Please use an equation step by step and please show the numbers do not use words

The missing values are highlighted in bold, which are approximate to four decimal places (with the exception of B = 90 in problem 3).

Lowercase letters a,b,c are side lengths; Uppercase letters A,B,C are angles opposite the sides mentioned.

The drawings are shown below.

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Explanation:

Problem 1

Use the Law of Cosines to solve for side c

c^2 = a^2 + b^2 - 2*a*b*cos(C)

c^2 = 3^2 + 4^2 - 2*3*4*cos(40)

c^2 = 6.61493337

c = sqrt(6.61493337)

c = 2.57195128

c = 2.5720

Now apply the Law of Sines to find angle A

sin(A)/a = sin(C)/c

sin(A)/3 = sin(40)/2.57195128

sin(A) = 3*sin(40)/2.57195128

sin(A) = 0.74976647

A = arcsin(0.74976647)

A = 48.57015285

A = 48.5702

Once we know two angles of a triangle, we can then subtract their sum from 180 to get the third missing angle.

A+B+C = 180

B = 180 - (A+C)

B = 180 - (48.57015285+40)

B = 91.42984715

B = 91.4298

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Problem 2

Like with the previous problem, we can use the Law of Cosines to solve for the missing side.

b^2 = a^2 + c^2 - 2*a*c*cos(B)

b^2 = 3^2 + 2^2 - 2*3*2*cos(110)

b^2 = 17.10424172

b = sqrt(17.10424172)

b = 4.13572747

b = 4.1357

Now use the Law of Sines to find angle A

sin(A)/a = sin(B)/b

sin(A)/3 = sin(110)/4.13572747

sin(A) = 3*sin(110)/4.13572747

sin(A) = 0.68164014

A = arcsin(0.68164014)

A = 42.9719427

A = 42.9719

Then we can wrap things up like so

A+B+C = 180

C = 180 - (A+B)

C = 180 - (42.9719427+110)

C = 27.0280573

C = 27.0281

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Problem 3

Use the Law of Cosines to find angle A.

a^2 = b^2 + c^2 - 2*b*c*cos(A)

12^2 = 13^2 + 5^2 - 2*13*5*cos(A)

144 = 194 - 130*cos(A)

-130*cos(A) = 144 - 194

-130*cos(A) = -50

cos(A) = (-50)/(- 130)

cos(A) = 0.38461538

A = arccos(0.38461538)

A = 67.38013505

A = 67.3801

We could use the Law of Cosines to find angle B, but I'll use the Law of Sines instead.

sin(A)/a = sin(B)/b

sin(B) = b*sin(A)/a

sin(B) = 13*sin(67.38013505)/12

sin(B) = 0.99999999998574

sin(B) = 1

B = arcsin(1)

B = 90

It turns out we have a 5-12-13 right triangle (though usually c is the longest side instead of b).

Now we could use the Law of Cosines to find angle C, but the steps shown below are much quicker in my opinion that don't involve any trig functions.

A+B+C = 180

C = 180 - (A+B)

C = 180 - (67.38013505 + 90)

C = 22.61986495

C = 22.6199

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Problem 4

The steps will basically be identical to problem 3, but with different numbers of course.

First we need the Law of Cosines to find angle A.

a^2 = b^2 + c^2 - 2*b*c*cos(A)

5^2 = 8^2 + 9^2 - 2*8*9*cos(A)

25 = 145 - 144*cos(A)

-144*cos(A) = 25 - 145

-144*cos(A) = -120

cos(A) = (-120)/(-144)

cos(A) = 0.83333333

A = arccos(0.83333333)

A = 33.55730976

A = 33.5573

Now use the Law of Sines to find angle B.

sin(A)/a = sin(B)/b

sin(B) = b*sin(A)/a

sin(B) = 8*sin(33.55730976)/5

sin(B) = 0.88443328

B = arcsin(0.88443328)

B = 62.18186103

B = 62.1819

Lastly,

A+B+C = 180

C = 180 - (A+B)

C = 180 - (33.55730976 + 62.18186103)

C = 84.26082921

C = 84.2608

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Side notes:

Answer:

Supplementary

Step-by-step explanation:

VSW and TSW combine and make 180. Complementary is when they make up to 90

Add total people:

5 + 20 + 40 + 30 + 20 = 115 people

Add people 6-10 to 21-25 = 20 + 20 = 40

Divide the two age ranges by total people:

40/115 = 0.34782609

Multiply by 100 to get percent:

0.34782609 x 100 = 34.782609%  Round off as needed

Answer:

B. 42.

Step-by-step explanation:

x/35 = 30/25

25x = 30*35

x = (30*35)/25

  = 1050/25

  = 42.

Answer:

True

Step-by-step explanation:

3x5=15

15+8=23

23=23

Answer:

True

Step-by-step explanation:

3 x 5 = 15

15 + 8 = 23

Answer:

d.f(x)=(×2 +1)/3).

Step-by-step explanation:

I think that was my answer

Answer:

120 miles.

Step-by-step explanation:

Use long division to find how many miles the car travels in 1 hour then we multiply by 4

: (7÷210=30)×4=120miles. Hope this helped ;D

Answer:7541

Step-by-step explanation:

all you have to do is add the bottom

Answer:

Rhombus

Square

Step-by-step explanation:

Rhombuses and squares have sides that are always congruent.

Answer:

See below.

Step-by-step explanation:

x+9>17

  -9  -9

x>8

-hope it helps

Answer: five hundred sixty-two thousand nine hundred thirty-two

Step-by-step explanation: Student instructed to give the word form of a given value.

Answer:

The correct word form is:

Five hundred sixty-two thousand nine hundred thirty-two.

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Thank you so much for participate in the community of Brainly.com

I hope help you :)

Kind regards, Antonio.

Answer:

first find the average per day. 5/3= 1 & 2/3... 2/3 of a minute is 40 is 60/3=20 seconds. so 4 days would be the full 5 minutes plus another 1 minute and another 40 seconds.. so by day 4 it would be 6 min and 40 seconds.

Answer:

$91 per ounce

Step-by-step explanation:

If 3 ounces cost $273, we can divide both sides by 3 to find the unit rate. To make this clearer, we use the variable [tex]x[/tex] for ounces. Then, we have the equation

[tex]3x=273[/tex].

Dividing both sides by 3, we have

[tex]x=91[/tex].

The cost of one ounce is $91.

The percentage of those that did not like both of them is 76%

Let the total number of people in the community be 100%

n(u) = 100

If 58% like to listen to the radio only and 18% like to watch the T.V. only, then;

n(R) = 58 - x

n(T) = 118 - x

where x is the percentage of people who do not like both of them. Taking the sum;

58 + x + 18 = 100

x + 76 = 100

x = 100 - 76

x = 24

Hence 24% of people like both of them.

The percentage of those that did not like both of them is 76%

Learn more on sets here: https://brainly.com/question/13458417

Answer:

I have no clue thats why is got this app

Answer:

57 units³

Step-by-step explanation:

Volume = length • width • height

Fill in the numbers:

V = 3 4/5 • 2 1/2 • 6

I am making them into improper fractions to make it easier:

V = 19/5 • 5/2 • 6

Multiplying the length and the width:

V = 95/10 • 6

Multiplying the height in:

V = 57

Answer:

Maximum height = 16 yards

This occurs 20 yards from the quarterback.

Step-by-step explanation:

Given function:  [tex]f(x)=-0.025x^2+x+6[/tex]

To find the maximum (turning point), differentiate the function:

[tex]f('x)=-0.05x+1[/tex]

Set the derivative to zero and solve for [tex]x[/tex]:

[tex]\implies f'(x)=0[/tex]

[tex]\implies -0.05x+1=0[/tex]

[tex]\implies 0.05x=1[/tex]

[tex]\implies x=20[/tex]

Substitute found value of [tex]x[/tex] into the function to find the maximum height:

[tex]f(20)=-0.025(20)^2+(20)+6=16[/tex]

Therefore, the maximum height is 16 yards.

This occurs 20 yards from the quarterback.

The maximum height of the football can be 16 yards and this occurs 20 yards from the quarterback. The concepts of differentiation are used to solve this problem.

