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2 years ago

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Which of these ordered triples indicates where the plane cuts the x-axis for this equation? 7x +2y +3z =42 A. (14,0,0) B. (7,0,0

) C. (21,0,0) or D. (6,0,0)

2 answers:

Drupady [299]2 years ago

6 0

Answer:

Option D is correct.

Step-by-step explanation:

Given Equation of plane is 7x + 2y + 3z = 42

We need to find ordered triplet where plane cuts the x-axis.

To find point of x-axis when plane cuts it. we put other coordinates equal to 0.

So, put y = 0 and z = 0 in equation plance to get x-coordinate of the required ordered triplet.

7x + 2 × 0 + 3 × 0 = 42

7x + 0 + 0 = 42

7x = 42

$x=\frac{42}{7}$

x = 6

⇒ ordered triplet = ( 6 , 0 , 0 )

Therefore, Option D is correct.

pickupchik [31]2 years ago

4 0

My answer is: D. <span>(6,0,0)

Given:
</span><span> 7x +2y +3z =42

I assumed that the format in the given choices is (x,y,z). So, I substituted each number to its corresponding variable.

A. </span>(14,0,0) → 7(14) +2(0) +3(0) = 42 → 98 + 0 + 0 ≠ 42 NOT THE ANSWER<span>
B. (7,0,0) </span>→ 7(7) +2(0) +3(0) = 42 → 49 + 0 + 0 ≠ 42 NOT THE ANSWER<span>
C. (21,0,0) </span>→ 7(21) +2(0) +3(0) = 42 → 147 + 0 + 0 ≠ 42 NOT THE ANSWER<span>
D. (6,0,0) </span>→ 7(6) +2(0) +3(0) = 42 → 42 + 0 + 0 = 42 CORRECT ANSWER.

<span>The ordered triples indicated where the plane cuts the x-axis for this equation is D. (6,0,0). </span>

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in triangleABC the side lengths are b=13, ac=21 and bc=x. write a compound inequality the represents the range of possible value

tankabanditka [31]

Answer:

8 < x < 34

Step-by-step explanation:

ab = 13, ac = 21, bc = x

The longest side of a triangle must be less than the sum of the other two sides.

If 21 is the longest side:

21 < 13 + x

8 < x

If x is the longest side:

x < 13 + 21

x < 34

Therefore, 8 < x < 34.

3 0

2 years ago

Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D = {(x, y) |

Bas_tet [7]

Answer:

$M=168k$

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

Step-by-step explanation:

Let's begin with the mass definition in terms of density.

$M=\int\int \rho dA$

Now, we know the limits of the integrals of x and y, and also know that ρ = ky², so we will have:

$M=\int^{9}_{1}\int^{4}_{1}ky^{2} dydx$

Let's solve this integral:

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}21dx$

$M=21k\int^{9}_{1}dx=21k*x|^{9}_{1}$

So the mass will be:

$M=21k*8=168k$

Now we need to find the x-coordinate of the center of mass.

$\bar{x}=\frac{1}{M}\int\int x*\rho dydx$

$\bar{x}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}x*ky^{2} dydx$

$\bar{x}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}x*y^{2} dydx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*\frac{y^{3}}{3}|^{4}_{1}dx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*21 dx$

$\bar{x}=\frac{21}{168}\frac{x^{2}}{2}|^{9}_{1}$

$\bar{x}=\frac{21}{168}*40=5$

Now we need to find the y-coordinate of the center of mass.

$\bar{y}=\frac{1}{M}\int\int y*\rho dydx$

$\bar{y}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}y*ky^{2} dydx$

$\bar{y}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}y^{3} dydx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{y^{4}}{4}|^{4}_{1}dx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{255}{4}dx$

$\bar{y}=\frac{255}{672}\int^{9}_{1}dx$

$\bar{y}=\frac{255}{672}8=\frac{2040}{672}$

$\bar{y}=\frac{85}{28}$

Therefore the center of mass is:

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

I hope it helps you!

