Solve each question (a, b, c) and show your work. Thank you <3

Solve Each Question (a, B, C) And Show Your Work. Thank You &lt;3

Answers

Answer 1

Answer:

a) 112 ft.

b) 256 ft. and 3 seconds

c) 7 seconds

Step-by-step explanation:

a) The model rocket is lauched from a platform. To find the height of the platform, we need to find h when t = 0, because the rocket starts from the platform when no time has elapsed:

[tex]h=-16t^2+96t+112[/tex]

[tex]h=-16*0+96+0+112\\\\h=112[/tex]

Therefore, the height of the platform is [tex]\fbox{112}[/tex] ft.

b) If you learned calculus before, we can find the maximum height easily. We take the derivative of h and set it equal to 0. Remember, the derivative of a function is simply the slope of it at an instantaneous point. At the maximum point of a function, it's slope equals to 0.

[tex]h=-16t^2+96t+112\\h'=-32t+96+0\\h'=-32t+96[/tex]

Ok! Let's set the derivative of h to 0!

[tex]0=-32t+96\\-96=-32t\\t=3[/tex]

We now know how long it takes for the rocket to reach maximum point (t represents seconds), but we also need to find the maximum height. We can simply plug our t=3 into the function of h, because t=3 is the point where the rocket reaches maximum height:

[tex]h(3)=-16(3)^2+96*3+112\\h(3)=-144+288+112\\h(3)=256[/tex]

The maximum height of the rocket is [tex]\fbox{256}[/tex] ft and the rocket takes [tex]\fbox{3}[/tex] seconds to reach the height.

c) The rocket reaches the ground when h equals 0. We can set up the equation to solve for it:

[tex]h=-16t^2+96t+112\\0=-16t^2+96t+112\\0=-16(t+1)(t-7)\\0=(t+1)(t-7)\\t=-1, t=7[/tex]

However, time can never be negative.

Therefore, it takes the rocket [tex]\fbox{7}[/tex] seconds to reach the ground.

I hope this helps! Let me know if you have any questions :)


Related Questions

Select all the numbers that are rational.

Answers

Answer:

-14/2 , 1/3 and 0.325 are the rational numbers

Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.

Answers

Given:

In the given circle, the measure of major arc TV is 220 degrees.

To find:

The measure of angle TUV.

Solution:

In a circle, the measure central angle of arc is equal to its corresponding arc measure and according to central angle theorem, the measure of subtended angle on an arc is half of the measure of central angle of that arc.

So, the measure of subtended angle is half of the measure of its corresponding arc.

[tex]m\angle TUV=\dfrac{1}{2}\times \text{Measure of major arc TV}[/tex]

[tex]m\angle TUV=\dfrac{1}{2}\times 220^\circ[/tex]

[tex]m\angle TUV=110^\circ[/tex]

Therefore, the measure of angle TUV is 110 degrees.

Given the line segment AB=36 cm and a point C on directed line segment AB that partitions AB into the ratio 1 to 2, find the lengths of the line segments AC and CB

Answers

the lengths of AC is 24 and CB is 12

Explanation: so we know that the ratio is 2:1, which can be expressed as 2x and x.

we know that 2x+x must equal 36, so we can set up the equation 2x+x=36

we then add 2x to x to make 3x=36, divide both sides by 3, and get x=12.

now that we know what x equals, 2(12) is 24 and (12) is 12 :)

Graph the Image of AKLM after a translation 1 unit left and 7 units up.​

Answers

You are basically just moving the graph as a whole, so k will be at (3.10), m will be at (1,6) and l will be at (7,10)

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Pick a point (such as K, L, or M). Count one grid square to the left and 7 up. That is its new location.

Nadia has $1.35 in nickels. How many nickels
does she have?

Answers

Answer:

27 Nickels

Step-by-step explanation:

Divide 1.35 by 0.05

= 27

Which of these strategies would eliminate a variable in the system of equations?
-7x + 2y = 5
3x - 5y = -5

A. Add the equations
B. Multiply the top equation by 3, multiply the bottom equation by 7, then add the equations.
C. Multiply the top equation by 5, multiply the bottom equation by 2, then add the equations.

