Find the measure of angle

C. For each term in this expression, you can just apply the power rule.

[tex]y = 3x^2 - \sqrt x + \dfrac2x = 3x^2 - x^{\frac12} + 2x^{-1}[/tex]

[tex]\implies \dfrac{dy}{dx} = 2\cdot3x^{2-1} - \dfrac12 x^{\frac12-1} + (-1)\cdot2x^{-1-1}[/tex]

[tex]\implies \dfrac{dy}{dx} = 6x - \dfrac12 x^{-\frac12} - 2x^{-2}[/tex]

[tex]\implies \dfrac{dy}{dx} = 6x - \dfrac1{2\sqrt x} - \dfrac2{x^2}[/tex]

Every other choice involves composite functions that do require the chain rule to differentiate.

Option C  : [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex]  can be differentiated without using chain rule.

The differentiation of  [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex]   without using chain rule can be done as follows:

[tex]\begin{aligned}\dfrac{dy}{dx} &= \dfrac{d}{dx}(3x^2 - \sqrt{x} + \dfrac{2}{x})\\\\&= \dfrac{d}{dx}(3x^2 - x^{\frac{1}{2}} + 2x^{-1})\\&= 6x - (1/2)x^{-\frac{3}{2}} -2x^{-2}\\\end{aligned}[/tex]

The rest of the functions are composite, which means, that after differentiating them with some other base, you need to change the base and differentiate again, thus applying chain rule.

Thus, the function [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex]   can be differentiated without using chain rule.

Thus, option C:   [tex]y = 3x^2 - \sqrt{x} + \dfrac{2}{x}\\[/tex]   is correct option.

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Answer:

1. -3 × A1 + A2 --> B2

2. [tex]-\frac{1}{7}[/tex] × B2 --> C2

Step-by-step explanation:

1. -3 × A1 + A2 --> B2

(4x × -3) + 12x = -12x + 5x = -7x

(2y × -3) + 6y = -6y + 6y = 0y

(-10 × -3) + -9 = 30 - 9 = 21

2. [tex]-\frac{1}{7}[/tex] × B2 --> C2

-7x × [tex]-\frac{1}{7}[/tex] = 1x

21 × [tex]-\frac{1}{7}[/tex] = -3

Same process as last time

Answer:

B

Step-by-step explanation:

<STR = <SRT                      Given the markings of the triangle

<STR + <STU = 180            Supplementary angles

(2x - 9) + 7x = 180               Remove the brackets

2x - 9 + 7x = 180                 Combine

9x - 9 = 180                         Add 9 to both sides

9x = 180 + 9                        Combine

9x = 189                              Divide by 9

9x/9 = 189/9

x = 21

Answer:

Step-by-step explanation:

According to given we have (x, y) pairs:

Work out the equation of the line.

Find the slope:

Find the y- intercept using one pair of coordinates:

The line is:

Find the value of y when x = 14 and x = 15:

Answer:

1. 6²=36

2. 289[tex]\frac{1}{2}[/tex] = 17

3. [tex]14^{-2}[/tex] = [tex]\frac{1}{196}[/tex]

4. 10³=1000

5. [tex]5^{4}[/tex]=625

Step-by-step explanation:

Answer:

1. 6² = 36

2. 289^1/2 = 17

3. 14^-2 = 1/196

4. 10³ = 1000

5. 5⁴ = 625

Step-by-step explanation:

I just used the rule that logₓy = n means that xⁿ = y and a logarithm without a base, has a base of 10 (called a "common logarithm").

As the hint suggests, convert to spherical coordinates using

x = p cos(u) sin(v)

y = p sin(u) sin(v)

z = p cos(v)

dV = dx dy dz = p² sin(v) dp du dv

Then U is the set

[tex]U = \left\{ (p,u,v) \mid 0\le p\le2 \text{ and } 0\le u\le \dfrac{\pi}2 \text{ and } 0\le v\le\dfrac{\pi}2\right\}[/tex]

and the integral of y over U is

[tex]\displaystyle \iiint_U y \, dV = \iiint_U p\sin(u)\sin(v) \cdot p^2 \sin(v) \, dV[/tex]

[tex]\displaystyle \iiint_U y \, dV = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \int_0^2 p^3 \sin(u) \sin^2(v) \, dp \, du \, dv [/tex]

[tex] \displaystyle \iiint_U y \, dV = \frac{2^4-0^4}4 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \sin(u) \sin^2(v) \, du \, dv [/tex]

[tex]\displaystyle \iiint_U y \, dV = 4 \cdot \left(-\cos\left(\frac\pi2\right) + \cos(0)\right) \int_0^{\frac\pi2} \sin^2(v) \, dv [/tex]

[tex]\displaystyle \iiint_U y \, dV = 4 \cdot \frac12 \int_0^{\frac\pi2} (1-\cos(2v)) \, dv [/tex]

[tex]\displaystyle \iiint_U y \, dV = 2 \left(\left(\frac\pi2 - \frac12 \sin\left(2\cdot\frac\pi2\right)\right) - \left(0 - \frac12 \sin\left(2\cdot0\right)\right) \right)[/tex]

[tex]\displaystyle \iiint_U y \, dV = \pi - \sin(\pi) = \boxed{\pi}[/tex]

Answer:

Step-by-step explanation:

Multiply the length and width, or c and b to find their area. Multiply this measurement by two to account for both sides. Add the three separate measurements together. Because surface area is the total area of all of the faces of an object, the final step is to add all of the individually calculated areas together.

