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3 years ago

3. An airplane flies 105 miles in ½ hour. How far can it fly in 1 ¼ hours at the same rate of speed?

Mathematics

2 answers:

ella [17]3 years ago

6 0

Answer:

105 at 30 min.

<em>x</em> at 75 min.

105 mph x 2 = 210 mph at one hour

There is still 15 min to go soooo...

210/4 = 52.5

210 + 52.5 = 262.5 mph for 75 min

Check by dividing

262.5/75=3.5

raketka [301]3 years ago

5 0

262.5 miles
explanation 1/4 is half of 1/2 so 52.5 is half of 105 and then 210 for an hour of travel

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Is anyone able to figure this out, I can't do this

katrin [286]

Answer:

C. √2 - 1

Step-by-step explanation:

If we draw a square from the center of the large circle to the center of one of the small circles, we can see that the sides of the square are equal to the radius of the small circle (see attached diagram)

Let r = the radius of the small circle

Using Pythagoras' Theorem $a^2+b^2=c^2$

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

to find the diagonal of the square:

$\implies r^2 + r^2 = c^2$

$\implies 2r^2 = c^2$

$\implies c=\sqrt{2r^2}$

So the diagonal of the square = $\sqrt{2r^2}$

We are told that the radius of the large circle is 1:

⇒ Diagonal of square + r = 1

$\implies \sqrt{2r^2}+r=1$

$\implies \sqrt{2r^2}=1-r$

$\implies 2r^2=(1-r)^2$

$\implies 2r^2=1-2r+r^2$

$\implies r^2+2r-1=0$

Using the quadratic formula to calculate r:

$\implies r=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\implies r=\dfrac{-2\pm\sqrt{2^2-4(1)(-1)}}{2(1)}$

$\implies r=\dfrac{-2\pm\sqrt{8}}{2}$

$\implies r=-1\pm\sqrt{2}$

As distance is positive, $r=-1+\sqrt{2}=\sqrt{2}-1$ only

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2 years ago

Read 2 more answers

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3 years ago

Simplify (4ab^2)^3<br><br> Any help is appreciated

Pie

Answer:

$64a^{3} b^{6}$

Step-by-step explanation:

1) Distribute the exponent outside of the parentheses to the terms inside the parentheses. In this case, multiply the 3 outside the parentheses with the exponent of each of the terms inside:

$(4ab^{2} )^3$

$4^{3}$ · $a^{3}$ · $b^{6}$

2) The variables are fine - you can't simplify them further. All you need to do now is multiply the $4^{3}$ out. Remember that it's kind of like asking, "what is 4 × 4 ×4?"

$4$ · $4$ · $4$ · $a^{3}$ · $b^{6}$

$16$ · $4$ · $a^{3}$ · $b^{6}$

$64a^{3} b^{6}$

Therefore, $64a^{3} b^{6}$ is the answer.

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2 years ago

The quotient is 71 2/3 what is the divisor

Genrish500 [490]

The divisor is 3.
It is 3 because to make the whole number and the remainder a mixed number you take the whole number then for the numerator you write what is left over(remainder) and for the denominator you will write the divisor. In this case the denominator is 3 so the divisor is 3.

Hope I helped ! :D

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2 years ago

The ratio table shows that 4 pounds of tomatoes cost $14. Complete the

valina [46]

Answer:

1 tomato: $3.50

2 tomatoes: $7

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Step-by-step explanation:

Ok, to start of if 4 tomatoes cost $14, that means 2 tomatoes cost $7. This probably means 1 tomato cost $3.50 and 3 tomatoes cost $10.50. Hope this helps!

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3 years ago