College Calculus - hyperbolic functions (see attachment)

Answer:

The length of BC is √105 cm or 10.2 cm.

Step-by-step explanation:

You have to apply Pythagoras Theorem, c² = a² + b² where c represents hypotenuse, a and b are the sides :

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

[tex]let \:a =BC \:, \: b = 8 \: , \: c = 13[/tex]

[tex] {13}^{2} = {BC}^{2} + {8}^{2} [/tex]

[tex]169 = {BC}^{2} + 64[/tex]

[tex] {BC}^{2} = 169 - 64[/tex]

[tex] {BC}^{2} = 105[/tex]

[tex]BC = \sqrt{105} [/tex]

[tex]BC = 10.2 \: cm \: (3s.f)[/tex]

Answer:

[tex] \boxed{\sf Length \ of \ BC = \sqrt{105} \ cm} [/tex]

Given:

AB = 13 cm

AC = 8 cm

To Find:

Length of BC

Step-by-step explanation:

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

[tex] \therefore \\ \sf {AC}^{2} + {BC}^{2} = {AB}^{2} \\ \sf \implies {8}^{2} + {BC}^{2} = {13}^{2} \\ \\ \sf {8}^{2} = 64 : \\ \sf \implies 64 + {BC}^{2} = {13}^{2} \\ \\ \sf {13}^{2} = 169 : \\ \sf \implies 64 + {BC}^{2} = 169 \\ \\ \sf Substract \: 64 \: from \: both \: sides : \\ \sf \implies (64 - 64) + {BC}^{2} = 169 - 64 \\ \\ \sf 64 - 64 = 0 : \\ \sf \implies {BC}^{2} = 169 - 64 \\ \\ \sf 169 - 64 = 105 : \\ \sf \implies {BC}^{2} = 105 \\ \\ \sf \implies BC = \sqrt{ 105 } \ cm [/tex]

So,

Length of BC = [tex] \sqrt{105} [/tex] cm

Answer:

a. $849.45

Step-by-step explanation:

In the above question, we are given the following information

Coupon rate = 10%

Face value = 1000

Maturity = n = 20 years

t = number of periods = compounded semi annually = 2

Percent yield = 12% = 0.12

Bond Value formula =

C/t × ([1 -( 1/ 1 + r/t)-^nt ÷] r/t) +( F/ (1 + r/t)^nt)

C = coupon rate × face value = 10% × 1000 = 100

Bond value:

= 100/2 × ( [1 - (1 /1 + 0.12/2)^-20×2]÷ 0.12/2)+ (1000/( 1 + 0.12/2)^20×2

= 50 × ( [1 - (1 /1 + 0.06) ^40] ÷ 0.06) + ( 1000/ (1 + 0.06) ^40

= 50 × ( [1 - (1/ (1.06) ^40] ÷ 0.06 ) + (1000/(1.06)^40)

= 50 × 15.046296872 + 97.222187709

= $849.45

Bond value = $849.45

Answer:

P = 110N + 1,900.

$4,540.

Step-by-step explanation:

Her base salary is $1,900, so your constant/y-intercept for the equation is $1,900.

She makes an additional $110 for each copy, so your slope is $110.

P (the total pay) = 110 * the number of copies sold + 1,900

P = 110N + 1,900.

She sells 24 copies.

P =  110 * 24 + 1,900

P = 2,640 + 1,900

P = 4,540.

So, her total pay is $4,540.

Hope this helps!

