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3 years ago

A triangle has a height of 15 in. and a area of 120 in. What is the length of it's base?

Mathematics

1 answer:

jek_recluse [69]3 years ago

7 0

Answer:

b=16

Step-by-step explanation:

Formula~ 1/2*b*h

1/2*15*b=120

7.5b=120

b=120/7.5

b=16

(you can substitute the value to check-i've done it below)

1/2*16*15=?

if you work it out, the ans will be 120, therefore the ans is correct!

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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

Assume that a spherical cell, with a diameter of 18 μm, has spherical mitochondria, each with a diameter of 0.18 μm. If mitochon

laiz [17]

Since the linear dimension of the mitochondria is 10^-2 times that of the cell, the volume as a proportion of cell volume will be (10^-2)^3 = 10^-6. In order to make up 0.134 of the cell volume, there must be

(1.34×10^-1)/(10^-6) = 1.34×10^5

mitochondria in the cell.

There are about 134,000 mitochondria.

4 0

3 years ago

What’s the relationship between these two angles?

Dovator [93]

Answer:

Co- interior angles

Step-by-step explanation:

Together they add up to 180°

So angle 5x= 115°

5 0

2 years ago

tony is taking a 5 year loan in the amount of $15,000. The interest is continuously compounded at an annual rate of 7%. How much

kobusy [5.1K]

Answer:

$21,038.28

Step-by-step explanation:

Use the equation 15000(1.07)^5 since 1.07 equals to 7% and you are loaning more money to Tony's account for 5 years. You should get $21,038.28 as your result.

7 0

3 years ago

Read 2 more answers

Pls help asap due tomorrow

Svet_ta [14]

Based on the information given, it should be noted that the least number of marbles that can be in the bag will be 10 marbles.

<h2>Solution to the probability.</h2>

If the bag contains 60 marbles, the number of red marbles will be:

= 1/5 × 60

= 12 marbles.

The number of white marbles will be:

= 3/10 × 60

= 18 marbles.

The number of blue marbles will be:

= 60 - (12 + 18)

= 60 - 30

= 30 marbles.

Furthermore, when the bag has 4 red marbles and 6 white marbles, there'll be 10 blue marbles.

Lastly, to find the probability of choosing a blue marble, we've to multiply 1/2 by the number given.

Learn more about probability on:

brainly.com/question/25870256

4 0

2 years ago