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2 years ago

A motorcycle daredevil is planning a stunt to perform at a county fair. A ramp must be built to give him a 20%

Mathematics

1 answer:

Shkiper50 [21]2 years ago

5 0

Answer: 95 feet

Step-by-step explanation:

Let the length of the horizontal run be represented by x.

Slope Grade = (Rise/Run) × 100

20 = (19/x) × 100

20 = 1900/x

20x = 1900

x = 1900/20

x = 95

Therefore, the length of the horizontal run must be 95 feet

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How to factor 4x^2+7x-15

GuDViN [60]

$4x^2+7x-15$

Break the expression into group:

$(4x^2+5x)+(12x-15)$

factor out x from 4x² - 5x : x (4x-5)
factor out 3 from 12x-15 : 3 (4x-5)

$=x(4x-5)+3(4x-5)$

factor out common term (4x-5) :

$= (4x-5)(x+3)$

hope this helps!

4 0

2 years ago

Carol bought 24 stamps for $6, and Charles paid $13 for 52 stamps. If the amount paid for the stamps is proportional to the numb

Vera_Pavlovna [14]

Answer:

Yes

Step-by-step explanation:

$24 divided by 6 equals 4

$52 divided by 13 equals 4

4 0

2 years ago

Read 2 more answers

. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum

Drupady [299]

Answer:

$r=1.05\ \text{ft}$

$h=2.12\ \text{ft}$

$20.91\ \text{ft}^3$

Step-by-step explanation:

r = Radius

h = Height

Volume of cylinder = $7.35\ \text{ft}^3$

$V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}$

Surface area is given by

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}$

Differentiating with respect to radius we get

$\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}$

Equating with zero we get

$0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05$

$\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0$

So, the value of the function is minimum at $r=1.05$

$h=\dfrac{7.35}{\pi r^2}=\dfrac{7.35}{\pi 1.05^2}\\\Rightarrow h=2.12$

So, the radius and height which would minimize the surface area is 1.05 feet and 2.12 feet respectively.

Surface area

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi \times 1.05^2+2\pi 1.05\times 2.12\\\Rightarrow A=20.91\ \text{ft}^3$

The minimum surface area is $20.91\ \text{ft}^3$ .

8 0

2 years ago

What is the equation of the circle with center (2, –5) that passes through the point (–2, 10)?

Travka [436]

The standard equation of a circle is

(x-h)^2 + (y-k)^2 = r^2

where the center is at point (h,k)

From the statement of the problem, it is already established that h = 2 and k = -5. What we have to determine is the value of r. This could be calculated by calculating the distance between the center and point (-2,10). The formula would be

r = square root [(x1-x2)^2 + (y1-y2)^2)]
r = square root [(2--2)^2 + (-5-10)^2)]
r = square root (241)
r^2 = 241

Thus, the equation of the circle is

$(x-2)^{2} + (y+5)^{2} =241$

4 0

2 years ago

-2(x-2)=-16 answer.

REY [17]

Answer:

-2x+4=-16

-2x = -16-4

-2x = -20

x = -20/-2

x = 10

3 0

2 years ago

Read 2 more answers