The rate at which the volume of the cone is changing is -5235.98 inches³/s when the radius of the circular cone is 50 inches and the height is 10 inches.
The formula for the circular cone can be given as;
V = 1/3 πr²h
Now we take the derivative with respect to time as follows;
V = 1/3 πr²h
dV/dt = 1/3π d/dt(r²h)
dV/dt = 1/3π [2r(dr/dt) × h + r²(dh/dt)]
Now we substitute the values in this equation as follows;
dV/dt = 1/3π [2 × 50 × 5 × 10 + (50²) (-4)]
dV/dt = 1/3π [ 5000 - 10000]
dV/dt = 1/3π [-5000]
dV/dt = -5235.98
Hence the negative sign indicates that the volume is decreasing over time and the rate of change is calculated to be -5235.98 inches³/s.
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Simplify -1(15+4 - 27) over 16
[tex] \frac{ - 1(15 + 4 - 27)}{16} \\ = \frac{ - 1(19- 27)}{16} \\ = \frac{ - 1( - 8)}{16} \\ = \frac{8}{16} \\ = 0.5[/tex]
ATTACHED IS THE SOLUTION
Answer:
= - 19 + 16^27
4.2(2) question 7 thankThe function f(x) = 3(x+15)² - 50
Domain are the inputs of the function. They are the x values of the function
The function gives a parabola. This means the values of x will be from negative infinty to positve infinity
[tex]\begin{gathered} In\text{ interval notation:} \\ \text{Domain: (}-\infty,\text{ }\infty)\text{ (option D)} \end{gathered}[/tex]Plotting the graph:
Range are the outputs of the function. They are the y values of the function
From the graph, we see tip of the parabola starts at y = -50 and extends upwards
The y value will be from -50 to positive infinity
[tex]\text{Range: \lbrack-50, }\infty)\text{ (option C)}[/tex]Question 1 - Write an equation in Standard Form of a line that passes through (-3,-7) and has a slope of 4.
Question 2 - Write an equation in Standard Form of a line that passes through (10,-2) and has a slope of -1/2
Question 3 - Write an equation in Point Slope Form of a line that passes through (-1,8) and has a slope of -3/4
Question 4 - Write an equation in Slope Intercept Form that passes through (-3,11) and (6,-7).
The equation is, 4x - y = -5
The equation is, x + 2y = 6
The equation is, [tex][tex]y = -\frac{3}{4}x + \frac{29}{4}[/tex][/tex]
The equation is, y = -2x + 5
What is standard form of equation of line?
When A and B are not both zero, a line has the usual form Ax + By = C. The standard form of equation with slope and the point is,[tex][tex]y - y_{1} = m(x - x_1)[/tex][/tex] ...(1)
1. Given:[tex][tex]x_1 = -3, y_1 = -7, m = 4[/tex][/tex]
Plug these values in the above equation,
[tex][tex]y - (-7) = 4(x - (-3)\\ y + 7 = 4(x + 3)\\\\y + 7 = 4x + 12\\y = 4x + 5\\\\4x - y = -5[/tex][/tex]
This is the equation in standard form of line.
2. Given:
[tex][tex]x_1 = 10, y_1 = -2, m = -\frac{1}{2}[/tex][/tex]
Plug these values in the equation (1),
[tex][tex]y - (-2) = -\frac{1}{2} (x - 10)\\y + 2 = -\frac{1}{2} x + 5\\[/tex][/tex]
Multiply both sides by 2.2y + 4 = -x + 10x + 2y = 6
This is the equation in standard form of line.
3. Given:
[tex][tex]x_1 = -1, y_1 = 8, m = -\frac{3}{4}[/tex][/tex]
Plug these values in the equation (1),[tex][tex]y - 8 = -\frac{3}{4}(x - (-1))\\ y -8 = -\frac{3}{4}(x + 1)\\ y - 8 = -\frac{3}{4}x - \frac{3}{4}[/tex][tex]y = -\frac{3}{4}x -\frac{3}{4} + 8\\ y = -\frac{3}{4}x + \frac{29}{4} \\[/tex][/tex]
This is the equation in point slope form.
4. Given:[tex][tex](x_1, y_1) = (-3, 11), (x_2, y_2) = (6, -7)[/tex][/tex]
First to find the slope from the given two points.
