Step-by-step explanation:
Taking the derivative of both sides with respect to x, we get
[tex]\dfrac{d}{dx}(x^3 + y^3) = \dfrac{d}{dx}(3)[/tex]
[tex]\Rightarrow 3x^2 + 3y^2\dfrac{dy}{dx} = 0[/tex]
Solving for [tex]\frac{dy}{dx}[/tex], we get
[tex]\dfrac{dy}{dx} = -\dfrac{3x^2}{3y^2} = -\dfrac{x^2}{y^2}[/tex]
100 Points + Brainliest Again. They deleted my other for being too easy :P
What is the circumference of a circle with a radius of 20 inches?
Answer:
125.66 inches
Step-by-step explanation:
Step 1: Calculate the circumference
The circumference formula is: C = πd
Another way of saying that is: C = 2πr
C = 2π(20)
C = 40π
C ≈ 125.66 inches
Answer: 125.66 inches
What is the volume of the cylinder shown below?
Answer:
c. 1500pi cubic units
Can someone help me find the answer?
Answer: C. is the correct answer.
Think of a situation in the real world where a relationship occurs between two sets. For example, I could list several different people and then list their birthdays. I could then form a relationship between these sets. First, illustrate the relationship using arrows. Then determine if the relationship is a function or not. State why?
Answer:
See Explanation
Step-by-step explanation:
Required
Determine if a real life situation is a function or not
I will give 2 instances
(1) Students and their ID
The relationship is as follows:
Student 1 -----> ID-1
Student 2 -----> ID-2
Student 3 -----> ID-3
Student 4 -----> ID-4
---------
----
--
Student n -----> ID-n
The above is a function because every student has a unique student ID.
In fact, the relation is a one-on-one function because no two students will have the same ID
(2) People and their year of birth
The relationship is as follows:
Person 1 -----> 2000
Person 2 -----> 2001
Person 3 -----> 2002
Person 4 -----> 2001
---------
----
Person n -----> 2005
The above is not a function because there is a possibility that a more than one person will have the same year of birth.
What is the simplest form of
Picture!
Answer:
Step-by-step explanation:
Factor the radicand.
If m ∥ n and n ⊥ p, then _____
Answer:
If m is parallel to n and n is perpendicular to p, then m is perpendicular to p.
Step-by-step explanation:
If you draw m parallel to n and then you run a line p through n such that n and p are perpendicular. The line p will also cross over m since lines go on forever and it will be perpendicular to m as well.
What is the y-intercept of the line y+11= -2(x+5)?
Answer:
y-intercept is (0, -21)
Step-by-step explanation:
For y-intercept, x = 0:
[tex]{ \sf{y + 11 = - 2(0 + 5)}} \\ { \sf{y + 11 = - 10}} \\ { \sf{y = - 21}}[/tex]
Use the Empirical Rule to answer the questions below:
The distribution of weights for newborn babies is approximately normally distributed with a mean of 7.6 pounds and a standard deviation of 0.7 pounds.
1. What percent of newborn babies weigh more than 8.3 pounds? %
2. The middle 95% of newborn babies weigh between and pounds.
3. What percent of newborn babies weigh less than 6.2 pounds? %
4. Approximately 50% of newborn babies weigh more than pounds.
5. What percent of newborn babies weigh between 6.9 and 9.7 pounds? %
Answer:
1. 16%
2. The middle 95% of newborn babies weigh between 6.2 and 9 pounds.
3. 2.5%
4. Approximately 50% of newborn babies weigh more than 7.6 pounds.
5. 83.85%
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 7.6 pounds, standard deviation of 0.7 pounds
1. What percent of newborn babies weigh more than 8.3 pounds?
7.6 + 0.7 = 8.3.
So more than 1 standard deviation above the mean.
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
Of those above the mean, 100 - 68 = 32% are more than one standard deviation above the mean. So
[tex]0.32*0.5 = 0.16[/tex]
16% of newborn babies weigh more than 8.3 pounds.
2. The middle 95% of newborn babies weigh between and pounds.
Within 2 standard deviations of the mean, so:
7.6 - 2*0.7 = 6.2 pounds
7.6 + 2*0.7 = 9 pounds.
The middle 95% of newborn babies weigh between 6.2 and 9 pounds.
3. What percent of newborn babies weigh less than 6.2 pounds?
More than 2 standard deviations below the mean, which is 5% of the 50% below the mean, so:
[tex]p = 0.05*0.5 = 0.025[/tex]
2.5% of newborn babies weigh less than 6.2 pounds.
4. Approximately 50% of newborn babies weigh more than pounds.
Due to the symmetry of the normal distribution, the mean, so 7.6 pounds.
Approximately 50% of newborn babies weigh more than 7.6 pounds.
5. What percent of newborn babies weigh between 6.9 and 9.7 pounds?
6.9 = 7.6 - 0.7
9.7 = 7.6 + 3*0.7
Within 1 standard deviation below the mean(68% of the 50% below) and 3 standard deviations above the mean(99.7% of the 50% above). So
[tex]p = 0.68*0.5 + 0.997*0.5 = 0.8385[/tex]
83.85% of newborn babies weigh between 6.9 and 9.7 pounds.
What is the value if x
Answer:
Step-by-step explanation:
Pls help me? I’m struggling
Answer: Number 1 is 150
Step-by-step explanation: If you put 72 / 48% in your calculator, you will get your answer.
There are 43 students in the orchestra and twice that number in the band. There are 31 boys and 10 girls in the choir. If each student only participates in one group, how many students total are there in the orchestra, the band, and the choir?
Answer:
170 students total
Step-by-step explanation:
43x2=86
86+43+31+10=170
help pls!!!!!
What is the inequality for this verbal description?
The value of y is greater than or equal to the sum of five times the value of x
and negative three.
Answer:
y ≥ 5x+ (-3)
Step-by-step explanation:
greater than or equal to ≥
The sum means add
y ≥ 5x+ (-3)
Answer:
Option D, y ≥ 5x + (-3)
Step-by-step explanation:
Step 1: Make an expression
The value of y is greater than or equal to the sum of five times the value of x and negative three.
The value of y is greater than or equal to ← y ≥
The sum of five times the value of x and negative three ← 5x + (-3)
y ≥ 5x + (-3)
Answer: Option D, y ≥ 5x + (-3)
Determine if the function f is an exponential function. If so, identify the base. If not, why not?
f(x)=(1/e)^x
A. This is not an exponential function because the variable is in the exponent position.
B. The base is x.
C. This is a polynomial.
D. The base is e^−1.
Answer: D) The base is e^(-1)
We use the rule that x^(-k) = 1/(x^k). That allows us to say e^(-1) = 1/(e^1) = 1/e
The 1/e is the base of the exponential (1/e)^x
In general, the exponential b^x has base b.
What is the area if measurements are 6m x 5.2m
Answer:
33.00 355.2
5.0m x 6.7m 33.50 360.6
5.0m x 6.8m 34.00 366.0
5.0m x 6.9m 34.50 371.4
5.1m x 6.0m 30.60 329.4
5.1m x 6.1m 31.11 334.9
5.1m x 6.2m 31.62 340.4
5.1m x 6.3m 32.13 345.8
5.1m x 6.4m 32.64 351.3
5.1m x 6.5m 33.15 356.8
5.1m x 6.6m 33.66 362.3
5.1m x 6.7m 34.17 367.8
5.1m x 6.8m 34.68 373.3
5.1m x 6.9m 35.19 378.8
50 POINTS
Use the function f(x) to answer the questions.
f(x) = −16x2 + 22x + 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
work and answers below
Answer:
[tex]\text{Part A.}\\(-\frac{1}{8},0),\\(\frac{3}{2},0)\\\\\text{Part B.}\\(\frac{11}{16},\frac{169}{16})\\\\\text{Part C.}[/tex]
Draw a parabola concave down with vertex at [tex](\frac{11}{16},\frac{169}{16})[/tex]. Since the leading coefficient of the equation is -16, the parabola should appear thinner than its parent function [tex]y=x^2[/tex]. Ensure that the parabola passes through the points [tex](\(-\frac{1}{8},0)[/tex] and [tex](\frac{3}{2},0)[/tex].
Step-by-step explanation:
Part A:
The x-intercepts of a function occur at [tex]y=0[/tex]. Therefore, let [tex]y=0[/tex] and solve for all values of [tex]x[/tex]:
[tex]0=-16x^2+22x+3[/tex]
The quadratic formula states that the real and nonreal solutions to a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex].
In [tex]-16x^2+22x+3[/tex], assign:
[tex]a\implies -16[/tex] [tex]b\implies 22[/tex] [tex]c\implies 3[/tex]Therefore, the solutions to this quadratic are:
[tex]x=\frac{-22\pm\sqrt{22^2-4(-16)(3)}}{2(-16)},\\x=\frac{-22\pm 26}{-32},\\\begin{cases}x=\frac{-22+26}{-32}=\frac{4}{-32}=\boxed{-\frac{1}{8}},\\x=\frac{-22-26}{-32}=\frac{-48}{-32}=\boxed{\frac{3}{2}}\end{cases}[/tex]
The x-intercepts are then [tex]\boxed{(-\frac{1}{8},0)}[/tex] and [tex]\boxed{(\frac{3}{2},0)}[/tex].
Part B:
The a-term is negative and therefore the parabola is concave down. Thus, the vertex will be the maximum of the graph. The x-coordinate of the vertex of a quadratic in standard form [tex]ax^2+bx+c[/tex] is equal to [tex]x=\frac{-b}{2a}[/tex]. Using the same variables we assigned earlier, we get:
[tex]x=\frac{-22}{2(-16)}=\frac{-22}{-32}=\frac{11}{16}[/tex]
Substitute this into the equation of the parabola to get the y-value:
[tex]f(11/16)=-16(11/16)^2+22(11/16)+3,\\f(11/16)=\frac{169}{16}[/tex]
Therefore, the vertex of the parabola is located at [tex]\boxed{(\frac{11}{16},\frac{169}{16})}[/tex]
For the next school year, you must take math, English, science, and one elective. You must take all four classes in one day. How many class schedules are possible if the math class cannot be the first class of the day?
18
4
12
24
Answer:
24
Step-by-step explanation:
ESSE
Combine these radicals.
27-3
O √24
O 23
O-23
0 -3/2
here's the answer to your question
Which equation does the graph represent?
A. x^2 + y^2 = 4
B. x^2/3^2 + y^2/4^2 = 1
C. (X - 1)^2 / 3^2 + y^2/4^2 = 1
D.X^2 / 4^2 + (y + 1)^2 / 3^2 = 1
9514 1404 393
Answer:
B. x^2/3^2 + y^2/4^2 = 1
Step-by-step explanation:
The graph looks like a circle, but is not. It is a unit circle scaled by a factor of 3 in the x-direction and a factor of 4 in the y-direction. Thus, its equation is ...
(x/3)^2 +(y/4)^2 = 1
x^2/3^2 +y^2/4^2 = 1
I need help solving 10gallons = miles
Answer:
50?
Step-by-step explanation:
Because its 50 miles per gallon, so gallon time 50 will be the miles? I'm not sure but i think it is
Simplify (5^-2)^4. Plsss help
Answer:
1/5^8
Step-by-step explanation:
We know that a^b^c = a^(b*c)
(5^-2)^4
5^(2*-4)
5^-8
We know that a^-b = 1/a^b
1/5^8
The planet Mercury travels in an elliptical orbit with eccentricity 0.203. Its minimum distance from the Sun is 4.5 x 10^7 km. If the perihelion distance from a planet to the Sun is a(1 - e) and the aphelion distance is a(1 + e), find the maximum distance (in km) from Mercury to the Sun.Pick from the following:1. 7.7 x 10^7 km.2. 6.6 x 10^7 km.3. 6.8 x 10^7 km.
Answer:
Option C
Step-by-step explanation:
From the question we are told that:
Eccentricity [tex]e=0.203[/tex]
Minimum distance from the Sun [tex]d_s= 4.5 x 10^7 km[/tex]
Perihelion distance from a planet to the Sun is [tex]r= a(1 - e)[/tex]
Aphelion distance [tex]r'=a(1 + e)[/tex]
Generally the equation for Perihelion distance is mathematically given by
[tex]4.5 * 10^7= a(1 - 0.203)[/tex]
[tex]4.5 * 10^7 = 0.797a[/tex]
[tex]a = 56.46 * 10^6 km[/tex]
Generally the equation for Aperihelion distance is mathematically given by
[tex]r' = a(1 + e)[/tex]
[tex]r' = 56.4617 * 10^6 (1 + 0.203)[/tex]
[tex]r'=6.8 * 10^7 km[/tex]
Option C
Fine the area and circumference of each circle and round to the nearest tenth.
Answer: A=πr²
A=3.14(1.6inch)² r=d/2⇒3.2/2⇒1.6
A=3.14×2.56in²
A=8.0384in²
A≈8.04
now circumference,
C=2πr
C=2×3.14×1.6in
C=10.048in
C≈10.05
Which statement can be proved true using the given theorem?
Answer:
BF = 16
Step-by-step explanation:
18/12 = 1.5 * 6 = 9
Since DE and BF are parallel and DB and EF are parallel, they comprise a parallelogram. This means that DB = EF
DB = EF = 9
24/1.5 = 16
DE = 16
BF = 16
The statement which can be proven true using the given theorem (congruence) is Segment BF = 16.
Congruence theoremBy the congruence theorem;
We can conclude that triangles ABC and EFC are congruent triangles and as such have the ratio of corresponding sides to be equal.Hence, AE/EC = BF/FC.
Therefore; 12/18 = BF/24
Hence, BF = 24× 12/18
BF = 16Read more on congruent triangles;
https://brainly.com/question/1675117
Suppose f(x) = loga(x) and f(7) = 2. Find f(343)
Answer:
6
Step-by-step explanation:
The given function to us is ,
[tex]\rm\implies f(x)= log_a(x) [/tex]
And its value at 7 is 2 , that is ,
[tex]\rm\implies f(x)= log_a(7) =2[/tex]
Taking this ,
[tex]\rm\implies 2= log_a(7) [/tex]
In general we know that ,
[tex]\bf\to log_a b = c ,\ then \ a^c = b [/tex]
Using this , we have ,
[tex]\rm\implies a^2 = 7 [/tex]
Squarerooting both sides ,
[tex]\rm\implies a =\sqrt{ 7 }[/tex]
Therefore , when x is 343 ,
[tex]\rm\implies f(343)= log_{\sqrt7} ( 343) [/tex]
We can write , 343 as 7³ ,
[tex]\rm\implies f(343)= log_{\sqrt7}7^3 [/tex]
[tex]\rm\implies f(343)= log_{7^{\frac{1}{2}}} 7^3 [/tex]
This can be written as ,
[tex]\rm\implies f(343)= \dfrac{ 3}{\frac{1}{2}} [/tex]
[tex]\rm\implies \boxed{\blue{\rm f(343)= 6 }}[/tex]
Hence the required answer is 6.
Plz help me find side x on the triangle
Answer:
x=71
Step-by-step explanation:
Since this is an isosceles triangle as indicated by the lines on the sides, the sides lengths are equal.
When the sides are equal, the base angles are equal
x=71
Can someone please help me .?
Answer:
5
Step-by-step explanation:
5+7
A map that was created
using a scale of 1 inch : 3 miles
shows a lake with an area of
18 square inches. What is the
actual area of the lake?
9514 1404 393
Answer:
162 mi²
Step-by-step explanation:
The area on the map is ...
18(1 in)²
Then the area on the ground will be ...
18(3 mi)² = 18·9 mi² = 162 mi²
PLEASE HELP FAST!! I MIGHT GIVE BRAINLIEST TO FASTEST AND ACCURATE
After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly.
The relationship between the elapsed time t, in seconds, and the number of bacteria, B(t) in the petri dish is modeled by the following function:
B(t) = 9300 x (1/64)^t
Complete the following sentence about the rate of change of the bacterial culture
The bacterial culture loses 1/2 of its size every_______ seconds
Answer:
1/6
Step-by-step explanation:
We want to find how long it takes for the bacteria to lose half its size. We can do this by taking one point of the bacteria and finding how long it takes to go to half its size. When t=0, 9300 * (1/64)^t = 9300 * 1 = 9300 as anything to the power of 0 is 1. Therefore, we can solve for t when the end result of the bacteria is 9300/2= 4650, making our equation
4650 = 9300 * (1/64)^t
divide both sides by 9300
1/2 = (1/64)^t
First, we can tell that 2^6 = 64*. Because of this, we can say that (1/2)^6 = 1^6/2^6 = 1/64, so (1/64)^(1/6) = 1/2. We know this because
(1/2)^6 = 64
take the 6th root of both sides
(1/2) = (64)^(1/6)
. This means that t=1/6, so the bacterial culture loses 1/2 of its size every 1/6 seconds
* if this is harder to figure out, e.g. 3 and 729, we can plug (log₃729) into a calculator
Answer:
0.17 seconds
Step-by-step explanation:
i got this correct on Khan :)
i hope it helps
I need help with the question below
Answer:
a: 1/12
b: 1/6
c: 1/2
d: 1/2
e: 1/12
f: 1/3
Step-by-step explanation:
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x=t−t−1, y=1+t2, t=1
Answer:
Step-by-step explanation:
First, I would find the point on the curve. By substituting t=1, I get (x, y). Next, I will try to eliminate the t and make a xy equation. In this case, the t's will cancel out in 'x=t-t-1" which wouldnt make this a curve. To find the equation of the tangent line, find the deretitave of the xy equation, and subsitute x in to find the slope at that point. Next, use point slope form to find the equation at the point.
