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3 years ago

PLZ!!! HELP!!!!! What is the slope

Mathematics

1 answer:

pentagon [3]3 years ago

4 0

Answer:

zero slope

Step-by-step explanation:

horizontal lines are zero slope because they are not slanted (slope)

this is a horizontal line.

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You want to get from a point A on the straight shore of the beach to a buoy which is 54 meters out in the water from a point B o

anyanavicka [17]

Answer:

$x =\dfrac{45 \sqrt{6}}{ 2}$

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

$\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}$

In order to estimate the point along the shore, x meters from B, the runner should stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

i.e

The differential of V(x) = V'(x) =0

= $\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0$

$-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0$

$\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}$

$\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}$

$\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}$

$\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}$

squaring both sides; we get

$\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}$

$\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}$

By cross multiplying; we get

$49x^2 = 25(54^2+x^2)$

$49x^2 = 25 \times 54^2+ 25x^2$

$49x^2-25x^2 = 25 \times 54^2$

$24x^2 = 25 \times 54^2$

$x^2 = \dfrac{25 \times 54^2}{24}$

$x =\sqrt{ \dfrac{25 \times 54^2}{24}}$

$x =\dfrac{5 \times 54}{\sqrt{24}}$

$x =\dfrac{270}{\sqrt{4 \times 6}}$

$x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}$

$x =\dfrac{45 \sqrt{6}}{ 2}$

8 0

3 years ago

Three times a number x is more than 18.

poizon [28]

Answer:

3x>18

Step-by-step explanation:

Three times the number x will be called 3x. If an expression is more or greater than a number, we use the greater symbol: >

So, we can write,

3x>18

5 0

2 years ago

How can I factor -2x^2+2x+4=0 ?

Shtirlitz [24]

Because all are a multiple of 2, you can factor out 2, 2(-x^2+x+2)=0

4 0

3 years ago

HELP ME PLEASE ECPLAIN WHY

stiv31 [10]

Answer:

A≈110.11

using formula 1/4 $\sqrt5(5+2\sqrt5)a2$

Step-by-step explanation:

8 0

3 years ago

For the given decision algorithm, find how many outcomes are possible. HINT [See Example 1.] Step 1: Step 2: Alternative 1: 1 ou

Kruka [31]

Answer:

the total number of outcome in step 1 = 1+2+3= 6

the total number of outcome in step 2 = 2 +2+3 = 7

hence total number of outcome = 6 x7

= 42

Step-by-step explanation:

7 0

3 years ago