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3 years ago

Find the equation of a line that is perpendicular to x+y=8 and passes through the point (8, 10).

Mathematics

2 answers:

ArbitrLikvidat [17]3 years ago

6 0

Answer:

Y = -x + 2

Step-by-step explanation:

y = -x + 8

y = 1x + b

10 = 8 + b

b = 2

VladimirAG [237]3 years ago

5 0

Answer:

y-y1=m(x-x1)

y-10=8(x-8)

y-10=8x-64

y-10+64-8x

y+54-8x

y-8x+54

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The spherical balloon is inflated at the rate of 10 m³/sec. Find the rate at which the surface area is increasing when the radiu

rjkz [21]

The balloon has a volume $V$ dependent on its radius $r$ :

$V(r)=\dfrac43\pi r^3$

Differentiating with respect to time $t$ gives

$\dfrac{\mathrm dV}{\mathrm dt}=4\pi r^2\dfrac{\mathrm dr}{\mathrm dt}$

If the volume is increasing at a rate of 10 cubic m/s, then at the moment the radius is 3 m, it is increasing at a rate of

$10\dfrac{\mathrm m^3}{\mathrm s}=4\pi (3\,\mathrm m)^2\dfrac{\mathrm dr}{\mathrm dt}\implies\dfrac{\mathrm dr}{\mathrm dt}=\dfrac5{18\pi}\dfrac{\rm m}{\rm s}$

The surface area of the balloon is

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and differentiating gives

$\dfrac{\mathrm dS}{\mathrm dt}=8\pi r\dfrac{\mathrm dr}{\mathrm dt}$

so that at the moment the radius is 3 m, its area is increasing at a rate of

$\dfrac{\mathrm dS}{\mathrm dt}=8\pi(3\,\mathrm m)\left(\dfrac5{18\pi}\dfrac{\rm m}{\rm s}\right)=\dfrac{20}3\dfrac{\mathrm m^2}{\rm s}$

4 0

2 years ago

In this system of linear equations with no solution

Ksivusya [100]

Two line with the same slope are parallel, if two parallel lines have a different y-intercept they will never cross each other.

(Any two lines with different slopes will always intersect at some point)

3 0

3 years ago

Kensington City Cafe recently introduced a new flavor of coffee. They served 28 grande cups

Dmitrij [34]

Answer:

jumbo 23 oz, grande 16 oz

Step-by-step explanation:

Use g for grande and j for jumbo

The first equation: 28g + 33j = 1207

The second equation: 28g + 53j = 1667

Subtract the first from the second

28g + 53j = 1667

- 28g + 33j = 1207

Equal 20j = 460

j = 23

Put 23 in for j in either equation and solve for g:

28g + 33(23) = 1207

28g + 759 = 1207

28g = 448

g = 16

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2 years ago

Simplify and solve each equation for the x

Olegator [25]

Answer:

19y - 7y = 1 + 4(x+2x)

y = 1/12 + x

x = y - 1/12

I hope this helps!

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2 years ago

Please answer ASAP!!!!

trasher [3.6K]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers