Using implicit differentiation, it is found that the radius is increasing at a rate of 0.0081 cm per minute.
What is the volume of a sphere?The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
In this problem, we have that:
[tex]\frac{dV}{dt} = 500, r = 70[/tex]
Hence the rate of change of the radius is given as follows:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
[tex]19600\pi\frac{dr}{dt} = 500[/tex]
[tex]\frac{dr}{dt} = \frac{500}{19600\pi}[/tex]
[tex]\frac{dr}{dt} = 0.0081[/tex]
The radius is increasing at a rate of 0.0081 cm per minute.
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NEED HELP ASAP PLEASE
Answer:
y = 2x^2 + 8x + 3
Step-by-step explanation:
Step 1: use the vertex form of the quadratic equation
y = a*(x - h)^2 + k
vertex = (-2, -5) = (h, k)
y = a*(x + 2)^2 - 5
Step 2: determine a using the given point
point = (0, 3)
y = a*(x + 2)^2 - 5
3 = a*(0+2)^2 - 5
3 + 5 = a*(2)^2
8 = a*4
a = 2
vertex equation is now y = 2*(x + 2)^2 - 5
Step 3: simplify vertex equation to standard quadratic equation
quadratic equation = Ax^2 + Bx + C
y = 2*(x + 2)^2 - 5
y = 2*(x^2 + 4x + 4) - 5
y = 2x^2 + 8x + 8 - 5
y = 2x^2 + 8x + 3
Match each pair of rational numbers with their sum
The match each pair of rational numbers with their sum is:
[tex]\frac{2*(a-b)}{a^2b^2} = \frac{-2}{a^2b}+\frac{2}{ab^2}[/tex]
[tex]\frac{a-b^2}{a^2b^3} }=\frac{1}{ab^3} +\frac{-1}{a^2b}[/tex]
[tex]\frac{2ab-1}{4a^2b^2} }=\frac{1}{2ab} +\frac{-1}{4a^2b^2}[/tex]
[tex]\frac{2*(1-ab^2)}{a^2b^3} =\frac{2}{a^2b^3}+\frac{-2}{ab}[/tex]
FactoringIn math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.
When you factor an expression using the rule a factor out a common term, it is possible simplify an expression
Then, you should factor and simplify each given algebraic expression.
[tex]\frac{2*(a-b)}{a^2b^2} =\frac{2a-2b}{a^2b^2}=\frac{2a}{a^2b^2} -\frac{2b}{a^2b^2} =\frac{2}{ab^2} +\frac{-2}{a^2b}[/tex][tex]\frac{a-b^2}{a^2b^3} }=\frac{a}{a^2b^3} -\frac{b^2}{a^2b^3} =\frac{1}{ab^3} +\frac{-1}{a^2b}[/tex][tex]\frac{2ab-1}{4a^2b^2} }=\frac{2ab}{4a^2b^2} -\frac{1}{4a^2b^2} =\frac{1}{2ab} +\frac{-1}{4a^2b^2}[/tex][tex]\frac{2*(1-ab^2)}{a^2b^3} =\frac{2-2ab^2}{a^2b^3}=\frac{2-2ab^2}{a^2b^3}=\frac{2}{a^2b^3}+\frac{-2}{ab}[/tex]
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1. Create an ungrouped frequency distribution table with the data from the survey concerning the age of the people, which attend the gym. The results of a survey are presented below.
Answer:
firstly ,we need to put the set of ages into categories
Example: (Category1 = age 19 ; category2 = age 20 ; ........ )
→ The frequency of a certain value (age) is equal to the number of times that specific age appears in the data set.
Step-by-step explanation:
Write 320 g as a fraction of 2 kg. Give your answer in its simplest form.
Answer:
4/25
Step-by-step explanation:
320 grams over 2kj(which is 2000grams) is 320/2000, simplified is 4/25
Evaluate
11
% of
953.23
m
Give your answer rounded to 2 DP.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{11\% of 953.23}}{\left( \cfrac{11}{100} \right)953.23}\implies 104.86[/tex]
5/8 multiplied by 4/10 (pls answer asap)
Answer:Flying potatox x plus y yes
Step-by-step explanation:
Answer:
the answer is 1/4 if the question is a fraction
tìm số hữu tỉ
(x-5/6)^2=1/36
Answer:
x = [tex]\frac{2}{3}[/tex] , x = 1
Step-by-step explanation:
(x - [tex]\frac{5}{6}[/tex] )² = [tex]\frac{1}{36}[/tex] ( take square root of both sides )
x - [tex]\frac{5}{6}[/tex] = ± [tex]\sqrt{\frac{1}{36} }[/tex] = ± [tex]\frac{1}{6}[/tex] ( add [tex]\frac{5}{6}[/tex] to both sides )
x = [tex]\frac{5}{6}[/tex] ± [tex]\frac{1}{6}[/tex] , then
x = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
x = [tex]\frac{5}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{6}{6}[/tex] = 1
You have been given data about gas prices in 15 states.
2018 Gas Price Data
Max: $2.42
Min: $2.03
Mean: $2.098
Median: $2.06
Mode: $2.04
Variance: 0.0121
Standard Deviation: $0.1098
What does the range, standard deviation, and variance say about gas prices in 2018?
The range, standard deviation, and variance say about gas prices in 2018 discussed below
What is standard deviation and variance?Variance is the average squared deviations from the mean, while standard deviation is the square root of this number.
As the variance in 2018 is 0.0121.
A model with low variance means sampled data is close to where the model predicted it would be.
As the standard deviation in 2018 is 0.1098.
Low standard deviation means data are clustered around the mean
A small range means low variability in a distribution.
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Please help me!! High School algebra 2 math. Big Ideas Math
Answer:
x = 8
Step-by-step explanation:
Hello!
The missing angle in the triangle can be found by subtracting 90° and 45° from 180°. The missing angle is 45°.
This means that the triangle is isosceles, as there are two congruent base angles, 45° and 45°.
The side lengths opposite these two angles are congruent.
We can see that 8 is opposite 45°, and x is opposite 45°. Therefore, x must be equal to 8.
The value of x is 8.
Answer:
x = 8
Step-by-step explanation:
The interior angles of a triangle sum to 180°.
The given triangle is a right triangle, so the missing angle is 45°
⇒ 180° - 90° - 45° = 45°
As the triangle has 2 equal angles, this means it is an isosceles triangle (with its vertex at the right angle). An isosceles triangle has legs of equal measure, therefore [tex]x=8[/tex].
Proof
This can be proven by using the tan trigonometric ratio to calculate the value of x.
Tan trig ratio
[tex]\sf tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta[/tex] = 45°O = 8A = xSubstituting the given values into the equation and solving for x:
[tex]\implies \tan (45^{\circ})=\dfrac{8}{x}[/tex]
[tex]\implies x=\dfrac{8}{\tan (45^{\circ})}[/tex]
[tex]\implies x=\dfrac{8}{1}[/tex]
[tex]\implies x=8[/tex]
f(x) = 3 and g(x) = x – 2
3 = x – 2
5 = x
Answer:
3=1×5-2
Step-by-step explanation:
you minus 5-2 is 3 and one threes three
Write the following expression without negative exponents and without parentheses.
(5x)^−3
Answer:
[tex] \dfrac{1}{125x^3} [/tex]
Step-by-step explanation:
[tex] (5x)^{-3} = \dfrac{1}{(5x)^3} = \dfrac{1}{5^3x^3} = \dfrac{1}{125x^3} [/tex]
If you bought 4 candies for a
total of $3.28, how much did it
cost you for 3 candies?
Answer:
2.46
Step-by-step explanation:
3.28/4=0.82(for one candy)
0.82×3=2.46(for 3 candies)
Pls help no links or troll answers ill report them
Answer:
insufficient
Step-by-step explanation:
What is the question?
What is the slope of the line that passes through (-2, 7) and (4, 9)
Answer: The slope is 1/3
Step-by-step explanation:
m = y2-y1/x2-x1
m =9-7/4+2
m=2/6
m=1/3
Answer:
The slope is 1/3
Step-by-step explanation:
m=y2-y1/x2-x1
m=9-7/4-(-2)
m=2/6
m=1/3
please help with geometry!!!! ‼️‼️‼️‼️ i will mark brainliest
Answer:
P = 156 units
Step-by-step explanation:
the perimeter (P) is the sum of the 3 sides of the triangle.
tangents from an external point to the circle are congruent , that is
HK = HJ ( substitute values )
13x - 8 = 7x + 4 ( subtract 7x from both sides )
6x - 8 = 4 ( add 8 to both sides )
6x = 12 ( divide both sides by 2 )
x = 2
Then
HK = HJ = 7x + 4 = 7(2) + 4 = 14 + 4 = 18
and
KI = IL = 21
then
GL = GJ = 60 - 21 = 39
Thus
P = HK + KI + IG + GJ + JH = 18 + 21 + 60 + 39 + 18 = 156 units
how do you do .22 x .4
Answer: 0.088
Step-by-step explanation:
There are two ways. My way is complicated, but never wrong!
0.22 converted to a fraction is 22/100,
explanation: you know this because the denominator must be 10, 100, 1000, 10000 etc... and must be one more digit than the numerator.
and 0.4 into a fraction is 4/10. but we have to have same denominators so we multiply 4/10 by 2 4 x 10 = 40; 10 x 10 = 100.
now multiply...
40 x 22 = 880
100 100 100
and turn it into a decimal, by reversing how we turned it into a decimal.
so it's 0.088!
Find the value of x.
9 + 4(x + 2) - 3x
What is the term for best describes 3
An expression is defined as a set of numbers, variables, and mathematical operations. The term that best describes 3 is coefficient.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of 3 in the expression, 9 + 4(x + 2) - 3x, is that it is the coefficient of x in the third term.
Hence, the term that best describes 3 is coefficient.
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Please help me!
1. Determine whether the following table represents an exponential function. Explain why or why not.
X: 0, 1, 2, 3
Y: 12, 16, 32, 52
Does the table represent an exponential function? Why or why not?
A. No, all of the X values have a constant difference, but all of the Y values do not have a constant ratio
B. Yes, all of the X values have a constant ratio, but all of the Y values have a constant difference
C. No, all of the X values have a constant ratio, but all of the Y values do not have a constant difference.
D. Yes, all of the X values have a constant difference, and all of the Y values have a constant ratio
2. Determine whether the rule represents an exponential function. Explain why or why not.
Y=9x5^x
Choose the correct answer below
A. Since the independent variable X is the exponent, Y=9×5^x represents an exponential function
B. Since the independent variable X is not the base, Y=9×5^x does not represent an exponential function
C. Since the independent variable X is the base, Y=9×5^x does represent an exponential function
D. Since the independent variable X is not the exponent, Y=9×5^x does not represent an exponential function
3. A population of 55 foxes in a wildlife preserve quadrupled in size every 11 years. The function y=55x4^x, where X is the number of 11 year periods, models the population growth. How many foxes will there be after 22 years?
After 22 years there will be ____ foxes (type an whole number)
4. Since 2006, the amount of money spent that restaurant in a certain country has increased at a rate of 8% each year. in 2006, about $360 billion were spent at restaurants. If the trend continues, about how much will be spent at restaurants in 2015.
About $______ billion will be spent at restaurants in 2015 if the trend continues.
5. A bird drops a stick to the ground from a height of 90 feet. The function h=-16t^2+90 gives the sticks approximate height H above the ground, in feet, after T seconds. Add about what time does the stick hit the ground?
The stick hits the ground at about _____ seconds. (Round to one decimal place as needed)
6. During halftime of a soccer game, a slingshot launches T-shirt at the crowd. A T-shirt is launch from a height of 3 feet with an initial upward velocity of 80 ft./s. Use the equation h(t) = -16t^2+80t+3, where t is time in seconds and h(t) is height. How long will it take the T-shirt to reach its maximum height? What is the maximum height?
The T-shirt takes _____ Second(s) to reach its maximum height. (type an integer or a decimal)
The T-shirts maximum height is_____ feet above the field. (type an integer or a decimal)
Please help me I really need to get this done today! I will give you everything I have!
Answer:
a
Step-by-step explanation:
A. Z
B. <
C. S
D. >
E. =
F. 2
55? 35
Answer:
ABCD=EF
Step-by-step explanation:
A. Z
B. <
C. S
D. >
E. =
F. 2
55? 35
Shape A can be transformed to shape B by a rotation 90° clockwise about (-1, 1) followed by a translation by vector
(a b)
Find the values of a and b
The values of a and b if the coordinate is rotated 90° clockwise is -1 and -1
Rotation of coordinatesThe rotation is a transformation technique that changes the position of an object in an xy plane. If the coordinate (x, y) is rotated 90° clockwise, the resulting coordinate will be at (-y, x)
If the coordinate (-1, 1) is therefore rotated 90° clockwise about the origin, the resulting coordinate will be (-1, -1).
Comparing
a = -1 and b = -1
Hence the values of a and b if the coordinate is rotated 90° clockwise is -1 and -1
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Plsss help I’m so confused
Answer:
The answer is 1001101
Step-by-step explanation:
77 base 10 to base 2 is 1001101
A water tank that initially contained 200 gallons of water is leaking water at a constant rate of 4 gallons per minute. For the amount of time the tank has water, which of the following function models gives the number of gallons, G. in the tank t minutes after the leak started?
a. g(t) = 196 - t
b. g(t) = 200 - 4t
c. g(t) = 200t - 4
d. g(t) = 200t - 4r^2
e. g(t) = 200(3/4)^t
Answer:
b. g(t) = 200 - 4t
Step-by-step explanation:
I don't know how to explain this, but here is the answer.
4. Reid is building a fence around a square portion of his
yard with an area of 200 square feet. Which point
below best represents the side length of one side of the
fence?
A. Point A
B. Point B
C. Point C
D. Point D
The point that best represents the length of one side of the fence of the square portion of the garden area is: B. Point B.
What is the Area of a Square?Area of a square = s², where s is the side length of the square.
Area of the square portion of his yard = 200 square feet
Side length of one side of the fence = √200 = 14.1 feet.
From the number line given, point B best represents 14.1 feet. Therefore, the side length is best represented by: B. Point B.
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3. () Triangle ABC is transformed to create Triangle A'B'C'. What type of rigid transformation is this? (1 pt)
If triangle A'B'C' is reflected over the y-ands, what are the coordinates of triangle A"B"C"? (3 pts)
-
A' (1.3)
B' (4.1)
A" (_
B (______
C' (6,5)
-
C" (
111
Answer:
see the attachment photo!
Which of the following shows the true solution to the logarithmic equation 3 log Subscript 2 Baseline (2 x) = 3
x = negative 1
x = 1
x = negative 1 and x = 1
x = 0, x = negative 1, and x = 1
The value of x is 1 , option B is the correct answer.
What is an Equation ?When two algebraic expressions are equated using an equal sign , the mathematical equation formed is called an Equation.
The equation is given by 3log₂(2x)=3
3log₂(2x)=3
log₂(2x) = 3/3
log₂(2x) = 1
The base of the logarithm is 2
it can also be written as
[tex]\rm 2^{log_{2}(2x)} = 2 ^1[/tex]
2x = 2
x = 1
Therefore the value of x is 1 , option B is the correct answer.
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Leah's family took a road trip to Mount Rushmore. Leah fell asleep 44% of the way through the trip. If Leah fell asleep after they had travelled 132 miles, what was the total length of the trip?
Leah's family took a road trip to Mount Rushmore. Leah fell asleep 44% of the way through the trip. the total length of the trip is 190.08 miles.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Leah's family took a road trip to Mount Rushmore. Leah fell asleep 44% of the way through the trip.
If Leah fell asleep after they had traveled 132 miles
So,
44% of 132
= 0.44 x 132
= 58.08
Add in the miles they already traveled
132 + 58.08
= 190.08
Thus, the total length of the trip is 190.08 miles.
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Q varies inversely with x. if q = 12 when x = 5, find the value of q when x = 12.
q varies inversely as x: qx = k, such k is constant
Given values:
q = 12x = 5To determine the constant of variation, substitute the first two given values of q and x to the equation of variation.
qx = k(12)(5) = k60 = kTo determine the value of q, substitute the second given value of x together with the constant of variation.
x = 12, q = ?qx = 6012q = 60q = 60/12q = 5Answer:
The value of q is 5.Wxndy~~
3. In the expression 25-5+7x3 ÷ 1, which operation should be done first?
O division
O addition
O subtraction
O multiplication
Answer:
division
Step-by-step explanation:
please mark me as brainlest
4.3 Mr Mokwebo 's two sons, Refentse and Tokelo have just passed grade 7 and grade 9 respectively. He will give them some money to buy chocolates at Jubilee Mall as a reward for their hardwork. Refentse will receive R21 less than Tokelo. Altogether they will need R253 to buy the chocolates. Set up an equation and calculate how much each will get. Let Tokelo 's money be x 4.3.1 Write down Refentse 's money in terms of x. (1) 4.3.2 Set up an equation and calculate how much each will get. (4) [22] Total: 60
The amount of money each of Mr Mokwebo 's two sons; Tokelo and Refentse will get is R116 and R95 respectively.
How to write and solve equation:Amount needed to buy chocolate = R253Tokelo's money = xRefentse's money = x - 21Total amount needed = Tokelo's money + Refentse's money
253 = x + (x - 21)
253 = x + x - 21
253 = 2x - 21
253 - 21 = 2x
232 = 2x
divide both sides by 2
x = 232/2
x = 116
Therefore,
Tokelo's money = x = R116
Refentse's money = x - 21
= 116 - 21
= R95
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