A curve is described by the following parametric equations:x = 2 - t
y = x^2 + 1
Which statement best describes the curve?
The curve is a parabola with a vertex at (2, 1) and is traced from left to right for increasing values of t.
The curve is a parabola with a vertex at (2, 1) and is traced from right to left for increasing values of t.
The curve is a parabola with a vertex at (-2, -1) and is traced from left to right for increasing values of t.
The curve is a parabola with a vertex at (-2, -1) and is traced from right to left for increasing values of t.
Answers
So substituting
So this equation represents a parabola where
The curve is a parabola with a vertex at (2,1) and is traced from left to right for increasing values of t.
A curve is described by parametric equations x = 2 - t;
y = x^2 + 1 statement the curve is a parabola with a vertex at (2,1) and is traced from left to right for increasing values of t is the best-described curve.
We use a parameter to describe equations then we are talking about Parametric Equations, that isWe can write both as functions of a parameter.
We have given the parametric equation
What is the parametric equation?
The parametric equation defines a group of quantities as functions of one or more independent variables called parameters.
So substituting the value of x in y we get,
So this equation represents a parabola where y is the dependent variable and t is the independent variable.
This equation is shown in the following figure, the best statement that describes the curve.
Therefore we can say that the curve is a parabola with a vertex at (2,1) and is traced from left to right for increasing values of t.
To learn more about the parametric equation visit:
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Write the equation for each transformation of f(x)= |x| described below.a. translate left 9 units, stretch vertically by a factor of 5, and translate down 23 units. b. translate left 12 units, stretch horizontally by a factor of 4, and reflect over the x-axis. need steps don't understand how to do!
Answers
Answer: 3
Step-by-step explanation:
(x + 4i) is a root which means its conjugate (x - 4i) is also a root
(x + 4i)(x - 4i) = x² + 16
Use Long Division for 2x⁵ - 13x⁴ + 22x³ - 187x² - 160x + 336 ÷ x² + 16
2x³ - 13x² - 10x + 21
x² + 16 ) 2x⁵ - 13x⁴ + 22x³ - 187x² - 160x + 336
- (2x⁵ + 0x⁴ + 32x³) ↓ ↓ ↓
-13x⁴ - 10x³ - 187x² ↓ ↓
- (-13x⁴ +0x³ - 208x²) ↓ ↓
-10x³ + 21x² - 160x ↓
- (-10x³ + 0x² - 160x) ↓
21x² + 0x + 336
- (21x² + 0x + 336)
0
Use Synthetic Division to divide (x - 7) by the reduced polynomial (2x³ - 13x² - 10x + 21)
7 | 2 -13 -10 21
| ↓ 14 7 -21
2 1 -3 0 ← remainder is 0
Use grouping to factor the reduced polynomial (2x² + x - 3)
2x² - 2x + 3x - 3
= 2x(x - 1) +1(x - 1)
= (2x + 1)(x - 1)
The factors are: (x - 7) (2x + 1) (x - 1) (x + 4i) (x - 4i)
The first 3 are real roots and the last 2 are complex roots
The zeros of a polynomial function are the factors of the function.
The number of real zeros of f(x) is 3
The function is given as:
Two of the factors are given as:
x - 7 ad x + 4i
The factor x + 4i is a complex factor.
If a polynomial function has a complex factor, then the conjugate of the complex factor is also a factor of the polynomial.
This means that f(x) has 2 complex factors
The degree of the polynomial is 5.
So, the number (r) of real zeros is the difference between the degree of the polynomial and the number of complex factors.
This gives
Hence, the number of real zeros of f(x) is 3
Read more about zeros of polynomials at:
Answers
Answers
560(t)+500(t) =2000, since we are given a 2000 distance limit. Then we are to find the time when they are at this distance. Solve for t, which is equal to 0.53 hours or 32 minutes.
b. The number is not divisible by 5.
c. The number is even or less than 12.
d. The number is neither prime nor composite.
e. The square root of the number is less than 3.
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a) 2 is part of the set and 2 is not greater than 2. NO
b) 5 and 10 in the set are divisible by 5. NO
c) 2,4,6,8,10 are even but the rest are odd ( BUT note the word "or"). the rest are less than 12. YES
d) 0 and 1 are the only numbers that are neither prime nor composite (they're not even part of the set). NO
e) the square root of 9 is 3 so the maximum number is 9 (but what happened to 10?) NO
For our given sample, the only true statement is:
c. The number is even or less than 12.
Which event, covers the entire sample space of this experiment?
The sample for the experiment is the set:
{2, 3, 4, 5, 6, 7, 8, 9, 10}
So, we need to see which ones of the statements are true for every digit in that set.
For example:
a "The number is greater than 2."
Is false, because the outcome can be 2, as 2 belongs to the set.
The true statement is:
c. The number is even or less than 12. (all the numbers are less than 12).
If you want to learn more about sets:
#SPJ5
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When you're reading out loud and you come to " 0.3 ",
you say "three tenths".
"Three tenths" is the fraction " 3/10 ".
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To find : - area of EBFD
Solution : - We have, area of square ABCD = 3 x 3 = 9 units.
Thus, (ar)EBFD = ar ABCD - ar DAE - arDCF
arDAE = 1/2 x base x height
=1/2 x 1.5 x 3 ( AE is 1/2 of AB = 1.5, DA is altitude)
= 2.25
arDFC = 1/2 x base x height
= 1/2 x 1.5 x 3 (FC is 1/2 of BC, DC is altitude)
= 2.25
Thus, (ar) EBFD = arABCD - arDAE - arDCF
= 9 - 2.25 - 2.25
= 4.5 units.
Thus, area of quad EBFD is 4.5 units.