Answer:

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

Step-by-step explanation:

Answer:

its 1

Step-by-step explanation:

it literly says it on the grid and its really simple

Answer:

c

Step-by-step explanation:

because the rest are just way off

Answer:

The answer is C, bro

Step-by-step explanation:

hope this helped.

Answer:

Step-by-step explanation:

87

Answer:

630 in.³

Step-by-step explanation:

To find the volume of a rectangular prism, you can multiply the height, times the width, times the length. So, let's go ahead and do that with the values of the given prism.

7 × 10 × 9 = 70 × 9 = 630

So, our volume is 630...but not so fast. We also have to put in our units. Our units are inches × inches × inches, or inches³. So our final value is 630 in.³

Hopefully that's helpful! :)

Answer:

x = 3

y = 0

z = 8

Step-by-step explanation:

a) 3x + 3y - z = 1

b) z = 8

c) -x -3y + 2z = 13

a) 3x + 3y - 8 = 1 (substitution)

a) 3x + 3y = 9

c) - x - 3y + 2(8) = 13 (substitution)

c) -x - 3y + 16 = 13

c) -x - 3y = -3

(3x + 3y = 9) + (-x -3y = -3)

= 2x = 6

x = 3

a) 3(3) + 3y - 8 = 1

9 + 3y - 8 = 1

y = (1 -9 + 8)/3

y = 0

answer:

6.4

Step-by-step explanation:

4^2+5^2=c^2

16+25

square root of 41

c^2=6.4

Answer:

g = he - 10h

Step-by-step explanation:

The definition of a rate in math is, the speed of something being gained in a problem, let's say we have a hot pipe that can full up a pool in 6 hours, our rate would be 1/6 of the pool per hour.

Answer 12

Step-by-step explanation:

A shipment of 12 microwave ovens contains three defective units. A vending company has ordered four units, and because each has identical packaging, the selection will be random. What is the probability that (a) all four units are good, (b) exactly two units are good, and (c) at least two units are good?

 I hope that helped?

Answer:

18 π ≈ 56.52

Step-by-step explanation:

The formula for the volume of a cylinder is V = π · r² · h.

This cylinder has a height (h) of 2 and a radius (r) of 3.

Therefore the volume is:

V =  π · r² · h = π · 3² · 2 = 18 π ≈ 56.52.

Answer:

3000×0.07=210 tins

Step-by-step explanation:

210 tins

Step-by-step explanation:

3000÷100×0.07

=2.1

Answer:

10% 0f 70 is 7

Step-by-step explanation:

70÷10=7

10%=7

Could be -24 if you are raising the -30 by 6.

Answer:

Step-by-step explanation:

500 mph with a flight time of 10 hours and 20 minutes  [(20 min)*(1 h/60 min) = 0.333 hr]

Distance = Speed * Time

Time = 10.333 hours

Distance = (500 miles/hr)*(10.333 hrs) = 5166.5 miles

The pilot's numbers indicate a distance of 5167 miles, compared to Mark's number of 4944 miles.  That is a 4.3% reduction from the pilot's numbers.  Not too bad, so we might question 1) Mark's knowledge, or 2) the impact that the approach and landing speeds have of the total miles flow.

My preference would be to trust the pilot's data.  I don't know where Mark got his math education.

9514 1404 393

Answer:

  1

Step-by-step explanation:

Any (non-zero) number divided by itself is 1.

_____

This is a fact that has many uses in problem solving and units conversion.

Answer:

Over 30

Step-by-step explanation:

There is no definite answer if you don't know how many pages each person. All you have to do is multiply 5 by 6

Answer:

The function is negative for all real values of x where

-6 < x < -2.

Step-by-step explanation:

f(x) = (x +2)(x + 6)

 x + 2 = 0    or   x + 6 = 0

x = -2     or x = -6

 After graphing the function is negative between -6 < x < -2

The true statement about the graph is (a) The function is negative for all real values of x where -6 < x < -2.

The equation of the function is given as:

[tex]f(x) = (x + 6)(x + 2)[/tex]

From the graph, we have the following highlights

The above means that:

The function is negative for all real values of x where -6 < x < -2.

Hence, the true statement about the graph is (a)

Read more about quadratic graphs at:

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Steps are in the attachment.

________

Hope it helps :)) ⚜

Question 2: -4/3

Question 3: -7/20

F(x) = -4 means y = -4. That means whatever the x is, the answer is going to be -4.