A catapult launches a boulder with an upward velocity of 184 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h= -16t^2 + 184t + 20. How long does it take the boulder to reach its maximum height? What is the boulder's maximum hieght

Answers

Answer 1

For this case we have the following equation:
h = -16t ^ 2 + 184t + 20
Deriving we have:
h '= -32t + 184
We equal zero and clear t:
-32t + 184 = 0
32t = 184
t = 184/32
t = 5.75 s
Then, the maximum height is given by:
h (5.75) = -16 * (5.75) ^ 2 + 184 * (5.75) + 20
h (5.75) = 549 feet
Answer:
It takes the boulder to reach its maximum height about:
t = 5.75 s
the boulder's maximum hieght is:
h (5.75) = 549 feet

Answer 2

Answer:

The answer should be C.

Related Questions

The function f(x)=35+15x represents the amount of money, in dollars, mr. lewis earns for working x hours. how much money does mr. lewis earn for working 25 hours?

Answers

410.

You can get this by plugging in the 25 for x in the above equation.

Final answer:

By substituting x with 25 in the equation f(x)=35+15x, we find out that Mr. Lewis would earn $410 for working 25 hours.

Explanation:

The function provided is f(x)=35+15x, which represents the amount of money Mr. Lewis earns for working x hours. In the case of Mr. Lewis working for 25 hours, we substitute the value of x with 25 in the equation to calculate his earnings. Therefore, f(25)=35+15(25)=35+375=$410. Hence, Mr. Lewis would earn $410 for working 25 hours.

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A piggy bank contains the same number of quarters, nickels, and dimes. the coins total $4.40. how many of each type of coin does the piggy bank contain?

Answers

Let the number of each coin be n.

The total sum of these coins is $4.40. So we can write:

n Nickles + n Dimes + n Quarters = 4.40

0.05n + 0.10n + 0.25n = 4.40

0.40n = 4.40

n = 11

So this means, there are 11 coins of each type.

Answer: 11 of each type

Step-by-step explanation:

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Ratios

Ms. Grande brought 24 apples and 18 oranges for a party after a class play. Find the ratio of the number of apples to the total number of fruits Ms. Grande bought.

There are 44 chicken and fish filets altogether in a freezer. There are 12 chicken filets. Which is the ratio of the number of chicken filets to the number of fish filets in the freezer?

There were 12 boys and 18 girls in a class. Then, 3 more boys joined the class and 2 girls left. What is the ratio of the number of boys to the number of girls in the class now?

Monica had $42 and Naomi had $18 at first. Monica then gave $6 to Naomi. What is the ratio of the amount of money Monica has to the amount of money Naomi has in the end?

Answers

1) 6:3
2) 11:3
3) 15:16
4) 3:2

Final answer:

To find the ratio of the number of apples to the total number of fruits, divide the number of apples by the total number of fruits. Simplify the ratio by dividing both numbers by their greatest common factor. For the ratio of chicken filets to fish filets, divide the number of chicken filets by the total number of filets. Simplify the ratio if possible. To find the ratio of boys to girls, determine the new number of boys and girls after some changes. For the ratio of money, calculate the amounts each person has and simplify the ratio.

Explanation:

To find the ratio of the number of apples to the total number of fruits, we divide the number of apples (24) by the total number of fruits (24 apples + 18 oranges = 42). This gives us a ratio of 24:42. We can simplify this ratio by dividing both numbers by their greatest common factor, which is 6. So the simplified ratio is 4:7.

For the second question, we need to find the ratio of the number of chicken filets to the number of fish filets. There are 12 chicken filets and a total of 44 filets in the freezer. So the ratio is 12:44. This can also be simplified by dividing both numbers by 4, giving us a simplified ratio of 3:11.

In the third question, we start with 12 boys and 18 girls. Then, 3 more boys join and 2 girls leave. So the new number of boys is 12 + 3 = 15, and the new number of girls is 18 - 2 = 16. The ratio of boys to girls is therefore 15:16.

In the fourth question, Monica has $42 and Naomi has $18. When Monica gives $6 to Naomi, Monica will have $42 - $6 = $36 left, and Naomi will have $18 + $6 = $24. The ratio of the amount of money Monica has to the amount of money Naomi has is 36:24, which can be simplified to 3:2.

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What is the surface area of the prism? Include steps.

Answers

First things first. This is a rectangular prism, so it's faces are all rectangles.

Area of a rectangle: Area = Length x Height

- Rectangular Prism Dimensions:

Length: 3m
Width: 4m
Height: 2m

To calculate the surface area of a rectangular prism we first need to realize that he has 3 pairs of equal rectangles.

- The first pair (Photo 1):

Two rectangles with the same measure, so we can say that the area of this pair is: (L x H) x (L x H) or 2 x (L x H).

-> Area (Pair 1) = 2 x (3 x 2) = 2 x 6 = 12m^2

But if we will do the same thing to 3 different pairs, we can describe that:

- Total Surface Area (At):

At = 2 x (L x H) + 2 x (L x H) + 2 x (L x H)

-> At = 2 x ((L x H) + (L x H) + (L x H))

So now, just put the values inside de formula,

- Pair 1: Length = 3m ; Height = 2m

- Pair 2: Length = 4m ; Height = 2m

- Pair 3: Length = 4m ; Height = 3m

*I know that this pair doesn't have a "real Height" but this doesn't change anything when solving, you can consider the 4m as height and the 3m as length or vice versa, the order of the factors doesn't change the product.

-> At = 2 x ((3 x 2) + (4 x 2) + (4 x 3))
-> At = 2 x (6 + 8 + 12)
-> At = 2 x (26)

-> At = 52 m^2

How many solutions are there for the system of equations shown on the graph?

No solution

One solution

Two solutions

Infinitely many solutions

Answers

If one line on top of the other then Infinitely many solutions.

If the lines are parallel then No solution.

Answer:

D. Infinitely many solutions

Step-by-step explanation:

We have been given an image of two lines on coordinate plane. We are asked to find the number of solutions for our given lines.

Upon looking at our given graph, we can see that both lines are same. Since both lines coincide, therefore, each point on the line will be solution of our given lines.

Therefore, our given lines will have infinitely many solutions and option D is the correct choice.

triston is baking specity bread for the school bake sale. she has 10 1/2 cups of flour. the recipe for 1 loaf of bread calls for 2 1/3 cups of flour. How many whole loaves of bread can she make.

Answers

Triston can make a total of 4 loafs

Triston can make 4 whole loaves of bread using her 10 1/2 cups of flour. This was determined by dividing the total flour available by the flour required per loaf. Fractional or partial loaves are not counted.

To determine how many whole loaves of bread Triston can make, we need to perform a simple division of the total amount of flour by the amount required for one loaf.

First, let's convert the mixed numbers to improper fractions:

10 1/2 cups of flour = 21/2 cups of flour2 1/3 cups of flour = 7/3 cups of flour

Next, we will divide the total flour by the flour needed per loaf:

(21/2) ÷ (7/3) = (21/2) × (3/7) = (21 × 3) / (2 × 7) = 63/14 = 4.5 loaves

Since we can only make whole loaves, Triston can make 4 whole loaves of bread.

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What is the average rate of change of the function over the interval x = 0 to x = 6? f(x)=2x−1
____
3x+5

Answers

[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\ -------------------------------\\\\ f(x)=\cfrac{2x-1}{3x+5} \qquad \begin{cases} x_1=0\\ x_2=6 \end{cases}\implies \cfrac{f(6)-f(0)}{6-0}[/tex]

[tex]\bf \cfrac{\left[ \frac{2(6)-1}{3(6)+5} \right]~~-~~\left[ \frac{2(0)-1}{3(0)+5} \right]}{6}\implies \cfrac{\left[ \frac{11}{23}\right]~~-~~\left[-\frac{1}{5} \right]}{6} \\\\\\ \cfrac{\frac{11}{23}+\frac{1}{5}}{6}\implies \cfrac{\quad \frac{78}{115}\quad }{\frac{6}{1}}\implies \cfrac{78}{115}\cdot \cfrac{1}{6}\implies \cfrac{13}{115}[/tex]

In the circle below, radius mn = 1.4 m and mlmn = 52°. determine the length of arc ln. round your answer to the nearest tenth and use π = 3.14.

Answers

The arc length is given by:
Arc length=θ/360×π×d
θ=52
d=2×1.4=2.8 m
thus
Arc length will be:
52/360×3.14×2.8
=1.27 m

Answer:

1.27 is the answer

Step-by-step explanation:

Stan's cookie recipe makes 242424 cookies and calls for exactly 384384384 sprinkles. He is wondering how many sprinkles (p)(p)left parenthesis, p, right parenthesis he will need to make 606060 cookies. He assumes each cookie will have the same number of sprinkles. How many sprinkles does Stan need to make 606060 cookies?

