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3 years ago

I will upvote and give brainliest answer

Mathematics

1 answer:

Lana71 [14]3 years ago

7 0

Answer:

x = 58°

Step-by-step explanation:

Fact 1) Recall the fact that angles in a triangle add to 180°

Fact 2) Recall the fact that angles on a straight line add to 180°

The first angle we can work out is BAC using fact 2

114 + ? = 180

? = ( 180 - 114 )

? = 66

∠ BAC = 66

Now that we have angle BAC we can utilise the fact angles in a triangle add to 180°, so we can set this equation up

x + 66° + 56° = 180°

x + 122° = 180°

x = ( 180 - 122 )

x = 58°

You might be interested in

A submarine is at 89 feet below the surface of the ocean. If it descends another 42 feet, what will be it’s position in relation

jeyben [28]

add the 2 numbers:

89 + 42 = 131 feet below the surface,

which can also be written as -131 feet

8 0

3 years ago

Consider F and C below. F(x, y, z) = 2xz + y2 i + 2xy j + x2 + 9z2 k C: x = t2, y = t + 3, z = 3t − 1, 0 ≤ t ≤ 1 (a) Find a func

Ray Of Light [21]

Answer:

a)∇f = 2y + 2x + 18z

b) $\int\limits^._C {F} \, dr$ =108

Step-by-step explanation:

Given:

f (x,y,z ) = $(2xz+ y^{2})i + (2xy) j +(x^{2} + 9z^{2})k$

The curve C :

$x=t^{2} ,\\y= t+3\\z= 3t-1$

where 0 ≤ t ≤ 1

Required:

(a) F = ∇f =? (F is a vector here)

(b) $\int\limits^._C {F} \, dr$ =?

Solution

First we will find the directional derivative F = ∇f

for that , we will use the formula :

∇f = $F_{x}i+ F_{y} j+F_{z}k$

Fx= δf/δx = δ/δx $(2xz+ y^{2})i$ = 2z i

Fy= δf/δy=δ/δy (2xy)j = 2x j

Fz= δf/δz=δ/δz $(x^{2} + 9z^{2})k$ = 18z k

∇f = (2z) i .i + (2x) j.j + (18z) k.k

∇f = 2z + 2x + 18z

For part b):

we will use line integral formula:

$\int\limits^._C {F} \, dr$

to calculate dr, we will need the curve C:

r = x(t)+y(t)+z(t)

r= $(t^{2})i + (t+3) j +(3t-1) k$

$\frac{dr}{dt}=\frac{dx}{dt} +\frac{dy}{dt} + \frac{dz}{dt}$

$\frac{dx}{dt} = 2t$

$\frac{dy}{dt} = 1$

$\frac{dz}{dt} = 3$

$\int\limits^._C {F} \, dr$ = $\int\limits^1_0 {F_{x} } \, dx+ F_{y} dy +F_{z} dz$

= $\int\limits^1_0 {(2z(2t) + 2x(1) + 18z (3)} \, )$

put values of y, x and z

= $\int\limits^1_0 {2(3t-1) + 2(t^{2}) +18 (3) (3t-1)} \,$

= ${2t^{2} + 6t+162t -54-2}\, |^1_0$

= ${ 2t^{2}+ 168t - 56} \,|^1_0$ (Note : f(1)-f(0))

=2(1)+162(1)+2(0)+162(0)-56

= 2+162 -56

$\int\limits^._C {F} \, dr$ =108

3 0

3 years ago

The price per gallon of gasoline changes often. Most drivers pay close attention to those changes. Find the percent change in pr

Jlenok [28]

A) The amount of change is .20 (20 cents) so we need to find what percent of $4.00 is .20...
4 * x = .20
x = .20/4 = .05

Multiply by 100 (move decimal 2 places to the right) to change decimal to percent.

.05 = 5% increase

b)The increase is .75. What percent of 3.00 is .75

3 * x = .75
x = .75/3
x = .25 x 100 = 25% increase

c) The amount of change is .75 but this time we are going from 3.75 to 3.00 so we find out what percent .75 is of 3.75.

3.75 * x = .75
x = .75/3.75
x = .20 x 100 = 20% decrease

6 0

3 years ago

50 points plus brainilest for correct answer and step by step.

creativ13 [48]

Answer:

80 miles

Step-by-step explanation:

Speed is 30 miles/hour

Time is 2 hours 40 minutes or 2 2/3 hours or 8/3 hours

Distance is speed x times

so distance is 30 x 8/3 = 80 miles

7 0

2 years ago

Consider T(h) = 10h, which gives the total money earned, T, after a specific number of hours worked, h. Find T(30).

Lubov Fominskaja [6]

Answer:

T (30) = 300

Step-by-step explanation:

Explanation:-

Given T(h) = 10h

where 'T' gives the total money earned, T

and a specific number of hours worked' h'

Put h = 30

T(h) = 10h

T (30) = 10 × 30

T (30) = 300

6 0

2 years ago