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1 year ago

Find the remainder when f(x) = 2x3 − 12x2 + 11x + 2 is divided by x − 5. (2 points) 7 −3 3 −7

Mathematics

2 answers:

Nutka1998 [239]1 year ago

6 0

Synthetic division shows the remainder to be 7. Evaluating the function at x=5 shows the same thing.

Dafna1 [17]1 year ago

3 0

Answer:

Step-by-step explanation:

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2 years ago

Becky lives 5 5\8 miles from school steve

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1 year ago

Emanuel was charged \$32$32dollar sign, 32 for a 14\dfrac29 \text{ km}14 9 2 km14, start fraction, 2, divided by, 9, end fract

mash [69]

Answer:

The cost per kilometer was $2.25

Step-by-step explanation:

The correct question is

Emanuel was charged $32 for a 14 2/9 km

What was the cost per kilometer?

To find out the cost per kilometer (unit rate) divide the total cost by the total kilometers

Convert mixed number to an improper fraction

$14\frac{2}{9}\ km=\frac{14*9+2}{9}=\frac{128}{9}\ km$

Find the unit rate

$\frac{32}{\frac{128}{9}}=\frac{32*9}{128}=\$2.25\ per\ kilometer$

therefore

The cost per kilometer was $2.25

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2 years ago

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2 years ago

EXAMPLE 5 If F(x, y, z) = 4y2i + (8xy + 4e4z)j + 16ye4zk, find a function f such that ∇f = F. SOLUTION If there is such a functi

Valentin [98]

If there is such a scalar function f, then

$\dfrac{\partial f}{\partial x}=4y^2$

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}$

$\dfrac{\partial f}{\partial z}=16ye^{4z}$

Integrate both sides of the first equation with respect to x :

$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to y :

$\dfrac{\partial f}{\partial y}=8xy+4e^{4z}=8xy+\dfrac{\partial g}{\partial y}$

$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to y :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with f , then differentiate both sides with respect to z :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to z :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

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1 year ago