The vector function is, r(t) = [tex]\bold{ < t,2t^2,9t^2+4t^4 > }[/tex]
Given two surfaces for which the vector function corresponding to the intersection of the two need to be found.
First surface is the paraboloid, [tex]z=9x^2+y^2[/tex]
Second equation is of the parabolic cylinder, [tex]y=2x^2[/tex]
Now to find the intersection of these surfaces, we change these equations into its parametrical representations.
Let x = t
Then, from the equation of parabolic cylinder, [tex]y=2t^2[/tex].
Now substituting x and y into the equation of the paraboloid, we get,
[tex]z=9t^2+(2t^2)^2 = 9t^2+4t^4[/tex]
Now the vector function, r(t) = <x, y, z>
So r(t) = [tex]\bold{ < t,2t^2,9t^2+4t^4 > }[/tex]
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Please, help me. I have no idea.
Which of the following options are examples of how you can name the angle? Select all that apply.
Answer:
∠A
∠EAU
∠UAE
Step-by-step explanation:
You can name an angle by their middle vertex letter which, in this case, is A.
You can also name an angle using the three letters provided: E, A, U.
However, the vertex letter should always be in the middle. So, it could be ∠EAU and ∠UAE.
Let me know if you don't understand or need more explanation.
Type a digit that makes this statement true. 8,353,05_
The digits that make the given statement true are 3 or 7.
5,156,936 is divisible by 4.5,156,976 is divisible by 4.What are the rules of divisibility of 4?The basic rule for divisibility by 4 is that if the number formed by the last two digits of a number is divisible by 4, the original number is divisible by 4 as well; this is because 100 is divisible by 4, and so adding hundreds, thousands, and so on is simply adding another number that is divisible by 4.So, 5,156,9_6 to be divisible by 4:
If the last two digits are divisible by 4, the sum is divisible by 4.As a result, _6 must be divisible by 4.There are two options here: 3 (as in 36) or 7. (as in 76).Therefore, the digit that makes the given statement true is 3 or 7.
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The correct question is given below:
Type a digit that makes this statement true.
5,156,9_6 is divisible by 4.
In a school election there were four candidates: Tom, Rebecca, Olly and Wendy.
540 students voted in the election.
5% of the votes were for Tom
of the votes were for Rebecca
The ratio of the number of votes for Olly to the number of votes to Wendy was 1:2
How many votes were for Wendy?
5% of votes were for Tom: 27
2/9 of the votes were for Rebecca: 114
213 votes are for Wendy
Examine the distribution of the target variable. what is the proportion of individuals who purchased organic products?
The proportion of individuals who purchased organic products is 24.77%.
The target variable is the variable whose values are modeled and predicted by other variables. A predictor variable is a variable whose values will be used to predict the value of the target variable
The target variable (also called the dependent variable) used in the analysis for this tutorial is a categorical variable that differentiates clinicians in the study that indicated that they would be Highly Likely to Use Product X from those that had a Low Likelihood to Use the new product
Organic food is grown without the use of synthetic chemicals, such as human-made pesticides and fertilizers, and does not contain genetically modified organisms (GMOs). Organic foods include fresh produce, meats, and dairy products as well as processed foods such as crackers, drinks, and frozen meals.
According to the plot the distribution of target variable is as follows
0’s: 167181’s
5505
The proportion of individuals who purchased organic products are: 5505/22223
= 0.2477
=24.77%
That is around 24.77% people have purchased organic products.
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[tex]y \geq \frac{1}{3}x+4\\[/tex]
In linear equation, y ≥ x + 12/3 is simple version .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.It has the formula Ax + B = 0, with A and B being any two real numbers and x being an ambiguous variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.y ≥ 1/3 x + 4
y ≥ x/3 + 4
y ≥ x + 12/3
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Which of the following options are examples of how you can name the angle?
Answer:
3rd and 4th
Step-by-step explanation:
Answer:
∠C and ∠DCB and ∠BCD
Step-by-step explanation:
We can name an angle either using one letter that represents it or use all three letters together.
When we use a single letter to represent or point an angle we must choose the center letter, C in this case.
And when we use all three letter to point an angle we must place the center letter, again C in this case, in the middle
Therefore the angle can be named as
∠C or ∠DCB or ∠BCD
The ratio of a to b is constant, and
a = 9 when b = 6. What is the value of
b when a = 2?
Answer:
Step-by-step explanation:
a : b
9 : 6
2 : x
Cross multiply
6*2 = 9x
12 = 9x
12/9 = x
4/3 = x
WILL GIVE BRAINLIEST
Enrollment at a golf academy has grown exponentially since the academy opened. A graph depicting this growth is shown. Determine the percentage rate of growth.
1.5%
5%
50%
0.5%
GRAPH IS BELOW
Answer:
We can see that after 2 years, enrollment becomes 35 instead of 15.
35/15=2.333...)
Since it's exponential, take sqrt(2.333...)=about 1.5
So the growth is 50%
answer this question
The equation of the function g(x) is g(x) = -2|x - 2| + 5
How to determine the equation of the function g(x)?The function f(x) is given as
f(x) = 2|x - 2| - 5
The rule of the transformation is a reflection across the x-axis
This is represented as
g(x) = -f(x)
So, we have
-f(x) = -2|x - 2| + 5
Substitute g(x) = -f(x) in -f(x) = -2|x - 2| + 5
g(x) = -2|x - 2| + 5
Hence, the equation of the function g(x) is g(x) = -2|x - 2| + 5
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6.
Part A: Annotate the expressions.
Expression C
20-(-3)
Expression D
-20-(-3)
Part B: How are the expressions similar?
Part C: Explain the steps you would take in simplifying
Expression D.
Answer:
expression d is your right answer
if i walked 4 miles for 180 days how much miles would i have walked
Answer:
720
Step-by-step explanation:
4x180=720 u have to multiply because 4 miled in 180 days is the same as 4x180
Ms. Jordan bought a box of 32 granola bars. Every day each of her three children ate one granola bar for lunch. Now there are only 11 bars left. Which equation can be used to find the number of days, n, that the children ate the bars for lunch? 32 =-11 32 = 3n - 11 ○ 32 = 3 +11 32 = 3n+ 11
The equation that can be used to find the number of days is 32 - 3n = 11
How to determine the equation that can be used to find the number of days?The given parameters are
Initial amount = 32
Rate = 3 i.e. 3 children
Amount left = 11
Let the number of days be n
So, we have:
Initial amount - number of days * rate = amount left
This gives
32 - 3n = 11
Hence, the equation that can be used to find the number of days is 32 - 3n = 11
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Which equation can be used to find the answer to 30 divided by 5
Answer:
[tex]30 \div 5[/tex]
Way A
• 5 divided by 0 is 0.
• 5 divided by 3 is 0.6, flip the number, and you get 6.
Way B
• Divide 30 by 5 to get 6.
What is the remainder when f(x) = x4 + 7x3 + 17x2 + 20x is divided by x2 + 4?
a
\large x^2+13x+7+\frac{-52}{x^2+4}
b
\large x^2+7x+\frac{13x-8}{x^2+4}
c
\large x^2+7x+13+\frac{5x-52}{x^2+4}
d
\large x^2+1+\frac{1}{x^2+4}
The reminder by dividing f(x)= x⁴ + 7x³ + 17x² + 20x is divided by x² + 4 is x² + 7x + (-13x² - 8x)/(x² + 4) so none of the given option is correct.
What is a number system?The number system is a way to represent or express numbers.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
Given the dividend f(x)= x⁴ + 7x³ + 17x² + 20x and diviser x² + 4
The first time it will go to x²
Then,
Quotient = x²
Remainder = 7x³ - 13x²
The second time goes to 7x
Quotient = 7x
Remainder = -13x² - 28x
The third time it is not divisible so (-13x² - 8x)/(x² + 4) will be the reminder.
Together it is x² + 7x + (-13x² - 8x)/(x² + 4).
Hence "The reminder by dividing f(x)= x⁴ + 7x³ + 17x² + 20x is divided by x² + 4 is x² + 7x + (-13x² - 8x)/(x² + 4)".
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One bridge design has supports that form an X in the center. Find the measure of each numbered angle.
The measure of angle is 52, 128 and 132
What are angles?A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
Given:
one angle = 52
So,
<2 = 52 (vertically opposite angle)
<1 + <2 = 180 ( linear pair)
<1 + 52 = 180
<1 = 128
and, <1 = < 3 ( vertically opposite angle)
<3 = 132
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Each leg of an isosceles triangle is twice as long as its base. Express the perimeter in terms of the length of the base.
The perimeter of the triangle in discuss expressed in terms of the length of the base as required in the task content is; Perimeter= 5x.
What is the perimeter of the isosceles triangle in terms of the length of the base?According to the task content, it follows that the perimeter of the triangle in terms of the length of the base is to be determined.
Let x = length of the base
Therefore, length of each leg = 2x.
Therefore, since the perimeter of the triangle is the sum of all sides; it follows that we have;
Perimeter = x + 2x +2x
Perimeter = 5x.
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R, S, and T are collinear. S is between R and T. RS =2w + 1, ST = w - 1, and RT = 18. Use the Segment Addition Postulate to slove for w. Then determine the lenght of RS.
R, S, and T are collinear . Then 13 is the length of RS.
What do collinear points mean?
Collinear points are those that are situated along a single or shared straight line. In Euclidean geometry, two or more points are said to be collinear if they are located on a line either near or far from one another.The question to know
RS + ST = RT
RS = w + 1 , ST = w - 1
RT = 18
2w + 1 + w - 1 = 18
3w = 18
w = 18/3
w = 6
RS = 2 * 6 + 1 = 13
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which set of points are collinear? d, s, y startfragment, d, s, y, p, t, y startfragment, p, t, y, y, d, h startfragment, y, d, h, h, t, s
The set of points (A) P, T, and Y are collinear.
What are collinear points?Collinear points are those that are on the same straight line or in the same plane. In Euclidean geometry, two or more points on a line that is close to or far from each other are said to be collinear.In general, three points A, B, and C are collinear if the sum of the lengths of any two line segments between AB, BC, and CA equals the length of the remaining line segment, that is, AB + BC = AC, AC +CB = AB, or BA + AC = BC.In response to the question -
Only one set of points - (P, T, Y) - can be seen to be on the same straight line. One of the options mentioned is - (P, T, Y).Therefore, the set of points (A) P, T, and Y are collinear.
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The correct question is given below:
Which set of points is collinear?
(A) P, T, Y
(B) D, S, Y
(C) H, T, S
(D) Y, D, H
7. On a recent math test, the boys averaged
81 and the girls averaged 90. If there are twice
as many boys in the class as girls, what was
the overall average for the class?
A recipe uses both carrots and onions. The recipe uses 4 times more carrots than onions. If the recipe uses a total of 25 ounces of chopped carrots and onions, how many ounces of onions does the recipe use?
The ounces of onions is 5 ounces.
How to calculate the value?Let the onions be represented by x.
The recipe uses 4 times more carrots than onions. The carrots will be 4 × x = 4x.
Therefore, the equation will be:
4x + x = 25
5x = 25
Divide by 5
x = 25/5
x = 5
Therefore, the ounces of onions is 5 ounces.
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Answer:
Step-by-step explanation:
The ounces of onions is 5 ounces.
The recipe uses 4 times more carrots than onions. The carrots will be 4 × x = 4x.
Therefore, the equation will be:
4x + x = 25
5x = 25
Divide by 5
x = 25/5
x = 5
Therefore, the ounces of onions are 5 ounces.
Adeli opened a savings account with an initial deposit of $2000 and will not make any additional deposits or withdrawals the account earns 5% interest compounded annually what is the total amount that adele will have in her account in the end of the 3 years
The total amount that Adele will have in her account at the end of the 3 years is $2,315.25.
Given that, principal=$2000, rate of interest=5% and time period=3 years.
How to calculate the compound interest?The compound interest formula is used to calculate compound interest, sometimes known as "interest on interest". The formula for compound interest is [tex]A = P(1 + \frac{r}{100})^{nt}[/tex], where P= principal balance, r= interest rate, n= number of times interest is compounded per time period and t= number of time periods.
Now, A=2000(1+5/100)³
=2000(1+0.05)³
=2000(1.05)³
=$2,315.25
Therefore, the total amount that Adele will have in her account at the end of the 3 years is $2,315.25.
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I need help finding the m with m
The value of x in the angles is 17
How to determine the value of x?The angles are given as
3x + 10 and 2x - 5
These angles are complementary angles
So, we have
3x + 10 + 2x - 5 = 90
Collect the like terms
So, we have
3x + 2x + 10 - 5 = 90
Evaluate the like terms
So, we have
5x = 85
Divide both sides by 5
x = 17
Hence, the value of x in the angles is 17
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-23/20 in a decimal form long division
(-23/20) in a decimal form long division will be equal to (-1.15)
As per the question statement, we are provided with a fraction: (-23/20).
We are required to calculate the simplest form of the fraction in decimals using to the long division method.
The long division method works with 4 component: dividend, divisor, quotient and remainder. And the steps to perform the long division method are as follows:
Step 1: To take the first digit of the dividend from the left and check if this digit is greater than or equal to the divisor.
Step 2: Then, to divide it by the divisor and write the answer on top as the quotient.
Step 3: To subtract the result from the digit and write the difference below.
Step 4: To bring down the next digit of the dividend (if present).
Step 5: To Repeat the same process.
Hence, converting the fraction (-23/20) to decimal values using the process of long division method mentioned above, we get (-1.15).
Long Division method: In Mathematics, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals that is simple enough to perform by hand, by breaking down a division problem into a series of easier steps, as mentioned above.To learn more about Long Division method, click on the link below.
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Find constants and in the function ()= such that (12)=1 and the function has a local maximum at =12
When the function changes from increasing to decreasing, a local maximum occurs. The value of a = 5e.
What is meant by local maximum?A local maximum point on a function is a point (x, y) on the function's graph whose y coordinate is greater than all other y coordinates on the graph at "close to" points (x, y).
When the function changes from increasing to decreasing, a local maximum occurs. This means that the function's derivative will shift from positive to negative.
Let the function be [tex]&F(x)=a x e^{b x} \\[/tex]
[tex]&F '(x)=d / d x\left(a x e^{b x} ) \\[/tex]
[tex]&=a(d / d x)\left(x e^{b x}) \\[/tex]
simplifying the above equation, we get
[tex]&=a\left[\left(d / d x* x\right) e^{b x} +\left(x* d / d x* e^{b x} )\right] \\[/tex]
[tex]&=a\left[e^{b x} +b x e^{b x} \right] \\[/tex]
[tex]$&=a[1+b x] e^{b x}[/tex]
For critical points, set [tex]$f^{\prime}(x)=0$[/tex] and solve for x
[tex]&a[1+b x] e^{b x} =0 \\[/tex]
simplifying the above equation, we get
1 + bx = 0
bx = -1
x = -1/b
The value of x = -1/b
Given that f(x) has local max at 1/5, critical point x = 1/5 then
-1/5 = -1/b
Therefore, b = -5
[tex]&F(x)=a x e^{-5x}\\[/tex]
[tex]&F(1 / 5)=a / 5 e^{-1}\\[/tex]
1 = a/5e
Therefore, the value of a = 5e.
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Factoring All Methods
Answer:
5(3n - 4)(3n - 10)
Step-by-step explanation:
15n² - 110n + 200 ← factor out 5 from each term
= 5(3n² - 22n + 40) ← factor the quadratic
consider the factors of the product of the coefficient of the n² term and the constant term which sum to give the coefficient of the n- term.
product = 3 × 40 = 120 and sum = - 22
the factors are - 12 and - 10
use these factors to split the n- term
3n² - 12n - 10n + 40 ( factor the first/second and third/fourth terms )
3n(n - 4) - 10(n - 4) ← factor out (n - 4) from each term
(n - 4)(3n - 10)
then
15n² - 110n + 200 = 5(n - 4)(3n - 10)
Answer:
Hello,
Step-by-step explanation:
[tex]15n^2-110n+200=15(n^2-\dfrac{22}{3}x +\dfrac{40}{3} )\\[/tex]
1. I am thinking about 2 numbers with sum=22/3 and product=40/3.
Those numbers are 4 and 10/3 since 4*10/3=40/3 and 4+10/3=22/3
[tex]15(n^2-\dfrac{22}{3}x +\dfrac{40}{3} )=15(n-\dfrac{10}{3} )(n-4)=5*(3n-10)(n-4)[/tex]
2.
[tex]15(n^2-\dfrac{22}{3}x +\dfrac{40}{3} )=15(n^2-2*\dfrac{11}{3} x+(\dfrac{11}{3})^2 -\dfrac{121}{9} +\dfrac{120}{9})\\\\=15((n-\dfrac{11}{3})^2 -\dfrac{1}{9})\\\\=15( n-\dfrac{11}{3} -\dfrac{1}{3})*(n-\dfrac{11}{3} +\dfrac{1}{3})\\=15(n-\dfrac{10}{3})(n-4)\\\\=5(3n-10)(n-4)\\[/tex]
3.
Using discriminant ...
The solution set of a linear system whose augmented matrix is [ 1 2 3 ] is the same as the solution set of =, if =[ 1 2 3 ].
x+2x+x=d is solution set of a linear system whose augmented matrix.
What does matrix mean?
A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.First statement
[ 1 2 3 | d][x]
[ 1 2 3]x=d
x+2x+3x=d
Second statement
Ax=d
Given that A = [ 1 2 3]
[ 1 2 3]x=d
x+2x+3x=d
x+2x+x=d
Then, they are going to have the same solution
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Verify if f(x)= 5-3x/2 and g(x)= 5-2x/3 are inverses. Please show step by step.
Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.
Inverse of functionsIn order to determine if the function f(x) and g(x) are inverses of each other, the composite function f(g(x)) = g(f(x))
Given the function
f(x)= 5-3x/2 and
g(x)= 5-2x/3
f(g(x)) = f(5-2x/3)
Substitute
f(g(x)) = 5-3(5-2x)/3)/2
f(g(x)) = (5-5+2x)/2
f(g(x)) = 2x/2
f(g(x)) = x
Similarly
g(f(x)) = 5-2(5-3x/2)/3
g(f(x)) = 5-5+3x/3
g(f(x)) = 3x/3
g(f(x)) =x
Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.
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Which equation best represents the graph shown below? Explain in detail how you arrived at your answer by stating each of the mathematical transformations necessary and to produce the graph
Answer step by step
A. Y = (x - 2)^2 - 3
B. Y = (x + 2)^2 - 3
C. Y = - ( x - 2 )^2 - 3
D. Y = 1/2 ( x + 2)^2 - 3
The quadratic equation is:
y = (x - 2)^2 - 3
So the correct option is A.
Which equation best represents the graph shown below?
The graph clearly is the graph of a quadratic equation, there we can see that:
The y-intercept is y = 1.
The vertex is (2, -3)
Remember that if we know that a quadratic equation has a vertex (h, k), then the equation can be written as:
y = a*(x - h)^2 + k
In this case, the vertex is (2, -3), replacing that we get:
y = a*(x - 2)^2 - 3
Now, we can find the value of a, the leading coefficient, by using the fact that the y-intercept is y = 1, evaluating in zero we should get:
1 = a*(0 - 2)^2 - 3
1 = a*4 - 3
1 + 3 = a*4
4/4 = a = 1
Then we conclude that the quadratic equation is:
y = (x - 2)^2 - 3
So the correct option is A.
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a phrase that describes a set of real numbers is given. express the phrase as an inequality involving an absolute value. all real numbers x more than 2 units from 0
All real numbers x more than 2 units from 0 will be |x - 2| ≤ 0.
What does "real number" mean?
In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions. In contrast to the natural numbers 1, 2, 3,... that result from counting, real numbers are utilized in measurements of continuously altering quantities such as size and time.All real numbers x at most 2 units from 0
This means if x is centered at 2 then it can move at the max 2 units on either side (i.e. 4 units after 2 and 0 units before 2)
This will be |x - 2| ≤ 0
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