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2 years ago

A line passes through the point (-8,-5) and has a slope of 3/4. Write an equation in point slope form for this line.

Mathematics

1 answer:

timurjin [86]2 years ago

3 0

Answer:

y+5 = 3/4(x+8)

Step-by-step explanation:

The point slope form of the equation of a line is

y - y1 = m(x-x1) where m is the slope and ( x1,y1) is a point on the line

The slope is 3/4 and the point is (-8,-5)

y - -5= 3/4( x - -8)

y+5 = 3/4(x+8)

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Find the solution of the differential equation dy/dt = ky, k a constant, that satisfies the given conditions. y(0) = 50, y(5) =

irga5000 [103]

Answer: The required solution is $y=50e^{0.1386t}.$

Step-by-step explanation:

We are given to solve the following differential equation :

$\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.

From equation (i), we have

$\dfrac{dy}{y}=kdt.$

Integrating both sides, we get

$\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}]$

Also, the conditions are

$y(0)=50\\\\\Rightarrow ae^0=50\\\\\Rightarrow a=50$

and

$y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.$

Thus, the required solution is $y=50e^{0.1386t}.$

8 0

2 years ago

Read 2 more answers

Suppose that w and t vary inversely and that t = 5/12

Svetlanka [38]

Answer:

Option B. t=5/3w ;1/3

Step-by-step explanation:

We are told that $w$ varies Inversely with $t$ thus generally speaking $w$ ∝ $\frac{1}{t}$ since they are inverted, <u>otherwise</u> if they were proportionally varied then $w$ ∝ $t$ . This means that there is a constant value ( $a$ ) for which $w$ is inversely proportional to $t$ and can be mathematically expressed as:

$w=\frac{a}{t}$ Eqn. (1)

Now since we are given the values of $w=4$ and $t=\frac{5}{12}$ , we can plug them in Eqn. (1) and find our constant of proportionality $a$ as follow:

$w=\frac{a}{t}\\ \\a=wt\\\\a=(4)(\frac{5}{12} )\\\\a=\frac{5}{3}$

Now that we have our constant we can find the new $t$ value for the second value of $w=5$ as follow:

$w=\frac{a}{t} \\\\t=\frac{a}{w}\\ \\t=\frac{\frac{5}{3} }{5}\\\\t=\frac{5}{15}\\ \\t=\frac{1}{3}\\$

Therefore based on the options give, we can see that Option B. is correct since

$t=\frac{5}{3w}$ and for $w=5$ , then $t=\frac{1}{3}$

8 0

2 years ago

What is 0.644 in expanded form

Brrunno [24]

I hope this helps you

0,644

644/1000

161/250

4 0

2 years ago

(please!!!) What fraction is equivalent to 38%?

Aleks04 [339]

Answer: 19/50

Step-by-step explanation: To write a percent as a fraction in lowest terms, first remember that a percent is a ratio that compares a number to 100. In this case, 38% can be written as the ratio 38 to 100 or 38/100. Notice however that 38/100 is not in lowest terms so we need to divide the numerator and denominator by the greatest common factor of 38 and 100 which is 2.

38 ÷ 2 = 19

100 ÷ 2 = 50

<em>Therefore, 38% can be written as the fraction 19/50 which is in lowest terms.</em>

8 0

2 years ago

Read 2 more answers

Carol is one-sixth of an inch taller than dave.dave is fifty-eight and a half inches tall.how tall is carol

katrin2010 [14]

C=1/6 of x
D=55/1/2
1/6 of 111/2=110.167
55.08
=55 inches

5 0

2 years ago