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2 years ago

An airplane descends 1.6 miles to an elevation of 6.95 miles. Find the elevation of the plane before its

Mathematics

1 answer:

kolezko [41]2 years ago

8 0

Answer:

Step-by-step explanation: First, let's call the starting elevation of the plane: e

We can then write an equation representing this problem as:

e−1.5mi=5.25mi

Now, add 1.5mi to each side of the equation to solve for e

while keeping the equation balanced:

e−1.5mi + 1.5mi=5.25mi + 1.5mi

e−0=6.75mi

e=6.75mi

The plane's starting elevation was 6.75 miles

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Write a fraction, less than 1 with a denominator of 6 that is greater than 3/4

guajiro [1.7K]

6>3/4... a number greater than one can be expressed as a fraction with a numerator greater than the denominator. Hope this helps...

5 0

2 years ago

<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx....%7D%20%7D%20%7D%20%7D%20%20%3D%20%

andrey2020 [161]

First observe that if $a+b>0$ ,

$(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}$

Let $a=0$ and $b=x$ . It follows that

$a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}$

Now let $b=1$ , so $a^2+a=4x$ . Solving for $a$ ,

$a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2$

which means

$a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}$

Now solve for $x$ .

$x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2$

(note that we assume $2x-1\ge0$ )

$4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}$

(we omit $x=0$ since $2\cdot0-1=-1\ge0$ is not true)

3 0

1 year ago

The local newspaper has letters to the editor from 70 people. If this number represents 5% of all of the newspaper's readers, h

Alex Ar [27]

Answer:

This shows us that there are 1400 readers.

Step-by-step explanation:

To work this out you would first need to find how many times 5% goes into 100%, You can do this by dividing 100 by 5, this gives you 20. This is because the whole amount is equivalent to 100%.

To work out the total number of readers you would multiply 70 by 20, this gives you 1400. This is because we know that 70 is equivalent to 5% and that 5% goes into 100% 20. So by multiplying 70 by 20 we are working out the total (100%), and that this shows us there are 1400 readers.

1) Divide 100 by 5.

$100/5=20$

2) Multiply 70 by 20.

$70*20=1400$

8 0

2 years ago

The radius of a cylindrical gift box is (4x + 1) inches. The height of the gift box is three times the radius. What is the sur

user100 [1]

Answer:

S = 128πx² + 64πx + 8π

Step-by-step explanation:

Suraface area of a cylinder is given by:

S = 2πrh + 2πr²

We know that the height is 3 times as big as the radius, hence:

h = 3r

so we can plug in the new h value and rewrite the S equation as:

S = 2πrh + 2πr²

S = 2πr(3r) + 2πr²

S = 6πr² + 2πr²

S = 8πr²

We're given in the question that the radius is (4x + 1) inches, so plug that into r.

Given: r = 4x + 1

Therefore,

S = 8πr²

S = 8π(4x + 1)²

S = 8π(16x²+8x+1)

S = 128πx² + 64πx + 8π

8 0

3 years ago

Read 2 more answers

What is the y-value of sin(x) when x= -180°?

Andreyy89

In trigonometry, we start from the point (1,0), so this is the 0-degree point. Then, we start rotating counter clockwise along the unit circle.

Note that rotating 180 or -180 degrees is actually the same, because you travel half the circumference clockwise or counter clockwise. In both cases, you start from the rightmost point of the circle, (1,0), and arrive at the leftmost point, (-1,0).

Now, for every point (x,y) on the unit circle, given by a certain angle $\alpha$ , we have

$\cos(\alpha)=x,\quad \sin(\alpha)=y$

So, in this case, the angle of -180 is associated with the point (-1,0), and thus we have

$\sin(-180)=0$

8 0

2 years ago