Tell whether the given side lengths form a right triangle.
6, 11, 16

Answer:

The equation of the position at time t will be:

[tex]y(t)=-\frac{1}{2}9.81t^{2}+64t+15[/tex]

Step-by-step explanation:

We can start by saying that the acceleration here is g = -9.81 m/s². The minus sign is because the gravity acceleration is a vector downward (negative value), and the ball is going upward (positive value).

And we know that acceleration can be written as a second derivative:

[tex]g=\frac{d^{2}y}{dt^{2}}=y''[/tex] (1)

Now, we can take the integral in each side:

[tex]\int gdt=\int y''dt[/tex]

[tex]\int y''dt=\int -9.81dt[/tex] (2)

Solving the integral in each side we have:

[tex]y'(t)=-9.81t+C[/tex] (3)

Where y'(t) is the velocity at t time (v = dy/dt = y' ) and c is a constant value.

Now, the initial conditions are:

initial height y(0) = 15 feet

initial velocity y'(0) = v(0) = 64 feet/s

Using this condition we can find C. Let's evaluate equation (3) at t = 0.

[tex]y'(0)=-9.81(0)+C[/tex]

[tex]C=64\: feet/s[/tex]

So we have:

[tex]y'(t)=-9.81t+64[/tex] (4)

Now, we need to take the integral of equation (4) to get the position function:

[tex]\int y'(t)dt=\int (-9.81t+64)dt[/tex]

Solving this new integral we have:

[tex]y(t)=-\frac{1}{2}9.81t^{2}+64t+D[/tex] (5)

Using the same method above, we can find D evaluating (5) at t = 0, we have:

[tex]y(0)=-\frac{1}{2}9.81(0)^{2}+64(0)+D[/tex]

[tex]D=y(0)[/tex]

[tex]D=15\: feet[/tex]

Finally, the equation of the position at time t will be:

[tex]y(t)=-\frac{1}{2}9.81t^{2}+64t+15[/tex]

I hope it helps you!

Answer:

maybe

Step-by-step explanation:

Answer:

X= 8 and y= 138

Step-by-step explanation:

IF ANS IS CORRECT COMMENT BACK FOR EXPLANATION

Answer:

6% growth

Step-by-step explanation:

The equation =

A = 2300(1.06)⁷

What does 0.06 represent in the equation?

The formula for Exponential growth =

y = a (1 +r)^t

Where

y = Size after time t

a = Initial size

r = Growth rate in Percentage

t = Time t

Equating both Equations together

y = a (1 +r)^t = A = 2300(1.06)⁷

1 + r = 1.06

r = 1.06 - 1

r = 0.06

Converting to percent

r = 0.06 × 100

r = 6% growth rate

Answer:

Step-by-step explanation:

y = -x - 9

y = 2x + 3

Find point of intersection

2x + 3 = -x - 9

x = -4

Intersection: (-4,-5)

Question :

Cone is formed from 3200 ft³ of gravel, if the height of the cone is 24 ft what is the radius in feet of the base of the cone

Answer:

11.3 feet

Step-by-step explanation:

The volume of a cone = πr²h/3

We are asked to find the radius

The formula is given as:

r = √3V/πh

V = 3200 ft³

h = 24 ft

r = √3 × 2400/π × 24

r = 11.28379 ft

Approximately = 11.3 ft

The radius in feet = 11.3 ft

Answer:

the answer is 7x^2-12x square root of 14 +72 (option 2)

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

you rise up from the line where it is exactly going throw another line. (like it would make a point) fine another time where it happens and rise count up or down and count up and run count left or right. then you'll have a fraction

Answer:

The correct answer is;

The replacement cone holds 4·π cubic inches more than the volume of the original cone  

Step-by-step explanation:

The given measurements of the cones are;

