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3 years ago

34 less than the product of 14 and an unknown number is 78.

1 answer:

7 0

$n-an\ unknown\ number\\14\cdot n=14n-the\ product\ of\ 14\ and\ an\ unknown\ number\\34\ less\ than...-subtract\ 34\\\\so,\ we\ have\ an\ equation:\\\\14n-34=78\ \ \ \ |add\ 34\ to\ both\ sides\\14n=112\ \ \ \ |divide\ both\ sides\ by\ 14\\\boxed{n=8}$

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Keisha needs to save $331. To earn money she plans to babysit and charge $11 per hour. Write two estimates Keisha could use to d

Maru [420]

M=11h, let M=331
so 331/11=h

4 0

2 years ago

Read 2 more answers

Find the mass of the solid paraboloid Dequals={(r,thetaθ,z): 0less than or equals≤zless than or equals≤8181minus−r2, 0less th

Lubov Fominskaja [6]

Answer:

M = 5742π

Step-by-step explanation:

Given:-

- Find the mass of a solid with the density ( ρ ):

ρ ( r, θ , z ) = 1 + z / 81

- The solid is bounded by the planes:

0 ≤ z ≤ 81 - r^2

0 ≤ r ≤ 9

Find:-

Find the mass of the solid paraboloid

Solution:-

- The mass (M) of any solid body is given by the following triple integral formulation:

$M = \int \int \int {p ( r ,theta, z)} \, dV\\\\$

- We can write the above expression in cylindrical coordinates:

$M = \int\limits\int\limits_r\int\limits_z {r*p(r,theta,z)} \, dz.dr.dtheta \\\\M = \int\limits\int\limits_r\int\limits_z {r*[ 1 + \frac{z}{81}] } \, dz.dr.dtheta\\\\$

- Perform integration:

$M = \int\limits\int\limits_r{r*[ z + \frac{z^2}{162}] } \,|_0^8^1^-^r^2 dr.dtheta\\\\M = \int\limits\int\limits_r{r*[ 81-r^2 + \frac{(81-r^2)^2}{162}] } \, dr.dtheta\\\\M = \int\limits\int\limits_r{r*[ 81-r^2 + \frac{6561 -162r + r^2}{162}] } \, dr.dtheta\\\\M = \int\limits\int\limits_r{r*[ 81-r^2 + 40.5 -r +\frac{r^2}{162} ] } \, dr.dtheta\\\\M = \int\limits\int\limits_r{[ 121.5r-r^2 -\frac{161r^3}{162} ] } \, dr.dtheta\\\\$

$M = 2*\int\limits_0^\pi {[ 121.5r^2-r^3 -\frac{161r^4}{162} ] } |_0^6 \, dtheta\\\\M = 2*\int\limits_0^\pi {[ 121.5(6)^2-(6)^3 -\frac{161(6)^4}{162} ] } \, dtheta\\\\M = 2*\int\limits_0^\pi {[ 4375-216 -1288] } \, dtheta\\\\M = 2*\int\limits_0^\pi {[ 2871] } \, dtheta\\\\M = 5742\pi kg$

- The mass evaluated is M = 5742π

8 0

2 years ago

√48a^4 b^5 c^3 d simplify and keep it in radical form

Morgarella [4.7K]

I will assume the square root extends all the way across.

$\sqrt{48a^4b^5c^3}$

$\sqrt{2^4\cdot3\cdot a^4b^5c^3}$

$\sqrt{(2^2)^2\cdot3\cdot(a^2)^2\cdot(b^2)^2\cdot b\cdot c^2\cdot c}$

$\sqrt{(4)^2\cdot3\cdot(a^2)^2\cdot(b^2)^2\cdot b\cdot c^2\cdot c}$

$\sqrt{(4\cdot a^2 \cdot b^2 \cdot c)^2\cdot3\cdot b\cdot c}$

$4\cdot a^2\cdot b^2\cdot c\sqrt{3\cdot b\cdot c}$

$\boxed{4a^2b^2c\sqrt{3bc}}$

3 0

3 years ago

The quadratic function in vertex form of a parabola vertex 1,1 and passes through 4,19

Grace [21]

Answer:

y = 2(x - 1)² + 1

Step-by-step explanation:

The equation of a quadratic function in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (1, 1), thus

y = a(x - 1)² + 1

To find a substitute (4, 19) into the equation

19 = a(4 - 1)² + 1

19 = 9a + 1 ( subtract 1 from both sides )

18 = 9a ( divide both sides by 9 ), thus

a = 2

y = 2(x - 1)² + 1 ← in vertex form

5 0

3 years ago

Find the volume of the sphere. Round your answer to the nearest tenth.

shepuryov [24]

Answer:

179.50

Step-by-step explanation:

The formula for calculating pi is as followed: 4/3·π·r³

The question is either asking to calculate using 3.14 for π or add π at the end of your answer instead of completing it. I will substitute π for 3.14.

∴V=4/3·3.14·3.5³

V=179.503333333

Round your answer to the nearest hundredth:

179.503333333 rounded to the nearest hundredth becomes 179.50

∴V=179.50

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Another way to answer this question is to use the same formula; but not substitute 3.14 into the answer.

V=π.4/3·r³

V=π·57.1666666667

Round 57.1666666667: 57.17

V=57.17π

Either one would work. Hope this works.

5 0

2 years ago