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3 years ago

Which word in the sentence is the indirect object? I gave Serena some flowers.

Mathematics

1 answer:

Pepsi [2]3 years ago

7 0

I gave. gave what? flowers= direct object
gave flowers to who? Serena=indirect object.
I hope this helped. :)

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Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integ

atroni [7]

Answer: $y=Ce^(^3^t^{^9}^)$

Step-by-step explanation:

Beginning with the first differential equation:

$\frac{dy}{dt} =27t^8y$

This differential equation is denoted as a separable differential equation due to us having the ability to separate the variables. Divide both sides by 'y' to get:

$\frac{1}{y} \frac{dy}{dt} =27t^8$

Multiply both sides by 'dt' to get:

$\frac{1}{y}dy =27t^8dt$

Integrate both sides. Both sides will produce an integration constant, but I will merge them together into a single integration constant on the right side:

$\int\limits {\frac{1}{y} } \, dy=\int\limits {27t^8} \, dt$

$ln(y)=27(\frac{1}{9} t^9)+C$

$ln(y)=3t^9+C$

We want to cancel the natural log in order to isolate our function 'y'. We can do this by using 'e' since it is the inverse of the natural log:

$e^l^n^(^y^)=e^(^3^t^{^9} ^+^C^)$

$y=e^(^3^t^{^9} ^+^C^)$

We can take out the 'C' of the exponential using a rule of exponents. Addition in an exponent can be broken up into a product of their bases:

$y=e^(^3^t^{^9}^)e^C$

The term e^C is just another constant, so with impunity, I can absorb everything into a single constant:

$y=Ce^(^3^t^{^9}^)$

To check the answer by differentiation, you require the chain rule. Differentiating an exponential gives back the exponential, but you must multiply by the derivative of the inside. We get:

$\frac{d}{dx} (y)=\frac{d}{dx}(Ce^(^3^t^{^9}^))$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*\frac{d}{dx}(3t^9)$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*27t^8$

Now check if the derivative equals the right side of the original differential equation:

$(Ce^(^3^t^{^9}^))*27t^8=27t^8*y(t)$

$Ce^(^3^t^{^9}^)*27t^8=27t^8*Ce^(^3^t^{^9}^)$

QED

I unfortunately do not have enough room for your second question. It is the exact same type of differential equation as the one solved above. The only difference is the fractional exponent, which would make the problem slightly more involved. If you ask your second question again on a different problem, I'd be glad to help you solve it.

7 0

2 years ago

Use a compass and straightedge to construct an equilateral triangle using the length (AB) ̅ for the sides.

Nostrana [21]

For a better understanding of the solution provided here please go through the diagram in the file attached.

Let us begin the construction of the triangle in a step by step fashion.

Step 1 Take AB as the base.

Step 2 Take the point of the compass and place it on A and take the width of the compass to be AB.

Step 3 Make an arc (as shown in green for convenience).

Step 4 Now, take the point of the compass and place it on B keeping the width of the compass to be AB.

Step 5 Make an arc (as shown in yellow for convenience) such that it intersects the arc made in Step 3 at the point C.

Step 6 Join the points A and C, and B and C.

The made triangle is the required equilateral triangle, $\Delta ABC$ . All the sides will be equal to the length AB.

3 0

3 years ago

How can I improve in math if I don't like it and if I can't focus a lot in that class

EastWind [94]

If I were you I would do after school math tutoring.

5 0

3 years ago

Read 2 more answers

Find the equation of a line that has slope, m, of 4 and passes through the point (10, 15).

Fantom [35]

Step-by-step explanation:

m=4 , (10, 15)

straight line equation:

y= mx +c

substituting the values:

15=4(10) + c

15 = 40 + c

15 - 40 = c

c = -25

therefore,

y = 4x - 25 (ans)

hope this helps :)))

4 0

3 years ago

which one of yu geniuses can answer this question ???

madreJ [45]

Answer:

B. 20

Step-by-step explanation:

x + 40 = 3x

x - x + 40 = 3x - x

40 = 2x

20 = x

3 0

3 years ago