Answer:

15 pt

Step-by-step explanation:

to convert qt to pt you multiply by 2 so 7 and 1/2 times 2 is 15

Answer:

The probability that the person is between 65 and 69 inches is 0.5403

Step-by-step explanation:

Mean height = [tex]\mu = 66[/tex]

Standard deviation = [tex]\sigma = 2.5[/tex]

We are supposed to find What is the probability that the person is between 65 and 69 inches i.e.P(65<x<69)

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

At x = 65

[tex]Z=\frac{65-66}{2.5}[/tex]

Z=-0.4

Refer the z table for p value

P(x<65)=0.3446

At x = 69

[tex]Z=\frac{69-66}{2.5}[/tex]

Z=1.2

P(x<69)=0.8849

So,P(65<x<69)=P(x<69)-P(x<65)=0.8849-0.3446=0.5403

Hence the probability that the person is between 65 and 69 inches is 0.5403

Answer: The concentration will be 8 milligrams per liter at 2 hours and 4 hours.

Step-by-step explanation:

GIven: The concentration of a certain painkiller supplied by serum varies in its effectiveness over time according to the following function, [tex]C (t) = - t^2 + 6t[/tex] where C is the concentration of the painkiller in the serum measured in milligrams per liter so that it takes effect during t hours.

Put C(t)=8, then we get

[tex]8=-t^2+6t\\\\\Rightarrow\ t^2-6t+8=0\\\\\Rightarrow\ t^2-2t-4t+8=0\\\\\Rightarrow\ t(t-2)-4(t-2)=0\\\\\Rightarrow\ (t-2)(t-4)=0\\\\\Rightarrow\ t=2,4[/tex]

At t=2, [tex]C(t)=-(2)^2+6(2)=-4+12=8[/tex]

At t=4, [tex]C(t)=-(4)^2+6(4)=-16+24=8[/tex]

Hence, the concentration will be 8 milligrams per liter at 2 hours and  4 hours.

Answer: 12-i

               12-(√-1)

Step-by-step explanation:

[tex]18-\sqrt{-25}[/tex]   Original Question

[tex]18-(\sqrt{25} * \sqrt{-1} )[/tex]   Split

[tex]18-5*(\sqrt{-1} )[/tex]   Solve for square root

[tex]12-\sqrt{-1}[/tex]   Subtract

You can substitute [tex]\sqrt{-1}[/tex] for i

[tex]12-i[/tex]   Substitute

Answer:

18-5i

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the measure of third angle be X

The sum of interior angle of triangle = X

Let's create an equation

[tex]x + 32 + 90 = 180[/tex]

Add the numbers

[tex]x + 122 = 180[/tex]

Move constant to R.H.S and change its sign

[tex]x = 180 - 122[/tex]

Subtract the numbers

[tex]x = 58[/tex] °

Hope this helps...

Best regards!!

Answer:

236

Step-by-step explanation:

The interquartile range is the right edge of the box minus the left edge of the box

The right edge of the box is 301

The left edge of the box is 65

301 -65 =236

The interquartile range is 236

Answer:

65

Step-by-step explanation:

To find interquartile range, you substract upper quartile( 130 in this problem) and the lower quartile(65 in this problem)

Finally, you get the answer 65.

Hope this helps!

Answer:

3 is not a solution

Step-by-step explanation:

6x – 7 = 12?

Substitute 3 in for x and see if the equation is true

6*3 - 7 = 12

18-7 = 12

11 =12

This is false so 3 is not a solution

Answer:

3 grams will be left after 6 half-lives

Step-by-step explanation:

Half-live:

Time it takes for the substance to be reduced by hall.

After n half lives:

The amount remaing is:

[tex]A(n) = A(0)(0.5)^{n}[/tex]

In which A(0) is the initial amount and n is the number of half-lives.

Starting with 210 grams of a radioactive isotope, how much will be left after 6 half-lives?

This is A(6) when A(0) = 210. So

[tex]A(n) = A(0)(0.5)^{n}[/tex]

[tex]A(6) = 210(0.5)^{6} = 3.3[/tex]

Rounding to the nearest gram

3 grams will be left after 6 half-lives

Answer:

Look for perpendicular lines or corresponding angles or alternate interior angles.

Step-by-step explanation:

When you want to show that a quadrilateral is a parallelogram you need to show that the oposite sides are parallel. In order to show that two segments are parallel there are various theorems and definitions you can use.