[tex][tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\m = \frac{-7-11}{6-(-3)}\\ m = \frac{-18}{9\\}\\ m = -2[/tex][/tex]
Now plug m = -2 and one of the given point in the equation (1), we ge[tex]t[tex]y - 11 = -2(x - (-3))\\y - 11 = -2(x + 3)\\y - 11 = -2x - 6\\y = -2x + 5[/tex][/tex]
This is the equation in slope intercept form.
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A and B are complementary angles. If mA = (2x +27)° and mB =
(2x-21), then find the measure of A.
Answer:
mA = 69 degrees
Step-by-step explanation:
A complementary angle has a measure of 90 degrees.
(2x + 27) + (2x - 21) = 90
Simplify
4x + 6 = 90
-6
4x = 84
/4
x = 21
mA: 2(21) + 27 = 69
Answer:
A = 69°
Step-by-step explanation:
Complementary angles sum 90°
A + B = 90°
(2x + 27) + (2x-21) = 90°
4x + 27 - 21 = 90°
4x + 6 = 90°
4x = 90 - 6
4x = 84°
x = 84°/4
x = 21
Then A:
A = 2x + 27
A = 2*21 + 27
A = 42 + 27
A = 69°
B = 2x - 21
B = 2(21) + 27
B = 42 - 21
B = 21°
Check:
69 + 21 = 90
Hello can you help me on my 7th grade math worksheet show all work
ANSWER:
78.5 ft
STEP-BY-STEP EXPLANATION:
One trip equals the circumference of the circle.
The circumference of a circle is calculated by means of the following formula:
[tex]\begin{gathered} c=\pi\cdot d \\ \\ d=\text{ diameter = 25 ft} \end{gathered}[/tex]Therefore, we substitute and calculate the distance the pony would walk for a trip:
[tex]\begin{gathered} c=(3.14)(25) \\ \\ c=78.5\text{ ft} \end{gathered}[/tex]That is, the number of feet the pony walks is 78.5
what is the missing measurement (w) for the poster of spongebob.
To make a poster you have to keep the ratio between lenght and height (otherwise it will look weird)
This is:
[tex]\frac{12\operatorname{cm}}{20\operatorname{cm}}=\frac{w}{36\operatorname{cm}}[/tex]Each person gets 3 scoops of ice cream. Is this relationship between the number of people and the number of scoops proportional?
Yes, the number of scoops proportional.
Define Proportional
A linear relationship between two amounts or variables is indicated by proportionality. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.
Hence, It is proportional. This is because as the number of people increases, the number of scoops also increase.
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Use the given endpoint R and midpoint M of RS¯ to find the coordinates of the other endpoint S.
R(3, 0), M(0, 5)
Step-by-step explanation:
the midpoint coordinates between 2 points A and B are
((xa + xb)/2, (ya + yb)/2)
xa = 3
ya = 0
and so we get
(3 + xb)/2 = 0
3 + xb = 0
xb = -3
(0 + yb)/2 = 5
yb = 10
therefore, S = (-3, 10)
For f(x) = 2x² - 1, what is (f. f)(−2)?
(See image below)
f is 7. The process of composing small units into larger units that solve larger problems is known as composition.
What is Composition function?A function composition is an operation that produces a new function, h, by combining two functions, f and g, in such a way that h(x) = g(f(x)). That is, function g is being applied to function x.In essence, one function is applied to the output of another. A composite function is one that is reliant on another.A composite function is created when one function is substituted for another. For example, f(g(x)) is the composite function formed by replacing x in f with g(x) (x). The expression f(g(x)) is pronounced "f of g of x."Therefore,
f = 2 (-2)² - 1 : f = 7
Steps
f = 2 (-2)² - 1
2 (-2)² =2³
f = 2³-1
2³ = 8
f = 8-1
Subtract the numbers:
8 - 1 = 7
f = 7
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Write down the integer values satisfied by this diagram. O -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 n
Reason:
The diagram describes values between -1 and 3. We exclude -1 because of the open hole. We include 3 because of the closed endpoint.
Find the circumcenter of the triangle ABC.
A(-5, -6), B(-8,6), C(-5,6).
The circumcenter is
(Type an ordered pair)
Answer: a b C D
Step-by-step explanation:
the measure of the angles of a triangle are shown in the figure below. solve for x
64°
x°
40°
Answer:
Sum of angles in a triangle add up to 180°.
x = 180 - 64 - 40
= 76°
Salomon tracks the weight of his new puppy every 2 weeks. She weighs 10 lbs the
day he brings her home. His list for her first 6 "weighs" is as follows: (10, 13, 16, 19,
22, 25}
Which equation represents the growth of the puppy?
