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3 years ago

7. Diana took 2 hours to cycle from town X to town Y. Her average speed was 10 kilometers per

Mathematics

1 answer:

motikmotik3 years ago

7 0

Answer:

a.) 20 kilometers

b.)1.67 hours

Step-by-step explanation:

a.) formula= speed =distance/time

Speed= 10km/hr

Distance=unknown

Time=2hrs

Therefore from formula, distance=speed x time

10 x 2

20 kilometers

b.) If average speed is increased by 2km/hr then

total speed= 2+10=12km/hr

Distance remains constant therefore distance= 20km

Therefore time =distance/speed

20/12

= 1.67 hours

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Find the slope of line passing through the two points, (7, 1) and (-2, 1).

Mamont248 [21]

Answer: m = 0

Step-by-step explanation:

Slope (m) = y2 - y1/,x2 - x1 : meaning increase in y divided by increase in x . it can also be written as ∆y/∆x

y1= 1, y2 = 1, x1 = 7, x2 = -2

Substitute for those values in the equation above

m = 1 -1/-2 - 7

= 0/-9

Therefore,

m = 0

The slope of the line passing through those coordinates = 0

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3 years ago

6ax^2+6ax+6a find the greatest common factor?

adelina 88 [10]

The GCF (Greatest Common Factor) is 6a.

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2 years ago

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Which of the following are perfect squares? 2, 4, 6, 16, 20,25, x², x³, x¹⁵, x²⁰, x²⁵

coldgirl [10]

Answer:

4, 16, 25, $x^{2}$ , $x^{20}\\$ .

Step-by-step explanation:

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2 years ago

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How to differentiate ?

Bas_tet [7]

Use the power, product, and chain rules:

$y = x^2 (3x-1)^3$

• product rule

$\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm d(x^2)}{\mathrm dx}\times(3x-1)^3 + x^2\times\dfrac{\mathrm d(3x-1)^3}{\mathrm dx}$

• power rule for the first term, and power/chain rules for the second term:

$\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(x-1)^2\times\dfrac{\mathrm d(3x-1)}{\mathrm dx}$

• power rule

$\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(3x-1)^2\times3$

Now simplify.

$\dfrac{\mathrm dy}{\mathrm dx} = 2x(3x-1)^3 + 9x^2(3x-1)^2 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2 \times (2(3x-1) + 9x) \\\\ \boxed{\dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2(15x-2)}$

You could also use logarithmic differentiation, which involves taking logarithms of both sides and differentiating with the chain rule.

On the right side, the logarithm of a product can be expanded as a sum of logarithms. Then use other properties of logarithms to simplify

$\ln(y) = \ln\left(x^2(3x-1)^3\right) \\\\ \ln(y) = \ln\left(x^2\right) + \ln\left((3x-1)^3\right) \\\\ \ln(y) = 2\ln(x) + 3\ln(3x-1)$

Differentiate both sides and you end up with the same derivative:

$\dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac2x + \dfrac9{3x-1} \\\\ \dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \times x^2(3x-1)^3 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(15x-2)(3x-1)^2$

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2 years ago

Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent switc

s344n2d4d5 [400]

Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent switches, each one set on or off. The receiver (wired to the door) must be set with the same pattern as the transmitter. If six neighbors with the same type of opener set their switches independently.The probability of at least one pair of neighbors using the same settings is 0.65633

Step-by-step explanation:

Step 1

In the question it is given that

Automatic garage door opener utilizes a transmitter control with four independent switches

So .the number of Combinations possible with the Transmitters =

2*2*2*2= 16

Step 2

Probability of at least one pair of neighbors using the same settings = 1- Probability of All Neighbors using different settings.

= 1- 16*15*14*13*12*11/(16^6)

Step 3

Probability of at least one pair of neighbors using the same settings=

= 1- 0.343666

Step 4

So the probability of at least one pair of neighbors using the same settings

is 0.65633

3 0

2 years ago