The telescope shape and the characteristic equations of the telescope parameters are the same as parabolic equations
The distance between the focus and the vertex, of the parabola is 3.375 meters
The process for obtain the above values is as follows:
The known parameters of the parabola are;
The location of the vertex of the parabola= The origin = (0, 0)
The height of the parabola = 9 meters
The width of the parabola = 12 meters
The unknown parameter;
The distance between the focus and the vertex
Method:
Finding the coordinate of the focus from the general equations of the the parameters of a parabola
The equation of the parabola in standard form is y = a·(x - h)² + k
From which we have;
(x - h)² = 4·p·(y - k)
The coordinates of the focus, f = (h, k + p)
Where;
(h, k) = The coordinates of the vertex of the parabola = (0, 0)
∴ a = 1/(4·p)
From the question, we have the following two points on the parabola,
given that the parabola is 12 meters wide at 9 meters above the origin and
it is symmetric about the y-axis;
Points on the parabola = (9, 6), and (9, -6)
Plugging in the values of the vertex, (h, k) and the two known points, in the equation, y = a·(x - h)² + k, we get;
6 = a·(9 - 0)² + 0 = 81·a
a = 6/81 = 2/27
p = 1/(4·a)
∴ p = 1/(4 × 2/27) = 27/8
The coordinate of the focus, f = (h, k + p)
∴ f = (0, 0 + 27/8) = (0, 27/8)
The coordinate of the focus f = (0, 27/8)
Given the vertex and the focus of the parabola have the same x-values of 0, we have;
The distance between the focus and the vertex, d = the difference in their y-values;
∴ d = 27/8 - 0 = 27/8 = 3.375
The distance between the focus and the vertex, d = 3.375 meters
Learn more about parabola here;
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area of a triangle 5cm base and 4 cm height
Answer:
1/2 base×height
1/2 .5×4
1/2.20
20 divided by 2 is 10
1/1×10
10cm2
ans
The sum of two numbers is 41. The larger number is 17 more than the smaller number. What are the numbers?
Larger number:
Smaller number:
Solve the system of equations.
6x−y=−14
2x−3y=6
whats the answer please C:
Answer:
Step-by-step explanation:
10a+5(a-3)=15 I don’t know the answer I keep checking and it’s wrong
Answer:
[tex]10a + 5(a - 3) = 15 \\ 10a + 5a - 15 = 15 \\ 15a = 30 \\ a = \frac{30}{15} \\ a = 2 \\ 10 \times 2 + 5(2 - 3) = 15 \\ 20 + - 5 = 15 \\ 15 = 15 \\ lhs = rhs\\ thank \: you[/tex]
Answer: a = 2
Solve:
Given
10a + 5 (a - 3) = 15
Expand parentheses and apply the distributive property
10a + 5 · a - 5 · 3 = 15
10a + 5a - 15 = 15
Combine like terms
(10a + 5a) - 15 = 15
15a - 15 = 15
Add 15 on both sides
15a - 15 + 15 = 15 + 15
15a = 30
Divide 15 on both sides
15a / 15 = 30 / 15
[tex]\boxed{a=2}[/tex]
Check:
Left-hand side = 10a + 5 (a - 3)
Left-hand side = 10(2) + 5 (2 - 3)
Left-hand side = 20 + 5(-1)
Left-hand side = 20 - 5
Left-hand side = 15
Right-hand side = 15
15 = 15, therefore, [tex]\boxed{a=2}[/tex] would make the equation true.
Hope this helps!! :)
Please let me know if you have any questions
Fewer and fewer customers have been coming into the restaurant, so Bill, the manager, decides to change the entire menu. After he does this, he finds out that people loved the food, but the service has been driving people away. This represents what kind of problem in the decision-making process? O a) Failure to develop enough options O b) Failure to correctly define the problem c) Failure to act on a decision O d) Failure to evaluate the decision
Answer:
failure to correctly define the problem
Step-by-step explanation:
He changes the menu without identify that the real problem was the service.
solve the equation
0.09w+1.8
Step-by-step explanation:
0.09w + 1.8 = 0
0.09w = 0 - 1.8
0.09w = - 1.8
0.09w ÷ 0.09 = - 1.8/ 0.09
w = - 20
Which of the following is true because of the Associative Law of Addition?
A. 1000 + 2000 + 6 = 3006
B. (1000) + 2000 + 6 = 1000 + (2000) + 6
C. 1000 + 2000 + 6 = 2000 + 1000 + 6
D. 1000 + (2000 + 6) = (1000 + 2000) + 6
Answer:
d part is correct because in associative property the brackets and the numbers CAN be shifted
Find the shortest distance from A
to C
in the diagram below.
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Answer:
5√13 m
Step-by-step explanation:
The length of the space diagonal is the "Pythagorean sum" of the lengths of the edges of the cuboid.
AC = √(8² +6² +15²) = √325 = √(13·25)
AC = 5√13 . . . meters
__
AB is the hypotenuse of the right triangle with legs 6 and 8, so is 10 units. AC is the hypotenuse of right triangle ABC, so is ...
AC = √(AB² +BC²) = √(10² +15²)
look at the image for the quetion
Answer:
Does the answer help you?
While organizing the magazines at the doctor's office, Camille put 12 magazines in the first pile, 15 magazines in the second pile, 18 magazines in the third pile, 21 magazines in the fourth pile, and 24 magazines in the fifth pile. If this pattern continues, how many magazines will Camille put in the sixth pile?
Answer:
27
Step-by-step explanation:
since you are adding 3 to the pile each time, on the 6th pile you would have 27 because 24 + 3 = 27
the factor of 12 are ...............
Answer:
1, 2, 3, 4, 6, and 12
Step-by-step explanation:
Answer:
1,2,3,4,6,12
Step-by-step explanation:
because they divide the numbers without any remainder.
What is the solution to 4x + 2 = 6(-2x - 5) ?
O2
O 16
0-2
O -16
Please need help on this
4x+2=6(-2x-5)
<=>4x+2=-12x-30
<=>16x+32=0
<=>x=-2
What is the derivative of (x + 1) sin x?
Answer:
By the Sum Rule, the derivative of 1−sin(x) 1 - sin ( x ) with respect to x x is ddx[1]+ddx[−sin(x)] d d x [ 1 ] + d d x [ - sin ( x ) ] .
Picking a card and spinning a spinner are independent events.
True
False
Answer:
True
Step-by-step explanation:
Both happened in different times and are seprate events
Is u=−12 a solution of 8u−1=6u?
Answer:
No, -12 is not a solution.
Step-by-step explanation:
8u-1=6u
8(-12)-1=6(-12)
-96-1=-72
-97=-72
Untrue, to it’s not a solution
If the prism has 3 layers, what would the volume of the
prism be in cubic centimeters?
OA) 4 cubic centimeters
OB) 8 cubic centimeters
OC) 12 cubic centimeters
OD) 16 cubic centimeters
Answer:
OD) 16 cubic centimeters
5404 buttons are produced by a factory in Jebel Ali in a week. If the factory produced same number of buttons every day of the week, buttons produced in a day is _________________
We need to find the number of buttons the company produced per day
The company produced 772 buttons per day
Total bottons produced in a week = 5404
There are 7 days in a week
If the factory produced same number of buttons every day of the week
Then,
Buttons produced per day = Total bottons produced in a week / Total number of days in a week
= 5404 / 7
= 772 buttons
The company produced 772 buttons per day
Read more: https://brainly.com/question/24368335
The probability that a patient recovers from a disease is 0.3.
If 6 people are known to have contacted the disease, what is the probability that at least 4 survive?
Answer:
0.07047
Step-by-step explanation:
at least 4 people survive is
4 people survive and 2 don't +
5 people survive and 1 doesn't +
all 6 people survive
the probability of 4 people to survive is the product of the individual probabilities :
0.3×0.3×0.3×0.3 = 0.3⁴ = 0.0081
times the probability 2 don't survive
0.7×0.7 = 0.49
0.0081×0.49 = 0.003969
now, the chance that 4 out of 6 survive is that probabilty times how many times we can select 4 out of 6.
to select 4 out of 6 is
[tex] \binom{6}{4} [/tex]
= 6! / (4! × (6-4)!) = 6! / (4! × 2!) = 6×5/2 = 30/2 = 15
so, the probability of having 4 survivors is
15×0.003969 = 0.059535
the probability of 5 people surviving is 0.3⁵ times one not
0.3⁵×0.7 = 0.001701
we have 6 over 5 combinations to pick 5 out of 6 = 6.
so, in total for 5 survivors we get
6×0.001701 = 0.010206
and the probabilty of all 6 surviving is
0.3⁶ = 0.000729
so, the probability of at least 4 out of 6 surviving is
0.059535 +
0.010206 +
0.000729
---------------
0.070470
Hello I'm new can anyone help me with this question?
Thank you so much! <3 xoxo
Kathy stood on the middle rung of a ladder. She climbed up 3 rungs, moved down 5 rungs, and then climbed up 9 rungs. Then she climbed up the remaining 4 rungs to the top of the ladder. How many rungs are there in the whole ladder?
Answer:
There are fourteen rungs on the ladder
If K = (AB)/(A+B) , then B = ?
(a) (A)/(1−A)
(b) (AK)/(A−K)
(c) (AK)/(K−A)
(d) (A+K)/(A)
(e) (A−K)/(AK)
Lets do
[tex]\\ \sf\longmapsto K=\dfrac{AB}{A+B}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{K}=\dfrac{A+B}{AB}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{K}=\dfrac{1}{A}+\dfrac{1}{B}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{B}=\dfrac{1}{K}-\dfrac{1}{A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{B}=\dfrac{K-A}{AK}[/tex]
[tex]\\ \sf\longmapsto B=\dfrac{AK}{K-A}[/tex]
what is the tan invers of 3i/-1-i
z = 3i / (-1 - i )
z = 3i / (-1 - i ) × (-1 + i ) / (-1 + i )
z = (3i × (-1 + i )) / ((-1)² - i ²)
z = (-3i + 3i ²) / ((-1)² - i ²)
z = (-3 - 3i ) / (1 - (-1))
z = (-3 - 3i ) / 2
Note that this number lies in the third quadrant of the complex plane, where both Re(z) and Im(z) are negative. But arctan only returns angles between -π/2 and π/2. So we have
arg(z) = arctan((-3/2)/(-3/2)) - π
arg(z) = arctan(1) - π
arg(z) = π/4 - π
arg(z) = -3π/4
where I'm taking arg(z) to have a range of -π < arg(z) ≤ π.
Paul bought a student discount card for the bus. The card allows him to buy daily bus passes for $1.70.
After one month, Paul bought 16 passes and spent a total of $35.20.
How much did he spend on the student discount card?
He spent $22.5 on the student discount card.
This question is solved using proportions.
The cost of each card is of $1.50.
Paul bought 15 passes, that is, 15 cards.
Considering that he bought 15 cards, each for $1.50, his spending was of:
He spent $22.5 on the student discount card.
URGENT! WILL GIVE BRAINLIEST (PICTURE INCLUDED)
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Answer:
x > -1 and x ≠ 3
Step-by-step explanation:
The function value will be positive when there are an even number of negative factors. The factors change sign at x = -1, are zero at x = 3. The expression is positive for ...
x > -1 and x ≠ 3
Which is a graph of g(c) = (0.5)x+3^ -4
Answer:
I've attached a graph with this, that's your answer
Can someone please help me solve the equation?
Answer:
B opition is right
Step-by-step explanation:
The domina a function of
Labour costs, totalling $47.25, account for 63%
of a car repair bill. Calculate the total bill.
Answer:
75
Step-by-step explanation:
Let x = total bill
x*63% = 47.25
x *.63 = 47.25
Divide each side by .63
x*.63/.63 = 47.25/.63
x=75
Which of the following is not a rational number?
What are all possible integer solutions for b & p in the equation?
Answer:
4
Step-by-step explanation:
7+sqrt(7) is an irrational number
Answer:
p = 8 when b = 16 and p = -8 when
b = -16
Step-by-step explanation:
x² + bx + 64 = x² + 2px + p²
Cancel x² on both sides,
bx + 64 = 2px + p²
Now, by comparing both sides, you'll get the following equations,
1. b = 2p
2. p² = 64
From equation (2),
p = ±√64
= 8 or -8
Substitute p = 8 and p = -8 into equation (1),
b = 2(8) and b = 2(-8)
b = 2(8) and b = 2(-8) = 16 = -16
Therefore, p = 8 when b = 16 and p = -8 when
b = -16
WILL GIVE BRAINLIEST
Combine like terms.
2x – 3 – 5x + 8 = [ ? ]x + [ ]
Answer:
-3x + 5
Step-by-step explanation:
like terms are the ones that have x and the ones that don't.
hope this makes sense
Answer:
-3x + 5
Step-by-step explanation:
2x - 3 - 5x + 8 can also be written as 2x - 5x - 3 + 8
→ Using the rewritten method collect the x terms
-3x - 3 + 8
→ Now collect the integers
-3x + 5
please help!!!!!!!!!!
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Answer:
-203.1875
Step-by-step explanation:
The ends of the interval are ...
(-4, g(-4)) = (-4, 1023 15/16)
(1, g(1)) = (1, 8)
The average rate of change is the slope of the line between these two points:
m = (y2 -y1)/(x2 -x1)
m = (8 -(1023 15/16))/(1 -(-4)) = (-1015 15/16)/5 = -203 3/16
The average rate of change on the interval is -203 3/16.
