In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measured 40 cm tall and 90 cm wide. Find an equation of the parabola with its vertex at the origin.

Answers

Answer 1

Equation of a parabola that opens up with vertex at it's origin: x^2=4py
point on the parabola:(45,40)
equation:
45^2=4p(40)
4p=45^2/40=40.625
thus
x^2=(50.625)y

Answer: x^2=(50.625)y

Related Questions

What is sin (51)?
Answer Choices : 1.23 , 0.63 , 0.51 , 0.78

Answers

The correct answer is .78
Make sure your calculator is in degrre mode when doing these.

Using calculator I got 0.77714.....
so the answer is 0.78

Write the expression 5x+4x^2(2x+7)-6x^2-9x as a polynomial in standard form

Answers

5x + 4x²(2x + 7) - 6x² - 9x
5x + 8x³ + 28x² - 6x² - 9x

8x³ + 22x² - 4x

This can be simplified to:

2x(4x² + 11x - 2)

I don't know which of those answers you are looking for.

Answer:

8x^3 + 22x^2 - 4x

Step-by-step explanation:

5x+4x^2(2x+7)-6x^2-9x

Open the bracket

5x + 8x^3 + 28x^2 - 6x^2 - 9x

= 8x^3 + 28x^2 - 6x^2 - 9x + 5x

= 8x^3 + 22x^2 - 4x

In standard form, the polynomial 5x+4x^2(2x+7)-6x^2-9x is 8x^3 + 22x^2 - 4x

Wai recorded the length of each wire needed for a science project. What is the total length of wire needed?

Answers

the picture in the attached figure

we know that
the attached figure is a frequency table

Multiply each number of Length by its frequency
The product is the total amount for that value
Add the products
so
(1/8)*1+(1/4)*1+(1/2)*3+(3/4)*8+(1)*4+1 3/8*(2)
1 3/8----> 11/8
=(1/8)*1+(1/4)*1+(1/2)*3+(3/4)*8+(1)*4+11/8*(2)
=(1/8)+(1/4)+(3/2)+(6)+(4)+11/4
=(1+2+12+48+32+22)/8
=117/8-----> 14.625-----> 14 5/8 ft

the answer is
14.625 ft or 14 5/8 ft

Answer:

14 5/8

Step-by-step explanation:

multiply each number by it's frequency the product is the total value .

What is the area of a regular hexagon with a side length of 12 cm

Answers

The answer is about 374.
More exactly would be 374.12.
Hope this helps!

The answer is 72 cm. Because 12*6=72.

A bag contains 5 5 green marbles, 10 10 yellow marbles, 4 4 red marbles. two marbles are drawn without replacement which means that once the first marble is selected it is not put bag into the bag. it is not replaced. what is the probability of drawing a green marble then a red marble?

Answers

The probability of drawing a green marble will be 5/19, then for a red marble it will be 4/18 because there are less marbles in the bag. Also the probability of drawing a green or red marble the second draw will be the same probability. Hope this helps!

Total number of marbles = 5 + 10 + 4 = 19

Number of green marbles = 5
Number of red marbles = 4

P(Green, then red) = (4/19)(5/18) = 5/28

Answer: 5/28

Which set of ordered pairs could be generated by an exponential function?
(0, 0), (1, 1), (2, 8), (3, 27)
(0, 1), (1, 2), (2, 5), (3, 10)
(0, 0), (1, 3), (2, 6), (3, 9)
(0, 1), (1, 3), (2, 9), (3, 27)

Answers

For this case we must find the set of ordered pairs that form an exponential function.