Select one:
O
O
y = x + 3
y = 3x + 10
y = 10x + 3
y = x + 10
Equation (B) "y = 3x + 10" represents the growth of the puppy.
What are equations?An equation is a mathematical formula where the "equal to" sign appears between two expressions having the same value. Like 3x plus 5 equals 15, for example. Different types of equations exist, such as linear, quadratic, cubic, and others. The three primary forms of linear equations are the slope-intercept form, standard form, and point-slope form.So, the equation that represents the situation:
The weight increase is: (10, 13, 16, 19, 22, 25)We can observe that every time, there is a rise of 3lbs of weight.Now, let 10 be a constant as the weight is starting from 10 lbs.And 'x' be the number of time Salomon tracks the weight.Then:
y = 3x + 10For example, Salomon checks the weight for the 6th time then:
y = 3x + 10y = 3(5) + 10y = 15 + 10y = 25So, the equation is correct.
Therefore, equation (B) "y = 3x + 10" represents the growth of the puppy.
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The correct question is given below:
Salomon tracks the weight of his new puppy every 2 weeks. She weighs 10 lbs the day he brings her home. His list for her first 6 "weighs" is as follows: (10, 13, 16, 19, 22, 25}
Which equation represents the growth of the puppy? Select one:
A. y = x + 3
B. y = 3x + 10
C. y = 10x + 3
D. y = x + 10
Find the value of x.
(8x - 11)
5x°
(2x+6)°
Answer: x=37/3
Step-by-step explanation:
8x-11+5x+2x+6=180 ==> three angles of a triangle add up to 180 degrees
8x+5x+2x-11+6=180
13x+2x-5=180
15x-5=180
15x=185
x=185/15
x=37/3
What is the slope of the line x=4?
O A. 0
O B. Undefined
O C. 4
• D.1
Answer:
B. Undefined
Step-by-step explanation:
x = 4 is a vertical line, and vertical lines are Undefined because they go straight up.
Add −1 3/10+2/5 using the number line.
Select the location on the number line to plot the sum.
The location on the number line to plot the sum of the given number is shown in the image attached below.
What is a number line?In Mathematics, a number line simply means a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.
Note: Each interval on this number line represents 1/10.
Next, we would add the given numbers together as follows:
Number = −1 3/10 + 2/5
Number = −13/10 + 2/5
Number = (-13 + 4)/10
Number = -9/10 or -0.9.
Therefore, the sum would be located between -4/5 and -1.
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professor smith loves dark chocolate, and she would like to find out the proportion of the population that shares her preference. she randomly sampled 150 people, and 120 people choose dark chocolate. to construct a 95% confidence interval, she should use:
Use 1-Prop Z Int to create a 95% confidence interval.
Z test should be employed because there is only one set of samples collected and the sample size is huge.
An observed percentage is compared to a theoretical one using a one proportion z-test. The test statistic is determined as follows:
z = (p-p0) / √(p0(1-p0)/n)
where:
p = observed sample proportion
p0 = hypothesized population proportion
n = sample size
You can reject the null hypothesis if the p-value associated with the test statistic z is less than your selected level of significance (popular choices are 0.10, 0.05, and 0.01).
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Find the slope of the line that passes through (4,2) and (2,1)
Given
Points (4,2) and (2,1)
Find
Slope of the line
Explanation
Slope of line is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]so ,
[tex]\begin{gathered} m=\frac{1-2}{2-4} \\ \\ m=-\frac{1}{-2} \\ \\ m=\frac{1}{2} \end{gathered}[/tex]Final Answer
Hence , the slope of line is m = 1/2
I need help with this math question all parts please
we have the function
[tex]P(t)=\frac{60(1+0.4t)}{0.01t+3}[/tex]Part A
For t=0
substitute
[tex]\begin{gathered} P(t)=\frac{60(1+0.4(0))}{0.01(0)+3} \\ \\ P(t)=\frac{60(1)}{3} \\ \\ P(t)=20 \end{gathered}[/tex]The initial population was 20 insectsPart B
For t=5 years -------> Convert to months
t=60 months
substitute
[tex]\begin{gathered} P(t)=\frac{60(1+0.4(60))}{0.01(60)+3} \\ \\ P(t)=\frac{60(1+24)}{0.6+3} \\ \\ P(t)=\frac{1500}{3.6} \\ \\ P(t)=416.67 \end{gathered}[/tex]The answer is 417 insectsPart C
Determine horizontal asymptote
[tex]\begin{gathered} P(t)=\frac{60\left(1+0.4t\right)}{0.01t+3} \\ \\ rewrite \\ P(t)=\frac{60+24t}{0.01t+3} \end{gathered}[/tex]The horizontal asymptote is given by the ratio of
[tex]\frac{24}{0.01}=2,400[/tex]P(t)=2,400 ---------> horizontal asymptote
that means
as the value of time t increases ------> the value of the population tends to 2,400 insects
the population cannot be greater than 2400 insects
The range for the function P(t) is the interval [20, 2400)
All real numbers greater than or equal to 20 insects and less than 2400 insects
Part D
Using a graphing tool
Please help me. Much Appreciated Each part of problem mark as either a, b, c
Given:
Total number of people surveyed = 205
a) Percentage of the survey respondents that do not like both hamburgers and burritos.
Number of people that do not like both = 54
To find the percentage of the respondents that do not like both, we have:
[tex]\begin{gathered} \text{ \% that do not like both = }\frac{Number\text{ that }do\text{ not like both}}{\text{Total surveyed}}\ast\frac{100}{1} \\ \\ \text{ \% that do not like both = }\frac{54}{205}\ast100\text{ = }26.3\text{ \%} \end{gathered}[/tex]Therefore, the percentage of the survey respondents that do not like both hamburgers and burritos is 26.3%
b) Marginal relative frequency of all customers that like hambugers.
Given:
Number of customers that like hamburgers = 110
To find the marginal relative frequency, we have:
[tex]M=\frac{110}{250}=0.54=54\text{ \%}[/tex]The marginal relative frequency of all customers that like hambugers is 54%
c) Conditional relative frequencies:
i) Conditional relative frequency that a person likes hamburgers given that the person does not like burritos:
[tex]\frac{110-29}{135}=\frac{81}{135}=0.6=60\text{ \%}[/tex]ii) Conditional relative frequency that a person likes burritos, given that the person does not like hamburgers:
[tex]\frac{41}{41+54}=\frac{41}{95}=0.43=43\text{ \%}[/tex]you are playing a game of hide - and - seek with two friends . while one of your friends counts , you and your other friend are given a chance to hide in one of five possible hiding spots . you are each allowed to pick a hiding spot , and are permitted to share a hiding spot . your friend finishes counting and checks one of the five hiding spots . assuming that everyone's decisions are made uniformly at random , what are the chances that your friend does not find anyone in the first spot that they check ?
The probability the friend finds no one in the first spot is 60%.
What is probability?Probability is the chance or likelihood that an expected event occurs when there are many possible outcomes or events.
For instance, the probability that when the counting friend goes to the hiding spot, they can or cannot find a friend there.
The two friends can only hide in 2 spots, leaving 3 spots with nobody.
The number of hiding spots = 5
The number of friends hiding = 2
The number of counting friends = 1
The number of spots they can hide = 2 out of 5
The probability of finding a person in a hiding spot = 2/5 or 40%
The probability of not finding a person in a hiding spot = 3/5 (1 - 2/5) or 60% (1 - 40%).
The chances that your friend finds anyone in the first spot are 60%.
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Select the correct answer.
Which of these graphs represents a function?
A. W
B. X
C. Y
D. Z
Answer:
The second graph (B: X?)
Step-by-step explanation:
The second graph (B?) is a function because the graphed line passes the vertical line test (no two points are vertically on top of each other).
Find the midpoint of the segment below and enter its coordinates as anordered pair. If necessary, express coordinates as fractions, using the slashmark (/) for the fraction bar.
Each midpoint's coordinate is given by the mean of the respective coordinates of the two endpoints of the segment. Then, if we say M is the midpoint of that segment, we have:
Mx = (-4 + 4)/2 = 0/2 = 0
My = [6 + (-2)]/2 = (6 - 2)/2 = 4/2 = 2
Therefore, writing those coordinates as an ordered pair, we have:
M = (0, 2)
Write an exponential expression equivalent to 8^3 that has a base of 2.
The exponential expression equivalent to 8^3 that has a base of 2 is 2^9.
What is exponential expression?
Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied.
Applying the laws of indices,
The expression 8^3 can be written as,
8 x 8 x 8 = (2^3) x (2^3) x (2^3)
= 2^(3+3+3) ...{If a^m x a^n then a^(m+n) }
8 x 8 x 8 = 2^9
Therefore, the exponential expression equivalent to 8^3 that has a base of 2 is 2^9.
