URGENT! The range of y=Arccosx is (-pi/2,pi/2). True or False?

Answer:

21.7 m

Step-by-step explanation:

The question above is a right angle triangle and we would be using the trigonometric function of tangent to solve for it.

tan θ = Opposite/ Adjacent

Opposite side = Height = unknown

Adjacent = 20sqrt(3) m

θ = Angle of Elevation = 30°

Hence, we have:

tan 30° = Opposite/ 20√3

Opposite = tan 30° × 20√3m

Opposite = 20m

Height of the tower = Height of the observer + Height (Opposite side)

Height = 20m

Height of the the observer as given in the question is = 1.7m

Height of the tower = 20m + 1.7m

= 21.7m

Therefore, the height of the tower = 21.7m

Answer:

C 39.0

Step-by-step explanation:

To find the approximate angle, x, that the second tree makes with the ground, we can use the concept of similar triangles Therefore the correct option is B.

Let's calculate the height of the first tree using the given information. We can use the formula for the opposite side in a right triangle: opposite = adjacent * tan(angle). Therefore, the height of the first tree is approximately [tex]19 * tan(32°) = 19 * 0.6249 ≈ 11.873[/tex]  feet. Now, we can set up a proportion between the two trees based on their heights. Let x be the angle the second tree makes with the ground.

We have the following proportion: (height of first tree)/(height of second tree) = (length of first tree)/(length of second tree). Substituting the known values, we have [tex]11.873/16 = 19/x[/tex]. Cross-multiplying gives us [tex]11.873x = 304,[/tex]  and dividing both sides by 11.873 yields[tex]x ≈ 25.63°.[/tex]  The approximate angle, x, that the second tree makes with the ground is closest to 35.0°.

Hence the correct option is B

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Answer:

Step-by-step explanation:

From ohms law the expression for voltage is given as

[tex]V= IR[/tex]

Now given that

Voltage, V= [tex]2.4*10^3[/tex] volts

Resistance R= [tex]2*10^6[/tex] ohms

Applying ohms law the current can be calculated by making I the subject of formula

that is I= V/R

[tex]I= \frac{2.4*10^3}{2*10^6} \\\\I= \frac{2.4}{2} *10^(^3^-^6^)\\\\I=1.2*10^-^3[/tex]

The current in amps is 1.2 milli amps

Answer:

Step-by-step explanation:

The general form of a quadratic equation is ax²+bx+c = 0

Given the quadratic equation x²+4x+9=0 in its standard form, on comparing with the general equation we can get the value of the constant a, b and c as shown;

ax² = x²

a = 1

bx = 4x

b = 4

c = 9

The quadratic formula is given as x = -b±√(b²-4ac)/2a

Substituting the constant;

x = -4±√(4²-4(1)(9))/2(1)

x = -4 ±√(16-36)/2

x = -4±√-20/2

x = -4±(√-1*√20)/2

Note that √-1 = i

x = -4±(i√4*5)/2

x = (-4±i2√5)/2

x = -4/2±i2√5/2

x = -2±i√5

The solution to the quadratic equation are  -2+i√5 and  -2i-√5

Answer:

True

Step-by-step explanation:

Microsoft Excel is a great tool and has saved me on countless occasions in graphs and tables. I agree with the earlier answer by Hedland.

Answer:

[tex]slope=3[/tex]

Step-by-step explanation:

Use the following equation the find the slope:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}[/tex]

Rise over run is the change in the y-axis over the change in the x-axis from one point to the other. This is also known as the "slope". Insert the known values:

[tex](-10_{x1},8_{y1})\\\\(-15_{x2},-7_{y2})\\\\\\\frac{-7-8}{-15-(-10)}\\\\\frac{-7-8}{-15+10}[/tex]

Solve:

[tex]\frac{-7-8}{-15+10}=\frac{-15}{-5}[/tex]

Simplify. Two negatives make a positive:

[tex]\frac{-15}{-5}=\frac{15}{5}[/tex]

Simplify fraction by dividing top and bottom by 5:

[tex]\frac{15}{5}=\frac{3}{1} =3[/tex]

The slope is 3.

:Done

The slope of the line that passes through the points (-10, 8) and  (-15, -7) is 3 and thsi can be determined by using the point-slope formula.

Given :

The line that passes through the points (-10, 8) and  (-15, -7).

The following steps can be used in order to determine the slope of the line that passes through the points (-10, 8) and  (-15, -7):

Step 1 - The slope formula when two points are given is:

[tex]\rm m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

where m is the slope and [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points on the line.

Step 2 - Substitute the known terms in the above formula.