When observing, the last set of ordered pairs is an exponential function of the form:

[tex]y = 3 ^ x[/tex]

For x = 0:

[tex]y = 3 ^ 0 = 1[/tex]

We have the ordered pair:

[tex](x, y): (0, 1)[/tex]

For x = 1:

[tex]y = 3 ^ 1 = 3[/tex]

We have the ordered pair:

[tex](x, y): (1, 3)[/tex]

For x = 2:

[tex]y = 3 ^ 2 = 9[/tex]

We have the ordered pair:

[tex](x, y): (2, 9)[/tex]

For x = 3:

[tex]y = 3 ^ 3 = 27[/tex]

We have the ordered pair:

[tex](x, y): (3, 27)[/tex]

Answer:

The set of ordered pairs that form an exponential function is:

[tex](0, 1), (1, 3), (2, 9), (3, 27)[/tex]

Answer:

Step-by-step explanation:

Share 450 in the ratio of 4:5

Answers

Let's represent the ratio in variable form:
4n + 5n = 450
9n = 450
n = 50
Now we multiply into the ratio:
200:250
Or
200 and 250

4 : 5 → 4 + 5 = 9

450 : 9 = 50

4 · 50 = 200
5 · 50 = 250

Answer: 200 and 250.

suzie divided a 3-pound bag of apples into 2 equal piles. How many lbs of apples are in each pile

Answers

3/2 = 1.5 Lbs per pile.

3 pounds divided by 2 piles = 1.5 pounds per pile

Final answer:

Suzie's 3-pound bag of apples divided into two equal piles will result in each pile weighing 1.5 pounds. This is a basic arithmetic problem often referred to as equal distribution.

Explanation:

Suzie is dividing a 3-pound bag of apples into two equal piles. This is a simple division problem where the total weight of apples (3 pounds) is distributed equally into two piles. Therefore, we simply divide the total weight by the number of piles.

To calculate the weight of apples in each pile, we divide the total weight (which is 3 lbs) by the number of piles (which is 2). So, 3 lbs ÷ 2 = 1.5 lbs. Each pile would weigh 1.5 lbs.

This type of problem is often referred to as an equal distribution problem in mathematics. It falls under the category of basic arithmetic and is typically taught in lower grades.

Learn more about Equal Distribution here:

https://brainly.com/question/34277990

#SPJ3

Evaluate the series 4 – 2 + 1 – 0.5 + 0.25 to S10. Round to the nearest hundredth.

Answers

The initial term of this geometric series is 4, and the common ratio is -1/2. The sum is given by

[tex]S_{n}=a_{1}\dfrac{r^{n}-1}{r-1}\\\\S_{10}=4\cdot \dfrac{(-\frac{1}{2})^{10}-1}{-\frac{1}{2}-1}=4\cdot \dfrac{(\frac{1}{1024}-1)}{(-\frac{3}{2})}\\\\=\dfrac{8}{3}\cdot \dfrac{1023}{1024}=\dfrac{341}{128}[/tex]

The sum is approximately 2.66.

Given v=(6,3) and w=(1,-2), what is the result of v-w

Answers

Here, v - w would be (6-1, 3-[-2]), or (5, 5).
I don't believe you need the word "result" here. At first I thought you'd meant "resultant." Here you're finding the "difference" v less w.

Final answer:

The result of v - w is (5, 5).

Explanation:

To find the result of v - w, we need to subtract the corresponding components of the two vectors. Given v = (6, 3) and w = (1, -2), we subtract their x-components and their y-components separately.

v - w = (6 - 1, 3 - (-2))

Therefore, v - w = (5, 5).

Learn more about Vector subtraction here:

https://brainly.com/question/4543959

#SPJ2

Find the surface area of each right regular pyramid. a pentagonal pyramid with base sides 1.5 meters, base area 3.9 m2, and slant height 4 meters

Answers

The answer is 18.9, i think, because there is a formula for finding the total surface area of such pyramids, but i used the simpler way of finding all the separate areas of each face using this information:

since the base area is 3.9 m2, we could just add that to the total at the end.

since the base edge is 1.5 m and the height is 4m, we could find the area of the face by doing (1.5 times 4)/2 which would give us 3m2.

Since there are 5 faces(pentagonal), we would multiply 3 times 5, and would get 15m total for all the triangle faces.

so to get the total surface area, you would add 15 + 3.9 (which was the base area) and get 18.9m2....

