The depth of the mirror of the cross-section of a searchlight would be 8.33 cm if the light bub has a vertex at 3 cm and the mirror is 20 centimeters across at the origin.
A cross-section is perpendicular to the axis of the symmetry goes through the vertex of the parabola. The cross-sectional shape of the mirrored section of most searchlights or spotlights is parabolic.
It helps in maximizing the output of light in one direction.The equation of the cross-section of the parabola is - [tex]y^{2} = 4ax[/tex], where a is the focus and x is the depth of the mirror from its origin.Given:
a = 3
y = [tex]\frac{20}{2}[/tex] cm = 10 cm
Solution:
from the equation [tex]y^{2} = 4ax[/tex]
[tex]y^{2} = 4*3*x\\ y^{2} = 12x[/tex]
putting x, 10 cm in the equation
[tex]x=\frac{10^{2} }{12} \\\\x= \frac{100}{12} \\\\x= 8.33 cm[/tex]
thus, the depth of the mirror would be - 8.33 cm
Learn more about other problems of the parabola:
https://brainly.com/question/12793264
What is the slope of the line below?
y=2/3 X - 3
Answer:
2/3
Step-by-step explanation:
Hey there!
Well in the equation,
y = 2/3x - 3
the slope is 2/3 because the equation shows 2/3x and wherever the x is in slope intercept that the slope.
Hope this helps :)
Suppose 100 users of a social networking site are chosen for a sample, but
only 25 respond. What is this an example of?
A. Response bias
B. Nonselection bias
O C. Selection bias
D. Nonresponse bias
Answer:
i think its d
Step-by-step explanation:
Answer: C
Step-by-step explanation:
Look at the pattern below. step 1 with 1 square step 2 with 3 squares step 3 with 6 squares step 4 with 10 squares How many squares will be in the pattern in step 6
Answer:
21 squares
Step-by-step explanation:
Here in this question, we are given a pattern and we want to determine what the values in that pattern will be at a specific step.
We proceed as follows;
What we can see in this pattern is that the difference in number of squares between a pattern and the next pattern increases by the addition of the next integer to the number of squares we have in the last pattern.
Thus for step 5, we shall be adding the next integer( 5) to the number of squares ;
That would be 10 + 5 = 15 squares
For step 6, we shall be adding the next integer (6) to the number of squares in step 5.
That would be 15 + 6 = 21 squares
How we got the initial next integer?
step 1 = 1 square
step 2 = 3 squares ( integer difference of 2)
step 3 = 6 squares ( integer difference of 3)
step 4 = 10 squares ( integer difference of 4)
so;
step 5 = 15 squares ( integer difference of 5)
step 6 = 21 squares( integer difference of 6)
If the function 5x + y = 1 has the domain {-2, 1, 6}, then what is the corresponding range?
Answer:
{ 11, -4, -29}
Step-by-step explanation:
5(-2) + y = 1
-10 + y = 1
y = 11
5(1) + y = 1
y = -4
5(6) + y = 1
30 + y = 1
y = -29
Answer:
The Range is the set: { -29, -4, 11 }
Step-by-step explanation:
You need to apply the given function to the x-values of the Domain, to find what values of the Range they are associated with. So let's start by isolating y on one side of the expression:
y = 1 - 5 x
Now let's find what values they result when x = -2, 1, and 6:
y = 1 - 5 (-2) = 1 + 10 = 11
y = 1 - 5 (1) = 1 - 5 = -4
y = 1 - 5 (6) = 1 - 30 = -29
Therefore the Range is the set: { -29, -4, 11 }
6 + x is an example of _____.
a formula
an expression
a constant
a variable
Answer:
An expression
Step-by-step explanation:
The constant in this case would be 6 because it never changes.
The variable would be x because the value of x can change.
A formula is a mathematical rule, which 6 +x is not.
Therefore, 6+x is an expression.
Which formula would you use to calculate the total enclosed space of Firm 1’s structure. Explain your choice.
What is the total enclosed space of Firm 1’s structure
Answer:
Total enclosed space = 6597.35 ft³
Step-by-step explanation:
Firm 1's structure is in the form of a cylinder, so the formula to get the enclosed space or volume of the cylinder will be,
Volume = πr²h
where r = radius of the structure
h = height of the Firm
By substituting the values of 'r' and 'h' in the given formula,
V = [tex]\pi (\frac{70}{2})^{2}(60)[/tex]
= [tex]\pi (35)\times 60[/tex]
= 6597.345
≈ 6597.35 cubic feet
Total enclosed space of Firm 1 is 6597.35 cubic feet.
Answer:
pi*r sqrq
Step-by-step explanation:
bc its a cirlce
total SA=10445.8 units sqrt
ur welcome
Rank the total mass of each stack
Answer:
Stack A (12M) > Stack D (9M) > Stack E (8M) > Stack B (6M) and Stack C (6M)
Step-by-step explanation:
Stack A has [tex] 6M + 2M + 4M = 12M [/tex]
Stack B has [tex] 2M + 2M + 2M = 6M [/tex]
Stack C has [tex] M + 5M = 6M [/tex]
Stack D has [tex] M + 3M + 5M = 9M [/tex]
Stack E has [tex] 5M + 3M = 8M [/tex]
The total mass of each stack from the highest to the least can be ranked as follows:
Stack A (12M) > Stack D (9M) > Stack E (8M) > Stack B (6M) and Stack C (6M)
The phone company offers to long-distance plans the first charges a flat value of five dollars per month plus $.99 each minute used and the second charge is $10 a month plus $.79 for each minute used if X represents the number of minutes use each month which system each of equations represent the amount of money why are you spin
Answer:
The systems of equation for the amount spent are as follows
[tex]Y= 0.99x+5[/tex]
[tex]Y= 0.79x+10[/tex]
Step-by-step explanation:
In this problem we are expect to give a model or an equation that represents the amount of money spent per month given a fix subscription amount and a variable fee which is based on extra minutes spent.
let Y represent the amount of money spent in total for the month
The first case:
Subscription =$5
charges per minutes = $0.99
therefore the amount spent can be modeled as
[tex]Y= 0.99x+5[/tex]
The second case:
Subscription =$10
charges per minutes = $0.79
therefore the amount spent can be modeled as
[tex]Y= 0.79x+10[/tex]
Please help this is really important
Can someone tell me if this is correct?
Answer:
yes it is correct it is not the first one
because the lines are not the same size and are in the right direction
Flying against the wind, a jet travels 1650 miles in 3 hours. Flying with the wind, the same jet travels 3480 miles in 4 hours. What is the rate of the jet in still air and what is the rate of the wind?
Step-by-step explanation:
Let the rate of the plane be x
The rate of the wind be y
Against the wind
Resultant velocity = x-y
1650/3 = x - y
550 = x - y
With the wind
Resultant velocity = x + y
3480/4 = x + y
870 = x + y
Solve equation simultaneously
Add both equations
870+550 = x+y+x-y
1420 = 2x
x = 710
x + y = 870
y=870 - 710
y = 160
The rate of jet in still air = 710 mph
The rate of wind = 160 mph
HOPE IT HELPS!
PRETTY PLEASE MARK ME BRAINLIEST :-)
plz help!! will mark brainliest!!
Answer:
correct me if I'm but i think the net cash flow is 3,790 because 2,040 a month income and 1,750 a month for other stuff. 2,040+1,750=3,790
Step-by-step explanation:
answer all three please
Answer:
Triangular prism
Volume = 100cm³
Rectangular prism
Volume = 480³
Total volume of Composite Figure 580cm³
Step-by-step explanation:
Erica can run 1 / 6 fraction of a kilometer in a minute. Her school is 3 / 4 of a kilometer away from her home. At this speed, how long would it take Erica to run home from school? answer quick plz
Answer:
the result is 4.5 minutes.
- Erica runs 1/6 km in a minute.
- The school is 3/1 km away from her home.
Step-by-step explanation:
Samuel has $20 in his savings account before he makes a deposit of $160 after two weeks he withdraws $160 how did Samuel savings account balance change
Find the slope and the y-intercept of the graph of the linear equation.
y=-7x+2
A) slope: - 1 y-intercept: 2
B) slope: 2; y-intercept: -7
C) slope: -7; y-intercept: 2
D) slope: 2; y-intercept: -7
Answer:
c) Slope;-7;y-intercept:2
Step-by-step explanation:
Samira and Sonia each have a bag containing 20 sweets. In each bag, there are 5 red, 6 green and 9 yellow sweets.
(a)
(b)
Samira chooses one sweet at random from her bag.
Write down the probability that she chooses a yellow sweet.
[1] Sonia chooses two sweets at random, without replacement, from her bag.
(i) Show that the probability that she chooses two green sweets is 3 . 38
(ii) Calculate the probability that the sweets she chooses are not both the same colour.
Step-by-step explanation:
there must be some typos here. but I try to address the right issues.
there is nothing under (a). so, really nothing to answer.
(b)
there are 20 sweets in her bag. 9 if the 20 are yellow.
so, the probability is the ratio of desired possibilities vs. total possibilities.
that is, tada! 9/20
that is the probabilty for Samira to pick a yellow sweet.
[1] (i)
again, 20 sweets to start with.
6 are green.
when she picks the first one, her probability to pick a green one is 6/20 = 3/10 = 0.3
and now, under the assumption that this came true, she picks another sweet.
this time she had only 19 left, and 5 of them are green.
so, this probabilty is 5/19
now both events need to happen for the case we are discussing. there is no overlapping, no ors, ifs and buts. it is just the product of both probabilities.
3/10 × 5/19 = 15/190 = 3/38
I think that is what the description asks for.
(ii)
that probability is
first selection is red and second is not red +
first selection is green and second is not green +
first selection is yellow and second is not yellow
so,
red and not red
5/20 = 1/4 red
15/19 not red (there are still 15 sweets of other colors in the bag, but again now only 19 total).
red and not red = 1/4 × 15/19 = 15/76 = 0.1974
green and not green
6/20 = 3/10 = green
14/19 = not green
green and not green = 3/10 × 14/19 = 52/190 = 26/95 =
= 0.2737
yellow and not yellow
9/20 = yellow
11/19 = not yellow
yellow and not yellow = 9/20 × 11/19 = 99/380 = 0.2606
so, now assuming up all 3 possibilities ("or" = sum) gives us the general possibility of selecting two different colors
= 0.7316
There are 50 teenagers at a swim meet. The ratio of locals to out-of-town
participants is 2:3. How many teenagers travelled from out-of-town to the swim
meet?
Answer:
There are 30 out of towners
Step-by-step explanation:
locals: out of town: total
2 3 2+3 = 5
There are 50 total 50/5 =10 so multiply each term by 10
locals: out of town: total
2*10 3 *10 5*10
20 30 50
There are 30 out of towners
Total teenagers = 50
Ratio = 2:3
Let the ratio people out of town be x
2x + 3x = 50
5x = 50
x = 10
Therefore 3× 10, 30 people out of town travelled to swim meet
Must click thanks and mark brainliest
Please help explanation if possible
Step-by-step explanation:
if we multiply gradient of the perpendicular line we are suppose to get -1the gradient of y=-x-2 is -1(gradient is the coefficient of x)therefore the gradient of other line is 1y =mx+c10=-5 +cc=15therefor the equation of the line is y=x+15What is the reason: if a+c=b+c then a=b
Step-by-step explanation:
Example 1:
a+c=b+c then a=b
First let the value of a and b be different (not equal)
a=5
b=7
c=10
a+c=b+c
5+10=7+10
15≠17
Example 2:
Let the value a and b be equal (the same)
a=5
b=5
c=10
a+c=b+c
5+10=5+10
15=15
So when,
a+c and b+c is equal, a and b are always equal.
Hope this helps ;) ❤❤❤
Answer:
a=b
Step-by-step explanation:
Reason:
a+c=b+c
a-b=c-c
c-c would be 0
if a-b=c-c=0
a-b=0
Only if a=b can a-b=0
You can also take it as:
b-a=c-c (a+c=b+c)
b-a=0=c-c
Therefore b=a
By the way even I am a BTS army
What is the equation for a circle centered at the origin (0,0)?
a) r sqt = x sqt + y sqt
b) r sqt =(/x+y) sqt
c) r= /x+y
d) r=x+y
Answer:
[tex]{ \sf{ \sqrt{r} = \sqrt{(x {}^{2} + {y}^{2} ) } }}[/tex]
Step-by-step explanation:
General equation:
[tex]{ \bf{ {x}^{2} + {y}^{2} + 2ax + 2by + c = 0}} \\ [/tex]
but a and b are 0:
[tex]{ \bf{ {x}^{2} + {y}^{2} = {r}^{2} }} \\ { \bf{ \sqrt{ {x}^{2} + {y}^{2} } = \sqrt{r} }}[/tex]
2p+8p>-20 help please ☺️
Answer:
p > -2
Step-by-step explanation:
2p + 8p > -20
10p > -20
10/10p > -20/10
p > -2
p is greater than -2
Which of the following choices is a linear function?
O f(x) = x2 – 3x+ 2
O f(x) = 3x3 – 3x + 2
O f(x) = -3x + 2
Answer:
f (x) = x2 - 3x + 2
Step-by-step explanation:
Answer:
f(x)=-3x+2
Step-by-step explanation:
The first one is a quadtratic function because it is in quadtratic form.
The second one is also not linear because it looks like a squiggly line. Sorry I forgot what they are called but I know it is not linear.
That leaves the last one is is linear and should be going down because there is a negative in front of the coefficient. It also has so exponent to prove why it is linear even further.
Hope this helps!
Bias can _____ be completely eliminated. a) always b)sometimes c) never
Answer:
the answer is c.
Step-by-step explanation:
c is the only reasonable option.
please help, not so good with this subject
Answer:
I believe the answer is d
Step-by-step explanation:
A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers.
In this case, since [tex]\sqrt{81}[/tex] can be simplified to 9 and 9 can be written as a fraction (9/1) it is a rational number.
I need help and fast!!!!
Answer:
H. b/a
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Step 1: Label our variables
y₂ = 2b
y₁ = b
x₂ = 2a
x₁ = a
Step 2: Plug into formula
m = (2b - b)/(2a - a)
Step 3: Evaluate
m = b/a
Answer:
b/a
Step-by-step explanation:
We have two points so we can use the slope formula
m = (y2-y1)/(x2-x1)
= ( 2b - b)/ ( 2a -a)
= b/a
1. What will be the sale price of the tennis racquet once the discount has been applied?
2. What is 25% of $12?
3. Which answer shows the discounted sale price for this tablet?
Answer:
150 is the answer of your question. I HOPE IT WILL HELP YOU.
Answer:
1) $150
2) $3
3) $150
Step-by-step explanation:
1) 25% times $200=$150
2) 25% times $12= $3
3) Half of $300 is $150, which 50% off is half off.
Please answer this question now
Answer:
298.3 square centimeters
Step-by-step explanation:
We are given
Slant height (l)= 14cm
Radius (r)= 5cm
Since we are given the slant height ,
the formula for surface area of a cone =
πrl + πr²
πr(l + r)
π = 3.14
Hence,
3.14 × 5(14 + 5)
3.14 × 5(19)
= 298.3 square centimeters
I am thinking of 3 consecutive numbers. The first is a multiple of 4, the second is a multiple of 5 and the third is a multiple of 6." What could the numbers be? Can you find 3 possible sets of numbers
Answer:
{4, 5, 6}, {64, 65, 66}, {124, 125, 126}
Step-by-step explanation:
x = 1st number
x + 1 = 2nd number
x + 2 = 3rd number
{4, 5, 6}, {64, 65, 66}, {124, 125, 126}
The possible set of numbers are {4,5,6}, {64,65,66} and {124,125,126}
What are consecutive number?Consecutive numbers are the numbers which follow each other in order from small to greater number.
Let three consecutive numbers are, x ,x+1 and x+2.
According to given condition,
The first number is a multiple of 4,
The second number is a multiple of 5,
And The second number is a multiple of 6.
Start from 4 and then try to find out sequence,
The numbers can be 4, 5 and 6.
Further, the number can be 64,65 and66
And The numbers can be 124,125 and 126
So, three sets of numbers are {4,5,6}, {64,65,66} and {124,125,126}
To know more about Consecutive number on:
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A triangle has sides of lengths 16, 63, and 65. Is it a right triangle? Explain.
Answer:
Yes
Step-by-step explanation:
If a triangle is a right triangle, the 3 side lengths will check out in the Pythagorean Theorem.
[tex]a^2+b^2=c^2[/tex]
where a and b are the legs and c is the hypotenuse.
The legs are the 2 shorter lengths and the hypotenuse is the longest length. The 3 side lengths are: 16,63 and 65. Therefore, 16 and 63 are the legs and 65 is the hypotenuse.
a=16
b=63
c=65
[tex]16^2+63^2=65^2[/tex]
Evaluate each exponent.
16^2=16*16=256
[tex]256+63^3=65^2[/tex]
63^2=63*63=3969
[tex]256+3969=65^2[/tex]
65^2=65*65=4225
[tex]256+3969= 4225[/tex]
Add 256 and 3969
[tex]4225=4225[/tex]
The statement above is true; 4225 is equal to 4225. Therefore, this is a right triangle because the side lengths check out when plugged into the Pythagorean Theorem.