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3 years ago

Not sure how to solve

Mathematics

1 answer:

Karolina [17]3 years ago

4 0

Answer:

(x, y, z) = (13/7, 19/7, 25/7)

Step-by-step explanation:

You know that the vector whose components are the coefficients of the equation of the plane is perpendicular to the plane. That is (1, 2, 3) is a vector perpendicular to the plane.

The parametric equation for a line through (1, 1, 1) with this direction vector is ...

(x, y, z) = (1, 2, 3)t +(1, 1, 1) = (t+1, 2t+1, 3t+1)

The point of intersection of this line and the plane will be the point in the plane closest to (1, 1, 1). That point has a t-value of ...

(t +1) +2(2t +1) +3(3t +1) = 18

14t +6 = 18

t = 12/14 = 6/7

The point in the plane closest to (1, 1, 1) is ...

(x, y, z) = (6/7+1, 2(6/7)+1, 3(6/7)+1)

(x, y, z) = (13/7, 19/7, 25/7)

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Let sin(−θ)=−3/5 and tanθ>0. What is the value of cos(−θ)?

Jobisdone [24]

Answer:

The value of Cos (-Ф) $\dfrac{\textrm 4}{\textrm 5}$ .

Step-by-step explanation:

Given Trigonometric function as :

sin( - Ф ) = $\frac{- 3}{5}$

- sin Ф = $\frac{- 3}{5}$

So, sin Ф = $\frac{ 3}{5}$

Now, as sin Ф = $\dfrac{\textrm perpendicular}{\textrm hypotenuse}$

So , $\dfrac{\textrm perpendicular}{\textrm hypotenuse}$ = $\frac{ 3}{5}$

So, perpendicular = 3

And hypotenuse = 5

Now, From Pythagoras Theorem

Base ² = Hypotenuse² - Perpendicular²

Or, Base ² = 5² - 3²

Or, Base ² = 25 - 9

Or, Base ² = 16

∴ Base = $\sqrt{16}$

I.e Base = 4

Now, Cos Ф = $\dfrac{\textrm base}{\textrm hypotenuse}$

So, Cos Ф = $\dfrac{\textrm 4}{\textrm 5}$

Now , Since

Cos ( - Ф ) = Cos Ф

So, Cos ( - Ф ) = Cos Ф = $\dfrac{\textrm 4}{\textrm 5}$

Hence The value of Cos (-Ф) $\dfrac{\textrm 4}{\textrm 5}$ . Answer

6 0

3 years ago

What is the best way to classify each equation? 22-3x+7x=4(x+5) ,6(2x-3=3(3-5), 6x-14=2(3x-7), 6x+3(x-4)=8(x-3)

Romashka-Z-Leto [24]

1. 22 - 3x + 7x = 4(x + 5)
 22 - 3x + 7x = 4x + 20
 +3x +3x +3x 
 22 + 10x = 7x + 20
 -7x -7x 
 22 + 3x = 20
 -22 -22
 3x = -2
 3 3
 x = -2/3

2. 6(2x - 3) = 3(3 - 5)
 12x - 18 = 3(-2)
 12x - 18 = -6
 +18 +18
 12x = 12
 12 12
 x = 1

3. 6x - 14 = 2(3x - 7)
 6x - 14 = -3x
 6x - 14 = 2(-7)
 6x - 14 = -14
 +14 +14
 6x = 0
 6 6
 x = 0

4. 6x + 3(x - 4) = 8(x - 3)
 6x + 3x - 12 = 8x - 24
 9x - 12 = 8x - 24
 -8x -8x 
 x - 12 = -24
 +12 +12
 x = -12

8 0

4 years ago

1. The product of two consecutive integers is 20. Find the values of these integers.

gulaghasi [49]

First find the factors of 20
1 & 20
2 & 10
4 & 5
-1 & -20
-2 & -10
-4 & -5

Now find the pairs that have a difference of 1

-4 & -5
4 & 5

4 0

3 years ago

Please help me. I need help thank you.

STatiana [176]

Answer:

Step-by-step explanation:

the ratio is 1:2

so,

$4*2=8\\7*2=14\\1*2=2$

the only shape with those numbers is C

Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day!

Stay Brainy!

7 0

3 years ago

Graph h(x)=-x^4 +3

Katyanochek1 [597]

Hope this helps, the y intercept is 3 ans the x intercepts are +1.3 and -1.3

8 0

3 years ago