2/3 (greater than less than or equal) 8/12

A line passes through the point (-2, 7) and has a slope of -5.

Ludmilka [50]

Answer:

-7

Step-by-step explanation:

3 0

3 years ago

I need to find the volume for number 10

kumpel [21]

Using the diagonal dimension and the height we can solve for the diameter of the cylinder using the Pythagorean theorem.

x^2 + 9.5^2 = 19.3^2

x^2 + 90.25 = 372.49

x^2 = 372.49 - 90.25

x^2 = 282.24

x = √282.24

x = 16.8

Now we know the diamteer and height, we can calculate the volume using the formula V = pi * r^2 * h

r = 1/2 the diameter = 16.8/2 = 8.4

using 3.14 for pi

Volume = 3.14 * 8.4^2 * 9.5

V = 3.14 * 70.56 * 9.5

v = 3.14 * 670.32

v = 2104.8 cubic meters

5 0

3 years ago

If f(x)=x^2- 4 and g(x)=x^2 plus 2 x,

gregori [183]

Answer:

$\huge\boxed{(f-g)\left(-\dfrac{1}{3}\right)=-3\dfrac{1}{3}}$

Step-by-step explanation:

$\text{We have}:\\\\f(x)=x^2-4\ \text{and}\ g(x)=x^2+2x\\\\(f-g)(x)=f(x)-g(x)\\\\\text{therefore}\\\\(f-g)(x)=(x^2-4)-(x^2+2x)=x^2-4-x^2-2x\\\\=(x^2-x^2)-2x-4=-2x-4\\\\(f-g)\left(-\dfrac{1}{3}\right)\to\text{put}\ x=-\dfrac{1}{3}\ \text{to the equation of the function}\ (f-g)(x):\\\\(f-g)\left(-\dfrac{1}{3}\right)=-2\left(-\dfrac{1}{3}\right)-4=\dfrac{2}{3}-4=-3\dfrac{1}{3}$

6 0

3 years ago

Chelsey put for $450 into an account with a simple interest rate of 2.5% when she withdrew the money she had earned a total of $

fgiga [73]

Answer:

5.66 years

Step-by-step explanation:

450 x 1.025^(n) = 450 + 67.50

450 x 1.025^(n) = 517.50

1.025^(n) =(517.50 / 450)

1.025^(n) = 1.15

n = ln(1.15) / ln(1.025)

n = 5.66

6 0

3 years ago

A 6m ladder leans against a wall. The bottom of the ladder is 1.3m from the wall at time =0sec and slides away from the wall at

icang [17]

Answer:

- 0.100

Step-by-step explanation:

Length of the ladder, H = 6 m

Distance at the bottom from the wall, B = 1.3 m

Let the distance of top of the ladder from the bottom at the wall is P

Thus,

from Pythagoras theorem,

B² + P² = H² .

or

B² + P² = 6² ..............(1) [Since length of the ladder remains constant]

at B = 1.3 m

1.3² + P² = 6²

or

P² = 36 - 1.69

or

P² = 34.31

or

P = 5.857

Now,

differentiating (1)

$2B(\frac{dB}{dt})+2P(\frac{dP}{dt})=0$

at t = 2 seconds

change in B = 0.3 × 2= 0.6 ft

Thus,

at 2 seconds

B = 1.3 + 0.6 = 1.9 m

therefore,

1.9² + P² = 6²

or

P = 5.69 m

on substituting the given values,

2(1.9)(0.3) + 2(5.69) × $(\frac{dP}{dt})$ = 0

or

1.14 + 11.38 × $(\frac{dP}{dt})$ = 0

or

11.38 × $(\frac{dP}{dt})$ = - 1.14

or

$(\frac{dP}{dt})$ = - 0.100

here, negative sign means that the velocity is in downward direction as upward is positive

5 0

4 years ago