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Sandra purchased $1,200 worth of electronic equipment on her new credit card, with an annual interest rate of 14.99%. If she has no other charges on the card and does not pay off the balance at the end of the month, how much money will she owe the credit card company after 1 month? Estimate the interest using the monthly periodic rate.
Given data:
The given amount of equipment purchased by the Sandra is A=$1,200.
Find the measure of
Answer: 93°
Step-by-step explanation:
[tex]\angle A \ and\ \angle B\ are\ vertical\ angles.\ Hence,\ \angle A \ = \ \angle B\\\\2x+19=3x-18\\\\2x+19+18=3x-18+18\\\\2x+37=3x\\\\2x+37-2x=3x-2x\\\\37=x\\\\Thus,\ x=37\\\\m\angle A=(2(37)+19)^0\\\\m\angle A=(74+19)^0\\\\m\angle A=93^0\\\\[/tex]
Nicholas was the lucky journalist assigned to cover the Best Beard Competition. He recorded the contestants' beard colors in his notepad. Nicholas also noted if the contestants were signed up for the mustache competition later in the day. Only in the beard competition Also in the mustache competition Red beard 2 5 Grey beard 2 06 2 What is the probability that a randomly selected contestant has a red beard or is only in the beard competition? Sm out Simplify any fractions
Sample space n(s)=2+2+5+7=16
Let P(E) be the probability of red beard or is only in the beard competition:
Total number of red beard=2+5=7
P(red beard)=2/7
Find the output when the input is n input 1,2,3,4,n output
-6,-8,-10,-12
The expression that represents the output value when the input is n is -4 - 2n
How to determine the output value for the input n?From the question, the input parameters are given as
Input 1,2,3,4,n
Similarly, the output parameters are given as
output: -6,-8,-10,-12
So, we have the following table of values
1,2,3,4,n
-6,-8,-10,-12
From the above table of values, we have the following parameters
Sequence type = arithmetic sequenceFirst term, a = -6Common difference, d = -2The output value for the input n is then calculated as
Tn = a + (n - 1) * d
So, we have
Tn = -6 + (n - 1) * -2
Open brackets
Tn = -6 - 2n + 2
Evaluate the like terms
Tn = -4 - 2n
Hence, the output value for the input n is -4 - 2n
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Which equation could represent the relationship shown in the scatterplot?
Scatter plot with x axis labeled variable x and y axis labeled variable y. Points go from lower left to upper right.
elmo makes sandwiches for a fundraiser. for each sandwich he uses globs of peanut butter at per glob and blobs of jam at per blob. the cost of the peanut butter and jam to make all the sandwiches is . assume that , , and are positive integers with . what is the cost of the jam elmo uses to make the sandwiches?
The cost of the jam Elmo uses to make the sandwiches =$1.65
What is the cost of the jam Elmo uses to make the sandwiches?
B globs of Peanut butter at 4 cents = 4B
J blobs of Jam at 5 cents = 5J
The number of sandwiches is given by the linear equation,
N(4B + 5J ) =$ 2.53
N(4B + 5J ) = 253 cents ---(1)
The factors of 253 = 1, 11, 23, 253.
Since N > 1 , N is 11 or 23
Considering N = 11
11(4B + 5J ) = 253
4B + 5J = 23 ---(2)
The possible values of B and J to satisfy the linear equation:
B = 2 and J = 3
Substituting B and J in (2)
4B + 5J = 23
4 (2) + 5(3) = 23
8 + 15 = 23
23 = 23
The linear equation is verified.
The cost of jam Elmo uses to make the sandwiches =N( 5J)
=11 (5*3)
= 11 *15
= 165 cents or $1.65
The complete question is:
elmo makes N sandwiches for a fundraiser. for each sandwich he uses B globs of peanut butter at 4 cents per glob and J blobs of jam at 5 cents per blob. the cost of the peanut butter and jam to make all the sandwiches is $2.53. assume that B, J, and N are positive integers with N>1. what is the cost of the jam elmo uses to make the sandwiches?
What is a linear equation?
Equations for straight lines are known as linear equations.As a one-degree equation, it also goes by that name. When an algebraic equation is graphed, a linear equation always produces a straight line since each term has an exponent of 1. In one variable and two variables, respectively, there are linear equations.To learn more about linear equations, refer:
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