On Mars, if you hit a baseball, the height of the ball at time "t" would be modelled by the quadratic function h=-1.85t^2+20t+1, where t is in seconds and h is in metres. When will the ball hit the ground?

Answers

Answer 1

Given that the height of the baseball is modeled by the equation:
h(t)=-1.85t^2+20t+1
where t is time in seconds and h is the height in meters
The time taken for the ball to hit the ground will be found as follows;
at the point when the ball hits the ground, h(t)=0, therefore our equation will be:
-1.85t^2+20t+1=0
solving the above quadratic equation for t we get:
t=[-b+/-sqrt(b^2-4ac)]/(2a)
substituting the values into the above formula we get:
t=[-20+\-sqrt(20^2+7.4)]/(-3.7)
t=-0.049771
or
t=10.8606
but since there is no negative time values we shall select:
t=10.8606
hence, we conclude that the time taken for the ball to hit the ground was:
t=10.8606 seconds

Related Questions

Evaluate. 5.4 - 1.3

Answers

5.4-1.3=4.1 is ur answer.

5.4 - 1.3= 4.1 is your answer

The distance between points (3, 7) and (x1, y1) is the square root of (x1 - 3)2 + (y1 - 7)2. A. True B. False

Answers

In analytical geometry, you can find the distance between two points situated on the same plane using the distance formula. The equation is

d = √[(x2-x1)^2+(y2-y1)^2]

This can be applied by first applying which is point 1 or point 2. Technically, it does not matter which is which, as long as you are consistent in pairing of the x,y coordinates. In this case, point 1 is (3,7) and point 2 is (x1,y1). Therefore, when you substitute the values, the distance would be

d = √[(x1-3)^2+(y1-7)^2]

The statement is TRUE.

Answer:

true

Step-by-step explanation:

took the test hope this helps

Start with a square piece of cardboard to produce a box that is 8 cm deep and whose capacity is exactly 1 liter. how large must the original square be

Answers

The formula for the volume of a square prism or box is calculated using the formula:

V = s^2 * h

where,

s is the measure of the sides of a square

h is the height of the prism or box = 8 cm

We are given that the volume capacity of the box must be 1 Liter. We know that 1 Liter is equivalent to 1000 cm^3. Therefore calculating for s:

1000 cm^3 = s^2 * (8 cm)

s^2 = 125 cm^2

s = 11.18 cm

Therefore the measure of the sides of the square must be about 11.18 cm. If the problem ask for the area of the square, A = s^2 = 125 cm^2.

The coordinates of a point are (4, –1). which matrix expression represents translating the point 3 units to the left and 7 units up?

Answers

The point (4, -1) is represented as:

| 4 |
|    |
|-1 |

Please, understand that the three vertical | represent a continuous line, which is the matrix representation.

The traslataion of 3 units to the left and 7 units up means that you have to add the matrix:

|- 3|
|    |
|7 |

So the representation is:

|4 |          |-3 |       |1 |
|    |    +    |    | =    |    |
|-1 |          |7 |       |6 |

Solve cos x +sqrt2 = -cos x for x over the interval (0,2pi) .

Answers

Final answer:

The equation cos x + sqrt(2) = -cos x is solved by combining like terms and isolating cos x, resulting in the solutions x = 3π/4 and 5π/4 over the interval (0,2π).

Explanation:

To solve the equation cos x + sqrt(2) = -cos x for x over the interval (0,2π), first combine like terms by adding cos x to both sides of the equation, resulting in:

2 cos x + sqrt(2) = 0

Isolate cos x by subtracting sqrt(2) from both sides:

2 cos x = -sqrt(2)

Divide both sides by 2 to solve for cos x:

cos x = -sqrt(2)/2

The value of cos x = -sqrt(2)/2 corresponds to angles in the second and third quadrants. So, the solutions for x in the interval (0,2π) are:

x = 3π/4, 5π/4

For large parties, a restaurant adds a 15% service charge to the bill. how much would be added to a bill of $638.40?

Answers

In restaurants, especially the fine dining ones, the bill includes a service charge. This payment is intended for the service given by the restaurant crew to make your experience in their premises worthwhile.

