write the domain and rang of h using interval notation

Answer:

x2 the left side and x3 the right side of the equation

Answer:

X = -2

First you cross multiply, and then you expand to get 15x+6

after that its basic algebra with adding/subtracting from each side, simplifying, and then divide both sides by -13.

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &4 \end{cases} \\\\\\ A=2000e^{0.08\cdot 4}\implies A=2000e^{0.32}\implies \boxed{A\approx 2754.26}[/tex]

Answer:

x = 4, -6

Step-by-step explanation:

x = 4, -6

Answer:

Shifted, reflected, and stretched

Step-by-step explanation:

Horizontal Shift: Right 1 Unit

Vertical Shift: Up 3 Units

Reflection about the x-axis: Reflected

Vertical Stretch: Stretched

Answer:

D) The number that is 5 to the right of -6 on the number line

Hope this helps :)

Answer:$373.50

Step-by-step explanation:

$498.00 divided by 40 is 12.45

12.45 times 30 is $373.50

Answer:

No, it is not a linear function, rather a rational function

Step-by-step explanation:

Because the term on the left-hand side contains both x and y, then neither variable varies directly with the other, hence, it's a rational function:

2yx=4

yx=2

y=2/x

Answer:

8.7

Step-by-step explanation:

8.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.78.7

Answer: 1300

Step-by-step explanation:

3300-1000=2000

2000-450=1550

1550-150=1400

1400-100=1300

Answer:

Step-by-step explanation:

1. Wear safety glasses

2. Be accompanied by an adult

3. Wear proper lab clothing

4. Alert Lab instructor if an accident were to happen

5. Follow all instructions given by lab instructor

Answer:

(1+y)^(3/2)-3(1+y)^(1/2)=(1+x)^(3/2)-3(1+x)^(1/2)+c

Step-by-step explanation:

This is separable.

Multiply x dx on both sides and divide both sides by (1+y)^(1/2) to obtain:

y/(1+y)^(1/2)=(1+x)^(-1/2) x dx

Using law of exponents to get rid of negative exponent by finding reciprocal:

y/(1+y)^(1/2)=x/(1+x)^(1/2) dx

Let u=(1+y)^(1/2).

Then u^2=1+y.

Differentiate: 2 u du=dy

[Let v=(1+x)^(1/2).]

Plug in our substitution:

(u^2-1) 2u du/u=(v^2-1) 2v dv/v

Simplify:

(u^2-1) 2 du=(v^2-1) 2 dv

Integrate both sides:

(u^3/3-u) 2+L=(v^3/3-v) 2+K

Divide both sides by 2:

u^3/3-u +L/2=v^3/3-v+K/2

K/2-L/2 is just a constant value C:

u^3/3-u=v^3/3-v+C

Use substitution again to put back in terms of x and y:

((1+y)^(1/2))^3/3-(1+y)^(1/2)=((1+x)^(1/2))^3/3-(1+x)^(1/2)+C

Simplify the exponent part a bit:

(1+y)^(3/2)/3-(1+y)^(1/2)=(1+x)^(3/2)/3-(1+x)^(1/2)+C

I don't like the division by 3 so multiply both sides by 3:

(1+y)^(3/2)-3(1+y)^(1/2)=(1+x)^(3/2)-3(1+x)^(1/2)+3C

3C is still just an unknown constant, c.

(1+y)^(3/2)-3(1+y)^(1/2)=(1+x)^(3/2)-3(1+x)^(1/2)+c

Answer:

69

Step-by-step explanation:

because 34plus 35 will give you 69

Answer:

8/64 = 0.125 = 12.5%

Step-by-step explanation:

8/64 = 0.125 = 12.5%

Answer:

70.2

Step-by-step explanation:

28.08 / 0.4 = 70.2

Answer:

3000

Step-by-step explanation:

Answer:

300

Step-by-3step explanation:

Answer:

82.5 miles in 1 1/2 hours

Step-by-step explanation:

Using the information the question gives us we can find the appropriate answer to this question by dividing the miles per hour by two, and then add that number to the additional miles per hour.

55 miles = one hour

2 hours = 110 miles

1 1/2 hours = 55 ÷ 2 = 27.5

55 + 27.5 = 82.5 miles

82.5 miles

Hope this helps

Answer:

Step-by-step explanation:

a) The height of the springboard above the water should be h(0) : Read, the height at t = 0

h(0) = -5(0) + 10(0) + 3

h(0) = 0 + 0 + 3

h(0) = 3

a) 3 meters

b)  The time it takes the diver to hit water should be, the positive 0 solution for t.  Remember, in a quadratic equation,  there are two values for t where a parabola crosses the horizontal axis, which in this case would be t.  Just by looking at the function, h(t) = -5t2 + 10t + 3 , one should be able to see that it cannot be factored easily, so it requires the Quadratic Formula to find the zeros ; x = -b ±√(b2-4ac)  / 2a

Substitute t for x, and use the coefficients for a, b, c:

t  =  (-10 ± √((102 - 4(-5)(3)))/2(-5)

t = (-10 ±√(100 + 60))/-10

t = (-10 ±√160)/-10) ; Now factor the 160 to simplify:

t = (-10 ±√(10*16))/-10

t = (-10 ±4√10)/-10 ; Factor out leading coefficient of -2 from the numerator:

t = -2(5 ± 2√10)/-10

t = (5 ± 2√10)/5

Using a calculator to find the zeros, and disregarding the negative zero (because t starts at 0):

t ≈ 2.265

b) approx. 2.265 seconds for diver to hit water.

c) To find this, set the function equal to 3 to find what other value for t would be equal to 3 (we know one is 0).

