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3 years ago

What is the value of r in the equation: 34r+3r=111 Show work

Mathematics

1 answer:

Murrr4er [49]3 years ago

6 0

Answer:

r = 3

Step-by-step explanation:

34r + 3r =111

add;

34r + 3r = 37r

37r = 111

dividedboth sides by;

$\frac{37r}{37} =\frac{111}{37}$

answer;

r = 3

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Answer:

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Step-by-step explanation:

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3 years ago

A candle is in the shape of a square pyramid. Its height is 5 cm and its slant height is 8 cm.

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Step-by-step explanation:

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3 years ago

A ball of radius 15 has a round hole of radius 5 drilled through its center. Find the volume of the resulting solid. Hint: The u

OverLord2011 [107]

Answer:

The volume of the ball with the drilled hole is:

$\displaystyle\frac{8000\pi\sqrt{2}}{3}$

Step-by-step explanation:

See attached a sketch of the region that is revolved about the y-axis to produce the upper half of the ball. Notice the function y is the equation of a circle centered at the origin with radius 15:

$x^2+y^2=15^2\to y=\sqrt{225-x^2}$

Then we set the integral for the volume by using shell method:

$\displaystyle\int_5^{15}2\pi x\sqrt{225-x^2}dx$

That can be solved by substitution:

$u=225-x^2\to du=-2xdx$

The limits of integration also change:

For x=5: $u=225-5^2=200$

For x=15: $u=225-15^2=0$

So the integral becomes:

$\displaystyle -\int_{200}^{0}\pi \sqrt{u}du$

If we flip the limits we also get rid of the minus in front, and writing the root as an exponent we get:

$\displaystyle \int_{0}^{200}\pi u^{1/2}du$

Then applying the basic rule we get:

$\displaystyle\frac{2\pi}{3}u^{3/2}\Bigg|_0^{200}=\frac{2\pi(200\sqrt{200})}{3}=\frac{400\pi(10)\sqrt{2}}{3}=\frac{4000\pi\sqrt{2}}{3}$

Since that is just half of the solid, we multiply by 2 to get the complete volume:

$\displaystyle\frac{2\cdot4000\pi\sqrt{2}}{3}$

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5 0

4 years ago

Martin throws a ball straight up in the air. the equation h(t) = -16t^2 + 40t + 5 gives the height of the ball, in feet, t secon

Lisa [10]

Answer:

2.62 seconds

Step-by-step explanation:

Let

t ----> the time in seconds

h(t) ----> he height of the ball, in feet

we have

$h(t)=-16t^2+40t+5$

we know that

When the ball hits the ground, the height is equal to zero

$-16t^2+40t+5=0$

The formula to solve a quadratic equation of the form

$at^{2} +bt+c=0$

is equal to

$t=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^2+40t+5=0$

$a=-16\\b=40\\c=5$

substitute in the formula

$t=\frac{-40\pm\sqrt{40^{2}-4(-16)(5)}} {2(-16)}$

$t=\frac{-40\pm\sqrt{1,920}} {-32}$

$t=\frac{-40+\sqrt{1,920}} {-32}=-0.12\ sec$

$t=\frac{-40-\sqrt{1,920}} {-32}=2.62\ sec$

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The solution is t=2.62 seconds

4 0

3 years ago

The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new functio

kap26 [50]

Answer:

The new function is (x + 7)² - 47 ⇒ the 3rd answer

Step-by-step explanation:

* Lets put the function f(x) in the vertex form at first and then make

the translation

∵ The general form of the quadratic function is

f(x) = ax² + bx + c

∵ The x-coordinate of the vertex of the function is -b/2a

∵ The y-coordinate of the vertex of the function is f(-b/2a)

- Lets find a , b from the function two find the vertex point

∵ f(x) = x² + 22x + 58

∴ a = 1 , b = 22 , c = 58

∵ x-coordinate of the vertex = -b/2a

∴ x-coordinate of the vertex = -22/2(1) = -11

∵ y-coordinate of the vertex = f(-11)

∴ f(-11) = (-11)² + 22(-11) + 58 = 121 - 242 + 58 = -63

∴ The vertex point is (-11 , -63)

- The vertex form of the quadratic function is f(x) = (x - h)² + k , where

(h , k) are the coordinates of the vertex point

∵ The vertex point is (-11 , -63)

∴ h = -11 , k = -63

∴ f(x) = (x - -11)² + -63

∴ f(x) = (x + 11)² - 63

* lets revise the rules of the translation

- If the function f(x) translated horizontally to the right

by m units, then the new function g(x) = f(x - m)

- If the function f(x) translated horizontally to the left

by m units, then the new function g(x) = f(x + m)

- If the function f(x) translated vertically up

by n units, then the new function g(x) = f(x) + n

- If the function f(x) translated vertically down

by n units, then the new function g(x) = f(x) – n

∵ f(x) will translate 4 units to the right

∴ m = 4

∵ f(x) ⇒ f(x - m)

∴ (x + 11)² ⇒ (x + 11 - 4)² = (x + 7)²

∵f(x) will translate 16 units up

∴ -63 will add by 16

∴ n = 16

∴ f(x) ⇒ f(x) + n

∵ -63 + 16 = -47

∴ The new function is (x + 7)² - 47

5 0

3 years ago

Read 2 more answers