Ask question

Ask question

All categories

3 years ago

11

Jay and David are Calculating their combined height Jay is 5 3/4 feet tall, and David is 6 1/8 feet tall. What is jay and David'

s combined height?

1 answer:

Murrr4er [49]3 years ago

6 0

Answer: $\dfrac{95}{8}\ ft$

Step-by-step explanation:

Given

The height of Jay is $5\frac{3}{4}\ ft$

The height of David is $6\frac{1}{8}\ ft$

Converting mixed to fraction and add the two heights for combined height

$\Rightarrow \dfrac{5\times 4+3}{4}+\dfrac{6\times 8+1}{8}\\\\\Rightarrow \dfrac{23}{4}+\dfrac{49}{8}\\\\\Rightarrow \dfrac{46}{8}+\dfrac{49}{8}\\\\\Rightarrow \dfrac{46+49}{8}=\dfrac{95}{8}\ ft$

Thus, the combined height of the two is $\frac{95}{8}\ ft$

You might be interested in

Evaluate the integral of the quantity x divided by the quantity x to the fourth plus sixteen, dx . (2 points) one eighth times t

Anika [276]

Answer:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c$

Step-by-step explanation:

Given

$\int\limits {\frac{x}{x^4 + 16}} \, dx$

Required

Solve

Let

$u = \frac{x^2}{4}$

Differentiate

$du = 2 * \frac{x^{2-1}}{4}\ dx$

$du = 2 * \frac{x}{4}\ dx$

$du = \frac{x}{2}\ dx$

Make dx the subject

$dx = \frac{2}{x}\ du$

The given integral becomes:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du$

Recall that: $u = \frac{x^2}{4}$

Make $x^2$ the subject

$x^2= 4u$

Square both sides

$x^4= (4u)^2$

$x^4= 16u^2$

Substitute $16u^2$ for $x^4$ in $\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du$

Simplify

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

In standard integration

$\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)$

So, the expression becomes:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)$

Recall that: $u = \frac{x^2}{4}$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c$

4 0

2 years ago

How many distinguishable 11 letter "words" can be formed using the letters in MISSISSIPPI?

SCORPION-xisa [38]

This is given by the multinomial coefficient:

$\dbinom{11}{1,4,4,2}=\dfrac{11!}{1!4!4!2!}=34650$

If you're not familiar with the multinomial coefficient, you may be able to see it more clearly if you count the number of possible combinations taking each distinct letter $n$ times, where $n$ is the number of times it shows up in the original word.

$\underbrace{\dbinom{11}1}_{\text{M}}\underbrace{\dbinom{10}4}_{\text{I}}\underbrace{\dbinom64}_{\text{S}}\underbrace{\dbinom22}_{\text{P}}=\dfrac{11!}{1!10!}\dfrac{10!}{4!6!}\dfrac{6!}{4!2!}\dfrac{2!}{2!0!}=\dfrac{11!}{1!4!4!2!}$

4 0

3 years ago

find the volume of a solid that is generated by rotating around the indicated axis the plane region bounded by the giveb curves:

Fofino [41]

Assuming the area below the line y=0 (i.e. x>1) does NOT count, the area to be rotated is shown in the graph attached.

A. Again, using Pappus's theorem,
Area, A = (2/3)*1*(1-(-1))=4/3 (2/3 of the enclosing rectangle, or you can integrate)
Distance of centroid from axis of rotation, R = (2-0) = 2
Volume = 2 π RA = 2 π 2 * 4/3 = 16 π / 3 (approximately = 16.76 units)

B. By integration, using the washer method
Volume = $2\pi\int_{-1}^1(1-x^2)(2-x)dx$
$=2\pi\int_{-1}^1(x^3-2x^2-x+2)dx$
$=2\pi[x^4/4-2x^3/3-x^2/2+2x]_{-1}^{1}$
$=2\pi([1/4-2/3-1/2+2]-[1/4+2/3-1/2-2])$
$=2\pi(8/3)$
= 16 π /3 as before

3 0

3 years ago

15 points with easy explanation please

GaryK [48]

Answer:

that would be 38 degrees

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Find 3 fractions between 2/8 and 3/8

Illusion [34]

5/16 multiply the denominator by 2 and add 1 to the numerator

9/32 multiply the denominator by 4 and add 1 to the numerator

10/32 multiply the denominator by 4 and add 2 to the numerator

5 0

3 years ago