The depth of the submarine is 50 ft below sea level when it starts to descend at a rate of 10.5 ft/s. It dives at that rate for 5 s. What are the constraints on the x- and y-values?

Answers

Answer 1

Answer:

The x represents time in seconds while y represents the depth of the submarine and the equation with constraint will be y = 10.5x + 50.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

As per the given,

The slope m = rate of descending = 10.5 ft/s

The y-intercept c = initial depth of submarine = 50 ft

Thus, y = mx + c converts as,

y = 10.5x + 50

Hence "The x represents time in seconds while y represents the depth of the submarine and the equation with constraint will be y = 10.5x + 50".

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Answer 2

Answer:

The constraints on the x-values or independent variable – time are:

0 s < time < 5 s

The constraints on the y-values or dependent variable – Depth are:

50 ft < Depth (below sea level) < 102.5 ft

Step-by-step explanation:

Boundary restrictions that are placed upon the variables in an equation are called the Constraints.

The x-values are the independent variables in an equation and in our case it is time.

The y-values are the dependent variables in an equation and in our case it is depth (below the sea level).

The rate of descend provided in the question is constant and is equal to 10.5 ft/s.

We can write our equation of Depth as follows:

Depth (below sea level) = 50 + 10.5*(time)

The constraints on the x-values or independent variable – time are:

0 s < time < 5 s

We can put the boundary values of x variable constraints in the equation of Depth to find the constraint on y-values or dependent variable.

Depth (below sea level) = 50 + 10.5*(time)

Depth (below sea level) = 50 + 10.5*(0), at time 0 s

Depth (below sea level) = 50 ft

Depth (below sea level) = 50 + 10.5*(5), at time 5 s

Depth (below sea level) = 102.5 ft

So the constraints on the y-values or dependent variable – Depth are:

50 ft < Depth (below sea level) < 102.5 ft

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The brackets for a shelf are in a shape of a triangle. Find the angles of the triangle if the measures of the angles are in the ratio x : 2x : 3x :

Answers

ok so remember that al angles add to 180
angles are x,2x,3x

add
x+2x+3x=6x
6x=180
divide 6
x=30

tmes 2
30*2=60

30*3=90

the angles are 30,60,90 degrees

so the angles are 30 60 and 90 degrees.

10ft 10ft 16ft height is 8 ft what's the area of a triangle

Answers

Answer:

The area is 64ft ^2.

Step-by-step explanation:

I believe this is an isosceles triangle and if so our base will be 16ft and our height will be 8ft, knowing this we can solve for the area.

Use the form A=bh/2

Now plug it in...

A=16x8/2

A=128/2

A=64ft ^2

Hope this helps :)

Simplify where possible 3a - 4a 6a

Answers

the answer is 5a. 3a- 4a is -1 then you add -1 and 6, and your outcome comes out to be 5a.

What are the solutions to the equation x-7/x=6? a. x=-7 and x=1
b. x=-6 and x=-1
c. x=-1 and x=7
d. x=1 and x=6

Answers

$x - (7)/(x) = 6$
$(x^(2))/(x) - (7)/(x) = 6$
$(x^(2) - 7)/(x) = 6$
$x^(2) - 7 = 6x$
$x^(2) - 6x - 7 = 0$
$x^(2) - 7x + x - 7 = 0$
$x(x) - x(7) + 1(x) - 1(7) = 0$
$x(x - 7) + 1(x - 7) = 0$
$(x + 1)(x - 7) = 0$
$x + 1 = 0$ $or$ $x - 7 = 0$
$x = -1$ $or$ $x = 7$

Answer:

Step-by-step explanation:

The equation is $x-(7)/(x)=6$

LCM of the denominator on the left side gives us:

$(x^(2)-7)/(x)=6$

Cross multiplying and arranging gives us:

$x^(2)-7=6x\nx^(2)-6x-7=0$

This is a binomial, to factor this, we have to think of 2 numbers that multiplied gives us $-7$ [the constant term] and added gives us $-6$ [the coefficient of x].

The two numbers are: $-7$ and $1$ .

Now we can write:

$x^(2)-6x-7=0\n(x-7)(x+1)=0$

Hence, either $(x-7)=0$ OR $(x+1)=0$ . This gives us two solutions, $x=7$ and $x=-1$ . Answer choice C is correct.

The formula a= bf-v1 is used to calculate acceleration as the change in velocity over a period of time. Solve the formula for the final velocity, bf in terms of initial velocity, v1, acceleration, a, and time,

Answers

Answer:

The formula for the final velocity, bf in terms of initial velocity, v1, acceleration, a, and time is given as

$bf=v1+a* t$

Step-by-step explanation:

Given:

$a=(bf-v1)/(t)$

To Find:

bf = ?

Solution:

Acceleration:

Acceleration is defined as the ratio between the change in velocity of an object and the time it takes for the object to change the velocity.

In formula, this is written as:

$a=(v_(f)-v_(i))/(t)$

Where,

'a' is the Acceleration.

'vf' is the final velocity.

'vi' is the initial velocity.

't' is the time it takes for the object to accelerate from vf to vi

Here it is given as

$a=(bf-v1)/(t)$

So,

Where,

'a' is the Acceleration

'bf' is the final velocity.

'v1' is the initial velocity.

't' is the time it takes for the object to accelerate from bf to v1.

On Solving the above equation 'bf' we get

$a=(bf-v1)/(t)\n\na* t=bf-v1\n\nbf=v1+a* t$ ....As required

Final answer:

In physics, the formula bf = a + v1 is used to calculate the final velocity in terms of the initial velocity, acceleration, and time. If acceleration is zero, final and initial velocities are equal, pointing to constant velocity. If acceleration is negative, the final velocity is less than the initial, indicating deceleration.

Explanation:

The equation a = bf - v1 is used to calculate acceleration, defined as the change in velocity over a period of time. To solve for the final velocity, bf, we simply need to rearrange the equation.

So, bf = a + v1. This equation tells us that the final velocity is equal to the sum of the initial velocity and the acceleration.

Other insights we can gather from this equation include: if acceleration is zero, the final and initial velocities are equal, pointing to constant velocity. This is because there's no change in speed. Conversely, if acceleration is negative, the final velocity is less than the initial, indicating a decrease in speed or deceleration.

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Solve the equation: 6x - 4 + 2(5x + 2) = 16x*1.) 0
2.) 1
3.) -2
4.) Infinitely Many
5.) No Solution

Answers

The answer is that there is no solution.

The problem would be 16x = 16x so there is no solution.

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