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4 years ago

I'll give 30 points I need help. Can someone please answer this question?

Mathematics

1 answer:

kirza4 [7]4 years ago

6 0

Answer:

1. 2 units to the left of g(x)

2. The function is not shifted vertically from g(x)

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Find the area enclosed by x2=2y and y2=16x

jekas [21]

Answer: $\dfrac{32}{3}$

Step-by-step explanation:

Given

The parabolas are $x^2=2y$ and $y^2=16x$

Find the point of intersection of two parabolas

$\Rightarrow \left(\dfrac{x^2}{2}\right)^2=16x\\\\\Rightarrow x^4=64x\\\Rightarrow x(x^3-64)=0\\\Rightarrow x=0,4$

Obtain y using x

$(x,y)\rightarrow (0,0)\ \text{and }(4,8)$

Area enclosed between the two is

$\Rightarrow I=\int\limits^4_0 ({4\sqrt{x}-\dfrac{x^2}{2}}) \, dx\\\\\Rightarrow I=\left ( 4\times \dfrac{2}{3}x^{\frac{3}{2}}-\dfrac{x^3}{2\times 3} \right) _0^4\\\\\Rightarrow I=\left ( \dfrac{8}{3}\times 8-\dfrac{4^3}{6} \right )-0\\\\\Rightarrow I=\dfrac{128-64}{6}\\\\\Rightarrow I=\dfrac{64}{6}\\\\\Rightarrow I=\dfrac{32}{3}$

Thus, the area bounded by the two parabolas is $\dfrac{32}{3}$ sq. units.

4 0

3 years ago

Astrid travels 130 km in 2 hours and then at 85 km/h for another 3 hours to reach her

Pie

Answer:

$\huge\boxed{\sf Speed = 77\ km/hr}$

Step-by-step explanation:

<h3><u>Formula to be used in the question:</u></h3>

Speed = Distance / Time

<h3><u>Distance for the first 2 hours:</u></h3>

= 130 km

<h3><u>Distance for the next 3 hours:</u></h3>

Speed = 85 km/h

Time = 3 hours

So,

Distance = Speed × Time

Distance = 85 × 3

Distance = 255 km

So,

<h3><u>Total distance from home to destination:</u></h3>

= 130 + 255

= 385 km

<h3><u>Speed on the return journey:</u></h3>

Total distance = 385 km

Time = 5 hours

Speed = Distance / Time

Speed = 385 / 5

Speed = 77 km/hr

$\rule[225]{225}{2}$

4 0

2 years ago

A pharmacist weighed eight different capsules of the same compound and recorded these measurements: 2312 mg, 2313 mg, 2315 mg, 2

Orlov [11]

median = 2317

mean = 2,316.875

8 0

3 years ago

you work for a telecommunications company and need to analyze the outcome of a proposed new cell tower project. cell phone radio

umka21 [38]

Answer:

The equations describing the area which each tower covers are given as

Tower A : $x^{2} + y^{2} = 16$

Tower B : $(x - 5)^{2} + (y - 4)^{2} = 9$

Tower C : $(x - 4)^{2} + (y + 4)^{2} = 25$

Step-by-step solution:

Cell phone radio towers broadcast a cell phone signal in circular pattern

Tower A at Adele Acres have position co-ordinates as (0,0) and a coverage radius of 4 ml. So, the area which it covers is given by the equation,

$x^{2} + y^{2} = 16$ -------------------------------(1)

Tower B at Brown Lake have position co-ordinates as (5,4) and a coverage radius of 3 ml. So, the area which it covers is given by the equation,

$(x - 5)^{2} + (y - 4)^{2} = 9$ -------------------------------(2)

Tower C at Cady City have position co-ordinates as (4,-4) and a coverage radius of 5 ml. So, the area which it covers is given by the equation,

$(x - 4)^{2} + (y + 4)^{2} = 25$ -------------------------------(2)

4 0

3 years ago

Part A: Max rented a motorbike at $465 for 5 days. If he rents the same motorbike for a week, he has to pay a total rent of $625

AleksAgata [21]

Answer: Our required equation will be

y-80x=65

Step-by-step explanation:

Since we have given that

Number of days Max rented a motorbike at $465 = 5 days

Number of days Max rented a motorbike at $625 = 7 days

According to question, we'll use " Equation of line using two points "

$(y-y_0)=\frac{y_2-y_1}{x_2-x_1}(x-x_0)\\\\(y-465)=\frac{625-465}{7-5}(x-5)\\\\(y-465)=80(x-5)\\\\y-465=80x-400\\\\y-80x=-400+465\\\\y-80x=65$

Hence, our required equation will be

y-80x=65

6 0

3 years ago