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3 years ago

Find two integers whose difference is -6. ( There are many!)

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

5 0

Step-by-step explanation:

There are infinitely many such integers.

x - y = -6 add y to both sides

x = -6 + y → x = y - 6

1. Choose any y value.

2. Substitute for the equation.

3. Calculate the value of x.

Examples:

for y = 0 → x = 0 - 6 = -6

check: -6 - 0 = -6

for y = 10 → x = 10 - 6 = 4

check: 4 - 10 = -6

for y = -9 → x = -9 - 6 = -15

check: -15 - (-9) = -15 + 9 = -6

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What is the volume of a right circular cylinder with a base diameter of 6 m and a height of 5 m?

ikadub [295]

Radius = 3 m
Cylinder Volume = π • r² • height

Cylinder Volume = 3.14159 * 3^2 * 5

Cylinder Volume = 141.372

OR PI * 45

6 0

3 years ago

ASAP: I need as soon as possible with this question I have taken a picture of. If you could tell me how to do it and the answer,

VladimirAG [237]

Answer:

The answer to your question is h = 125.85 ft = 126 ft

Step-by-step explanation:

Process

1.- Determine two equations to solve the problem

$tan 14 = \frac{h}{x}$ (1)

$tan 47 = \frac{h}{x - 386}$ (2)

from (1) h = xtan14

substitute in (2) tan 47 = $\frac{xtan14}{x - 386}$

solve for x tan47(x - 386) = xtan14

1.07x - 413.9 = 0.25x

1.07x - 0.25x = 413.9

0.82x = 413.9

x = 413.9/0.82

x = 504.76 ft

2.- Calculate h

h = 504.76 tan 14

h = 125.85 ft = 126 ft

4 0

3 years ago

5. The scale of a map says that 8 cm represents 5 km.

sleet_krkn [62]

Answer:

a. 12.8 cm b. 3.125

Step-by-step explanation:

To find any scale drawing use a proportion with one unit of values on the top and the other on the bottom. For example 8cm/5km = x/8km. So you would multiply 8 cm and 8 km and then divide by 5 to get 12.8 cm. For the second question plug in 5m in the numerator and solve for its denominator.

3 0

2 years ago

Read 2 more answers

A pair of congruent angles are described as follows: The degree measure of one angle is three more than twice a number, and the

Fiesta28 [93]

Answer:

The measure of the angles in degree is 57.5 degrees

Step-by-step explanation:

If two angles are congruent, they are equal in value

Let the number be x

2x + 3 = 3x-54.5

Thus;

3x-2x = 54.5 + 3

x = 57.5

6 0

3 years ago

Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare y

DiKsa [7]

The area of the surface is given exactly by the integral,

$\displaystyle\pi\int_0^5\sqrt{1+(y'(x))^2}\,\mathrm dx$

We have

$y(x)=\dfrac15x^5\implies y'(x)=x^4$

so the area is

$\displaystyle\pi\int_0^5\sqrt{1+x^8}\,\mathrm dx$

We split up the domain of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [4, 9/2], [9/2, 5]

where the left and right endpoints for the $i$ -th subinterval are, respectively,

$\ell_i=\dfrac{5-0}{10}(i-1)=\dfrac{i-1}2$

$r_i=\dfrac{5-0}{10}i=\dfrac i2$

with midpoint

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4$

with $1\le i\le10$ .

Over each subinterval, we interpolate $f(x)=\sqrt{1+x^8}$ with the quadratic polynomial,

$p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

Then

$\displaystyle\int_0^5f(x)\,\mathrm dx\approx\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It turns out that the latter integral reduces significantly to

$\displaystyle\int_0^5f(x)\,\mathrm dx\approx\frac56\left(f(0)+4f\left(\frac{0+5}2\right)+f(5)\right)=\frac56\left(1+\sqrt{390,626}+\dfrac{\sqrt{390,881}}4\right)$

which is about 651.918, so that the area is approximately $651.918\pi\approx\boxed{2048}$ .

Compare this to actual value of the integral, which is closer to 1967.

4 0

3 years ago