1 -  Remember that two lines perpendicular to the same segment are parallel.

2 - When two lines are cut by a secant and their alternate interior angles are congruent, then the resulting lines are parallel, I will attach a drawing to illustrate what I am saying.

3 - When two lines are cut by a secant and their CORRESPONDING angles are congruent, then the resulting lines are parallel, I will also attach a drawing to illustrate what I am saying.

4x+21+3x-5=121

7x+16=121

x=15

angle ABD =4(15)+21=81

A - No

B - No

C - Yes

D - Yes

.

C and D are alternate exterior angles

Answer:

b. the approx time it takes an investment to double in value

Answer:

B

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

[tex] \frac{42}{100} \times 350 = 147[/tex]

Concepts:

Answer:

First option and fifth option

-2x-1=3^(-x) and 2^(-x)+2= -5^x + 3 don't intersect.

Therefore, the graphs have no solution.

Answer:

number of children ticket sold = 70

number of adult ticket sold = 70 × 3 = 210

number of student ticket sold = 500 - 4(70) = 500 - 280 = 220

The number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.

We have a local theatre that sells out for their show. They sell all 500 tickets for a total purse of $8,040.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults.

Adult's ticket = [y]

Children's ticket = [x]

Student's ticket = [z]

and

y = 3x

Now -

x + y + z = 500

x + 3x + z = 500

4x + z = 500       ....[1]

and

12x + 18y + 15z = 8040

12x + 18(3x) + 15z = 8040

12x + 54x + 15z = 8040

66x + 15z = 8040     ....[2]

On solving [1] and [2], we get -

x = 90 and z = 140

and

y = 3x = 3 x 90 = 270

y = 270

Therefore, the number of Adult's ticket sold = 270, Children's ticket sold = 90 and Student's ticket sold = 140.

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

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Greetings from Brasil...

The equation is:

putting COS X for the 2nd member

- √(1 - 3.COS² X) = - COS X     ×(- 1)

√(1 - 3.COS² X) = COS X          everything squared

[√(1 - 3.COS² X)]² = (COS X)²

1 - 3.COS² X = COS² X

1 - 3.COS² X - COS² X = 0

1 - 4.COS² X = 0

making Y = COS X

1 - 4Y² = 0

- 4Y² = - 1     ×(- 1)

4Y² = 1

Y² = 1/4

Y = ±√1/4

Y = ± 1/2    

so, as we saw above

Y = COS X

1/2 = COS X   and   - 1/2 = COS X

so to get COS X = ± 1/2, then

X = π/3 = 60         (cos +)

X = 2π/3 = 120      (cos -)

X = 4π/3 = 240    (cos -)

X = 5π/3 = 300     (cos +)

So the only option that includes + and - its:

60° + n360° , 120° + n360°

Answer:

1. can

2. less

3. 5

Step-by-step explanation:

To find out if Waclaw could make it to the gas station using 10 miles, we need to add the number of miles he has to go in order to reach his destination.

[tex]4\frac{7}{8}+4\frac{3}{4} = 9\frac{5}{8}\\[/tex]

9 5/8 is less than 10, so he can make it to the gas station.

We can also find out the answer without even adding the numbers together, because both values are less than five, and when that happens, the sum cannot be 10 or more, so Waclaw can make it to the gas station.

Answer:

3

Step-by-step explanation:

Use this equation

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] substitute

-6-3/0-3 subtract

-9/-3 simplify

-3/-1 two negitives cansle out

3/1=3

Hope this helpes, if it did, please consider giving me brainliest, it will help me a lot. If you have any questions, feel free to ask.

Have a good day! :)

Answer:

3

Step-by-step explanation:

To find the slope, we use the slope formula

m= ( y2-y1)/(x2-x1)

   = ( -6 -3)/(0 -3)

    = -9/-3

    = 3

If it has a single zero that means it has to be just touching the x-axis with its tip.

