All categories

3 years ago

Show all your work please!

Mathematics

1 answer:

Tatiana [17]3 years ago

6 0

Answer:

-3 and 5

Step-by-step explanation:

f(n) = n² - 2n - 15

numbers whose product is -15 and sums up to -2 = -5 and 3

= n²- 5n+3n - 15

= n(n - 5) +3 (n - 5)

f(n) = (n + 3)( n - 5)

n + 3 = 0 n - 5 = 0

n = -3 n = 5

Roots = -3 and 5

You might be interested in

Use cylindrical coordinates. find the volume of the solid that is enclosed by the cone z = x2 + y2 and the sphere x2 + y2 + z2 =

sashaice [31]

Let $R$ be the solid. Then the volume is

$\displaystyle\iiint_R\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta$

which follows from the facts that

$\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=\zeta\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm d\zeta$
(by computing the Jacobian)

and

$z=x^2+y^2=r^2\implies z+z^2=72\implies z=-9\text{ or }z=8$
(we take the positive solution, since it's clear that $R$ lies above the $x$ - $y$ plane)
$r^2+z^2=72\implies z=\pm\sqrt{72-r^2}$
(again, taking the positive root for the same reason)
$z=r^2\implies 8=r^2\implies r=\sqrt8$

$\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}r(\sqrt{72-r^2}-r^2)\,\mathrm dr$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}(r\sqrt{72-r^2}-r^3)\,\mathrm dr$
$=\dfrac{32(27\sqrt2-35)\pi}3$

7 0

3 years ago

Hi, please help me with this thank you!

sdas [7]

5 hope this helps sorry if wrong

5 0

3 years ago

Name the constant(s) in the expression 7x + 9y + 3

mart [117]

The answer is B. 3

It is the only value not attached to a variable, thus remaining constant.

8 0

4 years ago

grigory [225]

For this case, what we must do is find the scale factor.
We have then that the scale factor is given by:
$k = \frac{L1}{L2}$
Where,
L1: side length of polygon ABCD
L2: side length of polygon PQRS
Note: both sides belong to the same side of each polygon
Substituting the values we have:
$k = \frac{6}{12}$
Rewriting we have:
$k = \frac{1}{2}$
Answer:
The scale factor of dilation is given by:
$k = \frac{1}{2}$

3 0

3 years ago

Read 2 more answers

What is SU?<br> SU = 5<br> SU = 7<br> SU = 12<br> SU = 13

alex41 [277]

Answer:

SU=5 the first option.

Step-by-step explanation:

I did the assignment.

8 0

4 years ago

Read 2 more answers