Answers

Answer:

Step-by-step explanation:

A

please help me please​

Answers

Answer:

30,000

Step-by-step explanation:

cos() =
O A. V
B.
173
2
OC.
OD.
-3

Answers

Answer:

-√3/2

Step-by-step explanation:

Given the expression:

Cos(7π/6)

Conver to degrees

=  Cos(7(180)/6)

= cos 210

= -√3/2

Hence the value of cos(7π/6) is -√3/2

what is the sum of the rational expressions x-4/2x+3x/2x-1​

Answers

Answer:

May the ans will help you.

Find two consecutive integers whose sum is 901.

Answers

the answer is :

x+1 and x+2

Answer:

900+1=901

Step-by-step explanation:

A city is designing a new trail system that will be
6 1/6 miles long. They plan on placing 49 mileage signs to show the distance. How far apart will each sign be?

Answers

Step-by-step explanation:

the answer is 6.125 and its will be divided by 125

A health clinic dietician is planning a meal consisting of three foods whose ingredients are summarized as follows: One Unit ofFood I Food II Food IIIUnits of Protein 10 15 20Units of Carbohydrates 1 2 1Units of Iron 4 8 11Calories 80 120 100The dietician wishes to determine the number of units of each food to use to create a balanced meal containing at least 40 units of protein, 6 units of carbohydrates, and 12 units of iron, and with as few calories as possible. Use solver to find how many units of each food should be used in order to minimize calories.

Answers

Answer:

z (min) = 360      x₁  =  x₃ = 0   x₂ = 3

Step-by-step explanation:

                             Protein      Carbohydrates    Iron      calories

Food 1  (x₁)               10                       1                   4              80

Food 2 (x₂)               15                       2                  8              120

Food 3 (x₃)               20                       1                  11              100

Requirements         40                        6                 12

From the table we get

Objective Function z :

z  =  80*x₁   +  120*x₂   +   100*x₃     to minimize

Subjet to:

Constraint 1.  at least 40 U of protein

10*x₁  +  15*x₂ + 20*x₃  ≥  40

Constraint 2. at least  6 U of carbohydrates

1*x₁  +  2*x₂  + 1*x₃    ≥  6

Constraint 3.  at least  12 U of Iron

4*x₁   +  8*x₂  +  11*x₃  ≥  12

General constraints:

x₁    ≥  0     x₂   ≥  0    x₃   ≥  0    all integers

With the help of an on-line solver after 6 iterations the optimal solution is:

z (min) = 360      x₁  =  x₃ = 0   x₂ = 3

What would be the amount of his last monthly bill in order. The bill amount to be 110 for all 12 months

Answers

Add up all the numbers the divide by the amount of numbers in the set.
1199/11 = 109
B. 109 answer

Find the angle measurements of the intersections for the two equations f(x) = 4x - 5 and g(x) = 2x^2 - 5.

Multiple answers

63
7 (This is one of the answers already)
20
76
90

Answers

Answer:

76° is the other one

Step-by-step explanation:

nope, no precise calculation here. the option are thankfully enough apart that solving it graphically is just fine. look at the screenshot. the upper intersection is the one with the 7° angle

the lower one is somewhat less than 90° :P

Answer:

76 is the other

Step-by-step explanation:

How should I tell my crush I like her? She's my friend and I asked her if she liked me yesterday and she said no but I think she was lying because she typed and then stoped typing and said no

Answers

Answer:

U just have to make her feel comfortable to trust u that she can tell u that she actually likes u....dont push anything just make her feel appreciated ok?

Step-by-step explanation:

that's all


Doris has a fish pond 15 by 18 ft. She wants to put grass in a strip of uniform with around the pond. She has enough grass seed for 234 ft squared. How wide will the strip be? Round your answer to the nearest tenth, when appropriate

Answers

Check the picture below.

so if we simply subtract the strip area with the pond and the area of the pond only, what's leftover is the area of the strip alone, so

[tex]\stackrel{\textit{area of the grass \underline{with} pond}}{(15+2x)(18+2x)}-\stackrel{\textit{area of the pond}}{(15)(18)}=\stackrel{\textit{their difference}}{232} \\\\\\ 270+30x+16x+4x^2-270=232\implies 46x+4x^2=232 \\\\\\ 23x+2x^2=116\implies 2x^2+23x-116=0[/tex]

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+23}x\stackrel{\stackrel{c}{\downarrow }}{-116}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x = \cfrac{-23\pm \sqrt{23^2-4(2)(-116)}}{2(2)}\implies x = \cfrac{-23\pm \sqrt{1457}}{4}[/tex]

now, the negative root will simply yield a negative value, which is not applicable here, so we'll only use the positive root, since it's the only feasible one for the phenomena

[tex]x = \cfrac{-23+ \sqrt{1457}}{4}\implies x \approx 3.792667341996157\implies \stackrel{\textit{rounded up}}{x = 3.8}[/tex]

Answer:

3 feet

Step-by-step explanation:

Let x be the width of the grass strip.