We know that if it has only one zero, the discriminant equals 0.

So,

[tex]D=b^2-4ac=0\implies (-k)^2-4(1)(9)=0[/tex]

Solving for k,

[tex]k=\pm\sqrt{36}=\boxed{\pm{6}}[/tex].

Hope this helps.

Answer:

60 cm

Step-by-step explanation:

You need to use ratios to solve.  If the scale is 1:30 then the wheel is 2:(?).  Cross-multiply the fractions and solve for x.

1/30 = 2/x

1x = 30*2

x = 60

The wheel is 60 cm in diameter.

Answer:

60 centimeters

Step-by-step explanation:

The scale is 1:30. The wheel diameter is 2 while the actual size of the wheel is unknown. Therefore, the scale for the wheel is 2:x

Let’s set up a proportion.

1/30=2/x

First, cross multiply. Multiply the numerator of the first fraction by the denominator of the second. Then, multiply the numerator of the second by the denominator of the first.

1*x= 2*30

1x=20*30

x=20*30

x=60

Add appropriate units, in this case centimeters (cm).

x= 60 cm

The actual diameter of the wheel is 60 centimeters.

Answer:7

Step-by-step explanation:

Answer:

X=7

Step-by-step explanation:

made a 100 on my quiz but i dont feel like puting my work in here and typing it

Answer:

We accept H₀

p-value = 0,1618

Step-by-step explanation:

We are going to solve a one tail proportion-test ( right tail)

We assume Normal distribution

Sample population 1000

Political strategist to test  wants to test:

Null hypothesis                             H₀           p = p₀       or   p = 26 %

Alternate hypothesis                    Hₐ           p > p₀        or  p > 26%

We assume CI  90 % then

α = 10 %     α = 0,1    and  z score for α = 0,1  is critical value

z = 2,32          ( note  2,32 is z score for α = 0,1017 "good approximation")

To compute z(s)

z(s)  =  ( p -p₀ ) / √ p₀q₀/n

z(s)  =  ( 0,29 - 0,26 ) /√ 0,26*0,74/1000

z(s)  = 0,03 / 0,014

z(s) = 2,14

We compare z(s) and z(c)

z(s) < z(c)

2,14 < 2,32

z(s) is in the acceptance region we accept H₀

The p-value for z(s) is from z-table

p-value = 0,1618

Answer:

Step-by-step explanation:

Given,

Radius ( r ) = 10

Height ( h ) = 6

pi ( π ) = 3.14

now, let's find the volume of given cone:

[tex]\pi {r}^{2} \frac{h}{3} [/tex]

Plug the values

[tex] = 3.14 \times {10}^{2} \times \frac{6}{3} [/tex]

Evaluate the power

[tex] = 3.14 \times 100 \times \frac{6}{3} [/tex]

Calculate

[tex] = 628 \: {units}^{3} [/tex]

Hope this helps..

Best regards!!

Answer:

The answer is 200π units³ .

Step-by-step explanation:

Given that the formula of volume of cone is V = 1/3×π×r²×h where r represents radius and h is height. Then, you have to substitute the value of radius and height into the formula :

[tex]v = \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]

[tex]let \: r = 10 \: , \: h = 6[/tex]

[tex]v = \frac{1}{3} \times \pi \times {10}^{2} \times 6[/tex]

[tex]v = \frac{1}{3} \times \pi \times 600[/tex]

[tex]v = 200\pi \: {units}^{3} [/tex]

Answer:

11 / 12 or 0.9167

Step-by-step explanation:

Given:

3/4 + 1/6

Find:

Value with expression

Computation:

"3/4 added to number 1/6"

3/4 + 1/6

By taking LCM

[9 + 2] / 12

11 / 12 or 0.9167

Answer:

5

Step-by-step explanation:

25/5

=5✖️5=25

=5/1

Answer:

25÷5 = 5 and 25/5 = 125

Step-by-step explanation:

hope this helps!