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dalvyx [7]
3 years ago
13

Alfonse and Melinda are taking a drive in a certain country. They know that a speed of 100 kilometers per hour is approximately

equal to 62 miles per hour. They are now driving on a road that has a speed limit of 105 kilometers per hour. How many miles per hour is the speed​ limit?
Mathematics
1 answer:
Alborosie3 years ago
5 0

Answer:

65.1 miles per hour

Step-by-step explanation:

According to the question 100 Km/hour = 63 miles/hour

It means in one hour 100 Km is traveled which is also equal to 62 miles.

hence 100 Km = 62 miles

dividing both sides by 100 we have

100/100 Km = 62/100 miles

Hence we can say that

1 Km = 0.62 miles

_________________________________________________

Multiplying both side by 105  we have

1 Km * 105 = 0.62 miles * 105

105 Km = 65.1 miles

Thus, 105 Km/hour is same as 65.1 miles per hour.

As 105 kilometres per hour is the speed limit in terms of yards/hour

speed limit will be  65.1 miles per hour.

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Find f(a), f(a+h), and<br> 71. f(x) = 7x - 3<br> f(a+h)-f(a)<br> h<br> if h = 0.<br> 72. f(x) = 5x²
Leni [432]

Answer:

71. \ \ \ f(a) \  = \  7a \ - \ 3; \ f(a+h) \  =  \ 7a \ + \ 7h \ - \ 3; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 7

72. \ \ \ f(a) \  = \  5a^{2}; \ f(a+h) \  =  \ {5a}^{2} \ + \ 10ah \ + \ {5h}^{2}; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 10a \ + \ 5h

Step-by-step explanation:

In single-variable calculus, the difference quotient is the expression

                                              \displaystyle\frac{f(x+h) \ - \ f(x)}{h},

which its name comes from the fact that it is the quotient of the difference of the evaluated values of the function by the difference of its corresponding input values (as shown in the figure below).

This expression looks similar to the method of evaluating the slope of a line. Indeed, the difference quotient provides the slope of a secant line (in blue) that passes through two coordinate points on a curve.

                                             m \ \ = \ \ \displaystyle\frac{\Delta y}{\Delta x} \ \ = \ \ \displaystyle\frac{rise}{run}.

Similarly, the difference quotient is a measure of the average rate of change of the function over an interval. When the limit of the difference quotient is taken as <em>h</em> approaches 0 gives the instantaneous rate of change (rate of change in an instant) or the derivative of the function.

Therefore,

              71. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{(7a \ + \ 7h \ - \ 3) \ - \ (7a \ - \ 3)}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{7h}{h} \\ \\ \-\hspace{4.25cm} = \ \ 7

               72. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{{5(a \ + \ h)}^{2} \ - \ {5(a)}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{{5a}^{2} \ + \ 10ah \ + \ {5h}^{2} \ - \ {5a}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{h(10a \ + \ 5h)}{h} \\ \\ \-\hspace{4.25cm} = \ \ 10a \ + \ 5h

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2 years ago
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BaLLatris [955]
N is greater than or equal to 11, I believe
3 0
3 years ago
Find YW. YW = _<br><br> I just need the answer for YW no explanation needed.
KATRIN_1 [288]

Answer:

YW=20\ units

Step-by-step explanation:

we know that

In a parallelogram the diagonals bisect each other

The figure XYZW is a parallelogram

so

VW=VY

VX=VZ

<em>Find the value of b</em>

VW=VY

substitute the given values

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solve for b

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YW=5b+b+8

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Gekata [30.6K]

Answer:

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Explanation:

\sf\:Given\:expression: log(\dfrac{x^2 y^3}{z} )

Logarithm rules:

\sf (i)  \ \sf log(ab) = log(a) + log(b)\\ \\ (ii) \  log(a/b) = log(a) - log(b)\\\\ (iii) \ log(a^n) = n log(a)

Breakdown of the expression:

\rightarrow \sf log\left(\dfrac{x^2y^3}{z}\right)

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\rightarrow \sf 2\log\left(x\right)+3\log \left(y\right)-\log \left(z\right)

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2 years ago
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