) and (−5,−1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
[tex](\stackrel{x_1}{-9}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{-5}-\underset{x_1}{(-9)}}} \implies \cfrac{-1 +4}{-5 +9} \implies \cfrac{ 3 }{ 4 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{ 3 }{ 4 }}(x-\stackrel{x_1}{(-9)}) \implies {\large \begin{array}{llll} y +4= \cfrac{ 3 }{ 4 } (x +9) \end{array}}[/tex]
find the local maximum and minimum values and saddle point(s) of the function. (enter your answers as a comma-separated list. if an answer does not exist, enter dne.)
There is no saddle point (DNE). However, there is local maximum at (1, 1/2) for the given function.
we have function of two variables f(x,y)= 9-2x+4y-x^2-4y^2
we will find the values by partial derivative with respect to x,y,xy
f ₓ= -2 -2x
[tex]f_{y}[/tex] = 4 -8y
to find the saddle point we should first find the critical points so equate
-2 -2x=0 and 4 -8y=0
we get x= 1 and y =1/2 so, critical points are (1,1/2)
to find local maximum or minimum we have to find [tex]f_{xx}[/tex] , [tex]f_{yy}[/tex] and [tex]f_{xy}[/tex]
formula is [tex]f_{xx}[/tex]* [tex]f_{yy}[/tex] - [tex]f_{2xy}[/tex] =0
[tex]f_{xx}[/tex] = -2
[tex]f_{yy}[/tex] = -8
[tex]f_{2xy}[/tex]=0
putting values in formula
(-2)*(-8) -0 =16 > 0, and [tex]f_{xx}[/tex] < 0 and [tex]f_{yy}[/tex] <0
so, here we have local maximum
we have no saddle point for this function by using the same formula we used to find extrema.
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what is the common denominator of "-1/4" + "-2/3"
Answer: 12
Step-by-step explanation:
The 4 in “-1/4” can be multiplied by three.
Three 3 in “-2/3” can be multiplied by four.
These give you the common denominator of 12!
Don’t forget to multiply the numerator by the amount you multiplied the denominator by!
Which of the following is most likely the next step in the series
Represent the following fractions and decimals in a number line
a. 4/7 b. 7/11 c. 8/5 d 0 /1 e. 2/5 f. 2.5 g. 4.3 h 1.2
Answer:
d, e, a, b, h, c, f, g
Step-by-step explanation:
if you convert them all to decimals you get
a = 0.57
b = 0.64
c = 1.6
d = 0
e = 0.4
f = 2.5
g = 4.3
h = 1.2
in order it goes 0, 0.4, 0.57, 0.64, 1.2, 1.6, 2.5, 4.3
The width of a rectangle is 3 units less than the length. The area of the rectangle is 18 units. What is the length, in units, of the rectangle?
Answer:
w=3units l=6 units
Step-by-step explanation:
The required length and width of the rectangle are 6 and 3 units
Given that,
The width of a rectangle is 3 units less than the length. The area of the rectangle is 18 units.
The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.
Here,
Let the length of the rectangle be l and the width of the rectangle is l -3
Now,
area of the rectangle,
18 = l [l - 3]
18 = l² - 3l
l² - 3l - 18 = 0
l² - 6l + 3l - 18 = 0
(l - 6) + 3 (l - 6) = 0
(l - 6)(l + 3) = 0
l = 6 {negative value of the l can be neglected.}
now,
width = 6 - 3 = 3
Thus, the required length and width of the rectangle are 6 and 3 units.
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A bird of species A, when diving, can travel four times as fast as a bird of species B top speed. If the total speeds for these two birds is 170 miles per hour, find the fastest speed of the bird of species A and the fastest speed of the bird of species B.
The fastest speed of the bird of species A is 136 mi/hr. and the fastest speed of the bird of species B is 34 mi/hr.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
A bird of species A, when diving, can travel four times as fast as a bird of species B at top speed which is given in the question.
Let b = the speed of bird species B.
So the speed of bird species A is 4b.
If the total speed for these birds is 170, then there is an equation :
⇒ 4b + b = 170.
⇒ 5b = 170
⇒ b = 170/5 = 34 mi/hr.
So the speed of bird species A will be 4×34 ⇒ 136 mi/hr.
Therefore, the fastest speed of the bird of species A is 136 mi/hr. and the fastest speed of the bird of species B is 34 mi/hr.
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Trisha is saving $25 a week to go on a vacation. She determines that she will need $350 for the vacation,
but she also wants to have over $100 left in her bank account after the trip. How many weeks should
Trisha save?
Answer:
Trisha should save for 18 weeks.
Step-by-step explanation:
1 week = $25
Total = $350
Also wants over $100
350+100 = 450
450 ÷ 25 = 18
The linear function m = 50 - 9d represents the amount m (in dollars) of money you have
left after buying d DVDs.
a. Interpret the terms and coefficient in the equation.
b. Find the domain of the function. Is the domain discrete or continuous? Explain.
c. Graph the function using its domain.
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
How can you tell whether a domain is continuous or discrete?A domain's discreteness or continuousness can be determined by examining the function's graph. The domain is continuous if the graph is a line. The domain is discrete if the graph consists of a collection of points.
What is a discrete domain example?Private Domain
The values that will be effective for the function are distinct from one another. The maximum number of children you can have, for instance, has a defined answer. You can have 0 children, 1, 2, 3, etc., but not 2,34.
How can you determine a discrete function's domain?Discrete graphs are those in which no lines connect the points. Start by locating all the x-coordinates in order to determine the domain and range of a discrete graph. The graph's entire set of x-coordinates makes up the domain. The graph's entire range of y-coordinates is considered to be the range.
What does a discrete structure's domain mean?The domain is the collection of all possible inputs for a function. The codomain is the collection of all permitted outputs.
What is an example of discrete structures?Graphs, logical assertions, and combinations are a few examples of discrete structures. Infinite or finite discrete structures are both possible. Contrary to continuous mathematics, which works with structures whose values can span the real numbers or have other non-separable qualities, discrete mathematics deals with discrete objects.
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Horizontal and parallel lines e and f are intersected by diagonal and parallel lines g and h. At the intersection of lines g and e, the bottom right angle is angle 2. At the intersection of lines h and e, the bottom right angle is angle 1. At the intersection of lines f and h, the top left angle is angle 3.
Statements Reasons
1. g || h 1. given
2. ∠1 ≅ ∠2 2. corresponding angles theorm
3. ∠2 ≅ ∠3 3. given
4. ∠1 ≅ ∠3 4. transitive property
5. e || f 5. ?
What is the missing reason in the proof?
vertical angles theorem
alternate exterior angles theorem
converse corresponding angles theorem
converse alternate interior angles theorem
The line e is parallel to f by converse alternate interior angles theorem.
What is converse alternate interior angle theorem?
Converse alternate interior angle theorem states that states if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.
What is parallel lines?
Two lines are said to be parallel when they do not meet at any point in a plane. Lines which do not have a common intersection point and never cross path with each other are parallel to each other. The symbol for showing parallel lines is ‘||’.
Given,
angle 1 is congruent to angle 2 and g is parallel to h.
similarly, angle 2 is congruent to angle 3,
by transitive property angle 1 is congruent to angle 3.
By converse alternate interior angle theorem, e is parallel to f.
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Solve the equation shown: 14 + 5/7x - 20 = 4/7x - 4
The value of x is determined by solving the equation 14 + 5/7x - 20 = 4/7x - 4, which is: x = 14.
How to Solve an Equation?When given an equation, to solve the equation means to find the value of the variable in the equation.
Given the equation:
14 + 5/7x - 20 = 4/7x - 4
Combine like terms
5/7x - 6 = 4/7x - 4
Add 6 to both sides
5/7x - 6 + 6 = 4/7x - 4 + 6
5/7x = 4/7x + 2
Subtract both sides of the equation by 4/7x:
5/7x - 4/7x = 4/7x + 2 - 4/7x [subtraction property of equality]
x/7 = 2
Multiply both sides by 7
x/7(7) = 2(7) [multiplication property of equality]
x = 14
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A deep-sea exploring ship is pulling up a diver at a rate of 25 feet per minute. The diver is 200 feet below sea level. How deep was the diver 10 minutes ago?
What is X in this equation
Answer:
13/4 or 3.25
Step-by-step explanation:
Since they are vertical angles, they are equal to each other. Thus, set the two equations together:
8x + 32 = 12x + 19
Isolate x
32 = 12x + 19 - 8x = 4x + 19
32 - 19 = 4x
4x = 13
4x/4 = 13/4 = 3.25
Can someone help me solve for
Calculate the value of x. Round to the nearest tenth. F 7.8 24 14.8
In this problem bout segment has the same distance so we can write an equation like:
[tex]\begin{gathered} x+7=13+8 \\ x=21-7 \\ x=14\approx14.8 \end{gathered}[/tex]So the answer is 14.8