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3 years ago

Write the following as a simple fraction in lowest terms

Mathematics

1 answer:

mrs_skeptik [129]3 years ago

3 0

(-6)^-4 / -6^(-3) = -6^(-4- -3) = (-6)^-1 = -1/6

(-6)^-2 / (-6)^-3 = (-6)^1 = -6

So the answer is - 6 1/6

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A person stands 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 meters

In-s [12.5K]

Answer:

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

Step-by-step explanation:

Given that,

A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.

From Pythagorean Theorem,

(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+

Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.

∴y²= x²+10²

$\Rightarrow y=\sqrt{x^2+100}$

Differentiating with respect to t

$\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}$

$\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}$

Since the car driving towards the intersection at 13 m/s.

so, $\frac{dx}{dt}=-13$

$\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)$

Now

$\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)$

$=\frac{24\times (-13)}{\sqrt{676}}$

$=\frac{24\times (-13)}{26}$

= -12 m/s

Negative sign denotes the distance between the car and the person decrease.

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

8 0

2 years ago

30 <img src="https://tex.z-dn.net/?f=30%5Cgeq%205" id="TexFormula1" title="30\geq 5" alt="30\geq 5" align="absmiddle" class="lat

Mila [183]

30 is more than 5 not exactlt know what ur looking for here?

3 0

2 years ago

Sierra has plotted two vertices of a rectangle at (3,2) and (8,2). What is the length of the sides of the rectangle

Eddi Din [679]

Answer:

5units

Step-by-step explanation:

Given the two vertices of a rectangle at (3,2) and (8,2). We are to calculate the distance between the two points.

Using the formula

D = √(x2-x1)²+(y2-y1)²

D = √(2-2)²+(8-3)²

D = √0+5²

D = √25

D = 5

Hence the length of the side of the rectangle is 5units

4 0

2 years ago

Can anyone help me with this problem?

Katen [24]

A because -2 -3 -4 ext are less than -1

6 0

2 years ago

Max has more than 5 carrots (number of carrots Max has = c)

Ainat [17]

Answer:

The right answer is five

4 0

1 year ago