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2 years ago

Consider the system of equations.

Mathematics

1 answer:

torisob [31]2 years ago

3 0

Answer:

the second equation converted to slope-intercept form is y = -1/3x -1

Step-by-step explanation:

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Sandra and Monica are both saving money. The equation y = 82x

Tanya [424]

Answer:

Step-by-step explanation:

328= 82 x 4

348/4 = 87

87 - 82 = 5

7 0

1 year ago

Need help with 8-9.

ANTONII [103]

So it is 5cm to 1m or 5cm to 1000cm
So the scale is the ratio which is 5:1000. this can be reduced to 1:200

10. if the room is 15cm on one side I can say that the ratio to actual size is 15/x. and scale is 1/200 so:
15/x = 1/200
3000 = x is one side

other side:
20/x = 1/200
4000 = x

7 0

2 years ago

cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides of the can costs 0

Dafna11 [192]

Answer:

Radius=2.09 cm

Height,h=14.57 cm

Step-by-step explanation:

We are given that

Volume of cylinderical shaped can=200 cubic cm.

Cost of sides of can=0.02 cents per square cm

Cost of top and bottom of the can =0.07 cents per square cm

Curved surface area of cylinder= $2\pi rh$

Area of circular base=Area of circular top= $\pi r^2$

Total cost,C(r)= $0.02\times 2\pi rh+2\pi r^2\times 0.07$

Volume of cylinder, $V=\pi r^2 h$

$200=\pi r^2 h$

$h=\frac{200}{\pi r^2}$

Substitute the value of h

$C(r)=0.02\times 2\pi r\times \frac{200}{\pi r^2}+2\pi r^2\times 0.07$

$C(r)=\frac{8}{r}+0.14\pi r^2$

Differentiate w.r.t r

$C'(r)=-\frac{8}{r^2}+0.28\pi r$

$C'(r)=0$

$-\frac{8}{r^2}+0.28\pi r=0$

$0.28\pi r=\frac{8}{r^2}$

$r^3=\frac{8}{0.28\pi}=9.095$

$r=(9.095)^{\frac{1}{3}}=2.09$

Again, differentiate w.r.t r

$C''(r)=\frac{16}{r^3}+0.28\pi$

Substitute the value of r

$C''(2.09)=\frac{16}{(2.09)^3}+0.28\pi=2.63>0$

Therefore,the product cost is minimum at r=2.09

h= $\frac{200}{\pi (2.09)^2}=14.57$

Radius of can,r=2.09 cm

Height of cone,h=14.57 cm

4 0

2 years ago

Can someone help idk if this is right

navik [9.2K]

Answer:

$a_n=-3 \cdot a_{n-1}$

$a_1=2$

You gave the explicit form.

Step-by-step explanation:

You gave the explicit form.

The recursive form is giving you a term in terms of previous terms of the sequence.

So the recursive form of a geometric sequence is $a_n=r \cdot a_{n-1}$ and they also give a term of the sequence; like first term is such and such number. All this says is to get a term in the sequence you just multiply previous term by the common ratio.

r is the common ratio and can found by choosing a term and dividing by the term that is right before it.

So here r=-3 since all of these say that it does:

-54/18

18/-6

-6/2

If these quotients didn't match, then it wouldn't be geometric.

Anyways the recursive form for this geometric sequence is

$a_n=-3 \cdot a_{n-1}$

$a_1=2$

5 0

2 years ago

The slope of the line whose equation is 5 x - 3 y = 4 is <br> 5/3 <br> 4/5 <br> -3/5

vlada-n [284]

The slope-intercept form: y = mx + b

m - slope

b - y-intercept

We have:

$5x-3y=4\qquad|\text{subtract 5x from both sides}\\\\-3y=-5x+4\qquad|\text{divide both sides by (-3)}\\\\y=\dfrac{5}{3}x-\dfrac{4}{3}$

<h3>Answer: 5/3</h3>

3 0

2 years ago