1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
finlep [7]
2 years ago
8

Tim and Cynthia leave Cynthia's house at the same time. Tim drives north and Cynthia drives west. Tim's average speed is 10 mph

slower than Cynthia's. At the end of one hour, they are 70 miles apart. Find Cynthia's average speed. (Round your answer to the nearest tenth.)
Mathematics
1 answer:
RSB [31]2 years ago
6 0

Answer:

  54.2 mph

Step-by-step explanation:

Since the drivers leave at the same time and travel in directions 90° from each other, their separation speed can be found using the Pythagorean theorem. Let c represent Cynthia's average speed. Then (c-10) will represent Tim's average speed. Their combined separation speed is 70 miles per hour, so we can write ...

  70² = c² +(c -10)²

  4900 = 2c² -20c +100 . . . . eliminate parentheses

  c² -10c -2400 = 0 . . . . . . . . divide by 2; put in standard form

  (c -5)² -2425 = 0 . . . . . . . . . rearrange to vertex form

  c = 5 ±5√97 . . . . . . . . . . . . solve for c, simplify radical

  c ≈ 54.244 ≈ 54.2 . . . . . . . use the positive solution

Cynthia's average speed was 54.2 miles per hour.

You might be interested in
Find the function y = f(t) passing through the point (0, 18) with the given first derivative.
monitta

Answer:

\displaystyle y = \frac{t^2}{16} + 18

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

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

<u>Algebra I</u>

  • Functions
  • Function Notation
  • Coordinates (x, y)

<u>Calculus</u>

Derivatives

Derivative Notation

Antiderivatives - Integrals

Integration Constant C

Integration Rule [Reverse Power Rule]:                                                                   \displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C

Integration Property [Multiplied Constant]:                                                             \displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

Point (0, 18)

\displaystyle \frac{dy}{dt} = \frac{1}{8} t

<u>Step 2: Find General Solution</u>

<em>Use integration</em>

  1. [Derivative] Rewrite:                                                                                         \displaystyle dy = \frac{1}{8} t\ dt
  2. [Equality Property] Integrate both sides:                                                        \displaystyle \int dy = \int {\frac{1}{8} t} \, dt
  3. [Left Integral] Integrate [Integration Rule - Reverse Power Rule]:                 \displaystyle y = \int {\frac{1}{8} t} \, dt
  4. [Right Integral] Rewrite [Integration Property - Multiplied Constant]:           \displaystyle y = \frac{1}{8}\int {t} \, dt
  5. [Right Integral] Integrate [Integration Rule - Reverse Power Rule]:              \displaystyle y = \frac{1}{8}(\frac{t^2}{2}) + C
  6. Multiply:                                                                                                             \displaystyle y = \frac{t^2}{16} + C

<u>Step 3: Find Particular Solution</u>

  1. Substitute in point [Function]:                                                                         \displaystyle 18 = \frac{0^2}{16} + C
  2. Simplify:                                                                                                             \displaystyle 18 = 0 + C
  3. Add:                                                                                                                   \displaystyle 18 = C
  4. Rewrite:                                                                                                             \displaystyle C = 18
  5. Substitute in <em>C</em> [Function]:                                                                                \displaystyle y = \frac{t^2}{16} + 18

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Integration

Book: College Calculus 10e

4 0
2 years ago
A super easy Math problem for 10 points...................
Oxana [17]

Answer:7.50

Step-by-step explanation: 3.00 + 0.50 times 9

7 0
3 years ago
What is the approximate curcumfrance of the circle shown below?​
Vikki [24]

Answer:

C.

Step-by-step explanation:

Circumference=PI*diameter

Circumference=3.14*19.5

Circumference=61.23 rounds to 61.2 so the answer is C

3 0
3 years ago
How do you become an administrator?
antoniya [11.8K]

How do you become an administrator?

I think answering a lot of questions and dont get warnings

8 0
3 years ago
there were 18 cans ona shelf. a customer bought 7 cans. then jake put 6 cans on the shelf. how many cans are on the shelf now?
Rainbow [258]
18-7+6=17

17 cans are on the shelf.
3 0
2 years ago
Read 2 more answers
Other questions:
  • Is the equation 3+z=-19 true false or open
    8·2 answers
  • Solve 2(x + 1) = 2x + 2.<br> A. All real numbers<br> B. No solution<br> C. 0<br> D. 1
    7·2 answers
  • Please help i will give a lot of points if corrected
    5·2 answers
  • Helppppp me please i need the answer fast &lt;3
    10·2 answers
  • explain how multiplying 4/10 and 3/10 is similar to multiplying 0.4 and 0.3 (please only answer if you for sure know the answer!
    9·1 answer
  • Hi I have some trouble understanding Mean,Median and Mode Comparisions can someone please help me with this problem
    13·1 answer
  • 24.783 is what percent of 75.1
    7·1 answer
  • Joe brought 17 packs of cola to a party, and each pack had 8 cans. Teresa brought 6 cans of juice. How many cans did they bring
    10·2 answers
  • Guys please help!!!!
    12·1 answer
  • To make her fruit punch for the end-of-year schoolcelebration, Yasmin uses 4 cups of papaya juice for every 6cups of pineapple j
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!