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3 years ago

How to solve it and the answer

Mathematics

1 answer:

Mandarinka [93]3 years ago

8 0

11.397058
comment If you want me to show my work

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Can someone please simplify these using product notation?

Contact [7]

A. 3a b. a^3 c. 4x d. 3pq e. 7^ef f. zxy^1

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3 years ago

Which number is divisible by both three and nine?

horrorfan [7]

Answer:

765 is divisible by 3 and 9 I hope that this helps

Step-by-step explanation:

765÷9=85

765÷3=255

7 0

2 years ago

Qu2.05 ML<br> Solve for x: 5|2x - 2] + 8 = 18.

Luda [366]

Answer:

512x−2+8=18

Step 1: Simplify both sides of the equation.

512x−2+8=18

512x+−2+8=18

(512x)+(−2+8)=18(Combine Like Terms)

512x+6=18

Step 2: Subtract 6 from both sides.

512x+6−6=18−6

512x=12

Step 3: Divide both sides by 512.

512x512=12/512

x= 3/128

Answer:

x=3/128

8 0

3 years ago

You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along

sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

$t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1$

To optimize this function we have to derive and equal to zero:

$\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\ \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\$

$x$

As $d_b=x$ , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0

3 years ago

Is it true or false that the measure of A is 45°

GrogVix [38]

The answer is false

8 0

3 years ago