The service charge accounts for a fixed percentage of your total expenses. If your total expenses amount to $638.40, then the service charge would be equal to 638.4(0.15) = $95.7. Therefore, $95.7 will be added to your original bill.

Answer:

Service charge added to a bill of $638.40 is $95.76 .

Step-by-step explanation:

As given

For large parties, a restaurant adds a 15% service charge to the bill.

Bill of the parties is $638.40 .

15% is written in the decimal form

[tex]= \frac{15}{100}[/tex]

= 0.15

Thus

Service charge = 0.15 × Bill of the parties .

= 0.15 × $638.40

= $ 95.76

Therefore service charge added to a bill of $638.40 is $95.76 .

Triangle XYZ is a right triangle. Angle Z is a right angle and m∠X = 68°. What is m∠Y?

Answers

interior angles of a triangle add up to 180

< X + < Y + < Z = 180
68 + Y + 90 = 180
158 + Y = 180
Y = 180 - 158
Y = 22 <==

m∠Y is 22°

What is right triangle?

Right triangle is defined as a triangle which one angle is a right angle or two sides are perpendicular.

Given,

ΔXYZ is a right triangle

m ∠Z = 90°

m∠X = 68°

Let m∠Y = x,

∵ Addition of interior angles of a triangle is 180°

So, m∠X + m∠Y +m ∠Z = 180°

Subsitute the values,

68° + x + 90° = 180°

x = 180 - 158

x = 22

Hence, m∠Y = 22°

Learn more about right triangle here

brainly.com/question/6322314

#SPJ2

What is the image of point (0,3) for mapping (x,y) (x-2,y-3)

Answers

When it asks for the image, that means what are your new coordinates after doing the rules they give you. In this, the rule is to subtract 2 from your x value and subtract 3 from the y value. So you subtract 2 from 0 and subtract 3 from 3. This will give you the values to use for the x and y of your answer:)

What are the zeros of the polynomial function f(x) = x3 − x2 − 12x?

a. 0, −4, −3
b. 0, −4, 3
c. 0, 4, −3
d. 0, 4, 3

Legit answer plz
this is important

Answers

x^3-x^2-12x=0 factor out x

x(x^2-x-12)=0 factor parenthetical expression

x(x^2-4x+3x-12)=0

x(x(x-4)+3(x-4))=0

x(x+3)(x-4)=0

So x=-3, 0, 4

So c) 0, 4, -3

Answer:

The correct option is c.

Step-by-step explanation:

The given function is

[tex]f(x)=x^3-x^2-12x[/tex]

Taking out the common factors.

[tex]f(x)=x(x^2-x-12)[/tex]

Now, factorize the parenthesis.

[tex]f(x)=x(x^2-4x+3x-12)[/tex]

[tex]f(x)=x(x(x-4)+3(x-4))[/tex]

[tex]f(x)=x(x-4)(x+3)[/tex]

Equate the function equal to 0, to find the zeros of the polynomial function f(x).

[tex]f(x)=0[/tex]

[tex]x(x-4)(x+3)=0[/tex]

Using zero product property, we get

[tex]x=0[/tex]

[tex]x-4=0\Rightarrow x=4[/tex]

[tex]x+3=0\Rightarrow x=-3[/tex]

The zeros of the polynomial function f(x) are 0,4,-3. Therefore the correct option is c.

The rectangle below has an area of x^2-15x+56 x 2 −15x+56 x, start superscript, 2, end superscript, minus, 15, x, plus, 56 square meters and a length of x-7x−7x, minus, 7 meters. what expression represents the width of the rectangle

Answers

The expression that represents the width of the rectangle is x - 8

Area of a rectangle:area = lw

l = length

w = width

area = x² + 15x + 56

length = x - 7

Therefore,

x² - 15x + 56 = (x - 7) w

divide both sides by x - 7

w = x² - 15x + 56 / x - 7

w = (x - 7)(x - 8) / x - 7

w = x - 8

learn more on rectangle here: https://brainly.com/question/4529723

Given the function f(x) = log3(x + 4), find the value of f−1(3

Answers

First of all, find f ⁻¹ (x), or the inverse function like so:
y = log(3x + 12)
e^y = 3x + 12
3x = e^y - 12
x = 1/3 (e^y - 12)
Now, swap x and y:
f ⁻¹ (x) = y = 1/3 (e^x - 12)

Secondly and finally, substitute 3 into this eq'n:
f ⁻¹ (3) = 1/3 (e³ -12) = 2.695.....
so 2.695 (to 4 sig.figs/ 3 d.ps)
or if asked for an exact answer then it is just: 1/3 (e³ -12), which can be simplfied to 1/3e³ - 4.

Answer:

Step-by-step explanation:

Given : [tex]f(x) = log_3(x + 4)[/tex]

To Find: [tex]f^{-1}(3)[/tex]

Solution:

[tex]y = log_3(x + 4)[/tex]

Replace y with x and x with y

[tex]x = log_3(y + 4)[/tex]

[tex]3^x = y + 4[/tex]

[tex]3^x-4 = y [/tex]

So, [tex]f^{-1}(x)=3^x-4[/tex]

Now substitute x= 3

[tex]f^{-1}(3)=3^(3)-4 [/tex]

[tex]f^{-1}(3)=27-4 [/tex]

[tex]f^{-1}(3)=23[/tex]

Hence the value of [tex]f^{-1}(3)[/tex] is 23

You invest an initial $2,000 in an account that has an annual interest rate of 6%, compounded daily. How much money will you have in the account after 15 years? Round your answer to the nearest whole number.

Answers

The formula is
A=p (1+r/k)^kt
A future value?
P present value 2000
R interest rate 0.06
K compounded daily 365
T time 15 years
A=2,000×(1+0.06÷365)^(365×15)
A=4,918.84

Use Gauss-Jordan elimination to solve the following linear system: 5x – 2y = –2 –x + 4y = 4 A. (–6,–5) B. (2,0) C. (0,1) D. (–1,0)

Answers

Im pretty sure its A.

The answer is C.(0,1)

5x - 2y = -2 -x + 4y = 4

5(0) - 2(1) = -2 -(0) + 4(1) = 4

What is the answer and steps if x=6

Answers

If "[tex]x[/tex]" equals 6

[tex]Then....[/tex]

[tex]Because, \\ \sqrt{6-5=y}^2 \\ y^2 - 1 = 0 \\ \sqrt{6 - 5} = 1 \\ 1 \neq -1 \\ Answer(maybe) : y = 1 [/tex]

What is the approximate area of a circle whose radius is 7? steps?

Answers

Area is 3.14* Radius^2
So plug in your numbers to get
3.14 * 7^2 = 153.94^2

Please help with this question

Answers

I believe the answer is c there is no x value as there is no solution

A dresser contains six pairs of shorts one each in the colors, red, black, blue, green, khaki, and gray. The dresser also contains four shirts one each in the colors black, navy, red, gray. Melanie has to get dressed in the dark, so she grabs A pair of shorts and a T-shirt at random. What is the probability that she selects a green pair shorts and a gray T-shirt?

(First of all, Melanie, you should really get a lamp. And second why is it you own more shorts than shirts?)

Answers

Answer: 1/24

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

Work Shown:

A = selects green pair of shorts
B = selects gray t-shirt

P(A) = probability of selecting green shorts
P(A) = (number of green shorts)/(number of shorts total)
P(A) = 1/6
P(B) = probability of selecting gray t-shirt
P(B) = (number of gray t-shirts)/(number of t-shirts total)
P(B) = 1/4

P(A and B) = probability of selecting green shorts AND gray t-shirt
P(A and B) = P(A)*P(B) ... since A and B are independent events
P(A and B) = (1/6)*(1/4)
P(A and B) = (1*1)/(6*4)
P(A and B) = 1/24

Note: The fraction 1/24 is approximately equal to 0.041667

The line y = x − 6 y=x−6 has exactly one point in common with the circle x 2 + y 2 = r 2 x2+y2=r2. what is the value of r 2 r2?

Answers

Given:
y = x - 6 (1)
for the line
x² + y² = r² (2)
for the circle

When the line intercepts the circle, the x and y values will be equal.
Equate the values of y by substituting (1) into (2).
x² + (x - 6)² = r²
x² + x² - 12x + 36 = r²
2x² - 12x + 36 = r²

Answer: r² = 2x² - 12x + 36

Please help with this question! thanks :)

Answers

the tallest line in the graph is 3

so 3 would be the answer

WILL GIVE A BRAINLIEST IF UR CORRECT PLEASE HELP!!

