The sum of two numbers is 48 and the difference is 10 . What are the numbers?

The expression means the product of 5 and the difference of three times r minus 10. If r = 4, the value of the expression is .

Morgarella [4.7K]

Answer:

10

Step-by-step explanation:

"three times r" = 3r

"three times r minus ten" = 3r - 10

"product of 5 and the difference of three times r minus ten"

= 5 (3r - 10)

given that r = 4,

the expression becomes

5 (3r - 10)

= 5 [3(4) - 10]

= 5 [12 - 10]

= 5 (2)

= 10

4 0

3 years ago

The base and height of a right triangle are 20 inches and 15 inches. Find the length of the hypotenuse.

Karolina [17]

Using the Pythagorean theorem:

Hypotenuse = sqrt( 20^2 + 15^2)

Hypotenuse = sqrt( 400 + 225)

Hypotenuse = sqrt(625)

Hypotenuse = 25

Answer: 25 inches

8 0

3 years ago

Read 2 more answers

In 2009 the life expectancy is about 80 life expectancy gains 5.7 years every decade. From 2009 in how many years would humanity

Dmitry [639]

Answer:

about 70 years

Step-by-step explanation:

Life expectancy (e) improves by 5.7 years every 10 years, so 5.7/10 = 0.57 years per year. For t years after 2009, it can be modeled by ...

e = 0.57t +80

We want to find when that is 120:

120 = 0.57t +80

40 = 0.57t

40/0.57 = t ≈ 70.2

About 70 years from 2009, humanity may achieve a life expectancy of 120 years.

3 0

3 years ago

2 consecutive even numbers add to equal 178. What is the smallest of the 2 numbers?

Diano4ka-milaya [45]

Answer:

The smallest number is 88

Step-by-step explanation:

Let

x ----> the first consecutive even number

x+2 --->the second consecutive even number

we know that

The linear equation that represent this problem is given by

$x+(x+2)=178$

solve for x

$2x=178-2\\2x=176\\x=88$

so

$x=88\\x+2=88+2=90$

therefore

The smallest number is 88

4 0

3 years ago

A right circular cylinder is inscribed in a sphere with diameter 4cm as shown. If the cylinder is open at both ends, find the la

SOVA2 [1]

Answer:

$8\pi\text{ square cm}$

Step-by-step explanation:

Since, we know that,

The surface area of a cylinder having both ends in both sides,

$S=2\pi rh$

Where,

r = radius,

h = height,

Given,

Diameter of the sphere = 4 cm,

So, by using Pythagoras theorem,

$4^2 = (2r)^2 + h^2$ ( see in the below diagram ),

$16 = 4r^2 + h^2$

$16 - 4r^2 = h^2$

$\implies h=\sqrt{16-4r^2}$

Thus, the surface area of the cylinder,

$S=2\pi r(\sqrt{16-4r^2})$

Differentiating with respect to r,

$\frac{dS}{dr}=2\pi(r\times \frac{1}{2\sqrt{16-4r^2}}\times -8r + \sqrt{16-4r^2})$

$=2\pi(\frac{-4r^2+16-4r^2}{\sqrt{16-4r^2}})$

$=2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})$

Again differentiating with respect to r,

$\frac{d^2S}{dt^2}=2\pi(\frac{\sqrt{16-4r^2}\times -16r + (-8r^2+16)\times \frac{1}{2\sqrt{16-4r^2}}\times -8r}{16-4r^2})$

For maximum or minimum,

$\frac{dS}{dt}=0$

$2\pi(\frac{-8r^2+16}{\sqrt{16-4r^2}})=0$

$-8r^2 + 16 = 0$

$8r^2 = 16$

$r^2 = 2$

$\implies r = \sqrt{2}$

Since, for r = √2,

$\frac{d^2S}{dt^2}=negative$

Hence, the surface area is maximum if r = √2,

And, maximum surface area,

$S = 2\pi (\sqrt{2})(\sqrt{16-8})$

$=2\pi (\sqrt{2})(\sqrt{8})$

$=2\pi \sqrt{16}$

$=8\pi\text{ square cm}$

4 0

3 years ago