PLS HELP WILL GIVE BRAINLIEST

A point moves along the curve y = √ x in such a way that the y-component of the position of the point is increasing at a rate of

Eduardwww [97]

Answer:

The value of x component changes at a rate of $\frac{dx}{dt}=4\sqrt{x}$ units per second

Step-by-step explanation:

We are given that $y=x^{\frac{1}{2}}$

Differentiating on both sides with respect to time we get

$\frac{dy}{dt}=\frac{d\sqrt{x}}{dt}\\\\\frac{dy}{dt}=\frac{1}{2}x^{\frac{-1}{2}}(\frac{dx}{dt})\\\\\frac{dy}{dt}=\frac{1}{2\sqrt{x}}\frac{dx}{dt}$

It is given that $\frac{dy}{dt}=2units/sec$

Solving for $\frac{dx}{dt}$ we get

$\frac{dx}{dt}=\frac{dy}{dt}\times 2\sqrt{x}\\\\\frac{dx}{dt}=4\sqrt{x}$

5 0

2 years ago

Alexandra purchases two donuts and three cookies at the donut shop and it's charged $3.30. Brianna purchases five donuts and two

Amiraneli [1.4K]

Given:

Cost of two donuts and three cookies = $3.30

Cost of five donuts and two cookies = $4.95

To find:

The cost of each donut.

Solution:

Let x be the cost of each donut and y be the cost of each cookie.

Cost of two donuts and three cookies = $3.30

$2x+3y=3.30$ ...(i)

Cost of five donuts and two cookies = $4.95

$5x+2y=4.95$ ...(ii)

Multiply equation (i) by 2.

$4x+6y=6.60$ ...(iii)

Multiply equation (ii) by 3.

$15x+6y=14.85$ ...(iv)

Subtracting (iii) from (iv), we get

$15x+6y-4x-6y=14.85-6.60$

$11x=8.25$

Divide both sides by 11.

$x=\dfrac{8.25}{11}$

$x=0.75$

Therefore, the cost of each donut is $0.75.

7 0

2 years ago

Olivia family drove to Disney land For spring break. Her mom and dad shared the driving duties for a total of 14 hours. her mom

Kay [80]

Mom drove for 11 hours.

Dad drove for 3 hours.

Step-by-step explanation:

Total hours = 14 hours

Total distance = 895 miles

Mom drove a speed of 65 mph

Dad drove a speed of 60 mph

Let 'x' be the number of hours drove by mom.

Let 'y' be the number of hours drove by dad.

x + y = 14 ---------------(1)

65x + 60y = 895 ---------(2)

Multiply eq(1) by 60 and subtract eq(2) from (1),

60x + 60y = 840

-(65x + 60y = 895)

-5x = -55

x = 55/5

x = 11

∴ Mom drove for 11 hours.

Substitute x=11 in eq(1)

11+y = 14

y = 3

∴ Dad drove for 3 hours.

6 0

3 years ago

Please help with this, 50 points. the question is in the photo.

Alex

Answer:

Creo que es de la siguiente forma

Step-by-step explanation:

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5 0

2 years ago

Read 2 more answers

The probability that a region prone to hurricanes will be hit by a hurricane in any single year is 0.1 and independent of other

ludmilkaskok [199]

Answer:

0.40951

Step-by-step explanation:

P(none in five years) = 1 - 0.1 = 0.9

P(at least one) = 1 - P(none in five years)

= 1 - $0.9^{5}$

= 1 - 0.59049

= 0.40951

So the probability of a hurricane hit at least once in the next 5 years is 0.40951

8 0

3 years ago