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katovenus [111]
3 years ago
11

The table lists the top four times for the 50-yard freestyle at a swim meet. Who had the fastest time?

Mathematics
1 answer:
Advocard [28]3 years ago
4 0

Answer:

Step-by-step explanation:

Nobody likes a short, one-word-answer. Let’s make sure other people understand everything.

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Two boats leave a dock at the same time. One boat travels south at 32 mi divided by hr32 mi/hr and the other travels east at 60
TEA [102]

Answer: the rate at which the distance between the boats is​ increasing is 68 mph

Step-by-step explanation:

The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.

Let x represent the length the shorter leg(south) of the right angle triangle.

Let y represent the length the longer leg(east) of the right angle triangle.

Let z represent the hypotenuse.

Applying Pythagoras theorem

Hypotenuse² = opposite side² + adjacent side²

Therefore

z² = x² + y²

To determine the rate at which the distances are changing, we would differentiate with respect to t. It becomes

2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1

One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that

dx/dt = 32

dy/dt = 60

Distance = speed × time

Since t = 0.5 hour, then

x = 32 × 0.5 = 16 miles

y = 60 × 0.5 = 30 miles

z² = 16² + 30² = 256 + 900

z = √1156

z = 34 miles

Substituting these values into equation 1, it becomes

2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60

68dz/dt = 1024 + 3600

68dz/dt = 4624

dz/dt = 4624/68

dz/dt = 68 mph

6 0
3 years ago
A car uses 30 gallons of gasoline for a trip of 800 miles. How many gallons would
antoniya [11.8K]

Answer:

26.25 gallons

Step-by-step explanation:

\frac{30 gallons}{800 miles} = \frac{x}{700 miles}

21000 = 800x

x = 26.25 gallons

6 0
3 years ago
544484454545454c454545x454544d5454d5w4ds5d45x45a45s4544444444444444444444444444444444444444449999999999999999xx599999999999994x5
MAXImum [283]

Answer:

uh. the answer to this is

8 0
2 years ago
Read 2 more answers
I need help with this question: Label: Coefficients, variables, terms, and constant. −2x2 + 9x − 3
iVinArrow [24]

Answer:

  coefficients: {-2, +9, -3}

  variables: {x}

  terms: {-2x^2, 9x, -3}

  constant: {-3}

Step-by-step explanation:

It is difficult to "label" here, so we'll list each, separated by commas.

<u>Coefficients</u>

Coefficients are the multiplicative factor of an expression. Depending on the expression of interest, it may consist of numbers, variables, or expressions. Here, we consider the expression of interest to be powers of x, so the coefficients are as listed. The last one (-3) is sometimes called a "constant coefficient." It multiplies x^0.

  coefficients: {-2, +9, -3}

<u>Variables</u>

A variable is usually a letter, symbol, or sequence of letters and symbols, that stands for something else--usually an unknown quantity. Its meaning and value will depend on the context. Generic variables are usually taken from the end of the alphabet: x, y, z. Their capitalization, font, or face may give special meaning. For example bold-face capital letters may be used to represent vectors or matrices.

  variables: {x}

<u>Terms</u>

A term is a product of coefficients and variables. Terms in a polynomial are separated by addition or subtraction symbols.

  terms: {-2x^2, 9x, -3}

<u>Constant</u>

"Constant" usually refers to a term containing no variables. It generally refers to a value that doesn't change.

  constant: {-3}

8 0
3 years ago
Which statement regarding the number of solutions for the linear equation shown below is true?
beks73 [17]
No Solutions. hope it helped
6 0
3 years ago
Read 2 more answers
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