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2 years ago

Simplify the expression. 7x^2+3-5(x^2-4) edguneity

Mathematics

1 answer:

Law Incorporation [45]2 years ago

4 0

Answer:

2x^2+23.

Step-by-step explanation:

Combine like terms.

This expression simplified is 2x^2+23.

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Use chain rule to find dw/dt w=ln(x^2 + y^2 + z^2)^(1/2) , x=sint, y=cost, z=tant

son4ous [18]

The chain rule states that

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}$

Since $\ln(x^2+y^2+z^2)^{1/2}=\dfrac12\ln(x^2+y^2+z^2)$ , you have

$\dfrac{\partial w}{\partial x}=\dfrac x{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial x}=\dfrac y{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial z}=\dfrac z{x^2+y^2+z^2}$

and

$\dfrac{\mathrm dx}{\mathrm dt}=\cos t$
$\dfrac{\mathrm dy}{\mathrm dt}=-\sin t$
$\dfrac{\mathrm dz}{\mathrm dt}=\sec^2t$

Also, since $x^2+y^2+z^2=\sin^2t+\cos^2t+\tan^2t=1+\tan^2t=\sec^2t$ , the derivative is

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\sin t\cos t}{\sec^2t}-\dfrac{\sin t\cos t}{\sec^2t}+\dfrac{\tan t\sec^2t}{\sec^2t}$
$\dfrac{\mathrm dw}{\mathrm dt}=\tan t$

4 0

3 years ago

A cyclist at a grocery store, 180m from his home decides to go to the post office which is 510m from his home in the same direct

KatRina [158]

A) -180m
b) 510-180=+330m
+330/45=7.333m/s
c) total distance = 840m
average speed = 840/105
= 8m/s

3 0

3 years ago

Which of the following can be classified as Discrete and Quantitative data. The number of students in your school. The different

WITCHER [35]

Answer:

a) The number of students in your school.

Step-by-step explanation:

Quantitative and Qualitative:

The data that can be expressed with the help of numerical are know as quantitative variable.
Qualitative variable is the non parametric variable and numerical does not describe the data

Discrete and Continuous data:

Discrete data are expressed in whole number and cannot take all the values within an interval.
Continuous variable can be expressed in decimals and can take any value within an interval.

a) The number of students in your school.

Since whole numbers are used to express number of children it is a discrete and continuous data.

b) The different colors of the eyes of your classmates.

These are qualitative data and numerical are not used to express them.

c) The height of all the people in your neighborhood.

These are continuous data as height is measured and can be expressed in decimals.

d) The acceleration of your car as you drive to school.

These are continuous data as acceleration is measured and can be expressed in decimals.

3 0

3 years ago

A cake company makes chocolate and vanilla cakes. The ratio of chocolate cakes to vanilla cakes is 3:4. What is the ratio of the

aleksley [76]

Answer:

4:7

Step-by-step explanation:

4:7

they make 7 cakes in total (3:4 = 7).

there are 4 vanilla cakes.

therefore, the ratio of vanilla cakes to the total number of cakes is 4:7.

6 0

2 years ago

Match each three dimensional figure to its volume based on the given dimensions.

Gre4nikov [31]

please attach a diagram

6 0

3 years ago