[tex]\rm m = \dfrac{-7-8}{-15+10}[/tex]

Step 3 - Simplify the above expression.

[tex]\rm m = \dfrac{15}{5}[/tex]

m = 3

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Answer:

4

Step-by-step explanation:

8 ^ 2/3

Rewriting 8 as 2^3

( 2^3) ^ 2/3

We know that a^ b^c = a^ (b*c)

2 ^ ( 3 * 2/3)

2 ^ 2

4

Answer:

Step-by-step explanation:

slope intercept form: y=mx+b

m= slope

b= y-intercept

y= 7x - 9

slope= 7

y-int.= -9

y= 3x - 1

slope 3

y-int.= -1

7x-9 = 3x-1

Add 9 to both sides: 7x = 3x +8

Subtract 3 from both sides: 4x = 8

Divide by 4 on both sides: x =2

Substitute 8 into the equation: y = 3(2) -1

y = 5

Solution: (2,5)

Answer:

Option C.

Step-by-step explanation:

It is given that,

[tex]P(A)=\dfrac{1}{4}[/tex]

[tex]P(B)=\dfrac{13}{20}[/tex]

It is given that events A and B are mutually exclusive. It means they have no common elements.

[tex]P(A\cap B)=0[/tex]

We know that,

[tex]P(A\ or\ B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

On substituting the values, we get

[tex]P(A\cup B)=\dfrac{1}{4}+\dfrac{13}{20}-0[/tex]

[tex]P(A\cup B)=\dfrac{5+13}{20}[/tex]

[tex]P(A\cup B)=\dfrac{18}{20}[/tex]

[tex]P(A\cup B)=\dfrac{9}{10}[/tex]

Therefore, the correct option is C.

The P (A or B) should be [tex]\frac{9}{10}[/tex]

Given that,

Based on the above information, the calculation is as follows:

[tex]= \frac{1}{4} + \frac{13}{20}\\\\= \frac{5+13}{20} \\\\= \frac{18}{20}\\\\= \frac{9}{10}[/tex]

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Answer:

  28 inches

Step-by-step explanation:

The point of intersection of the angle bisectors is the incenter. It is the center of a circle tangent to the three sides of the triangle. The circle has radius 2.

In the attached figure, we have labeled the points of tangency D, E, and F. We know that CE and CF are both of length 2, and we know that the points of tangency are the same distance from an external point where the tangents intersect. That means DA = FA and DB = EB.

The perimeter of the triangle is ...

  P = DA +DB +FA +EB +CF +CE

Using the above relations, this can be written as ...

  P = DA +DB +DA +DB +CF +CE = 2(DA +DB) +2(CE)

We are told that AB is 12 inches, so DA +DB = 12 inches. We also know that CE = 2 inches, so the perimeter is ...

  P = 2(12 in) + 2(2 in) = 28 in

The perimeter of triangle ABC is 28 inches.

Answer:

I may be wrong but I think 8 is your answer.

Step-by-step explanation:

(-1)^(3/7)  x 128^(3/7)

-1 x 128^3/7

128^(3/7) = 8

= 8

-5,3,-2,1 on a number line

<-|----|----|----|----|----|----|----|----|->

-5 -2 0 1 3

Answer:

Step-by-step explanation:

North-east has a bearing of 45 degrees

South-west has a bearing of 225 degrees.

Taken anticlockwise,

angle = south-west - north-east

=  (225-45)

= 180 degrees

answer

hope this helps....

Answer: [tex](y-1)=\dfrac{3}{2}(x+3)[/tex]

Step-by-step explanation:

Slope of the given line passing through (-2,-4) and (2,2) :

m=  [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]=\dfrac{2-(-4)}{2-(-2)}\\\\=\dfrac{2+4}{2+2}=\dfrac{6}{4}\\\\=\dfrac{3}{2}[/tex]

Parallel lines has same slope . That means  slope of required line would be [tex]\dfrac{3}{2}[/tex].

Equation of a line passing through (a,b) and has slope 'm' is given by :_

[tex](y-b)=m(x-a)[/tex]

Now, Equation of a line passing through(-3, 1) and has slope '[tex]\dfrac{3}{2}[/tex]' is given by

[tex](y-1)=\dfrac{3}{2}(x-(-3))\\\\\Rightarrow\ (y-1)=\dfrac{3}{2}(x+3)\ \ \to \text{Required equation in point slope form.}[/tex]

Hello there! :)

Answer:

[tex]\huge\boxed{x = 27}[/tex]

Given the equation:

3x - 4y = 65 where y = 4

Substitute in 4 for "y":

3x - 4(4) = 65

Simplify:

3x - 16 = 65

Add 16 to both sides:

3x - 16 + 16 = 65 + 16

3x = 81

Divide both sides by 3:

3x/3 = 81/3

x = 27.

Answer:

  all reals

Step-by-step explanation:

Simplified, you have ...

  20 -3n = 20 -3n

The equation is a tautology, true for all values of n.

The solution set is "all reals."

Answer:

Step-by-step explanation:

A fifth-grade polynomial requires a minimum of 6 different points to create an adequate graph. Let is [tex]X[/tex] the dominion of the polynomial, such that [tex]0[/tex], [tex]1[/tex], [tex]2[/tex], [tex]3[/tex], [tex]4[/tex], [tex]5[/tex] [tex]\in X[/tex]. The values of the function for each value are calculated herein:

x = 0

[tex]f(0) = 6\cdot 0^{5}+8\cdot 0^{4}-7\cdot 0^{3}-5\cdot 0^{2}+10[/tex]

[tex]f(0) = 10[/tex]

x = 1

[tex]f(1) = 6\cdot 1^{5}+8\cdot 1^{4}-7\cdot 1^{3}-5\cdot 1^{2}+10[/tex]

[tex]f(1) = 12[/tex]

x = 2

[tex]f(2) = 6\cdot 2^{5}+8\cdot 2^{4}-7\cdot 2^{3}-5\cdot 2^{2}+10[/tex]

[tex]f(2) = 254[/tex]

x = 3

[tex]f(3) = 6\cdot 3^{5}+8\cdot 3^{4}-7\cdot 3^{3}-5\cdot 3^{2}+10[/tex]

[tex]f(3) = 1882[/tex]

x = 4

[tex]f(4) = 6\cdot 4^{5}+8\cdot 4^{4}-7\cdot 4^{3}-5\cdot 4^{2}+10[/tex]

[tex]f(4) = 7674[/tex]

x = 5

[tex]f(5) = 6\cdot 5^{5}+8\cdot 5^{4}-7\cdot 5^{3}-5\cdot 5^{2}+10[/tex]

[tex]f(5) = 22760[/tex]

The table is now presented:

 x                 y

 0                10

 1                 12

 2               254

 3               1882

 4               7674

 5              22760

Finally, the graphic is now constructed by using an online tool (i.e. Desmos). The image is included below as attachment.

distance of a point [tex](x,y)[/tex] from origin is $\sqrt{x^2+y^2}$

so distance is $\sqrt{(-15)^2+(8)^2}=\sqrt{225+64}=\sqrt{289}=17$

Answer:

Distance=17 units

Step-by-step explanation:

Coordinates of the origin: (0, 0)

Coordinates of the point in question: (-15, 8)

Distance formula for any two points [tex](x_1,y_1), (x_2,y_2)[/tex] on the plane:

[tex]distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\distance=\sqrt{(-15-0)^2+(8-0)^2}\\distance=\sqrt{(15)^2+(8)^2}\\distance=\sqrt{225+64} \\distance=\sqrt{289} \\distance=17[/tex]

The order of a matrix is m×n where m is the number of rows and n is the number of columns.

can you count and find what are m and n here?

Answer:

Step-by-step explanation:

Number of rows X Number of columns

Rows = 3

Columns = 2

answer = 3x2

Answer:

$60

Step-by-step explanation:

Answer:

60$

Step-by-step explanation:

3 gallons per hr

multiply by 4

12gl  per 4hrs

5 dl per gl

multiply by 12

60 dl per 12 gl

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Answer:

C.

Step-by-step explanation:

When you replace x by x - h, the graph is shifted h units horizontally.

Here, x is replaced by x - 6.

x - h = x - 6

h = 6

6 is positive, so the shift is 6 units to the right.

Answer: C.

Answer:

All real numbers are solutions. 0=0

Step-by-step explanation:

(x+3)(x−5)=(x+3)(x−5)

Step 1: Simplify both sides of the equation.

x2−2x−15=x2−2x−15

Step 2: Subtract x^2 from both sides.

x2−2x−15−x2=x2−2x−15−x2

−2x−15=−2x−15

Step 3: Add 2x to both sides.

−2x−15+2x=−2x−15+2x

−15=−15

Step 4: Add 15 to both sides.

−15+15=−15+15

0=0

All real numbers are solutions.

Answer:

It is reduced to the equation of the Theorem of Pythagoras.

Step-by-step explanation:

Any triangle can be modelled by this formula under the Law of Cosine:

[tex]b = \sqrt{a^{2}+c^{2}-2\cdot a\cdot c\cdot \cos B}[/tex]

Where:

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Side lengths, dimensionless.

