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2 years ago

Match the solution set given in inequality with the best solution set given in interval notation

Mathematics

1 answer:

zimovet [89]2 years ago

7 0

There you go

I hope this help you

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What two consecutive whole numbers lie between the square root of 55?

Kamila [148]

$\boxed{7 \ \textless \ \sqrt{55} \ \textless \ 8}\\\\because\ 7^2=49 \ \textless \ 55\ and\ 8^2=64 \ \textgreater \ 55$

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2 years ago

Read 2 more answers

Whats the value of u+5v-w,if u=6, and w=9?

Vitek1552 [10]

To solve this we need only substitute values of u and w, and then calculate.

<span>u+5v-w = 6 + 5v - 9 = 5v +6 - 9 = 5v - 3</span>

3 0

2 years ago

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. (2 points)

n200080 [17]

Given:

$f(x)=\dfrac{8}{x}$

$g(x)=\dfrac{8}{x}$

To find:

Whether f(x) and g(x) are inverse of each other by using that f(g(x)) = x and g(f(x)) = x.

Solution:

We know that, two function are inverse of each other if:

$f(g(x))=x$ and $g(f(x))$

We have,

$f(x)=\dfrac{8}{x}$

$g(x)=\dfrac{8}{x}$

Now,

$f(g(x))=f(\dfrac{8}{x})$ $[\because g(x)=\dfrac{8}{x}]$

$f(g(x))=\dfrac{8}{\dfrac{8}{x}}$ $[\because f(x)=\dfrac{8}{x}]$

$f(g(x))=8\times \dfrac{x}{8}$

$f(g(x))=x$

Similarly,

$g(f(x))=f(\dfrac{8}{x})$ $[\because f(x)=\dfrac{8}{x}]$

$g(f(x))=\dfrac{8}{\dfrac{8}{x}}$ $[\because g(x)=\dfrac{8}{x}]$

$g(f(x))=8\times \dfrac{x}{8}$

$g(f(x))=x$

Since, $f(g(x))=x$ and $g(f(x))$ , therefore, f(x) and g(x) are inverse of each other.

6 0

2 years ago

A restaurant bill before tax is $15.50. How much is a 15% tip for this bill? How much money should be left for the whole bill?

ahrayia [7]

Answer:

The tip would be approximately $2.33. The total amount of money that should be left on the bill is $17.73.

Step-by-step explanation:

To determine the tip: 15.50 times 0.15 = 2.325 ≈ 2.33

To determine the total: 15.50 plus 2.33

4 0

3 years ago

Let S be the solid beneath z = 12xy^2 and above z = 0, over the rectangle [0, 1] × [0, 1]. Find the value of m > 1 so that th

jonny [76]

Answer:

The answer is $\sqrt{\frac{6}{5}}$

Step-by-step explanation:

To calculate the volumen of the solid we solve the next double integral:

$\int\limits^1_0\int\limits^1_0 {12xy^{2} } \, dxdy$

Solving:

$\int\limits^1_0 {12x} \, dx \int\limits^1_0 {y^{2} } \, dy$

$[6x^{2} ]{{1} \atop {0}} \right. * [\frac{y^{3}}{3}]{{1} \atop {0}} \right.$

Replacing the limits:

$6*\frac{1}{3} =2$

The plane y=mx divides this volume in two equal parts. So volume of one part is 1.

Since m > 1, hence mx ≤ y ≤ 1, 0 ≤ x ≤ $\frac{1}{m}$

Solving the double integral with these new limits we have:

$\int\limits^\frac{1}{m} _0\int\limits^{1}_{mx} {12xy^{2} } \, dxdy$

This part is a little bit tricky so let's solve the integral first for dy:

$\int\limits^\frac{1}{m}_0 [{12x \frac{y^{3}}{3}}]{{1} \atop {mx}} \right.\, dx =\int\limits^\frac{1}{m}_0 [{4x y^{3 }]{{1} \atop {mx}} \right.\, dx$

Replacing the limits:

$\int\limits^\frac{1}{m}_0 {4x(1-(mx)^{3} )\, dx =\int\limits^\frac{1}{m}_0 {4x-4x(m^{3} x^{3} )\, dx =\int\limits^\frac{1}{m}_0 ({4x-4m^{3} x^{4}) \, dx$

Solving now for dx:

$[{\frac{4x^{2}}{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right. = [{2x^{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right.$

Replacing the limits:

$\frac{2}{m^{2} }-\frac{4m^{3}\frac{1}{m^{5}}}{5} =\frac{2}{m^{2} }-\frac{4\frac{1}{m^{2}}}{5} \\ \frac{2}{m^{2} }-\frac{4}{5m^{2} }=\frac{10m^{2}-4m^{2} }{5m^{4}} \\ \frac{6m^{2} }{5m^{4}} =\frac{6}{5m^{2}}$

As I mentioned before, this volume is equal to 1, hence:

$\frac{6}{5m^{2}}=1\\m^{2} =\frac{6}{5} \\m=\sqrt{\frac{6}{5} }$

3 0

2 years ago