By first considering the angles on line abc show that ac is parallel to df

Alex wrote checks on Tuesday for $30 and $40. He also made a deposit in his

Ksivusya [100]

Alex finally had $(x+110) amount of money in his account i.e. He had $100 more then before!

Step-by-step explanation:

Alex wrote checks on Tuesday for $30 and $40. He also made a deposit in his checking account of $180. Let's solve it step by step :

Alex wrote checks on Tuesday for $30 and $40:

Let's suppose Alex initially had x amount of money out of which $30 & $40 is deducted! so left amount of money is $(x-70) .

He also made a deposit in his checking account of $180:

Out of left money $(x-70) , Alex deposited $180 in account so new money = $(x-70) + $180 = $(x+110)

Therefore, Alex finally had $(x+110) amount of money in his account i.e. He had $100 more then before!

6 0

2 years ago

Which of the following is the correct graph of the linear equation below? y+2 =3(x+1)

77julia77 [94]

Answer:

D

Step-by-step explanation:

3 0

2 years ago

Hello people ~

Luden [163]

Cone details:

height: h cm

radius: r cm

Sphere details:

radius: 10 cm

================

From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.

Using Pythagoras Theorem

(a)

TO² + TU² = OU²

(h-10)² + r² = 10² [insert values]

r² = 10² - (h-10)² [change sides]

r² = 100 - (h² -20h + 100) [expand]

r² = 100 - h² + 20h -100 [simplify]

r² = 20h - h² [shown]

r = √20h - h² ["r" in terms of "h"]

(b)

volume of cone = 1/3 * π * r² * h

===========================

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (\sqrt{20h - h^2})^2 \ ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20h - h^2) (h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20 - h) (h) ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} \pi h^2(20-h)$

To find maximum/minimum, we have to find first derivative.

(c)

First derivative

$\Longrightarrow \sf V' =\dfrac{d}{dx} ( \dfrac{1}{3} \pi h^2(20-h) )$

apply chain rule

$\sf \Longrightarrow V'=\dfrac{\pi \left(40h-3h^2\right)}{3}$

Equate the first derivative to zero, that is V'(x) = 0

$\Longrightarrow \sf \dfrac{\pi \left(40h-3h^2\right)}{3}=0$

$\Longrightarrow \sf 40h-3h^2=0$

$\Longrightarrow \sf h(40-3h)=0$

$\Longrightarrow \sf h=0, \ 40-3h=0$

$\Longrightarrow \sf h=0,\:h=\dfrac{40}{3}$

maximum volume: when h = 40/3

$\sf \Longrightarrow max= \dfrac{1}{3} \pi (\dfrac{40}{3} )^2(20-\dfrac{40}{3} )$

$\sf \Longrightarrow maximum= 1241.123 \ cm^3$

minimum volume: when h = 0

$\sf \Longrightarrow min= \dfrac{1}{3} \pi (0)^2(20-0)$

$\sf \Longrightarrow minimum=0 \ cm^3$

6 0

1 year ago

Read 2 more answers

Which of the following expressions is equivalent to -2-5?

Vanyuwa [196]

-7 Hope this helps. :)

6 0

2 years ago

Read 2 more answers

A student claims that the expression “9 times the sum of a number and 13" is translated to the algebraic expression 9n + 13. Is

FrozenT [24]

Answer:

No, the student is not correct. The correct expression is 9(n+13).

Step-by-step explanation:

"9 times the sum of a number and 13" means you must multiply 9 by the sum, not just by the number. 9n + 13 would be "the sum of 9 times a number and 13." Slightly different wording.

4 0

2 years ago

Read 2 more answers

By first considering the angles on line abc show that ac is parallel to df​

By first considering the angles on line abc show that ac is parallel to df