[tex]B[/tex] - Angle opposed to the side [tex]b[/tex], measured in sexagesimal degrees.

Now, let suppose that angle B is a right angle (90º), so that b is a hypotenuse and a and c are legs. Hence:

[tex]\cos B = 0[/tex]

And the equation is reduced to the form of the Theorem of Pythagoras, that is to say:

[tex]b = \sqrt{a^{2}+c^{2}}[/tex]

Answer:

3x+11y-3

Step-by-step explanation:

Hey! So here is what you do to solve the problem-

Combine like terms:

(x) 5x-2x=3x

(y) 3y+8y=11y

(#) 7-10 =-3

So....

3x+11y-3 is your answer!

Hope this helps!:)

Answer:

Step 1: Isolate the absolute value expression.

Step2: Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation.

Step 3: Solve for the unknown in both equations.

Step 4: Check your answer analytically or graphically.

Step-by-step explanation:

Answer:

Rewrite the absolute value equation as two separate equations, one positive and the other negative

Solve each equation separately

After solving, substitute your answers back into original equation to verify that you solutions are valid

Write out the final solution or graph it as needed

Step-by-step explanation:

Answer:

53 1/3 km/h

Step-by-step explanation:

average speed = (total distance)/(total time)

average speed = distance/time

time * average speed = distance

time = distance/(average speed)

250 km at 75 km/h

distance = 250 km

time = (250 km)/(75 km/h) = 3.33333... hours

350 km at 70 km/h

distance = 350 km

time = (350 km)/(70 km/h) = 5 hours

200 km at 30 km/h

distance = 200 km

time = (200 km)/(30 km/h) = 6.6666...  hour

total distance = 250 km + 350 km + 200 km = 800 km

total time = 3.33333... hours + 5 hours + 6.66666... hours = 15 hours

average speed = (total distance)/(total time)

average speed = (800 km)/(15 hours)

average speed = 53 1/3 km/h

The average speed of whole journey of the train is 45 km/hr

Average speed is the ratio of total distance travelled to total time taken. It is given by:

Average speed = total distance / total time

Given that a train travels 250 km with a average speed of 75 km/hr, hence:

75 = 250/time

time = 3.33 hours

It the travel 200 km with average speed of 30km/hr, hence:

30 = 200/time

time = 6.67 hours

The total distance = 200 km + 250 km = 450 km

The total time = 3.33 hr + 6.67 hr = 10 hours

Average speed = total distance/total time = 450 km/10 hours = 45 km/hr

The average speed of whole journey of the train is 45 km/hr

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Answer:

Increase in profit = 531.52

Step-by-step explanation:

I'll take your word for it.

What you'd need to do for each kind of pizza and price, multiply the number sold and profit/loss for each, and add them up.

Calculations have been tabulated and shown in the attached diagram.

Answer

Increase in profit

= 2221.88 - 1690.36

= 531.52

Answer:

Step-by-step explanation:

The function is f(x)=x^2 + ax + b

Derivate the function:

● f'(x)= 2x + a

Solve the equation f'(x)=0 to find a

The minimum is at (3,9)

Replace x with 9

● 0 = 2×3 + a

● 0 = 6 + a

● a = -6

So the value of a is -6

Hence the equation is x^2 -6x+b

We have a khown point at (3,9)

● 9 = 3^2 -6×3 +b

● 9 = 9 -18 + b

● 9 = -9 +b

● b = 18

So the equation is x^2-6x+18

Verify by graphing the function.

The vetex is (3,9) and it is a minimum so the equation is right

Answer:

JK = 6.86

Step-by-step explanation:

The parameters given are;

LJ = 14

JM = 48

LM = 50

[tex]tan(\angle JML )= \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length} = \dfrac{LK}{JM} = \dfrac{14}{48} = \dfrac{7}{24}[/tex]

[tex]tan \left( \dfrac{7}{24} \right)= 16.26 ^{\circ }[/tex]

∠JML = 16.26°

Given that ∠JML is bisected by KM, we apply the angle bisector theorem which states that a ray that bisects an interior angle of a triangle bisects the opposite (bisected angle facing side) in the proportion of the ration of the other two sides of the triangle.

From the angle bisector theorem, we have;

LM/JM = LK/JK

50/48 = LK/JK................(1)

LK + KJ = 14.....................(2)

From equation (1), we have;

LK = 25/24×JK

25/24×KJ + JK = 14

JK×(25/24 + 1) = 14

JK × 49/24 = 14

JK = 14×24/49 = 48/7. = 6.86.

JK = 6.86