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Mathematics

1 answer:

Umnica [9.8K]2 years ago

6 0

It’s a positive slope, constant slope, and increasing function. Because it’s a straight line going diagonally to the top right, you know the slope is positive, constant, and the function is positive.

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A geometric sequence is a sequence of numbers where the next term equals to

exis [7]

Answer:

Step-by-step explanation:

Let the first term be a and the common ratio be r.

ATQ, ar^4=24 and ar^6=144, r=sqrt(6) and a=24/(sqrt(6))^2=24/36=2/3

4 0

3 years ago

A bicyclist travels 13 km at a speed of 20 km/hr. how long does it take her to travel this distance?

aliina [53]

Answer:

${ \tt{time = \frac{distance}{time} }} \\$

speed is 20 km/hr
distance is 13 km

${ \tt{time = \frac{13}{20} }} \\ \\ { \boxed{ \tt{ \: time = 0.65 \: hours}}}$

3 0

2 years ago

Solve the differential equation.<br><br> (y^2 + xy^2)y' = 1

stira [4]

$(y^2 + xy^2)y' = 1 \ \Rightarrow\ (y^2 + xy^2)\frac{dy}{dx}= 1 \ \Rightarrow\\ \\
y^2(1 + x) \frac{dy}{dx} = 1 \ \Rightarrow\ y^2 dx = \frac{dx}{1 + x}\ \Rightarrow \\ \\
\int y^2 dx =\int \frac{dx}{1 + x} \ \Rightarrow\ \frac{1}{3}y^3 = \ln|1+x| + C\ \Rightarrow \\ \\
y^3 = 3 \ln|1 + x| + 3C\ \Rightarrow\ y = \sqrt[3]{3\ln|1+x| + K},\ \text{where $K = 3C$}
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