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Zanzabum
3 years ago
6

Select all the situations that can be modeled by the expression-80÷4. (multiple answers may be selected)

Mathematics
1 answer:
Masja [62]3 years ago
5 0

Answer:

Answer: C and D can be modeled using our expression

Step-by-step explanation:

The expression 80 / 4 is saying that you're splitting 80 into 4 equal parts.

80 / 4 = 20

Each part being 20.

Thus, you're looking for the situations where you're "splitting" 80 into 4 different things, all worth 20.

Option A.

Brady owed his mother 80, but repaid her 4. Brady is reducing his debt to his mom by 4. A good expression would be 80 - 4. You're not splitting up the debt, you're subtracting from it. Our expression doesn't fit.

Option B.

In total, the football team lost 80 yards across 4 plays. Our expression could be used here, but that would be assuming that they lost the same amount of yards (20) each play. This is unlikely, so we can't use our expression here. (E.g. they could lose 10, then 30, then 5, then 35 -- adding up to 80)

Option C.

Sam owed $80 to 4 friends, or, his $80 debt is split into 4 parts. Since he owes the same amount to each friend (all 4 parts are equal), we CAN use our expression here to find out how much he owed each friend.

Option D.

Taya received a total of 80, and divided it into 4 parts (one for each place she spent money at). Since we know she spent the same amount at each place (all parts are equal), our expression CAN be used here.

Option E.

Amanda withdrew $80 each day for 4 days. To find out the total, we'd have to multiply 80 by 4. $80 for each withdrawal, times four, as she did it 4 times. We are not splitting $80 up into parts, so our expression can't be used here.

Answer: C and D can be modeled using our expression

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By <em>direct</em> substitution and simplification, the <em>trigonometric</em> function z = cos (2 · x + 3 · y) represents a solution of the <em>partial differential</em> equation  \frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z.

<h3>How to analyze a differential equation</h3>

<em>Differential</em> equations are expressions that involve derivatives. In this question we must prove that a given expression is a solution of a <em>differential</em> equation, that is, substituting the variables and see if the equivalence is conserved.

If we know that z = \cos (2\cdot x + 3\cdot y) and \frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z, then we conclude that:

\frac{\partial t}{\partial x} = -2\cdot \sin (2\cdot x + 3\cdot y)

\frac{\partial^{2} t}{\partial x^{2}} = - 4 \cdot \cos (2\cdot x + 3\cdot y)

\frac{\partial t}{\partial y} = - 3 \cdot \sin (2\cdot x + 3\cdot y)

\frac{\partial^{2} t}{\partial y^{2}} = - 9 \cdot \cos (2\cdot x + 3\cdot y)

- 4\cdot \cos (2\cdot x + 3\cdot y) + 9\cdot \cos (2\cdot x + 3\cdot y) = 5 \cdot \cos (2\cdot x + 3\cdot y) = 5\cdot z

By <em>direct</em> substitution and simplification, the <em>trigonometric</em> function z = cos (2 · x + 3 · y) represents a solution of the <em>partial differential</em> equation  \frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z.

To learn more on differential equations: brainly.com/question/14620493

#SPJ1

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