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1 year ago

Use inductive reasoning to predict the next three numbers in the pattern (or sequence).

Mathematics

1 answer:

Arada [10]1 year ago

6 0

Answer:

28, 35, 43

Step-by-step explanation:

8-7 = 1

10-8 = 2

13-10 = 3

As you can see you need to add one extra numbers and the sequence goes on

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How does the volume of a sphere compare to that of the volume of a cylinder? What would you say the scale factor for Vol sphere:

borishaifa [10]

Answer:

The volume of a sphere is 2/3 times the volume of a similar cylinder

Scale factor : 2/3

Step-by-step explanation:

Let us consider a sphere of radius r. The volume of the sphere will be given as

$V_{s}=\frac{4}{3} \pi r^{3}$

Similarly, let us consider a cylinder with its height being twice the radius of the sphere. We will have its volume given as:

$V_{c}=\pi r^{2}h$

but h = 2r

Hence we have

$V_{c}= 2\pi r^{3}h$

We can divide the two volumes to get a constant that links them together

$\frac{V_{s}}{V_{c}}=\frac{\frac{4}{3} \pi r^{3}}{2\pi r^{3}h}$

this will give us 2/3

Hence the scale factor for Vol sphere: Vol cylinder is 2/3

3 0

3 years ago

How do you simplify (2xy2)3

pantera1 [17]

$(2xy^{2})^{3} = (2xy^{2})(2xy^{2})(2xy^{2})$
Now, we can just multiply it and obtain the result
$(2xy^{2})(2xy^{2})(2xy^{2})=(4x^{2}y^{4})(2xy^{2})=8x^{3}y^{6}$

I used law presented on this example
$2^{3}*2=2^{3}*2^{1}=2^{3+1}=2^{4}$

4 0

3 years ago

Show work please<br> \sqrt(x+12)-\sqrt(2x+1)=1

Nesterboy [21]

Answer:

$x=4$

Step-by-step explanation:

Given $\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1$ , start by squaring both sides to work towards isolating $x$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2$

Recall $(a-b)^2=a^2-2ab+b^2$ and $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1$

Isolate the radical:

$\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}$

Square both sides:

$\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2$

Expand using FOIL and $(a+b)^2=a^2+2ab+b^2$ :

$\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36$

Move everything to one side to get a quadratic:

$\displaystyle-\frac{1}{4}x^2+7x-24=0$

Solving using the quadratic formula:

A quadratic in $ax^2+bx+c$ has real solutions $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In $\displaystyle-\frac{1}{4}x^2+7x-24$ , assign values:

$\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24$

Solving yields:

$\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}$

Only $x=4$ works when plugged in the original equation. Therefore, $x=24$ is extraneous and the only solution is $\boxed{x=4}$

4 0

2 years ago

How did British scientists test Einstein theory of relativity

Stolb23 [73]

Answer: Arthur Stanley Eddington's 1919 expedition confirmed Einstein's prediction for the deflection of light by the Sun during the total solar eclipse of 29 May 1919 which helped to cement the status of general relativity as a true theory. Since then many observations have confirmed the correctness of general relativity.

Hope this helps. Also gimme brainliest.

8 0

2 years ago

Which are the correct classifications for the polygon?

katrin [286]

The correct classification for the polygon would be a concave hexagon.

6 0

2 years ago