....;);) hope this helps

What are the factors of x^2-64

Answers

Difference Of Two Squares
a^2 - b^2 = a^2 - b^2
so
x^2-64
=x^2 - 8^2
= (x + 8)(x - 8)

Final answer:

The factors of x^2 - 64 are (x - 8) and (x + 8), derived by recognizing the expression as a difference of squares and applying the formula a^2 - b^2 = (a - b)(a + b).

Explanation:

The question asks about the factors of x^2-64. This expression is a difference of squares, which can be factored using the formula a^2 - b^2 = (a - b)(a + b). In this case, x^2 is a^2, and 64 is b^2, with b being 8 since 82 = 64. Applying the formula, we get:

x^2 - 64 = (x - 8)(x + 8)

This shows that the factors of x^2-64 are (x - 8) and (x + 8). This process of factoring by recognizing patterns, especially the difference of squares, is a useful algebraic skill when simplifying expressions or solving equations.

New York City gift shop sells miniature Statue of Liberty sculptures that are 7.8 inches tall. the scale of the model to the actual statue is 1:232. what is the height of the actual statue to the nearest foot?

Answers

the correct answer is 151

I am first going to try finding the tangent line at this point:

Take the derivative:
dy/dx = (3x^2 - e^x)/2y
Solve using (0, 1)
dy/dx = (0 - 1)/6 = -1/6

I believe that -1/6 is the slope of the tangent line, so the slope of the normal line should be +6, right?

Answers

Yep, you're correct!

[tex]e^x-x^3+y^2=10[/tex]

[tex]y^2=x^3-e^x+10[/tex]

Take the derivative of both sides.

[tex]2y \dfrac{dy}{dx} = 3x^2-e^x [/tex]

[tex]\dfrac{dy}{dx}= \dfrac{3x^2-e^x}{2y}[/tex]

Plug in (0, 3) and you get -1/6.

The derivative of a function at a certain point is the slope of the tangent of that point.

This is because the derivative is supposed to represent the rate of change for the function, and the slope of a line represents a constant rate of change. The rate of change of a function at a certain point is constant, so a line can be used to represent it. This line is the tangent line.

It is a property of perpendicular lines to have slopes that are negative reciprocals of another. The negative reciprocal of -1/6 is 6, so you are correct.

You are correct on both counts. (Though, I suspect you mean "Solve using (0, 3)."

The slope of the normal is 6.

Mind helping someone out?
I've kinda been stuck on this problem and it's my last math problem for the day.

Answers

[tex]\bf 2a^3b^2\sqrt[3]{12b}\implies 2a^3b^2\sqrt[3]{12b^1}\implies \sqrt[3]{(2)^3(a^3)^3(b^2)^3~~~~12b^1} \\\\\\ \sqrt[3]{2^3a^{3\cdot 3}b^{2\cdot 3}~~~~12b^1}\implies \sqrt[3]{8a^9b^6~~~~12b^1}\implies \sqrt[3]{(8)(12)a^9b^6b^1} \\\\\\ \sqrt[3]{96a^9b^{6+1}}\implies \sqrt[3]{96a^9b^7}[/tex]

The base of a triangle is 15 centimeters and its height is 6 centimeters. What is the area of the triangle?
a.21 cm2
b.45 cm2
c.90 cm2
d.180 cm2 Submit

Answers

Hoi!

To calculate the area, multiply 15 and 6, then divide the product by 2.

15 × 6 = 90

90 ÷ 2 = 45

The area of this triangle is 45.

A new medical test provides a false positive result for hepatitis 2% of the time that is a perfectly healthy subject being tested for hepatitis will test as being infected 2% of the time. And research, the test is given to 30 healthy (not having hepatitis) subjects. Let X be the number of subjects who test positive for the disease

A. What is the probability that all 30 subjects will appropriately test as not being infected?
B. What are the mean and standard deviation of X?
C. To what extent do you think this is a viable test to use in the field of medicine?

Answers

A) You need to use the binomial distribution, for which the probability of an event X is given by:
[tex]P(X) = \frac{n!}{k!(n-k)!} p^{k} (1-p)^{n-k} [/tex]
where:
n = total number of events
k = number of success we want
p = probability of success

Therefore, since the problem tells you that X is the number of subjects who test positive for the disease, you will have:

[tex]P(X) = \frac{30!}{0!(30-0)!} 0.02^{0} (1-0.02)^{30-0} [/tex]

= 1 · 1 · 0.98³⁰
= 0.5455

Hence, the probability of none of the 30 subjects testing positive to the desease is 54.55%

B) In a binomial distribution, the mean is given by the formula:
μ = n · p
   = 30 · 0.02
   = 0.6

And the standard deviation is given by the formula:
σ = √[n·p·(1-p)]
   = √[30·0.02·0.98]
   = √0.588
   = 0.77

Hence, the mean is 0.6 and the standard deviation is 0.77

C) This test is not very viable: 30 subjects are a sample too small compared to the population (millions of people who need to be tested), the probability of finding that all the 30 subjects are healty is only a little bit over 50%, the standard deviation is too high compared to the mean, and 2% of false positive is a percentage too high to consider the test viable.

please help asap 50 pts

Answers

C. If you were to graph the parabola, you would find that the vertex is at (19,361). Therefore, the answer is C.

Your answer should be C.

[tex]The\; vertex\; is\; at\; 19,361\; so\; your\; answer\;is\;c![/tex]

Bob can type 2 letters in 4 hours while Bill can do it in 6. How many hours would it take them, working together, to type six letters?

Answers

Bob's production rate is given by:
r1 = 2/4 = 1/2 letter / hour
The production rate of Bill is given by:
r2 = 2/6 = 1/3 letter / hour
Thus, the production rate of both is:
r1 + r2 = 1/2 + 1/3 = 5/6 letter / hour
Then, the production of 6 letters is given by:
rate * time = letters
(5/6) t = 6
t = (6/5) 6
t = 36/5 = 7 1/5 hours = 7hr 12 min
Answer:
it would take them, working together, to type six letters about:
7hr 12 min

Answer:

It would take them 7.2 hours.

Am I correct in thinking that the answer to this derivative problem is B?

dy/dx = y/x^2

dy/y = dx/x^2

ln y * ln c = -1/x

cy = e^(-1/x)

y = ce^(-1/x)

Answers

y ' = x(1+y)
dy/dx = x(1+y)
dy/(1+y) = x dx .... separate variables
int[dy/(1+y)] = int[x dx] ... apply integral to both sides
ln(1+y) = (1/2)x^2+C ... see note below
1+y = e^{(1/2)x^2+C}
1+y = e^C*e^{(1/2)x^2}
1+y = Ce^{(1/2)x^2}
y = Ce^{(1/2)x^2}-1

Answer is actually choice C (not choice B)

note: we would use absolute value bars for the natural log on the left side, but because y > -1, this means 1+y > 0. So there's no need to worry about if 1+y is negative

-----------------------------------------------------

Checking the answer:

y = Ce^{(1/2)x^2}-1
dy/dx = d/dx[ Ce^{(1/2)x^2}-1 ]
dy/dx = d/dx[(1/2)x^2]*Ce^{(1/2)x^2}
dy/dx = (1/2)*2x*Ce^{(1/2)x^2}
dy/dx = x*Ce^{(1/2)x^2} ... we get some messy expression

x*(1+y) = x*(1+Ce^{(1/2)x^2}-1)
x*(1+y) = x*Ce^{(1/2)x^2} .... we get the same messy expression as before

So this shows that dy/dx = x*(1+y) is a true equation for y > -1 and y = Ce^{(1/2)x^2}-1, which confirms the right answer.

The figure below is the two-dimensional net of a rectangular prism. What is the surface area of the prism it can be folded to form? Show your work.

8 square units
20 square units
24 square units
28 square units

Answers

see the picture with letters attached to better understand the problem

we know that
surface area=area A +area B+area C+area D+area E+area F

area A=area F
area B=area area D
area C=area E
so
surface area=[2*1]+[4*2]+[4*1]+[4*2]+[4*1]+[2*1]----> 28 units²

the answer is
28 units²

Answer:

the answer is d:)

Step-by-step explanation:

i took the quiz on edge and got 100:D

What is the measure of the angle?