The radius of the original cone, r₁ = 3 inches

The height of the original cone, h₁ = 4 inches

The radius of the replacement cone, r₂ = 4 inches

The height of the replacement cone, h₂ = 3 inches

The volume of a cone, V = (1/3)·π·r²·h

The volume of the original cone, V₁ = (1/3)·π·r₁²·h₁

∴ V₁ = (1/3) × π × (3 in.)² × 4 in. ≈ 37.7 in.³

The volume of the replacement cone, V₂ = (1/3)·π·r₂²·h₂

∴ V₂ = (1/3) × π × (4 in.)² × 3 in. ≈ 50.27 in.³

The ratio of the volume of the two cones is given as follows;

Volume ratio = V₁/V₂

∴ Volume ratio = (1/3) × π × (3 in.)² × 4 in. /((1/3) × π × (4 in.)² × 3 in.) = 3/4

The difference in volume, ΔV = V₂ - V₁ = (1/3) × π × ((4 in.)² × 3 in. - (3 in.)² × 4 in. = 4·π in.³

Therefore, the volume of the replacement cone is 4·π in.³ more than the volume of the original cone.

Answer: 22/25

Step-by-step explanation:

54x+6x-30=7(x+2)+3x

60x-30=7(x+2)+3x

60x-30=7x+14+3x

60x-30=10x+14

60x-10x-30=14

60x-10x=14+30

50x=14+30

50x=44

x=22/25

Answer:

I was not aware of the "daily limit" thing for answers

Step-by-step explanation:

here you go hope this helps!

heyy dude just wanted points. so yeah.

Answer:

Monday, may 31, 2021

Step-by-step explanation:

:)))

Answer:

10 more shawties

Step-by-step explanation:

30-20 = 10

9514 1404 393

Answer:

  x = (9/2)√2 = 4.5√2

Step-by-step explanation:

We know the hypotenuse of an isosceles right triangle is √2 times the length of the side:

  9 = x·√2

  9√2 = 2x . . . . multiply by √2

  (9/2)√2 = x . . . divide by 2

Answer:

no

Step-by-step explanation:

Answer:

Cone: 100ft^3

Sphere: 200ft^2

Step-by-step explanation:

Firstly, the volume of a cone is 1/3 of the volume of the cylinder. It's literally in the formula:

[tex]V_{cone} = \frac{h \pi r^2}{3}\\\textrm{As you can notice, }\pi r^2\textrm{ is the area of the base, like in the cylinder formula}\\[/tex]

So we can just instantly tell that the volume of the cone is 100feet^3.

Not for the sphere - we can assume that if the height is the same, it's equal to two radiuses, or simply - to the diameter. Let's use the formula for the volume of a sphere, but substitute one of the radiuses with [tex]\frac{h}{2}[/tex]

[tex]V_{sphere} = \frac{4\pi r^3}{3} = \frac{2\pi r^2 h}{3} = \frac{2h\pi r^2}{3} = 2\cdot V_{cone}[/tex]

So we can instantly tell that the volume of the sphere is 200feet^3

Answer:

Hi! The answer to your question is 65

Step-by-step explanation:

☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆

☆Brainliest is greatly appreciated!☆

Hope this helps!!

- Brooklynn Deka

Answer:

Opens up

Step-by-step explanation:

x^2+2x-15

Standard form: ax^2+bx+c

If a<0, then the graph opens down

If a>0, then the graph opens up.

In this case: 1x^2+2x-15

a=1

Since 1>0 then the graph opens up.

Answer:

AT and H just straight down the middle from top to bottom. The x shape, from one point to is opposit point (an point works i think), and the heart, down the middle top to bottom, and the H can go middle from left to right

Step-by-step explanation:

the slope of this line is either A) 3 or C) 1

I think its 3

Answer:

The answer is the third option, 20.

Answer: 9/8

Step-by-step explanation:

Answer:

Expected population=  1,904,308 people

Step-by-step explanation:

Giving the following information:

Present Value (PV)= 1,350,000

Number of periods (n)=  10 years

Growth rate (g)= 0.035 per year

To calculate Future Value (FV), we need to use the following formula:

FV= PV*(1 + i)^n

FV= 1,350,000*(1.035^10)

FV= 1,904,308 people

Answer: there is no picture I will help if you repost it ? Brainliest if you can I need 4 more to rank up

Step-by-step explanation: