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4 years ago

What is the following difference? 56.4 – 27.39

Mathematics

2 answers:

Fudgin [204]4 years ago

7 0

Answer:

29.01

Step-by-step explanation:

You just have to do the math

ioda4 years ago

3 0

The answer is

29.01

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You were given a $20,000 gift towards University education by your grandparents. How much will this be in 17 years if it is inve

Nat2105 [25]

Answer:

$65,068.44

Step-by-step explanation:

A= 20000(1+ 0.07/4)^4(17)

A= 20000(1.0175)^68

A= 65,068.44

3 0

3 years ago

Read 2 more answers

Need help fast pls help

ValentinkaMS [17]

Answer:

Step-by-step explanation:

7 0

3 years ago

7. Phozia has three pieces of rope with lengths of 160 cm, 192 cm and

lianna [129]

Answer:

a) 16 cm, b) 37 pieces

Step-by-step explanation:

Part a

Finding the largest divisor of 160, 192 and 240

160 divisors: 1, 2, 4, 5, 8, 10, 16, 32, 40, 80 and 160.

// You can alternatively find them by factor pairs, which are (1, 160), (2, 80), (4, 40), (5, 32), (8, 20) & (10, 16). This way is much more faster. Also, you can simply search them in metanumbers.com

192 divisors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96 and 192

240 divisors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240

The largest divider that they all have in common is 16.

So 16 cm is the largest possible length of each of the shorter pieces of

rope

Part b

Now we have to count how many 16 cm pieces of rope can we get from the large rope pieces, which lengths are 160 cm, 192 cm and 240 cm

160/16 + 192/16 + 240/16 = 10 + 12 + 15 = 37

The answer is 37 pieces

3 0

3 years ago

Evaluate the interval (Calculus 2)

Darya [45]

Answer:

$2 \tan (6x)+2 \sec (6x)+\text{C}$

Step-by-step explanation:

<u>Fundamental Theorem of Calculus</u>

$\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))$

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

$\displaystyle \int \dfrac{12}{1-\sin (6x)}\:\:\text{d}x$

$\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int a\:\text{f}(x)\:\text{d}x=a \int \text{f}(x) \:\text{d}x$\end{minipage}}$

If the terms are multiplied by constants, take them outside the integral:

$\implies 12\displaystyle \int \dfrac{1}{1-\sin (6x)}\:\:\text{d}x$

Multiply by the conjugate of 1 - sin(6x) :

$\implies 12\displaystyle \int \dfrac{1}{1-\sin (6x)} \cdot \dfrac{1+\sin(6x)}{1+\sin(6x)}\:\:\text{d}x$

$\implies 12\displaystyle \int \dfrac{1+\sin(6x)}{1-\sin^2(6x)} \:\:\text{d}x$

$\textsf{Use the identity} \quad \sin^2 x+ \cos^2 x=1:$

$\implies \sin^2 (6x) + \cos^2 (6x)=1$

$\implies \cos^2 (6x)=1- \sin^2 (6x)$

$\implies 12\displaystyle \int \dfrac{1+\sin(6x)}{\cos^2(6x)} \:\:\text{d}x$

Expand:

$\implies 12\displaystyle \int \dfrac{1}{\cos^2(6x)}+\dfrac{\sin(6x)}{\cos^2(6x)} \:\:\text{d}x$

$\textsf{Use the identities }\:\: \sec \theta=\dfrac{1}{\cos \theta} \textsf{ and } \tan\theta=\dfrac{\sin \theta}{\cos \theta}:$

$\implies 12\displaystyle \int \sec^2(6x)+\dfrac{\tan(6x)}{\cos(6x)} \:\:\text{d}x$

$\implies 12\displaystyle \int \sec^2(6x)+\tan(6x)\sec(6x) \:\:\text{d}x$

$\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}$

$\boxed{\begin{minipage}{6 cm}\underline{Integrating $ \sec kx \tan kx$}\\\\$\displaystyle \int \sec kx \tan kx\:\text{d}x= \dfrac{1}{k}\sec kx\:\:(+\text{C})$\end{minipage}}$

$\implies 12 \left[\dfrac{1}{6} \tan (6x)+\dfrac{1}{6} \sec (6x) \right]+\text{C}$

Simplify:

$\implies \dfrac{12}{6} \tan (6x)+\dfrac{12}{6} \sec (6x)+\text{C}$

$\implies 2 \tan (6x)+2 \sec (6x)+\text{C}$

Learn more about indefinite integration here:

brainly.com/question/27805589

brainly.com/question/28155016

3 0

2 years ago

Quadratic formula, SOMEONE PLEASE HELP (30 points)

Anvisha [2.4K]

1. to create your own quadratic you have to just make up any numbers. so off the top of my head:
y = -5x^2 + 10x - 3

2. the equation to find the x value of the vertex uses is the equation -b/2a. You may notice that this is similar to the quadratic formula except for you take away the plus or minus square root part. if you think about it, it makes sense that this would be the vertex because the plus or minus parts are an equal distance away from the center of the parabola. so using the form ax^2 + bx + c we can plug in the a and b:
x = -10/2 (-5)
x = -10/-10
x = 1

so we have x and can plug into equation to get y value:
y = -5 (1)^2 + 10(1) -3
y= -10 + 10 - 3
y = -3

vertex is at point (1, -3)

3. the axis of symmetry is the line that runs straight up and down at the center of a parabola. the center of the parabola is the vertex so the line runs straight up and down through vertex. for a line to run straight up and down it is a constant x value. since the x of the vertex is 1, the line is:
x = 1

4. using quadratic formula :
x = [-b (+-) sqrt (b^2 - 4ac)]/2a
we get:
x = [-10 (+-) sqrt (10^2 - 4 (-5)(-3)]/2 (-5)
x = [-10 (+-) sqrt (100 - 60)]/-10
x= [-10 (+-) sqrt (40)]/-10
x= [-10 (+-) 2* sqrt (10)]/-10
x= [5 (+-) sqrt (10)]/5

that is the answer. You can use a calculator to solve easily.

5. the discriminant is the solution to what is under the squareroot sign. so the square root part was:
sqrt (b^2 - 4ac)

so discriminant is :
b^2 - 4ac

so for this function it is:
10^2 - 4 (-5)(-3)

solving this the discriminant is 40

6 0

4 years ago