Answers

Remember that the x-axis and the y-axis make an angle of 90° in the first quadrant. To find the measure of the angle we just need to add the smaller angle, 65°, and the right angle between the axis 90°:

Measure of the angle=65°+90°=155°

We can conclude that the measure of the bigger angle in the picture is 155°

The 65 degrees lies in the beginning of the 2nd quadrant where the second quadrant starts with 90 degrees.

So the angle is 90 degrees + 65 degrees = 155 degrees

The fourth one is the answer

Which represents a quadratic functionWhich represents a quadratic function? f(x) = 2x3 + 2x2 – 4 f(x) = –7x2 – x + 2 f(x) = –3x + 2 f(x) = 0x2 + 3x – 3

Answers

Answer:

[tex]f(x) = -7x^2 -x +2[/tex] represents a quadratic function.

Step-by-step explanation:

A polynomial of degree two is called quadratic function,

Also, degree of polynomial is the highest power of its monomial ( individual term with non zero coefficient ),

Since, [tex]f(x) = 2x^3 + 2x^2 -4[/tex] has degree 3,

⇒ [tex]f(x) = 2x^3 + 2x^2 -4[/tex] is not a quadratic function,

[tex]f(x) = -7x^2 -x +2[/tex] has degree 2,

⇒ [tex]f(x) = -7x^2 -x +2[/tex] is a quadratic function,

[tex]f(x) = -3x+2[/tex] has degree 1,

⇒ [tex]f(x) = -3x+2[/tex] is not a quadratic function,

[tex]f(x) = 0x^2 + 3x -3[/tex] has degree 1,

⇒ [tex]f(x) = 0x^2 + 3x -3[/tex] is not a quadratic function,

A group of 12 people attend a meeting. Every pair of people shook hands with each other. How many handshakes were there?

Answers

There are 12 people handshakes

The first person will shake the hand whit the other 11 people, the second with 10 because he has already shook his hand with the first, and so on.
So there will be 11+10+9+8+7+6+5+4+3+2+1=66 handshakes.

Hope this helped!

what is the following product 3 sqrt 2(5 sqrt 6-7 sqrt 3)

Answers

the answer in the attached figure

Answer:

[tex](30\sqrt{3}-21\sqrt{6})[/tex]

Step-by-step explanation:

We have to find the product of the expressions.

[tex]3\sqrt{2}(5\sqrt{6}-7\sqrt{3})\\[/tex]

= [tex]3\sqrt{2}\times 5\sqrt{6}-7\sqrt{3}\times 3\sqrt{2}[/tex] ( By distributive rule)

= [tex]3\times 5(\sqrt{2})(\sqrt{6})-7\times 3(\sqrt{3})(\sqrt{2})[/tex]

= [tex]15\sqrt{12}-21\sqrt{6}[/tex]

= [tex]15\sqrt{4\times 3}-21\sqrt{6}[/tex]

= [tex]30\sqrt{3}-21\sqrt{6}[/tex]

= [tex](30\sqrt{3}-21\sqrt{6})[/tex]

Quick need the answer!

Answers

The answer is “c” x=90.y=45

What is the remainder when the positive integer n is divided by 12 ? (1) when n is divided by 6, the remainder is 1. (2) when n is divided by 12, the remainder is greater than 5?

Answers

The remainder is 7.

The number n would be 31. In this case you could divide it by 6 and get 5 with a 1 remainder and then divide it by 12 and get 2 with a 7 remainder.

using his telescope, Tommy watches a bald eagle as it sits on the top of a cliff. the telescope is positioned so that the line of sight to the eagle forms a 38 degree angle of elevation. the telescope sits 1.3 m above the ground and the base of the telescope is 116 m away from the base of the cliff. to the nearest tenth of a meter, how high above the ground is the eagle?

Answers

the correct answer is B 91.9 m

I WILL MARK BRAINLIEST TO A CORRECT AND EXPLAINED ANSWER!!!!
Look at points C and D on the graph:

What is the distance (in units) between points C and D? Round your answer to the nearest hundredth.

A. 4.54 units
B. 5.00 units
C. 5.83 units
D. 34.00 units

Answers

C(-4;3)
D(1:0)

Image the right triangle between C, D and the point A(-4,0)

CA is 3-0=3; AD is 1-(-4)=1+4=5

CD is √3²+5²=√34=5.8309...

Answer:

Option C.

Step-by-step explanation:

Coordinates of the points C and D are (-4, 3) and (1, 0)

We have to find the distance CD.

Distance CD = [tex]\sqrt{(x-x')^{2}+(y-y')^{2}}[/tex]

CD = [tex]\sqrt{(1+4)^{2}+(0-3)^{2}}[/tex]

= [tex]\sqrt{25+9}[/tex]

= [tex]\sqrt{34}[/tex]

= 5.83 units

Therefore, Option C. distance CD = 5.83 units is the answer.

Suppose that there were a strong correlation between the variables n and p. Which of these is a true statement?
A. n may cause p.
B. p must cause n.
C. n must cause p.
D. n must not cause p.

Answers

Correlation is the measure of the type of association between two variables. There can be a positive, a negative or no association between two variables.

A correlation can be called association when it can be ascertained that the result in one variable is as a result of the result of the other variable. Though correlation is a condition for causation, but correlation does not imply causation.

Therefore, given that there were a strong correlation between the variables n and p, the true statement is "n may cause p".

Other Questions

Migrants who left the Great Plains behind during the 1930soften ended up living in poverty in crowded camps.gained great wealth and prosperity in California.had abundant food, clothing, and shelter.often ended up living comfortably in their own houses. #1. Complete each sentence below with the correct form of ser or estar.T _________ muy simptico #2. -Te duelen los ojos? -S, _______ mucho.#3. Write a complete sentence with the correct form of estar and a possessive adjective to say which family members the people are with right now.Sergio y usted (sobrino) _______#4. Complete each sentence below with the correct form of ser or estar.Nuestra casa _______ en la calle Bolvar. How does the elbow medical and lateral epicondylitis? In science class, students are learning about organic compounds. An acetic acid molecule is made of 2 carbon atoms, 2 oxygen atoms and 4 hydrogen atoms. What is the ratio of carbon atoms and hydrogen atoms The grey walls frowned on the plain below" is _____. simile, symbol, imagery, personification, metaphor. What are the major functions of the respiratory system? Under the normal curve, approximately what percent of scores fall between and -1 to +1 standard deviations around the mean? Generalize where orwell places the party and its beliefs in the stream of history Which explains how the Patriot Act has helped stop many terrorist plots ? Los estudiantes ocho horas por dis (dormir) Food preparation equipment shall be certified or classified for sanitation by Which formula represents a molecule of 2 - chlorobutane? A rectangular room measures 12 ft by 17 fr.Find the cost of installing a wall paper border around the room if the border costs $0.64 cents per foot How was the U.S. governments response to the Great Depression different after Franklin Roosevelts election than it was before?A. It began encouraging citizens to buy bonds in order to raise money.B. It took out loans from foreign countries experiencing hyperinflation. C. It attempted to save money by cutting government and military jobs. D. It increased spending based on Keynesian economic principles. Which form of commonly used state taxation adheres to the principle of sound taxation cited in this excerpt? What were United Nations inspectors looking for in Iraq prior to the Iraqi War? 1. The terrorist Osama bin Laden 2. Refugees from the Iran War 3. Weapons of mass destruction 4. An alleged slavery ring A key reason older adults suffer bone fractures is as a result of William gave 4 football cards to each of the 6 friends.Suppose he had 54 cards left. Write and solve an equation to find how many cards each friend a initially had. An ice cream cone has a diameter of 2 inches and a height of 5 inches. What is the volume of the ice cream cone? Round your answer to the nearest hundredth. (Use 3.14 for .) 10.47 in.3 20.93 in.35.23 in.3 15.7 in.3 This is an exit strategy when an entrepreneur sells his or her company to its managers