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solniwko [45]
3 years ago
12

SCALCET8 3.9.017.MI. Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west at 20 mi

/h. At what rate is the distance between the cars increasing two hours later
Mathematics
1 answer:
Veronika [31]3 years ago
3 0

Answer:

The rate at which the distance between the cars increasing two hours later=52mi/h

Step-by-step explanation:

Let

Speed of one car, x'=48 mi/h

Speed of other car, y'=20 mi/h

We have to find the rate at which the distance between the cars increasing two hours later.

After 2 hours,

Distance traveled by one car

x=48\times 2=96 mi

Using the formula

Distance=Time\times speed

Distance traveled by other car

y=20\times 2=40 mi

Let z be the distance between two cars after 2 hours later

z=\sqrt{x^2+y^2}

Substitute the values

z=\sqrt{(96)^2+(40)^2}

z=104 mi

Now,

z^2=x^2+y^2

Differentiate w.r.t t

2z\frac{dz}{dt}=2x\frac{dx}{dt}+2y\frac{dy}{dt}

z\frac{dz}{dt}=x\frac{dx}{dt}+y\frac{dy}{dt}

Substitute the values

104\frac{dz}{dt}=96\times 48+40\times 20

\frac{dz}{dt}=\frac{96\times 48+40\times 20}{104}

\frac{dz}{dt}=52mi/h

Hence, the rate at which the distance between the cars increasing two hours later=52mi/h

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lord [1]

Answer:

x = - 3 ± \sqrt{2}

Step-by-step explanation:

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x² + 6x = - 7

using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(3)x + 9 = - 7 + 9

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x + 3 = ± \sqrt{2} ( subtract 3 from both sides )

x = - 3 ± \sqrt{2}

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2 years ago
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Ksenya-84 [330]

Answer:

x = -4

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

Step-by-step explanation:

<u>Step 1: Define</u>

-15x + 5 = -10x + 25

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Add 15x on both sides:                    5 = 5x + 25
  2. Subtract 25 on both sides:              -20 = 5x
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  4. Rewrite:                                             x = -4
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Answer:

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Step-by-step explanation:

-15x^-10 * y ^ -3 * x^-9 * y^-9/3 (It's writing it like this.)

15 and 3 have a GCF of 3.

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Remove extraneous 1.

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Add integers.

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Negative powers change multiplication to division.

-5 / (x^19 * y^12) is the final answer.

Even with that, the simplified answer wouldn't have negative exponents because of the negative powers rule.

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Answer:

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