Find three solutions of the equation.

y = –3x
a.
(3, –9), (0, 0), (–1, 4)
c.
(–2, 6), (3, –9), (2, –7)
b.
(0, 0), (–3, 7), (–2, 6)
d.
(–2, 6), (3, –9), (–4, 12)

Answers

A pair of numbers is a solution of y = -3x if the second number, y, is -3 times the first number, x.

What about the pair (-1, 4)? If you replace x with -1, you get y = -3(-1) = 3, not 4. So (-1, 4) is NOT a solution.

For each answer choice, you have to check all three of the given pairs.

(0, 0) is a solution because if x = 0, then y = -3(0) = 0.
(3, -9) is a solution because if x = 3, then y = 3(-3) = -9.

Can you finish it?

When a line has an undefined slope what will any two points on the line have in common

Answers

y-coordinate
Good luck and have a nice day.

I think it y or k coordinate most likely y coordinate

A student performed the following steps to find the solution to the equation x^2-2x-8=0. Where did the student go wrong?

Step 1. Factor the polynomial into (x-4) and (x-2)
Step 2. x-4=0 and x-2=0
Step 3. x=4 and x=3

A. The student did not make any mistakes, the solution is correct
B. in step 1
C. in step 2
D. in step 3

Answers

In step 1, because you want to find factors that multiply to -8 and add to -2. So the correct factorization is (x-4)(x+2). The student got the minus sign wrong.

(Then in step 3 the x=3 is also very wrong, but that looks more like a typo).
(Also, it should be x-4=0 OR x+2=0, there is no x for which both factors are 0 at the same time!)

Is the sqr root of 1.21 rational or irrational?

Answers

sqr root of 1.2 = 1.1 = 11/10

answer
rational

Identify the cross section shown.

circle

trapezoid

rectangle

pentagon

Answers

The cross section shown in the picture below include the following: B. rectangle.

In Mathematics and Euclidean Geometry, a rectangle refers to a type of quadrilateral or polygon in which its opposite sides are equal and all the angles that are formed are right angles.

Generally speaking, a circle has no edge or sides. A trapezoid is a type of quadrilateral that has one pair of parallel sides and one pair of non-parallel sides. Additionally, a pentagon is a regular polygon that comprises 5 sides.

By critically observing the cross section shown in the picture below, we can logically deduce that it represents a rectangle because its opposite sides are equal.

juanita and lauren are painting a circular mural on one wall of the community center. the area of the mural is 66 square meters. what is the radius

Answers

Final answer:

The radius of Juanita and Lauren's circular mural with an area of 66 square meters is approximately 4.58 meters.

Explanation:

Juanita and Lauren's mural has an area of 66 square meters, and we need to find the radius of the circular mural. To find the radius, we can use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius. Since the area of the mural is 66 square meters, we have:

66 = πr²

To solve for the radius (r), we divide both sides of the equation by π:

r² = 66 / π

Then, take the square root of both sides to get:

r = √(66 / π)

Using a calculator to compute this, we find:

r ≈ 4.58 meters (rounded to two decimal places)

Therefore, the radius of the circular mural is approximately 4.58 meters.

(30 Points) Paysly is studying a mosquito with a mass of 2.5×10^-6 kilograms and a housefly with a mass of 2×10^-5 kilograms. Which statement is true?

Answers

Housefly with a mass of 2x10^-5 kiligrams

[tex] \cfrac{2*10^{-5}}{2.5*10^{-6}} =0.8*10^1=8[/tex]

B.The housefly is 8 times the mass of the mosquito.

The masses, in kg, of some bags on an airplane are shown below: 7, 6.2, 6.1, 6.8, 6.1, 6.2, 6.8, 5.8, 6.2, 6.3 Jack made the following box plot to represent the masses: box plot shows minimum at 5.8, first quartile at 6.1, median at 6.3, third quartile at 6.8 and maximum at 7 Which of the following did Jack show incorrectly on his box plot?

Answers

the correct answer would the median it should be 6.2 not 6.3

Answer:

The value that Jack show incorrectly on his box plot is:

Median ( As he showed median is 6.3 but median is 6.2)

Step-by-step explanation:

We are given the mass of the bags as:

7, 6.2, 6.1, 6.8, 6.1, 6.2, 6.8, 5.8, 6.2, 6.3

On arranging the data in the increasing order we have:

5.8 6.1 6.1 6.2 6.2 6.2 6.3 6.8 6.8 7

There are a total of 10 data points.

Also, the minimum value is: 5.8

Maximum value is: 7

The median is the central tendency of the data and lie in the middle of the data.

Hence, Median lie between 6.2 and 6.2

Hence, Median=6.2

Also, the lower set of data is: 5.8 6.1 6.1 6.2

The lower quartile or first quartile is the median of lower set of data is: 6.1

Also, the upper set of data is: 6.3 6.8 6.8 7

The upper quartile or Third quartile is the median of lower set of data is: 6.8

Hence, he showed median incorrectly in the box plot.

The sum of 2 numbers is 7. if one number is subtracted from the other, the result is -1. find the numbers

Answers

Let the two numbers be x and y.

Given,

x + y = 7

x = 7 - y

Also given,

x - y = -1

7 - y - y = -1

-2y = -8

y = 4

x = 7 - y = 7 - 3 = 4

Hence, the numbers are 3 and 4.

For the polynomial 8x3y2 – x?y2 + 3xy2 – 4y3 to be fully simplified and written in standard form, the missing exponent on the

Answers

A polynomial in standard form has terms arranged with the highest exponent on leftmost side and the lowest exponent on the right end. The variables are also arranged alphabetically.

Therefore, the exponent of the x-term must be 2 for the polynomial to be fully simplified and written in standard form.

Answer: 2

Step-by-step explanation: this answer is 100% correct for edge.nuity

triangle abc is a right triangle. If AC = 4 and BC = 10, find AB. Leave your answer in simplest radical form.

Answers

The answer is 2 radical 21

Other Questions

When total demand outpaces actual output in the economy, the economy usually enters? ___________ represent the most important issues or the main ideas you want your audience to understand and remember about your message If you eat foods that are compact and _______, more can fit into your stomach with less discomfort. What is the preferred technique for removing secretions from the mouth and nose of a newborn who requires resuscitation? The two naturally occurring isotopes of copper are copper-63 and copper-65. how many neutrons are in one atom of copper-65? 29 34 36 65 During activity and at rest, which type of body tissue burns the most calories? A common stockholder has no guarantee of receiving any cash inflows, but receives what is left after all other claims on the firm's income and assets have been satisfied. a. True b. False The human body can protect itself from infection. the ability to resist infection related to the height of an object dropped from the top of a 320-meter building is given by h(t)= -5t^2+320. how long will it take the object to hit the ground Margaret leased her life estate in the family home to her grandson, jeff, for six years. margaret, the governing life of the life estate, died prior to the expiration of the six-year lease. upon margarets death, what is the status of jeff's lease When photons with a wavelength of 310. nm strike a magnesium plate, the maximum velocity of the ejected electrons is 3.45 105 m/s. calculate the binding energy of electrons to the magnesium surface? Three words that describe Hermione Granger A student has some 1 and 5 bills in his wallet. he has a total of 14 bills that are worth 50 how many of each type of bill does he hae As people age there are changes in cognitive function, personality, social relationships, and other areas. ____________ use life milestones, membership in cohorts, and exposure to historical events to understand aging. How many lines of symmetry does the figure have?0123 An illness that affects the brain and reduces a person's ability to cope, to adjust to every day life changes, or to get along with others is called a(n) A comma may be used correctly to do any of the following Except blank.A.) Join sentences when used with a conjunctionB.) Set off introductory word, clause, or phraseC.) Set off interrupting words or expressionsD.) Call attention to what follows it If the exact terms of the listing agreement are met, the listing broker is entitled to a commission, even if the: Pathogens can be transmitted through contact with surfaces like doorknobs and countertops. Please select the best answer from the choices provided. T or F qu es ms importante para ti, tener la tecnologa ms avanzada o conservar el medio ambiente? Steam Workshop Downloader