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3 years ago

Which of the following expressions is equivalent to y+20−(1+5y)?

Mathematics

1 answer:

LuckyWell [14K]3 years ago

7 0

Answer:

19 - 4y

Step-by-step explanation:

y + 20 - (1 + 5y)

y + 20 - 1 - 5y

-4y + 19

19 - 4y

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A cone is 3 inches high and has a base with a surface area of 7 square inches. What is the volume of the cone?

lawyer [7]

Answer: the answer should be 7

Step-by-step explanation: V=πr2h

3=π·1.52·3

3≈7.06858

you can find the radius for the area of the base 7 by dividing by $\pi$ like such 7/3.1459 the squared because remember its in r2 form which give you 1.5 then plug this in for one of two ways to solve A· $\pi$ 1/3 or V=πr2h

4 0

3 years ago

Find the surface area of the solid generated by revolving the region bounded by the graphs of y = x2, y = 0, x = 0, and x = 2 ab

Nikitich [7]

Answer:

See explanation

Step-by-step explanation:

The surface area of the solid generated by revolving the region bounded by the graphs can be calculated using formula

$SA=2\pi \int\limits^a_b f(x)\sqrt{1+f'^2(x)} \, dx$

If $f(x)=x^2,$ then

$f'(x)=2x$

and

$b=0\\ \\a=2$

Therefore,

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+(2x)^2} \, dx=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx$

Apply substitution

$x=\dfrac{1}{2}\tan u\\ \\dx=\dfrac{1}{2}\cdot \dfrac{1}{\cos ^2 u}du$

Then

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx=2\pi \int\limits^{\arctan(4)}_0 \dfrac{1}{4}\tan^2u\sqrt{1+\tan^2u} \, \dfrac{1}{2}\dfrac{1}{\cos^2u}du=\\ \\=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0 \tan^2u\sec^3udu=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0(\sec^3u+\sec^5u)du$

Now

$\int\limits^{\arctan(4)}_0 \sec^3udu=2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17})\\ \\ \int\limits^{\arctan(4)}_0 \sec^5udu=\dfrac{1}{8}(-(2\sqrt{17}+\dfrac{1}{2}\ln(4+\sqrt{17})))+17\sqrt{17}+\dfrac{3}{4}(2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17}))$

Hence,

$SA=\pi \dfrac{-\ln(4+\sqrt{17})+132\sqrt{17}}{32}$

3 0

3 years ago

How could you find an even better estimate of the square root of 2

vodomira [7]

Answer:

First of all you need to know the $\sqrt {4}$ it's equal to 2 and

$\sqrt {1}$ which is the number is between 1 and 2 and between that number there maybe the possibilities of above 0.5 or under 0.5

After that Figure out which one was bigger? $\sqrt {2}$ or $\sqrt {3}$ ? The answer is $\sqrt {3}$ and $\sqrt {3}$ also near to $\sqrt {4}$ so it should be above 0.5 .

So we know that $\sqrt {2}$ is between 1 and 1.5.

Hopes that information was help you a lot

6 0

3 years ago

A cake shop can make 240 boxes of cakes for 8 days. How many cakes can the shop make in 12 days?

denpristay [2]

Answer:

<h2>360 cakes</h2>

Step-by-step explanation:

<h2>soln:</h2><h2>onecake =240\8=30</h2><h2>then 12 cakes =30×12=360</h2>

6 0

3 years ago

Read 2 more answers

Plz help I'm really bad at these

GREYUIT [131]

Y = mx + b, where m = slope = rise/run and b, the y intercept value

m = 1/1 = 1, then y = x + b.
We notice that y intercept is = - 1
And the equation is:

y = x - 1

6 0

3 years ago