3 0

2 years ago

Izumi is running on a quarter-mile oval track. After running 110 yards, his coach records his time as 16 seconds.

pickupchik [31]

Answer:

14.04 miles per hour

Step-by-step explanation:

The problem is asking for Izumi's speed. The formula of speed is:

s = $\frac{d}{t}$ , where "s" means speed, "d" means distance and "t" means time.

The problem is also asking for the unit<u> miles per hou</u>r ( $\frac{miles}{hour}$ ) so, this means that we have to know how many miles Izumi ran, given that the problem only mentioned<u> yards (110 yards).</u>

Let's convert 110 yards to miles, provided that he Izumi ran 1,760 yards in a mile.

110 yards ÷ 1760 $\frac{yards}{mile}$ = 0.0625 miles (this is the distance covered by Izumi in miles)

Let's go back again to the formula: s = $\frac{d}{t}$

s = $\frac{0.0625 miles}{16 seconds}$ = 0.0039 $\frac{miles}{sec}$

Since, the we arrived at a miles per second unit, we have to convert it to miles per hour.

So, if a minute has 60 seconds, then an hour has 3,600 seconds.

Thus, 0.0039 $\frac{miles}{sec}$ × 3,600 $\frac{seconds}{hour}$ = 14.04 miles per hour (the answer)

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2 years ago

A study found that a driver’s reaction time A(x) to audio stimuli and his or her reaction time V(x) to visual stimuli (both in m

amid [387]

Answer:

The required inequality is $0.0001 x^2 - 0.089 x - 7$ .

Step-by-step explanation:

The given inequalities are

$A(x) = 0.0051x^2 - 0.319x + 15$

$V(x)= 0.005x^2 - 0.23x + 22$

where, x is the driver's age (in years), A(x) is driver’s reaction time to audio stimuli and V(x) is his or her reaction time to visual stimuli, 16 ≤ x ≤ 70.

We need to find an inequality that can be use to find the x-values for which A(x) is less than V(x).

$A(x)$

$0.0051x^2 - 0.319x + 15< 0.005x^2 - 0.23x + 22$

$0.0051x^2 - 0.319x + 15- 0.005x^2 + 0.23x- 22$

Combine like terms.

$0.0001 x^2 - 0.089 x - 7$

where, 16 ≤ x ≤ 70.

Therefore, the required inequality is $0.0001 x^2 - 0.089 x - 7$ .

5 0

2 years ago

How many solutions does the equation sin(5x) = 1/2 have on the interval (0, 2PI]

Darina [25.2K]

Answer:

Step-by-step explanation:

Given the equation

Sin(5x) = ½

5x = arcSin(½)

5x = 30°

Then,

The general formula for sin is

5θ = n180 + (-1)ⁿθ

Divide through by 5

θ = n•36 + (-1)ⁿ30/5

θ = 36n + (-1)ⁿ6

The range of the solution is

0<θ<2π I.e 0<θ<360

First solution

When n = 0

θ = 36n + (-1)ⁿθ

θ = 0×36 + (-1)^0×6

θ = 6°

When n = 1

θ = 36n + (-1)ⁿ6

θ = 36-6

θ = 30°

When n = 2

θ = 36n + (-1)ⁿ6

θ = 36×2 + 6

θ = 78°

When n =3

θ = 36n + (-1)ⁿ6

θ = 36×3 - 6

θ = 102°

When n=4

θ = 36n + (-1)ⁿ6

θ = 36×4 + 6

θ = 150

When n =5

θ = 36n + (-1)ⁿ6

θ = 36×5 - 6

θ = 174°

When n = 6

θ = 36n+ (-1)ⁿ6

θ = 36×6 + 6

θ = 222°

When n = 7

θ = 36n + (-1)ⁿ6

θ = 36×7 - 6

θ = 246°

When n =8

θ = 36n + (-1)ⁿ6

θ = 36×8 + 6

θ = 294°

When n =9

θ = 36n + (-1)ⁿ6

θ = 36×9 - 6

θ = 318°

When n =10

θ = 36n + (-1)ⁿ6

θ = 36×10 + 6

θ = 366°

When n = 10 is out of range of θ

Then, the solution is from n =0 to n=9

So the equation have 10 solutions in the range 0<θ<2π

4 0

1 year ago