A cyclist travels3 km in 10 minutes.find his speed in km

Please help me I will really appreciate it!!!

slega [8]

Answer:

$\displaystyle r=\sqrt[3]{\frac{3V}{4\pi}}$

The last option matches the correct solution

Step-by-step explanation:

Equation Solving

We have the following equation:

$\displaystyle V=\frac{4}{3}\pi r^3$

And it's required to solve it for r.

Solving this equation needs to perform some operations to have the r isolated from any other variables or constants.

It can be done by conveniently operating on both sides as follows:

Eliminate the denominator by multiplying by 3:

$\displaystyle 3V=4\pi r^3$

Move $4\pi$ to the other side by dividing by $4\pi$ :

$\displaystyle \frac{3V}{4\pi}= r^3$

Swapping sides to have r at the left side:

$\displaystyle r^3=\frac{3V}{4\pi}$

Finally, take the cubic root and leave r alone:

$\displaystyle r=\sqrt[3]{\frac{3V}{4\pi}}$

The last option matches the correct solution

5 0

3 years ago

The owner of a grocery store wants to mix two kinds of condy together to make 15lb that he can sell for $5.00 per lb. He wants t

ankoles [38]

Answer: 6 pounds of sugar candy, and 9 pounds of chocolate candy.

Step-by-step explanation:

Let's define the variables:

C = pounds of chocolate candies used.

S = pounds of sugar candies used.

We know that he wants to make a total of 15lb, then:

C + S = 15

We also want that the price per pound to be equal to 5$.

This means that the price of the 15 pounds will be the same as the price of the un-mixed candies.

C*$7.00 + $2.00*S = $5.00*15

Then we have a system of equations:

C + S = 15

C*$7.00 + $2.00*S = $5.00*15

To solve this system, we need to start by isolating one of the variables, i will isolate C in the first equation:

C = 15 - S

now we can replace that in the other equation:

(15 - S)*$7.00 + $2.00*S = $5.00*15

Now we can solve this for S.

$105 - $5.00*S = $75

$105 - $75 = $5.00*S

$30 = $5.00*S

$30/$5 = S = 6

Then there are 6 pounds of sugar candy, and we can use the equation:

C + S = 15

C + 6 = 15

C = 15 - 6 = 9

There are 9 pounds of chocolate candy in the mix.

3 0

3 years ago

Read 2 more answers

(1+tan^2 A)cot A/cosec^2 A= tanA

Rufina [12.5K]

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

1 + tan²A = sec²A , secA = $\frac{1}{cosA}$ , cosecA = $\frac{1}{sinA}$ , cotA = $\frac{cosA}{sinA}$ , tanA = $\frac{sinA}{cosA}$

Consider the left side

$\frac{(1+tan^2A)cotA}{cosec^2A}$

= $\frac{sec^2AcotA}{cosec^2A}$

= $\frac{\frac{1}{cos^2A}(\frac{cosA}{sinA}) }{cosec^2A}$

= $\frac{\frac{1}{cosAsinA} }{\frac{1}{sin^2A} }$

= $\frac{1}{cosAsinA}$ × sin²A

= $\frac{sinA}{cosA}$

= tanA = right side , thus proven

4 0

3 years ago

Please help. All you have to do is write a simple expression but I don't fully under stand it so please help me. This is due tod

Semenov [28]

Answer:

1497 - 202

Step-by-step explanation:

The question is saying that the Las Vegas trip was longer so we know to put that first in the expression

we can also tell that the question is asking us for the difference (aka subtraction) between the two trip by the key words how much longer

and then it tells us that we are finding the difference between Las Vegas and Cheyenne so we know to use those two numbers

that is how we come up with the expression 1497 - 202

7 0

3 years ago

In the rational expression,

Travka [436]

Answer:

The reason why it is incorrect to cancel the 4x in the numerator with the 4x in the denominator is because 4x is not a factor of both the numerator and the denominator

Step-by-step explanation:

The denominator of the rational expression, x^2 + 4x - 12 given above is a quadratic equation. It is not factorizable. If we factorize the numerator, 4x - 8, we would have

4 (x - 2).

This means 4x is not a factor of the numerator(4x - 8) and neither is it a factor of the denominator (x^2 + 4x - 12). This is the reason why it is incorrect to cancel the 4x in the numerator with the 4x in the denominator. The factors of the denominator can only be gotten by using the general formula for solving quadratic equations

3 0

3 years ago