Answers

If these numbers are correct:

For every 242,424 cookies he needs 384,384,384 sprinkles. So how many sprinkles does he need for 606,060 cookies?

242,424/384,384,384 = 606,060/x

384,384,384 * 606,060 = 242,424 * x

232,959,999,767,040 = 242,424 * x

960,960,960 = x

To find the number of sprinkles needed for 60 cookies, determine the number of sprinkles per cookie by dividing 384 by 24, which is 16. Then multiply 16 by 60 to get 960 sprinkles.

The question asks us to calculate the number of sprinkles (p) needed for 60 cookies when a recipe for 24 cookies calls for 384 sprinkles.

To solve this, we start by finding the number of sprinkles per cookie:

Divide the total number of sprinkles (384) by the number of cookies in the recipe (24).Multiply the result by the number of cookies we want to make (60).

Therefore:

384 sprinkles ÷ 24 cookies = 16 sprinkles per cookie 16 sprinkles per cookie × 60 cookies = 960 sprinkles for 60 cookies

Stan would need 960 sprinkles to make 60 cookies.

Sara loves to go hiking this weekend she hiked 3 miles on Monday 4 miles on Tuesdays and 3 miles on Thursday .last week Sara hiked 8 miles. How many more miles did Sara hike this week than last week

Answers

This week: 4+3+3 = 10
Last week: 8
Difference: 10 - 8 = 2
Sarah walked two more miles this week than last week.

Answer:

2 miles

Step-by-step explanation:

Sara loves to go hiking.

She hiked 3 miles on Monday 4 miles on Tuesdays and 3 miles on Thursday.

Last week Sara hiked 8 miles

This week sara hiked = Monday + Tuesday + Thursday

= 3 + 4 + 3

= 10 miles

Last week hiked = 8 miles

Difference in two week hiked by Sarah = 10 - 8

= 2 miles

So, Sarah hike 2 miles more than last week.

For what value of a does (1/9)^a+1 = 81^a+1 x 27^2-a?

Answers

The answer for a should equal to -3 in the equation given

Solution:
(1/9)^(a+1)=81^(a+1) x 27^(2-a), then the answer would be a=-3.

Answer:

-4

Step-by-step explanation:

Next time use the internet :)

Stephanie rdes her bike 2 miles to the post office, and then another 50 yards to the train station. How many yards long was her trip?

Answers

There are 1,760 yards in a mile.

Multiply 1,760 by 2 = 3,520

Add 50 to 3,520 = 3,570

Stephanie's trip was 3,570 yards long.

geometry question!! 50 POINTS

Answers

Volume ratio is 686/250 = 2.74
Area ratio is
250 yd^3
radii? First solid has vol 250 yd^3 = (4/3)*pi*r^3; find r^3 = --------------
(4/3)*pi

Then r^3 = 187.5 yd^3, and r = 5.724 yd

Second solid has vol 686 yd^3 .... Please find the radius R using precisely the same method.

Then calculate the ratio of the surface areas of the 2 solids:

Solid 1 surface area 4*pi* R^2
----------------------------- = --------------- where R is the radius of the larger
Solid 2 surface area 4*pi*r^2 solid and r is the radius of the smaller

R^2
This ratio comes out to ----------
r^2

Scale factor? Obviously one solid is larger than the other. We have to figure out by how much, by comparing volumes. Actually, we've already done that (see above). We could also determine how much larger R is than r. That, too, would give us the scale factor.

Answer:

2.74

Step-by-step explanation:

Simplify i to the power 41

Answers

[tex]\bf \textit{recall that }i^4=1\\\\ -------------------------------\\\\ i^{41}\implies i^{40+1}\implies i^{40}\cdot i^1\implies i^{4\cdot 10}\cdot i\implies (i^4)^{10}\cdot i\implies 1\cdot i\implies i[/tex]

Answer:

It should be just "i"

students have 40 minuets to complete 50 questions on the aspire ___ test

A) math

B) reading

C) english

D) writing

Answers

I believe the answer to this is C. English.

Answer:

english C)

Step-by-step explanation:

sabendo que x2 + y2=74 e que xy=35, calcule valor de (x - y2)2

Answers

To solve this problem you must apply the proccedure shown below:

1. You have the following information given in the problem above:

- x²+y²=74
xy=35

2. Therefore, you have that (x-y)² is:

=(x-y)²
=x²-2xy+y²
=(x²+y²)-2xy

3. When you substitute the values given in the problem, you obtain:

=74-2(35)
=74-70
=4

4. Therefore, as you can see, the correct answer is: 4

Rewrite 0.85 as a fraction in lowest terms.

Answers

17/20 because it would be 85/100 and 5 goes into 85 17 times and 5 goes into 100 20 times.

simply and shortly put, we "use as many zeros at the bottom as there are decimals and lose the dot", what the dickens does that mean?

well, 0.85 has two decimals, so we use two zeros,00, at the bottom of the fraction and lose the dot, let's do so,

[tex]\bf 0.\underline{85}\implies \cfrac{085}{1\underline{00}}\implies \cfrac{85}{100}\implies \stackrel{simplified}{\cfrac{17}{20}}[/tex]

Factor each polynomial. Check your answer by distributing. 2x^2+5x+2

Answers

The answer of the factored polynomial is
(X+2)(2x+1)

What is 6.8 rounded to the nearest ones place?

Answers

6.8 ≈ 7

6.8 is nearer to 7 than to 6. so, 6.8 ≈ 7

↓
|------|------|------|------|------|------|-----|------|------|------|
6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7

Answer: 7

If you shift the linear parent function, f(x)=x, down 7 units what is the equation of the new function

Answers

To solve this problem you must apply the proccedure shown below:

1- You have that following parent function (the most basic function of the linear functions) given in the problem above:

f(x)=x

2- When you graph this parent function, you obtain the graph shown in the figure attached.

3- If you shift the linear parent function 7 units down, you have the following new function:

f(x)=x-7

4- The graph of the new function is shown in the second figure attached.

The answer is: f(x)=x-7

f(x)=x-7 is indeed the correct answer.just got it right

Is the mean value theorem for integrals the same as the mean value thoerem for derivatives?

Answers

Yes. The two theorems are equivalent statements given that the fundamental theorem of calculus is true.

Answer:

a^2 + b^2 =C^2

Step-by-step explanation:

Write an equation and solve: Twice a number, increased by 3 is 7.

Answers

the equation is 2x+3=7
2x +3=7
-3 -3
2x=4
divide both sides by 2
x=2
the answer is 2

A bus covered the 400-km distance between points a and b at a certain speed. on the way back the bus traveled at the same speed for 2 hours and then increased the speed by 10 km/hour until it reached a, thus spending 20 fewer minutes on the return trip. how long did the return trip take?

Answers

Let the speed going to B be x, the time taken be t and distance is 400 km
xt=400,
On the way back, the 2x+(x+10)(t-7/3), where it was total time minus 2 hours already driven minus 1/3 of hour, the 20 minutes.
2x+xt-(7/3)x+10t-70/3=400
2x+400-(7/3)x+10t-70/3=400
thus
-(1/3)x+4000/x=70/3
multiplying through by x we get:
-(1/3)x^2-(70/3)x+4000=0
x^2+70x-12000=0
x=(1/2)(-70+/-sqrt52900)
x=80 kmp
thus:
it took 5 hours to make the first trip
on way back 2 hours at 80 kph which means he traveled for 160 km at this speed
2 h 40 min at 90 k/h=90*8/3=240 km

The speed going to B is x, the time t and the distance, 400 km.

xt=400, x kph and t in hours

on the way back, the 2x+(x+10)(t-7/3), where it was total time minus 2 hours already driven minus 1/3 of an hour, the 20 minutes.

2x+xt-(7/3)x+10t-70/3=400

2x+400-(7/3)x+10t-70/3=400, 400 cancels, t=400/x

-(1/3)x+4000/x=70/3

multiply by x

-(1/3)x^2-(70/3)x+4000=0

x^2+70x-12000=0

x=(1/2)(-70+/- sqrt 52900); sqrt term=230

x=80 kph

took 5 hours to go there

on way back 2 hours at 80 kph=160 km

2h40m at 90kph=90*8/3=240 km

They add to 400 km.

The return trip took 4h40m

Find the first six terms of the sequence. a1 = -3, an = 2 ● an-1

Answers

The first term of the sequence is -3.

According to the formula each next term will be obtained by multiplying the previous term by 2.

So, next terms will be:

Second term = 2 x First Term = 2 x (-3) = - 6

Third term = 2 x (-6) = -12

Fourth term = -24

Fifth term = -48

Sixth term = -96

So, the sequence will be:

-3, -6, -12, -24, -48, -96 ...

Use double angle to rewrite 12sinxcosx

Answers

Final answer:

To rewrite 12sinxcosx using the double angle formula, multiply by (1/2) and use the formula for sin(2x) to obtain the answer of 12sin(2x).

Explanation:

To rewrite 12sin(x)cos(x) using the double angle formula, we need to know the formula for sin(2x) and cos(2x). The double angle formula for sine is sin(2x) = 2sin(x)cos(x), and for cosine it is cos(2x) = cos^2(x) - sin^2(x). Let's use these formulas to rewrite the expression:

12sin(x)cos(x) = 12 * (1/2) * 2sin(x)cos(x), since 1/2 is the value of cos^2(x) - sin^2(x).12 * (1/2) * 2sin(x)cos(x) = 6 * 2sin(x)cos(x).6 * 2sin(x)cos(x) = 12sin(2x). This is our final answer, using the double angle formula to rewrite the original expression.

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Final answer:

The expression 12sinxcosx can be rewritten as 6sin(2x) by using the double angle formula for sine.

Explanation:

The expression 12sinxcosx can be rewritten using the double angle formula for sine, which is sin(2a) = 2sina ⋅ cosa. By comparing this to the given expression, we can see that it is in the form of the right-hand side of the double angle formula, where a is equivalent to x. Therefore, the expression can be rewritten as 6sin(2x). Such double angle formulae are available for other trigonometric ratios as well.

In circle H, HJ¯¯¯¯¯ is a radius and JK¯¯¯¯¯ is a tangent segment. Which statement must be true?

A) HJ=JK
B) ∠HJK is an obtuse angle.
C) HJ=HK
D) ∠HJK is a right angle.

Answers

ITS RIGHT ANGLE YALL I FOUND IT

The Answer is D.

D) ∠HJK is a right angle.

On average, Scott drinks ½ of a 6-ounce glass of water in ⅔ hour. How much water does he drink in an hour?
a) 0.75 ounces b) 2 ounces c) 4.5 ounces d) 9 ounces

Answers

1/2 a 6 ounce glass is 3 ounces. He drinks 3 ounces in 2/3 of an hour.

3/2 = 1.5. He drinks 1.5 ounces in one third of an hour. 1.5 * 3 = 4.5

C. 4.5 ounces in one hour

24 inches is 250% of what length

Answers

24 inches is 250% of 9.6 inches, if that's not one of the options google "250% of (insert one of the options here)

The answer is: " 9.6 inches " .
________________________________________________________
Explanation:
________________________________________________________

24 = 250/100 * x ;

24 = 2.5 x ;

↔ 2.5 x = 24 ;

2.5 x / 2.5 = 24/ 2.5 ;

x = 9.6 ;

The answer is: " 9.6 inches " .
_________________________________________________________

Find the value of x.
The polygons are similar, but not necessarily drawn to scale.

Answers

[tex] \dfrac{12}{40} = \dfrac{3}{x} [/tex]

Cross multiply:
[tex]12x = 3 \times 40[/tex]

Evaluate RHS:
[tex]12x = 120[/tex]

Divide both sides by 12:
[tex]x = 10[/tex]

Answer:

[tex]x=10 units[/tex]

Step-by-step explanation:

Given: The polygons ABCD and JKLM are similar.

To find: The value of x.

Solution: Since, the given polygons are similar, therefore using the similarity condition, we have

[tex]\frac{AD}{JM}=\frac{CD}{LM}[/tex]

Substituting the given values, we get

[tex]\frac{12}{40}=\frac{3}{x}[/tex]

On cross multiplying, we get

[tex]\frac{3\times40}{12}=x[/tex]

[tex]x=10 units[/tex]

Therefore, the value of x is 10 units.

Use the table to determine the following probabilities. The probability that a randomly chosen person from this group has type B is . The probability that a randomly chosen person from this group has type AB is . The probability that a randomly chosen person from this group has type B or type AB blood is .

Answers

Use the table to determine the following probabilities.

The probability that a randomly chosen person from this group has type B is 3/25

The probability that a randomly chosen person from this group has type AB is 1/25

The probability that a randomly chosen person from this group has type B or type AB blood is 4/25

The probability that a randomly chosen person is:

first person: 3/25

second person: 1/25

third person: 4/25

Probability

Use the table to determine the following probabilities.

The probability that a randomly chosen person from this group has type B is 3/25.

The probability that a randomly chosen person from this group has type AB is 1/25.

The probability that a randomly chosen person from this group has type B or type AB blood is 4/25.

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