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1 year ago

Find the general form of the function that satisfies da/dt = -9a

2 answers:

8 0

Da/dt=-9a
t is variable. integral of -9adt= -9a*integral dt= -9a*t+c
The general form of funcion that satisfies differential equations da/dt=-9a is a=-9a*t+c

A solution of differential equation is a function which satisfies the equation.

posledela1 year ago

4 0

The given equation is
$\frac{da}{dt} =-9a$

This ODE (Ordinary Differential Equation) is separable.
That is,
$\frac{da}{a} = -9$

Integrate to obtain
$\int \frac{da}{a} =-9 \int dt \\\\ ln(a) = -9t + k \\\\ a(t) = c \, e^{-9t}$
where k, c are constants.

Answer: $a(t) = c \, e^{-9t}$ , c = constant.

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2 years ago

What does the digit 7 represent in 170,280?

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1 year ago

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Let us convert all figures into decimals so that we can compare them easily.

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1 year ago

ANSWER ALL 5 PARTS.

N76 [4]

A function $f$ from a set A to a set B is defined as a relation that assings to each element $x$ in the set A exactly one element $y$ in the set B. The set A is called the domain of the function while the set B is the range. So we have five statements and need to find some functions. Melissa decides to reserve a patch in her vegetable garden for growing bell peppers. If each side of the tomato patch is $x$ feet, then we have a square patch as shown in the Figure below.

1.a) Write the function Wa(x) representing the width of the bell pepper patch.

We know that she wants its width to be half the width of the tomato patch. Let $x$ be the width of the tomato patch, then the function that matches this statement is:

$\boxed{Wa(x)=\frac{x}{2}}$

1.b) Write the function La(x) representing the length of the bell pepper patch.

In this case Melissa wants its length to exceed the length of the tomato patch by 2 feet. To do this we enlarge the length of the tomato patch 2 feet. Therefore the function is the following:

 $\boxed{La(x)=x+2}$

2. Area of the bell pepper patch in terms of x.

Given that the bell pepper patch is a rectangle, then the area of a rectangle is the product of the length and width. So:

 $A=(\frac{x}{2})(x+2) \\ \\ \therefore \boxed{A=\frac{x(x+2)}{2}}$

3. Combined area of the tomato patch and the bell pepper patch.

This function is the sum of both the area of the tomato patch and the bell pepper patch. So:

 $Aar(x)=x^{2}+\frac{x(x+2)}{2} \rightarrow Aar(x)=x^{2}+ \frac{x^{2}}{2}+x \rightarrow Aar(x)=\frac{3x^{2}}{2}+x \\ \\ \therefore \boxed{Aar(x)=\frac{x(3x+2)}{2}}$

4. Write the function Aa(x) for the remaining planting area in the garden.

The remaining planting area in the garden are the rectangles in red. So we need to subtract the width of the bell pepper patch from the width of the tomato patch and multiply it by 2. In mathematical language this is given by:

 $Aa(x)=2(x-\frac{x}{2}) \rightarrow Aa(x)=x$

5. Find the area of the remaining space in the garden after planting tomatoes and bell peppers.

Given that Melissa wants the area of the bell pepper patch to be 31.5 square feet, then it is true that:

 $31.5=\frac{x(x+2)}{2} \rightarrow x^{2}+2x-64=0 \\ \\ solving \ for \ x: \\ x=7.06$

Therefore the area of the remaining space is:

 $\boxed{Aa(7.06)=7.06ft^{2}}$

6 0

2 years ago

Which absolute value function has a graph that is wider than the parent function, f(x) = |x|, and is translated to the right 2 u

Mariulka [41]

Case 1: If we multiply f(x) = |x| by a fraction greater than zero and less than 1, the width of the resulting graph will increase. If the vertex of the original function is moved 2 units to the right, then we'd replace |x| with |x-2| Only the coefficient (3/4) satisfies the "wider graph" requirement here.

Next time you list answr possibilities, please type them in only one per line, or separate them with commons, semicolons or the like.

4 0

2 years ago

Read 3 more answers