Answer:
b)
i) Focus ( 0,a) = [tex](0,\frac{1}{2} )[/tex]
ii) The equation of the directrix is
[tex]y = -\frac{1}{2} or y +\frac{1}{2} =0[/tex]
Step-by-step explanation:
Step(i):-
A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point (not in a line) in the plane
• The Fixed line is called the directrix of the parabola.
• The Fixed point is called the focus of the parabola.
• A line through the focus and perpendicular to the directrix is called the axis of the parabola.
• The point of intersection of parabola with the axis is called the vertex of the parabola.
Given Parabola x² = 2 y
Comparing x² = 4 a y
4 a = 2
[tex]a = \frac{1}{2}[/tex]
Focus ( 0,a) = [tex](0,\frac{1}{2} )[/tex]
Step(ii)
The equation of the directrix is y = -a or y +a=0
The equation of the directrix is
[tex]y = -\frac{1}{2} or y +\frac{1}{2} =0[/tex]
The equation of the directrix is 2 y +1 =0
Answer:
b.
Step-by-step explanation:
edg 2021
The sector has an area of 3 pi inches squared and a radius of 6 in. How many inches long is the arc for this sector? Use 3.14 for Pi and round to the nearest hundredth.
A sector with a radius of 6 inches and area of 3 pi inches squared.
Recall that Area of a sector = StartFraction n degrees over 360 degrees EndFraction (pi) (r squared) and StartFraction Arc length over Circumference EndFraction = StartFraction n degrees over 360 degrees EndFraction.
3.14
6.28
12.56
18.84
Answer: 6.28 inches.
Step-by-step explanation:
Formula :
i) Area of sector : [tex]A=\dfrac{x}{360}\times\pi r^2,[/tex], where x = central angle and r is radius
ii) Length of arc : [tex]l=\dfrac{x}{360}\times2\pi r[/tex]
Given , r= 6 in.
A = [tex]3\pi[/tex] inches
Put these values in (i) , we get
[tex]3\pi =\dfrac{x}{360}\times\pi (3)^2\\\\\Rightarrow\ 1=\dfrac{x}{120}\\\\\Rightarrow\ x=120^{\circ}[/tex]
Now , put values of x and r in (ii) , we get
[tex]l=\dfrac{120}{360}\times2\pi(3)\\\\\Rightarrow\ l=2\pi = 2(3.14)=6.28\text{ inches}[/tex]
Hence, the length of the arc is 6.28 inches.
Answer:
6.28
Step-by-step explanation:
Edge 2021
Pls help with this, I have a lot of work and I'm trying to get it done faster
Answer:
C = 3b
Step-by-step explanation:
If each bottle costs 3 dollars, then the cost of b bottles would be 3b.
Which subsets of real numbers does 2 1/3 belong to?
Answer:
rational numbers set
Step-by-step explanation:
rational numbers are fractions and 2 1/3 = 7/3
CORRECT ANSWER GETS BRAINLIEST!!! PLZ ANSWER FAST!!
Answer:
You Forgot the picture lol
If 15 x a = 90, then a=
Answer:
A = 6
Step-by-step explanation:
to find a, divide 90 by 15
90 / 15 = 6
The diagram shows a circle centre O work out the size of angle X work out the size of angle y
Answer:
x = 116° , y = 20°
Step-by-step explanation:
The angles are x = 116° & y = 20°
what is the circle theorem?When two angles are subtended by the same arc, the angle at the centre of a circle is twice the angle at the circumference i.e ∠O=2∠A
let the Points on the circumference be A,B,C then we have two traingles namely ΔABC & ΔOBC.
Given here ∠A=58°
therefore, by the circle theorem we get ∠O=116°
Again in ΔOBC it is a isosceles triangle with its two sides equal to the radius of the circle, so ∠OBC = ∠OCB
∠OCB +∠OBC+∠BOC=180°
2 ∠OBC=180°-116°
2 ∠OBC=64°
∠OBC=32°
Again, in ΔABC ∠C = 32° + 38° = 70° & ∠B= y +32°
therefore, y + 32° + 70° + 58° = 180°
y= 20°
Hence, the angles are x = 116° & y = 20°
Learn more about the circle theorem:
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you don't have to answer number 15. but pls answer the rest!
is 3kg equal to less than or greater than 3,000
there are more in the picture pls help ASP
BEST ANSWER GETS BRAINLESST AND FOLLOW ASP HURRY!!
Answer:
13) >
14)=
15)>
16)=
17)>
18)<
Step-by-step explanation:
my dad's old baseball card increased in value from $400 to $500. what was the percent increase?
Answer:
25%
Step-by-step explanation:
Quadrilateral ABCD has coordinates A (3, 1), B (4, 4), C (7, 5), D (6, 2). Quadrilateral ABCD is a
Answer:
Rhombus
I hope I helped!!!
Please make me brainliest
Which of the following points represents the center of a circle whose
equation is (x-3)2 + (y-2)2 = 16?
A. (3,-2)
B. (3,2)
C. (-3,-2)
D. (-3,2)
Answer:
B
Step-by-step explanation:
(x-3)² + (y-2)² = 16
(x-h)²+(y-k)²=16
r=4
h=3
k=2
center is at the point (h, k) ⇒ (3, 2)
What is meant by the term financial planning?
a Long-term goals are reached over an extended period of time, so your current income does not affect
them.
b. It is creating a road map of everything you do with your money.
c. It is hoping you will have enough money to pay all your bills on time.
d. If your income exceeds your expenses, you will be able to save money for the future.
Please select the best answer from the choices provided
B
ОООО
D
Save and Exit
Next
Submit
Matkathisandrum
Answer:
a Long-term goals are reached over an extended period of time, so your current income does not affect
them.
Step-by-step explanation:
Financial planning refers to long term goals that are planned and reached over an extended period of time to keep one solvent in cases of emergency without having a direct effect on current income.
Solvency simply means having more assets than liabilities to be able to stay afloat of one's debts.
What is the value of 2x3+12-13
Answer:
5
Step-by-step explanation:
According to PEMDAS the answer is five.
2x3+12-13
6+12-13
18-13
5
Lavern just turned 40 years old, so her credit score rose from 555 to 623,
According to the following table for a $150,000 mortgage, how much less per
year would Lavern have to pay on a $150,000 mortgage with the new credit
score?
FICO
Interest Monthly
Score
Rate Payment
720-850
5.59% $860
700-719
5.71% $872
675-699
6.25% $924
620-674
$1039
560-619
8.53% $1157
500-559
9.29% $1238
7.40%
A. $199
ООО
B. $1238
C. $1039
O D. $2388
Answer:
D
Step-by-step explanation:
($1238-$1039)×12=$2388
A catapult launches a boulder with an upward velocity of 120 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h = -16t^2 + 120t + 10. How long does it take to reach maximum height? What is the boulder's maximum height? What is the boulder's maximum height? Round to the nearest hundredth, if necessary.
Answer:
See below in bold.
Step-by-step explanation:
h = -16t^2 + 120t + 10
To find the height and time for maximum we convert to vertex form:
h = -16(t^2 - 7.5t) + 10
h = -16 [(t - 3.75)^2 - 14.0625] + 10
h = -16(t - 3.75)^2 + 225 + 10
h = -16(t - 3.75)^2 + 235
So the time to reach maximum height is 3.75 seconds and the maximum height = 235 ft.
Can anybody answer these questions. By the way the questions are seperated in different screenshots that i put.
Answer:
Sorry i can only answer one but the first one of the trapizoid is 76
Step-by-step explanation:
see picture
I need help tell me the answer plz
70,000
Answer:
round 5 up which makes 9 a 10 which makes 6 a 7
Answer:
70000
Step-by-step explanation:
You would look at the number that is in the hundreds place vaule, which is 500 in this case. Whenever a number is above or equal to 5, you would round up. You would round the number to the next thousand, which is 70000.
im really tired and my brain isnt working right please help i need help with part b
Answer:
hello! the answer is 2.5 hours :)
Answer:
the answer is 2.5 hours
Step-by-step explanation:
What are the missing amounts in this statement.
20% of $30= 40% of $____
Pls help me
Answer:
Step-by-step explanation:
20% of $30 = 40% of x
0.20 * 30 = 0.40 * x
[tex]\frac{0.2}{0.4}*30=x\\[/tex]
x = 15
A set of wrist watch prices are normally distributed with a mean of 767676 dollars and a standard deviation of 101010 dollars. What proportion of wrist watch prices are between 636363 dollars and 909090 dollars? You may round your answer to four decimal places. S
Answer:
0.8224
Step-by-step explanation:
Data
mean: $76standard deviation, sd: $10first value of interest, x1: $63second value of interest, x2: $90z-score for x1:
z1 = (x1 - mean)/sd = (63 - 76)/10 = -1.3
z-score for x2:
z2 = (x2 - mean)/sd = (90 - 76)/10 = 1.4
The proportion of wrist watch prices are between $63 and $90 is:
P(z1 < z < z2) = P(z < 1.4) - P(z < -1.3)
P(z < 1.4) = 0.9192 (see first picture attached)
P(z < -1.3) = 0.0968 (see second picture attached)
P(z1 < z < z2) = 0.9192 - 0.0968 = 0.8224
Seining bought 6 apples for $1.80. Jane brought 5 apples for $1.50.Are the rates in proportion
Answer:
Yes
Step-by-step explanation:
6 : 1.8 = 1 : 0.3
5 : 1.5 = 1 : 0.3
I need help on this.
Answer:
14
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
hopefully this helps
The area of a triangle is 30 square inches. The base of the triangle is 10
in. What is the height of the triangle? *
I will mark as Brainliest and give extra points help
Answer:
6 inches
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base and h is the height
30 = 1/2 (10) h
30 = 5h
Divide each side by 5
30/5 = 5h/5
6 = h
Answer:
Step-by-step explanation:
we know area of a triangle = 1/2 * base * height
1/2*10* height = 30
5* height =30
height = 30/5 = 6inches
hope it helps
I need help on this.
Answer:
2143-764=1379
Step-by-step explanation:
Question 16 (5 points)
The first two terms of an arithmetic sequence are a1 = 2 and a2 = 5. Find a6, the
sixth term of the sequence.
OA) 27
B) 20
OC) 14
D) 17
Answer:
D. 17.
Step-by-step explanation:
The nth term of an arithmetic sequence (an) is a1 + d(n - 1) where a1 = first term and d = the common difference.
In this sequence d = a2 - a1 = 5 - 2 = 3.
a6 = 2 + 3(6 - 1)
= 2 + 3*5
= 17.
Answer:
Step-by-step explanation:
probably 17
In the Pythagorean theorem (a + b2 = c), a and b stand for the lengths of the
shorter sides, and c stands for
A. the length of the legs
B. the area of the triangle
c. the length of the longest side
D. the height of the triangle
I WILL GIVE CORRECT ANSWER BRAINLIEST!! using the graph as your guide, complete the following statement. the discriminant of the function is______.
Answer:
B. Positive
Step-by-step explanation:
If there are 2 real roots, then the discriminant is always positive.
Answer:
B. position
Step-by-step explanation:
ap e x lol
Please help this is due at midnight!!!!!!!!!
Describe how to optimize a function given a set of constraints.
The setup for this problem is written as l(x,y)= f(x,y)+λg(x,y)
For example, a common economic problem is the consumer choice decision. Households are selecting consumption of various goods. However, consumers are not allowed to spend more than their income (otherwise they would buy infinite amounts of everything!!). Let’s set up the consumer’s problem:
Suppose that consumers are choosing between Apples (A) and Bananas (B). We have a utility function that describes levels of utility for every combination of Apples and Bananas.
11
A 2 B 2 = Well being from consuming (A) Apples and (B) Bananas.
Next, we need a set of prices. Suppose that Apples cost $4 apiece and Bananas cost $2 apiece. Further, assume that this consumer has $120 available to spend. The income constraint is
$2B+$4A≤$120
However, the problem requires that the constraint is in the form g(x, y)≥ 0. In
the above expression, subtract $2B and $4A from both sides. Now we have 0≤$120−$2B−$4A
g(A, B) Now, we can write out the lagrangian
11
l(A,B)= A2 B2 +λ(120−2B−4A)
f (A, B) g(A, B)
Step II: Take the partial derivative with respect to each variable We have a function of two variables that we wish to maximize.
Therefore, there will be two first-order conditions (two partial derivatives that are set equal to zero).
To know more about function follow
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If f(1) = 7 and f(n) = 5(n-1) + 2, then f(4) =
Answer:
f1 =7
f2 = 5(7) + 2 = 37
f3 = 5(37) + 2 = ?
f4 = 5(?) + 2 = ____
914
hopefully this makes sense
What’s the surface area of this prism?
Answer:
580
Step-by-step explanation:
1/2 6x10 x2 for the two bases is 60. for the rams is 20x8 x2 cause there is two ramps. then the bottom is 10 x 20 is 200. add them all up and get 580.
Answer:
760 m^2
Step-by-step explanation:
Please help me
Two exponential functions, fand g, are shown in the graph where g is a transformation of f.
Which of the rules given below shows the transformation of f?
A. g(x) = f(x-2)
B. g(x) = f(x) + 2
C. g(x) = f(x + 2)
D. g(x) = f(x) - 2
