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3 years ago

Twice the larger of two consecutive integers is equal to fifteen less than three times the smaller. Find the integers.

Mathematics

1 answer:

Alexxandr [17]3 years ago

7 0

Answer:

17,18

Step-by-step explanation:

let the smaller integer be "a" and the larger be "b"

Then 2b = 3a -15 ........................equ 1

but they are consecutive integers, b= a+1 ; substitute b into equ 1,thus,

2(a+1) = 3a - 15

2a + 2 = 3a-15

collect like terms,

2+15 =3a-2a

17 = a

b= a+1

b = 17+1

b=18.

The integers are 17,18

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A competitive knitter is knitting a circular place mat. The radius of the mat is given by the formula

Ilia_Sergeevich [38]

Answer: A. $A'(t)=\frac{4356\pi}{(t+11)^{3}}-\frac{527076\pi}{(t+11)^{5}}$

B. A'(5) = 1.76 cm/s

Step-by-step explanation: Rate of change measures the slope of a curve at a certain instant, therefore, rate is the derivative.

A. Area of a circle is given by

$A=\pi.r^{2}$

So to find the rate of the area:

$\frac{dA}{dt}=\frac{dA}{dr}.\frac{dr}{dt}$

$\frac{dA}{dr} =2.\pi.r$

Using $r(t)=3-\frac{363}{(t+11)^{2}}$

$\frac{dr}{dt}=\frac{726}{(t+11)^{3}}$

Then

$\frac{dA}{dt}=2.\pi.r.[\frac{726}{(t+11)^{3}}]$

$\frac{dA}{dt}=2.\pi.[3-\frac{363}{(t+11)^{2}}].\frac{726}{(t+11)^{3}}$

Multipying and simplifying:

$\frac{dA}{dt}=\frac{4356\pi}{(t+11)^{3}} -\frac{527076\pi}{(t+11)^{5}}$

The rate at which the area is increasing is given by expression $A'(t)=\frac{4356\pi}{(t+11)^{3}} -\frac{527076\pi}{(t+11)^{5}}$ .

B. At t = 5, rate is:

$A'(5)=\frac{4356\pi}{(5+11)^{3}} -\frac{527076\pi}{(5+11)^{5}}$

$A'(5)=\frac{4356\pi}{4096} -\frac{527076\pi}{1048576}$

$A'(5)=\frac{2408693760\pi}{4294967296}$

$A'(5)=1.76268$

At 5 seconds, the area is expanded at a rate of 1.76 cm/s.

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2 years ago

Select all that apply. (PLEASE HELP!!)

AlexFokin [52]

A and B are the answers.

If you need proof, just ask in the comments, and I’ll get back to you.

I hope this helps!

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3 years ago

A bicycle has a circumference of approximately 81.68 inches

Blizzard [7]

Answer:

Step-by-step explanation:

Don't ask

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3 years ago

Question 10: Each tablet in a bottle of 30 costs the pharmacy $4.60. The pharmacy has additional costs including supplies and sh

valentinak56 [21]

The pharmacy should charge $201.6 for the entire bottle

Cost price refers the price the seller bought the product

Selling price refers to the price the seller sells to the consumer.

Profit refers to the money earned by the seller above the cost price

Loss refers to the money paid by the seller above the cost price.

Profit= SP-CP

CP=30X$4.60=$138

TOTAL EXPENSES=$138+30X$1.40

= $180

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=$201.6

Therefore,the pharmacy should charge $201.6 for the entire bottle to make a profit of atleast 12%

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2 years ago

Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2?

Aliun [14]

Answer:

The last choice is the one you want

Step-by-step explanation:

First of all, a parabola has a minimum value if it is a positive parabola, one that opens upward. The first and the third parabolas are negative so they open upside down. That leaves us with choices 2 and 4. We find the side to side and up or down movement by finishing the completion of the square that has already been started for us. Do this by factoring what's inside the parenthesis into a perfect square binomial.

The second one factored becomes:

$g(x)=4(x-3)^2+1$

which reflects a shift to the right 3 and up 1. Not what we are asked to find.

The fourth one factored becomes:

$g(x)=8(x-3)^2-5$

which reflects a shift to the right 3 and down 5. That's what we want!

8 0

3 years ago

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