Stuart and Francisco designed a black rocket and a white rocket during an aerospace class. Both rockets were launched after class. During the launch, Stuart and Francisco recorded data of their rockets trajectories. Stuart modeled the black rockets distance from the ground, in feet, x seconds after it was launched with the graph. Francisco modeled the white rockets distance from the ground, in feet, x seconds after it was launched with the function g(x)= -16x^2 + 50x +7 . Both wanted to know what the greatest distance was from the ground for each rocket. Stuart obtained that his rockets greatest distance from the ground was [Drop down 1] while Francisco obtained a greatest distance of [Drop down 2].

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

[tex]x=-3+2cos\theta,\:y=5+2sin\theta\\\\x+3=2cos\theta,\: y-5=2sin\theta\\\\(x+3)^2=4cos^2\theta,\: (y-5)^2=4sin^2\theta\\\\(x+3)^2+(y-5)^2=4cos^2\theta+4sin^2\theta\\\\(x+3)^2+(y-5)^2=4(cos^2\theta+sin^2\theta)\\\\(x+3)^2+(y-5)^2=4(1)\\\\(x+3)^2+(y-5)^2=4[/tex]

Thus, the first option is correct. Trying all the other options will not get you the desired rectangular equation.

Problem 2

[tex]x=3-6cos\theta,\: y=-2+3sin\theta\\\\x-3=-6cos\theta,\: y+2=3sin\theta\\\\\frac{x-3}{-6}=cos\theta,\: \frac{y+2}{3}=sin\theta\\ \\ \frac{(x-3)^2}{36}=cos^2\theta,\: \frac{(y+2)^2}{9}=sin^2\theta\\ \\ \frac{(x-3)^2}{36}+\frac{(y+2)^2}{9}=cos^2\theta+sin^2\theta\\\\ \frac{(x-3)^2}{36}+\frac{(y+2)^2}{9}=1[/tex]

Therefore, the first option is correct. This equation is in the form of an ellipse with a horizontal major axis length of 12 (half is 6) and a vertical minor axis length of 6 (half is 3), with its center at (3,-2).

Problem 3

Not sure which equation needs to be used for this problem

Problem 4

[tex]x=-7cos\theta ,\:y=5sin\theta\\\\-\frac{x}{7}=cos\theta,\: \frac{y}{5}=sin\theta\\ \\ \frac{x^2}{49}=cos^2\theta,\: \frac{y^2}{25}=sin^2\theta\\ \\\frac{x^2}{49}+\frac{y^2}{25}=cos^2\theta+sin^2\theta\\ \\ \frac{x^2}{49}+\frac{y^2}{25}=1[/tex]

This equation is in the form of an ellipse with a horizontal major axis length of 14 (half is 7) and a vertical minor axis length of 10 (half is 5). See attached graph.

Problem 5

Eliminate the parameter:

[tex]x=-t^2-2,\:y=-t^3+4t\\\\x+2=-t^2\\\\-x-2=t^2\\\\\pm\sqrt{-x-2}=t\\\\y=-t^3+4t\\\\y=-(\pm\sqrt{-x-2})^3+4(\pm\sqrt{-x-2})[/tex]

Attached below is the graph of the curve, which corresponds with the first option.

Answer:

In two years erin grew 7 inches

Step-by-step explanation:

42 - 35 = 7

Answer:

atleast 7 inches

Step-by-step explanation:

35 inches - 42 inches = 7 inches

Two years ago, Erin was 35 inches tall.

To ride the roller coaster at a theme park, she must be at least 42 inches tall. So that means she grew atleast 7 inches

Answer:

3

Step-by-step explanation:

Divide 12 by 4 since the ratio is 12 to every 4 inches

Answer:15

Step-by-step explanation:

3+1/2=3/2

3/2*10=3*5=15

15

Answer:

sin C=20/25=4/5

cos C=15/25=3/5

tan C=20/15=4/3

Step-by-step explanation:

sine is opposite/hypotenuse

cosine is adjacent/hypotenuse

tangent is opposite/adjacent

=================================================

Here, we have to multiply fractions.

How to Multiply Fractions?

Here are the steps:-

So let's do it.

Step 1:-

[tex]\longmapsto\sf{3=\displaystyle\frac{3}{1}[/tex]

Step 2:-

[tex]\longmapsto\sf{\displaystyle\frac{3}{1} *\frac{7}{10}}[/tex]

[tex]\longmapsto\sf{\displaystyle\frac{21}{10} }[/tex]

We can't simplify this fraction, but there's something else we can do:-

Here's the answer:-

[tex]\boxed{\sf{2\displaystyle\frac{1}{10} }}[/tex]

=====================================================

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

Answer:

(-16, -4)

Step-by-step explanation:

4x - 13y = -12

x = 2y - 8

Substitute for x:

4(2y - 8) - 13y = -12

8y - 32 - 13y = -12

-5y - 32 = -12

-5y = 20

y = -4

Solve for x:

4x - 13(-4) = -12

4x + 52 = -12

4x = -64

x = -16

Solution to this system: (-16, -4)

I hope this helps!

Answer:

there are two methods

1. graphical method

2. elimination method

3. substitution method

Answer:

1.4.5m/s^2

2.6.25m/s^2

3.15m/s^2

4.0.05m/s^2

Step-by-step explanation:

a=v-u

----

t

27-0

------ = 27/6

6

=4.5m/s^2

u=4.5m/s

v=24.5m/s

t=3.2s

(24.5-4.5)÷3.2

=20/3.2

=6.25m/s^2

v=80m/s

u=50m/s

t=2s

(80-50)÷2

15m/s^2

v=0.80m/s

u=0.50m/s

t=6s

(0.80-0.50)÷6

=0.05m/s^2

Answer:

60 ft²

Step-by-step explanation:

A = 1/2 × b × h

A = 1/2 × 12ft × 10ft

A = 1/2 × 120 ft

A = 60ft²

Answer:

y + 1 = -1/4 (x - 1) Answer choice C is correct.

Step-by-step explanation:

Point Slope Formula: y - y1 = m (x-x1)

Your points:

(1,-1) and (5,-2)

You need to find the slope first:

Use the formula: y2 - y1 / x2 - x1

Your y2 is -2

y1 is -1

x2 is 5

x1 is 1

-2 - (-1)/5-1

-2 + 1 /4

-1/4 is your slope and the "m" in the formula.

Now we know our y1 is -1 and x1 is 1 you just need to plug them in

y + 1 = -1/4 (x - 1)

Notice that I didn't write y - (-1) this is because the negatives cancel into positives.

Answer choice C is correct.

Answer:

c. [tex]y+1=-\frac{1}{4} (x-1)[/tex]

Step-by-step explanation:

Hi there!

We are given the points (1, -1) and (5, -2)

We want to find the equation of that line using those points, in point-slope form

Point-slope form is written as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point

First, let's find the slope of the line

The formula for the slope (m) calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We already have everything we need to find the slope, but let's label the values of the points to avoid any confusion when calculating.

[tex]x_1=1\\y_1=-1\\x_2=5\\y_2=-2[/tex]

Now substitute:

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-2--1}{5-1}[/tex]

Subtract

m=[tex]\frac{-2+1}{5-1}[/tex]

m=[tex]\frac{-1}{4}[/tex]

The slope of the line is -1/4

Now substitute this into the formula to find point-slope form (remember that this is [tex]y-y_1=m(x-x_1)[/tex], and that m is the slope value)

Therefore:

[tex]y-y_1=-\frac{1}{4} (x-x_1)[/tex]

Now, let's substitute the values of [tex]x_1[/tex] and [tex]y_1[/tex], which we found earlier (which are 1 and -1 respectively) into the equation

[tex]y--1=-\frac{1}{4} (x-1)[/tex]

Simplify

[tex]y+1=-\frac{1}{4} (x-1)[/tex]

This equation matches option c, which is the answer.
Hope this helps!

The population model is an exponential decay because it decreases

The exponential model of the population is P = 3000(0.64^1/7)^t

The population decreases by 0.36 every 7 years.

This means that the function is an exponential decay.

An exponential decay function is represented as:

P = a((1 - r)^1/n)^t

Where:

So, we have:

P = 3000((1 - 0.36)^1/7)^t

Evaluate the difference

P = 3000(0.64^1/7)^t

Hence, the exponential model of the population is P = 3000(0.64^1/7)^t

Read more about exponential functions at:

https://brainly.com/question/11464095

11/2*3/4+1/78=9/8*5/8

5.5*3/4+1/78=9/8*5/8

16.5/4+1/78=9/8*5/8

4.125+1/78=9/8*5/8

4.125+0.013=9/8*5/8

4.125+0.013=1.125*5/8

4.125+0.013=5.625/8

4.125+0.013=0.703

4.138=0.703

the answer is 4.138=0.703

hope this helps

Answer:

$37.70

Step-by-step explanation:

56*.65

pls mark brainliest

With ϕ ≈ 1.61803 the golden ratio, we have 1/ϕ = ϕ - 1, so that

[tex]I = \displaystyle \int_0^\infty \frac{\sqrt[\phi]{x} \tan^{-1}(x)}{(1+x^\phi)^2} \, dx = \int_0^\infty \frac{x^{\phi-1} \tan^{-1}(x)}{x (1+x^\phi)^2} \, dx[/tex]

Replace [tex]x \to x^{\frac1\phi} = x^{\phi-1}[/tex] :

[tex]I = \displaystyle \frac1\phi \int_0^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx[/tex]

Split the integral at x = 1. For the integral over [1, ∞), substitute [tex]x \to \frac1x[/tex] :

[tex]\displaystyle \int_1^\infty \frac{\tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx = \int_0^1 \frac{\tan^{-1}(x^{1-\phi})}{\left(1+\frac1x\right)^2} \frac{dx}{x^2} = \int_0^1 \frac{\pi2 - \tan^{-1}(x^{\phi-1})}{(1+x)^2} \, dx[/tex]

The integrals involving tan⁻¹ disappear, and we're left with

[tex]I = \displaystyle \frac\pi{2\phi} \int_0^1 \frac{dx}{(1+x)^2} = \boxed{\frac\pi{4\phi}}[/tex]

Answer:

4556.25

Step-by-step explanation:

10:5:8=x:y:18

18/8=2.25

x=2.25x10=22.5

y=2.25x5=11.25

11.25x22.5x18=4556.25

Answer:

See below ↓

Step-by-step explanation:

ii.

Solving

Answer:

Brainliest please

Step-by-step explanation:

Answer:

it’s 3 x 2x 5 = 30

Then use that product and times it by 10. ( 10 x 30 )

Ans = 300 cubic centimeters

Step-by-step explanation:

3 x 5 x 2 = 30

30 x 10 = 300

Ans = 300 cubic centimeters

Answer: the value of x = 5

Answer:

Yes, the expressions are equivalent.

Step-by-step explanation:

Expanding (3x + 9)(x + 2) gives us [tex]3x^2 + 15x + 18[/tex] which is the same as when you expand (3x + 6)(x + 3).

Answer:

(3x+9)(x+2)

step:3xx+3x2+9x+9x2

3x2+6x+9x+9x2

answer is 3x2+15x+18

step:3xx+3x3+6x+6x3

3x2+6x+6x3

answer is 3x2+15x+18

Step-by-step explanation:

#Carry on learning#

Answer:

Answer: x = 10 degrees.

Step-by-step explanation:

Answer:

please try do the rest by yourself..Of you didn't get the answer you can ask me through comment..

Answer:

$636.17

Step-by-step explanation:

       First, we need to find the volume of the ball. Then, we will solve for the cost of it.

       Volume of a sphere and solving for the area:

V = [tex]\frac{4}{3}[/tex]πr³

V = [tex]\frac{4}{3}[/tex]π(7.5)³

V ≈ 1767.15 in³

       Now that we have the volume, next we need to find the cost. Since the lead costs $0.36 per in³, and our volume is in in³, we can multiply the volume by the cost.

1767.15 in³ * $0.36 = 636.174

       Money rounds to the hundredth place,

636.174 -> $636.17

          It will cost $636.17 to make one ball.

Answer:

Volume of a sphere = 4/3 Pi r³

if r = 7.5

= 4/3 pi 7.5³

= 4/3 pi 421.87

= 1687.5/3 pi

= 562.5 Pi

= 1767.15 in³

then

1767.15 x 0.36 = 636.17

if 1 in³ costs 0.36$

then 1767.15 in³ costs 636.17$

Answer:

Step-by-step explanation:

This is a Geometric Sequence  with common ratio 15/9 = 5/3

25/15  is also =  5/3

So the 10th term = ar^(n-1)

= 9*(5/3)^9

= 893.061 to nearest thousandth.

Hey there!

4 quarters = 1 dollar

To find how many quarters are in 20 dollars, we multiply 4 by 20

⇒ 4 × 20

⇒ 80

Therefore, 80 quarters are in 20 dollars

Answer:

  B.) y=csc x

Step-by-step explanation:

The cosecant function has a minimum magnitude of 1, so its range excludes any values in the range -1 < y < 1.

  y = csc(x) . . . has a range that does not include -0.8

Answer:

The expected value is $375

The profit is $6,500,000

Step-by-step explanation:

15000, 30000, 70000

1/100, 1/200, 1/400

So the expected value of the claim is:

15000 × (1/100) + 30000 × (1/200) + 70000 × (1/400) = 475

Given that an insurance policy sells for $800 and the expected value of the claim is $475.

So, the expected value of the companies profit is = $(800 – 475) = $325.

If the company sells 20,000 policies then the expected profit is = $(20000 × 325) = $6,500,000

Thus, The expected value (to the company) per policy sold is $375 and the expected profit is $6,500,000.

-TheUnknownScientist 72

Answer:

i think the answer is d which is 50°

To find the exact answer based on the last step, "[tex]2(3)^3+5[/tex]", you must use PEMDAS (attached image below)

          [tex]2(3)^3+5=2*27+5=54+5=59[/tex]

Thus the answer is 59.

Hope that helps!

Answer:

2b³ + 5 = 59

Step-by-step explanation:

Given information,

→ 2b³ + 5

→ b = 3

Let's solve the expression,

→ 2b³ + 5

→ 2(3)³ + 5

→ 2(27) + 5

→ 54 + 5 = 59

Hence, the answer is 59.

Answer:

Step-by-step explanation:

irrational number

Answer:

Irrational number

Step-by-step explanation:

It is a never-ending and non-repeating number.