So the length of the grass strip=18+2x

Area of the grass strip =2(18+2x)(x)+2(15)(x)=2(18x+2x^2)+2(15x)=(36x+4x^2)+30x=4x^2+66x^2

But the available grass seed is enough for 234 ft squared

4x^2+66x=234

4x^2+66x-234=0

x={-66+-[(66)^2–4(4)(-234)]^1/2}/2(4)

x={-66+-[4356+3744]^1/2}/8={-66+-[8100]^1/2}/8

x={-66+-(90)}/8

Two values of x: x=(-66+90)/8=24/8=3 and the other value of x=(-66–90)/8=-19.5. Adopt the positive value of x=3 feet (answer)

So the width of the strip is 3 feet.

Check for the area of grass strip around the fish pond : Area=2(18+6)(3)+2(15)(3)=2(24)(3)+90=144+90=234 square feet

Other area check =4x^2+66x=4(3)^2+66(3)=36+198=234 square feet

Therefore the strip is 3 feet wide

Please help please guys how are you doing

Answers

Answer:

the answer of the the triangle is 6

Answer:

6

Step-by-step explanation:

First row:

8 ÷ 2 = 4. → Square: 4

Second row:

14 - 4 = 10.

[two circles] = 10. So, 10÷2 = 5.

Circle = 5

Third Row:

[triangle] + 5 = 11

11 - 5 = 6

Triangle = 6

What number is missing here?
2, 3, 5, 8, 13. ?

Answers

Answer:

2, 3, 5, 8, 13 missing number is 18.

Question 35 of 49
Which description best describes parallel lines?
A. Lines that are not in the same plane and will never intersect
O B. Lines that intersect at a right angle
O C. Lines that intersect
D. Lines that lie in the same plane but will never intersect
SUBM

Answers

Answer:

D.lines that lie in the same plane but will never intersect

Step-by-step explanation:

parallel lie in the same plane but never meet


Use the table to approximate AB in the triangle below.

Answers

Answer:

Answer is 6.1 units

Step-by-step explanation:

The measure of length of AB in the triangle ABC is 6.1 units.

What are trigonometric ratios?

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

In the given triangle ABC, BC=5 and ∠A=55°.

We know that, sinθ= Opposite leg length/Hypotenuse length

Here, sinA=BC/AB

sin55°=5/AB

0.82=5/AB

AB=5/0.82

AB=6.1 units

Therefore, the measure of length of AB in the triangle ABC is 6.1 units.

Learn more about the trigonometric ratios here:

brainly.com/question/25122825.

#SPJ2

2)
110°
18x + 2
A) 8
C) 6
B) 12
D) -10

Answers

Answer:

C) 6

Step-by-step explanation:

Alternate interior angles are congruent meaning that they are equal to each other sp 18x+2=110 is simplified to 18x=108. Then divide by 18 to get x equal to 6. Hope this helped and post more :)

Simplify: (5x + 3) – (3x – 2)

Answers

Answer: 2x+5

Step-by-step explanation:

(5x + 3) – (3x – 2)

5x+3-3x+2

2x+5

Answer:

[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]

╭⋟───────────────

[tex](5x+ 3) - (3x - 2) \\ = 5x + 3 - 3x + 2 \\ = 5x - 3x + 3 + 2 \\ = 2x + 5[/tex]

───────────────⋞╯

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Find the measure of WX and show work

Answers

Ans : the measure of WX = 8

Seven times a number decreased by three-fourths of the same number is 25. What is the number?

Answers

Answer:

103/28

Step-by-step explanation:

Let the number be 'x'

Equation:-

7x - 3/4 = 25

7x = 25 + 3/4

7x = 100/4 + 3/4

7x = 103/4

x = 103/(4 x 7)

x = 103/28

Answer:

if we make this a algebraic equation it will look like this

7x-3/4x=25

6.25x=25

25 divided by 6.25=4

x=4

to check

28-3=25

Hope This Helps!!!

Choose each of the following that ARE a function

Answers

Ik that A and F are for sure but I think D maybe one as well.

Find the equation (in terms of x ) of the line through the points (-2,5) and (3,4)
y=

Answers

Answer:

y = (-1/5)x + 23/5

Step-by-step explanation:

Given:

Two points;

(-2,5) and (3,4)

Find:

Equation of slope

Computation:

y = mx + b

5 = m(-2) + b

5 = -2m + b .......... Eq1

4 = m(3) + b

4 = 3m + b .......... Eq2

Eq2 - Eq1

-1 = 5m

m = -1/5

5 = -2m + b

5 = -2(-1/5) + b

5 = 2/5 + b

b = 23/5

y = mx + b

y = (-1/5)x + 23/5

There are red, blue, and white buttons in a box. The ratio of the
number of red buttons to the number of white buttons is 4:7.
The ratio of the number of blue buttons to the number of red buttons
is 3:2. There are 280 white buttons.

How many buttons are there altogether?
Please help i’m very confused

Answers

Answer:

680

Step-by-step explanation:

Ratio of red to white 4 : 7

Number of white = 280

White + red buttons = x

7x / 11 = 280

7x = 280 * 11

7x = 3080

x = 3080 / 7

x = 440

Number of red buttons 440 - 280 = 160

Number of red bottons ;

Blue + red buttons = x

3 : 2 ; blue : red

3 + 2 = 5 ;

2x / 5 = 160

2x = 160 * 5

2x = 800

x = 800 / 2

x = 400

Number of Blue buttons :

400 - 160 = 240

Total :

White + red + blue

280 + 160 + 240 = 680 buttons

Consider rolling two fair dice and observing the number of spots on the resulting upward face of each one. Letting A be the event that at least one of the dice results in 6 spots on its upward face, and E be the event that exactly one of the dice results in 6 spots on its upward face, give the value of P(E|A). (Note: This value can be easily obtained by looking at p. 2.3 of the class notes and using a reduced sample space. In fact, such an approach makes the solution so trivial, that for this problem, you don’t have to give any justification for your answer.)

Answers

Answer:

[tex]P(E|A)= \frac{10}{11}[/tex]

Step-by-step explanation:

Given

Two rolls of die

[tex]E \to[/tex] one of the outcomes is 6

[tex]A \to[/tex] atleast one is 6

Required

P(E|A)

First, list out the outcome of each

[tex]E = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]

[tex]A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}[/tex]

So:

[tex]P(E|A)= \frac{n(E\ n\ A)}{n(A)}[/tex]

Where:

[tex]E\ n\ A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]

[tex]n(E\ n\ A) = 10[/tex]

[tex]n(A) = 11[/tex]

So:

[tex]P(E|A)= \frac{10}{11}[/tex]

You roll a die with the sample space s=1,2,3,4,5,6. you define A as (1,2,4) B as (2,3,4,5,6) C as (3,4) and D as (2,4,5). Determine which of the following events are exhaustive and/or mutually exhaustive.
Exhaustive Mutually exclusive
A and B
A and C
A and D
Band C

Answers

Answer:

A and B are exhaustive.

Step-by-step explanation:

Given

[tex]A = \{1,2,4\}[/tex]

[tex]B = \{2,3,4,5,6\}[/tex]

[tex]C =\{3,4\}[/tex]

[tex]D = \{2,4,5\}[/tex]

Solving (a): The mutually exclusive events

These are events that have no common or mutual elements

Events A to D are not mutually exclusive because each of the events have at least 1 common element with one another.

Solving (b): Exhaustive events.

Two events X and Y are said to be exhaustive if:

[tex]S = P(X\ n\ Y)[/tex]

i.e. if the sample space equals the intersection of X and Y

For events A to D, we have:

[tex]A\ n\ B = \{1,2,3,4,5,6\}[/tex]

and the sample space is:

[tex]S = \{1,2,3,4,5,6\}[/tex]

By comparison;

[tex]A\ n\ B = S[/tex]

Hence, A and B are exhaustive.

100 Brainly points!! Need help ASAP :)

In the image, two circles are centered at A. The circle containing B was dilated to produce the circle containing B’. What is the scale factor of dilation?

A. 1
B. 2
C. 0.5
D. -0.5

Answers

Answer:

B

Step-by-step explanation:

I'm not really shure tho

Answer:

D. -0.5

Step-by-step explanation:

AB dilated by scale factor -0.5 to produce AB'.

the length of AB = 4 units and the length of AB' = 2 units, the direction is backward, so the scale factor is - 2/4 = -0.5

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