Differentiation is a fundamental mathematical concept that is generally used to obtain the rate of change or slopes of a line.

It is given that the height of the football is modeled as the following function:

f(x) = -0.025x² + x + 6

where x is the ball's horizontal distance (in yards) from the quarterback.

To obtain the maximum height of the ball, the equation is needed to be differentiated and set equal to zero as follows:

[tex]\dfrac{d}{dx}f(x) = 0\\\dfrac{d}{dx}(-0.025x^2+x+6)=0\\-0.025\times2x +1 = 0\\-0.05x+1 = 0\\x = \dfrac{1}{0.05}\\x = 20[/tex]

Substitute this value of x in f(x) to find the maximum height,

f(20) = -0.025(20)² + 20 + 6

f(20) = -0.025 × 400 + 26

f(20) = -10 + 26

f(20) = 16

Therefore, the maximum height is 16 yards and this occurs 20 yards from the quarterback.

Learn more about Differentiation here:

https://brainly.com/question/33433874

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The complete question is as follows:

A quarterback tosses a football to a receiver 40 yards downfield. The height of the football, f(x), in feet, can be modeled by f(x) = -0.025x²+x+6, where x is the ball's horizontal distance, in yards, from the quarterback. What is the ball's maximum height and how far from the quarterback does this occur?​

Answer:

[tex](2,\, -3)[/tex].

[tex]r = \sqrt{6}[/tex].

Step-by-step explanation:

Let [tex](a,\, b)[/tex] denote the center of this circle. Let [tex]r[/tex] ([tex]r > 0[/tex]) denote the radius of this circle. The equation of this circle would be:

[tex](x - a)^{2} + (y - b)^{2} = r^{2}[/tex].

Expand to obtain an equivalent equation:

[tex]x^{2} + (- 2\, a) + y^{2} + (- 2\, b) + (a^{2} + b^{2} - r^{2}) = 0[/tex].

Since this equation and the given equation describe the same circle, their corresponding coefficients should match.

Notice that the coefficients of [tex]x^{2}[/tex] and [tex]y^{2}[/tex] in this equation are both [tex]1[/tex]. However, the corresponding coefficients in the given equation are both [tex]2[/tex]. Thus, divide both sides of the given equation by [tex]2\![/tex] to match the coefficients of the [tex]x^{2}[/tex] and [tex]y^{2}[/tex] terms:

[tex]x^{2} + (- 4\, x) + y^{2} + 6\, y + 7 = 0[/tex].

The constants should also match. Thus:

[tex]a^{2} + b^{2} - r^{2} = 7[/tex].

Substitute in [tex]a = 2[/tex] and [tex]b = (-3)[/tex]; given that [tex]r > 0[/tex], the value of [tex]r[/tex] would be:

[tex]r = \sqrt{2^{2} + 3^{2} - 7} = \sqrt{6}[/tex].

Answer:10 to the 2nd power

Step-by-step explanation:

Answer:

let's suppose

Diane: D= H – 8

Henry: H

Abdul: A = 3H

D+H+A=82

D=10

H=18

A=54

Answer:

f(0)=3

Step-by-step explanation:

f(0) = -3 x 0 + 3

f(0)=3

Answer:

3:2

Step-by-step explanation:

if they won 3/5 games, then the other 2 were lost so the ratio would be 3:2

Answer:

58

Step-by-step explanation:

65 + 57 = 122

A triangle is 180 degrees

180 - 122 = 58

58  is the missing measurement

Answer:

[tex]\dfrac{6\pi -9\sqrt{3} }{16}[/tex]

Step-by-step explanation:

You need to rewrite [tex]\cos^2 \theta[/tex] using cos double angle identity:

[tex]\cos 2\theta= \cos^2\theta-\sin^2\theta[/tex]

[tex]\implies \cos 2\theta= \cos^2\theta-(1-\cos^2\theta)[/tex]

[tex]\implies \cos 2\theta=2 \cos^2\theta-1[/tex]

[tex]\implies \cos^2\theta=\dfrac12(\cos 2\theta+1)[/tex]

Then substitute this into the integration.

Please see the attachment for the full integration (it was clearer for me to type this in MS word than use the equation editor here)

Recall the double angle identity for cosines

Using this the integral becomes :

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}\int_{\tiny \dfrac{\pi}{3}}^{\tiny \dfrac{\pi}{2}}\{3\cos (\theta)\}^{2}d\theta}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{1}{2}\int_{\tiny \dfrac{\pi}{3}}^{\tiny \dfrac{\pi}{2}}9\cos^{2}(\theta)d\theta}[/tex]

As we can take constant out of the integrand so we have

[tex]{:\implies \quad \displaystyle \sf \dfrac{9}{2}\int_{\tiny \dfrac{\pi}{3}}^{\tiny \dfrac{\pi}{2}}\cos^{2}(\theta)d\theta}[/tex]

Using the double angle identity for cosines ;

[tex]{:\implies \quad \displaystyle \sf \dfrac{9}{2}\int_{\tiny \dfrac{\pi}{3}}^{\tiny \dfrac{\pi}{2}}\bigg\{\dfrac{1+\cos (2\theta)}{2}\bigg\}d\theta}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{9}{4}\int_{\tiny \dfrac{\pi}{3}}^{\tiny \dfrac{\pi}{2}}\{1+\cos (2\theta)\}d\theta}[/tex]

Now , as integrals follow distributive property, so we now have

[tex]{:\implies \quad \displaystyle \sf \dfrac{9}{4}\bigg(\int_{\tiny \dfrac{\pi}{3}}^{\tiny \dfrac{\pi}{2}}d\theta+\int_{\tiny \dfrac{\pi}{3}}^{\tiny \dfrac{\pi}{2}}\cos (2\theta)d\theta \bigg)}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{9}{4}\bigg\{\bigg(\theta +\dfrac{\sin (2\theta)}{2}\bigg) \bigg|_{\tiny \dfrac{\pi}{3}}^{\tiny \dfrac{\pi}{2}}\bigg\}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{9}{4}\bigg[\dfrac{\pi}{2}-\dfrac{\pi}{3}+\dfrac{1}{2}\bigg\{\sin (\pi)-\sin \left(\dfrac{2\pi}{3}\right)\bigg\}\bigg]}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{9}{4}\bigg\{\dfrac{3\pi -2\pi}{6}+\dfrac{1}{2}\bigg(-\dfrac{\sqrt{3}}{2}\bigg)\bigg\}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{9}{4}\bigg(\dfrac{\pi}{6}-\dfrac{\sqrt{3}}{4}\bigg)}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{9}{4}\bigg(\dfrac{2\pi -3\sqrt{3}}{12}\bigg)}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{3(2\pi -3\sqrt{3})}{4\times 4}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \dfrac{6\pi -9\sqrt{3}}{16}}[/tex]

[tex]{:\implies \quad \displaystyle \bf \therefore \quad \underline{\underline{\int_{\tiny \dfrac{\pi}{3}}^{\tiny \dfrac{\pi}{2}}\{3\cos (\theta)\}^{2}d\theta =\dfrac{6\pi -9\sqrt{3}}{16}}}}[/tex]

Answer:

6.71 mm

Step-by-step explanation:

Find radius R

Volume = πR²H

4500π = πR²*100

R² = 45

so R = √45 = 3√5 = 6.71 mm

Answer:

  -225°, 135°, 495°

Step-by-step explanation:

Adding or subtracting multiples of 360° will give angle values that are coterminal with a given angle.

  -225° -360° = -595° (not on the list)

  -225° +0·360° = -225°

  -225° +360° = 135°

  -225° +2·360° = 495°

Angles -225°, 135°, 495° are coterminal with -225°.

Answer:

2x² + 4y²

according to your given information.......

Answer:

2 feet is equal to 0.609 meters

One meter is equal to roughly 3.281 feet.

So two feet is less than one meter.

To find how many meters a certain amount of feet is, you divide by 3.281

2 ÷ 3.281 = 0.609

2 feet is equal to 0.609 meters

Answer:

0.61 meter

Step-by-step explanation: