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3 years ago

If (m, −3) is on a circle with center (2, −3) and radius 7, what is a value of m?

1 answer:

3 0

Ok so
distance from (m,-3) to (2,-3) is 7 units

since the y value is the same, we don't even need to use distance formula

see how far 7 units from 2 is
-5 or 9
m can be -5 or 9
the point can be (-5,-3) or (9,-3)

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An aquarium measures 61 cm long, 30.5 cm wide, and 30.5 cm high.If the tank is only filled to 80% capacity with water, how much

LiRa [457]

Answer:

$V=45396.2\ cm^3$

Step-by-step explanation:

Given that,

The dimensions of an aquarium are 61 cm long, 30.5 cm wide, and 30.5 cm high.

The tank is filled to 80% capacity with water.

We need to find the water needed for this tank.

The volume of cuboid is given by :

$V=lbh$

As it is filled to 80% capacity, so,

$V=\dfrac{80}{100}\times lbh\\\\=0.8\times 61\times 30.5\times 30.5\\\\V=45396.2\ cm^3$

So, $45396.2\ cm^3$ of water is needed for this tank.

5 0

3 years ago

PLZ HELP!!! Use limits to evaluate the integral.

Marrrta [24]

Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:

$\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]$

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

$r_i=\dfrac{2i}n$

where $1\le i\le n$ . Each interval has length $\Delta x_i=\frac{2-0}n=\frac2n$ .

At these sampling points, the function takes on values of

$f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}$

We approximate the integral with the Riemann sum:

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3$

Recall that

$\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4$

so that the sum reduces to

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}$

Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:

$\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}$

Just to check:

$\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28$

4 0

3 years ago

Which formula could be used to find the volume of a cube with side length equal to s?

aliina [53]

Answer:

s cubed

Step-by-step explanation:

bc volume is length times width times height so it would be s times s times s which is s cubed

6 0

3 years ago

Can someone help me solve this question? It’s similar to the previous ones! Thank you!

luda_lava [24]

Answer:

$\boxed{\sf \ \ \ (-2x+-9)(1x+3)=-2x^2-15x-27 \ \ \ }$

the coefficient c is -27

Step-by-step explanation:

hello

$(-2x+-9)(1x+3)=(-2x-9)(x+3)=-2x(x+3)-9(x+3)=-2x^2-6x-9x-27\\=-2x^2-15x-27$

hope this helps

8 0

4 years ago

HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check all that apply.

Vesnalui [34]

It’s the third one - I tried :)

8 0

3 years ago