-5tt + 10t + 3 = 3

-5t2 + 10t = 0 ; factor out t

t(-5t + 10) = 0

We know t = 0:

We also know that -5t + 10 = 0

-5t = -10

t = 2

c) 2 seconds. This is the time that diver would equal height of t=0 which is where he started, and where he equals the height of the springboard.

d and e) The peak of the dive (parabola), is determined using the formula h = -b/2a (Derived from the Quadratic Formula) to find the y value (in this case, the h value, answering e) and then using that result in the function to find the x value (in this case, the t value answering d) of the point where the parabola (dive path) reaches a maximum(height), or minimum(in upward opening parabolas).

h = -10/2(-5)

h = -10/-10

h = 1

h(1) = -5(1)2 + 10(1) + 3

h(1) = -5 + 10 + 3

h(1) = 8

d) At t = 1 second, diver will have reached peak of dive.

e) At t = 1 second, diver will have reached a maximum height of 8 meters.

Answer:

-5x + 3

Step-by-step explanation:

1/3 x - 4x -5/3x + 1/3 x +3

2/3 x -4 -5/3x + 3

3/3x -4x +3

-1 1x -4x + 3

- 5x + 3

:)

Enter a problem...

Calculus Examples

Popular Problems Calculus Find the Domain and Range f(x)=5x-3

f

(

x

)

=

5

x

−

3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

(

−

∞

,

∞

)

Set-Builder Notation:

{

x

|

x

∈

R

}

The range is the set of all valid

y

values. Use the graph to find the range.

Interval Notation:

(

−

∞

,

∞

)

Set-Builder Notation:

{

y

|

y

∈

R

}

Determine the domain and range.

Domain:

(

−

∞

,

∞

)

,

{

x

|

x

∈

R

}

Range:

(

−

∞

,

∞

)

,

{

y

|

y

∈

R

}

Answer:

no its not since some dots are above each other and fail the vertical line test

Hope This Helps!!!

Answer:

no the x value repeat

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the missing leg x first using Pythagorean:

Now the 6 functions, considering angle α opposite to leg with length of 9:

sine = opposite/hypotenuse

cosine = adjacent/hypotenuse

tangent = opposite / adjacent

cotangent = adjacent / opposite

secant = hypotenuse / adjacent

cosecant = hypotenuse / opposite

B=

[tex]\\ \sf\longmapsto \sqrt{13^2-9^2}=\sqrt{169-81}=\sqrt{88}\approx9.5[/tex]

Now

[tex]\\ \sf\longmapsto sinA=\dfrac{P}{H}=\dfrac{9}{13}[/tex]

[tex]\\ \sf\longmapsto cosA=\dfrac{B}{H}=\dfrac{9.5}{13}[/tex]

[tex]\\ \sf\longmapsto tanA=\dfrac{P}{B}=\dfrac{9}{9.5}[/tex]

[tex]\\ \sf\longmapsto cotA=\dfrac{1}{tanA}=\dfrac{9.5}{9}[/tex]

[tex]\\ \sf\longmapsto secA=\dfrac{1}{cosA}=\dfrac{13}{9.5}[/tex]

[tex]\\ \sf\longmapsto cosecA=\dfrac{1}{sinA}=\dfrac{13}{9}[/tex]

Step-by-step explanation:

figure B is a scaled copy of figure B

by scale factor : 1/2

Answer:

2, -6

Step-by-step explanation:

x^2 + 4x - 12

A = 1

B = 4

C = -12

i used the "X" method to solve for the solutions. i think it's easier than using the quadratic formula but it doesn't always work

for the "X" method you have to multiply your A value and your C value together so 1 x (-12) = -12. that is going to be the top part of the X

the bottom part of the x will be your B value which is 4

we have to find multiples of -12 that will also add to 4

so -2 and 6 multiply to -12 but also add to 4 so we know these numbers will work

i added added two drawings to show how i found the solutions using the "X" method and the quadratic formula

Answer:

9×10^16

Step-by-step explanation:

Only if the power is the same, you can just add the first numbers

You just need to combine.

The rule (a) = a tells us we can just remove the parenthesis.

2*10^16 + 7*10^16

That would equal to 9 x 10^16 because when adding exponents, you keep them the same.

Answer:

ayo i think is ufo trying to communicate hey alien we come in peace

Step-by-step explanation:

[tex]\cos \theta(\tan \theta + \cot \theta)\\\\=\cos \theta \tan \theta + \cos \theta \cot \theta \\\\=\cos \theta \left (\dfrac{\sin \theta}{\cos \theta} \right)+ \cos \theta \left(\dfrac{\cos \theta}{\sin \theta} \right)\\\\\\=\sin \theta + \dfrac{\cos^2 \theta}{\sin \theta}\\\\=\dfrac{\sin^2 \theta + \cos^2 \theta}{\sin \theta}\\\\=\dfrac 1{\sin \theta}\\\\=\csc \theta[/tex]

Answer:

30%

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Answer:

609

Step-by-stepStep-by-step explanation:

nope

Answer:

if its me then i will bye the store. but the answer is 50%

Step-by-step explanation: