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3 years ago

How do you write out x <=-4

1 answer:

3 0

You can write it out multiple ways, such as x<=-4, x is (-infinity, -4], or {x | x<=4}. Even using a line, put -4 down, with a closed circle (including it means) and an arrow from there pointing left, for the included values to negative infinity.

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An engineer is using a polynomial function to model the height of a roller coaster over time x, as shown.

Anit [1.1K]

Answer:

Step-by-step explanation:

the first thing you have to do is to get the x and the y axis and add them to then decrease that by o,5 and then you get f of which you multiply it by 2 adn you get your answer.

8 0

2 years ago

Read 2 more answers

Answer if u love cats & dogs

eimsori [14]

Answer:

(7, 5.25) lies on the graph.

Step-by-step explanation:

We are given the following values

x = 4, 6, 8, 12 and corresponding y values are:

y = 3, 4.5, 6, 9

Let us consider two points (4, 6) and (6, 4.5) and try to find out the equation of line.

Equation of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given as:

$y=mx+c$

where m is the slope.

(x,y) are the coordinates from where the line passes.

c is the y intercept.

Here,

$x_{1} = 4\\x_{2} = 6\\y_{1} = 3\\y_{2} = 4.5$

Formula for slope is:

$m = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m = \dfrac{4.5-3}{6-4}\\\Rightarrow m = \dfrac{1.5}{2}\\\Rightarrow m = \dfrac{3}{4}$

Now, the equation of line becomes:

$y=\dfrac{3}{4}x+c$

Putting the point (4,3) in the above equation to find c:

$3=\dfrac{3}{4}\times 4+c\\\Rightarrow 3=3+c\\\Rightarrow c =0$

So, final equation of given function is:

$y=\dfrac{3}{4}x$

$4y=3x$

As per the given options, the point (7, 5.25) satisfies the equation.

So correct answer is $(7, 5.25)$ .

6 0

3 years ago

What is 4 ( x+2 )=10

Len [333]

Answer:

x= 1/2

Step-by-step explanation:

We can use Distributive property to solve this.

4(x+2)=10

4x+8=10

-8 -8

4x= 2

4x/4= 2/4

x= 1/2

Hope this is right!

6 0

3 years ago

Read 2 more answers

A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after subm

True [87]

Answer:

A) cooling constant = 0.0101365

B) $\frac{df}{dt} = k ( 60 - F )$

c) F(t) = 60 + 77.46 $e^{0.0101365t}$

D)137.46 ⁰

Step-by-step explanation:

water temperature = 60⁰F

temperature of Bar after 20 seconds = 120⁰F

temperature of Bar after 60 seconds = 100⁰F

A) Determine the cooling constant K

The newton's law of cooling is given as

= $\frac{df}{dt} = k(60 - F)$

= ∫ $\frac{df}{dt}$ = ∫ k(60 - F)

= ∫ $\frac{df}{60 - F}$ = ∫ kdt

= In (60 -F) = -kt - c

60 - F = $e^{-kt-c}$

60 - F = $C_{1} e^{-kt}$ ( note : $e^{-c}$ is a constant )

after 20 seconds

$C_{1}e^{-k(20)}$ = 60 - 120 = -60

therefore $C_{1} = \frac{-60}{e^{-20k} }$ ------- equation 1

after 60 seconds

$C_{1} e^{-k(60)}$ = 60 - 100 = - 40

therefore $C_{1} = \frac{-40}{e^{-60k} }$ -------- equation 2

solve equation 1 and equation 2 simultaneously

= $\frac{-60}{e^{-20k} }$ = $\frac{-40}{e^{-60k} }$

= 6 $e^{20k}$ = 4 $e^{60k}$

= $\frac{6}{4} e^{40k}$ = In(6/4) = 40k

cooling constant (k) = In(6/4) / 40 = 0.40546 / 40 = 0.0101365

B) what is the differential equation satisfied

substituting the value of k into the newtons law of cooling)

60 - F = $C_{1} e^{0.0101365(t)}$

F(t) = 60 - $C_{1} e^{0.0101365(t)}$

The differential equation that the temperature F(t) of the bar

$\frac{df}{dt} = k ( 60 - F )$

C) The formula for F(t)

t = 20 , F = 120

F(t ) = 60 - $C_{1} e^{0.0101365(t)}$

120 = 60 - $C_{1} e^{0.0101365(t)}$

$C_{1} e^{0.0101365(20)}$ = 60

$C_{1} = 60 * 1.291$ = 77.46

C1 = - 77.46⁰ as the temperature is decreasing

The formula for f(t)

= F(t) = 60 + 77.46 $e^{0.0101365t}$

D) Temperature of the bar at the moment it is submerged

F(0) = 60 + 77.46 $e^{0.01013659(0)}$

F(0) = 60 + 77.46(1)

= 137.46⁰

5 0

4 years ago

What is the slope of y=-4

Tpy6a [65]

Hello from MrBillDoesMath!

Answer:

Discussion:

y = -4 is a line of constant height and therefore has slope (m value) = 0

Thank you,

MrB

8 0

3 years ago