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3 years ago

3. Evaluate: 16+ 3.2 + 2(5 - 3)

Mathematics

2 answers:

Rufina [12.5K]3 years ago

7 0

Answer:

23.2

Step-by-step explanation:

16+3.2+2(5-3)

19.2+2(2)

19.2+4

23.2

Alina [70]3 years ago

6 0

Answer:

ugdffvgfftcxd

Step-by-step explanation:

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Find the modulus of the complex number 6-2i

Papessa [141]

Answer:

The modulus of the complex number 6-2i is:

$|z|\:=2\sqrt{10}$

Step-by-step explanation:

Given the number

$6-2i$

We know that

$z = x + iy$

where x and y are real and $\sqrt{-1}=i$

The modulus or absolute value of z is:

$|z|\:=\sqrt{x^2+y^2}$

Therefore, the modulus of $6-2i$ will be:

$z=6-2i$

$z=6+(-2)i$

$|z|\:=\sqrt{x^2+y^2}$

$|z|\:=\sqrt{6^2+\left(-2\right)^2}$

$=\sqrt{6^2+2^2}$

$=\sqrt{36+4}$

$=\sqrt{40}$

$=\sqrt{2^2}\sqrt{2\cdot \:5}$

$=2\sqrt{2\cdot \:5}$

$=2\sqrt{10}$

Therefore, the modulus of the complex number 6-2i is:

$|z|\:=2\sqrt{10}$

3 0

3 years ago

A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

sdas [7]

Answer:

$y=-\dfrac{13}{49}x^2$

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

$y=ax^2+bx+c$

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

$-13=a(-7)^2+b(-7)+c$

$49a-7b+c=-13$

(x,y) = (7,-13)

$-13=a(7)^2+b(7)+c$

$49a+7b+c=-13$

(x,y) = (0,0)

$0=a(0)^2+b(7)+c$

$c=0$

so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

$49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13$

$49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13$

we can solve these two equation using the elimination method, by simply adding the two equations

$\quad\quad49a-7b=-13\\+\quad49a+7b=-13$

------------------------------

$\quad\quad 98a=-26$

$\quad\quad a=-\dfrac{13}{49}$

Now we can plug this value of a in any of the two equations.

$49a-7b=-13$

$49\left(-\dfrac{13}{49}\right)-7b=-13$

$-13-7b=-13$

$-7b=0$

$b=0$

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

$y=\left(-\dfrac{13}{49}\right)x^2+0x+0$

$y=-\dfrac{13}{49}x^2$

$49y=-13x^2$

This our equation of the arch!

5 0

3 years ago

At a rate of 4 gallons per minute how long will it take to fill a 300 gallon swimming pool

Ivanshal [37]

Answer:

1 hour and 50 minutes will take to fill up a 300 gallon swimming pool explanation just do the quation/math

7 0

3 years ago

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Write the equation of a line in slope intercept form that passes through the points (0, 7) and (5, 3)

malfutka [58]

first you find the slope by making using the quation for slope

(7-3)/(0-5) and you find your slope is 4/-5. Then you can plug this into point slope form using on of the coordinates so:

y-y1=m(x-x1) --> y-3=-4/5(x-5)

then you distribute the -1 so -----> y-3=-4/5x+4 and then move the 3 over

so the answer is y= -4/5x+7

5 0

3 years ago

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Work out the surface area of a cylinder when the height = 18cm and the volume = 1715cm cubed

lara [203]

Answer:

813.4 cm² (nearest tenth)

Step-by-step explanation:

Volume of a cylinder

$\sf V=\pi r^2 h \quad\textsf{(where r is the radius and h is the height)}$

Given:

h = 18cm
V = 1715 cm³

Use the Volume of a Cylinder formula and the given values to find the radius of the cylinder:

$\implies \sf 1715=\pi r^2 (18)$

$\implies \sf r^2=\dfrac{1715}{18 \pi}$

$\implies \sf r=\sqrt{\dfrac{1715}{18 \pi}$

Surface Area of a Cylinder

$\sf SA=2 \pi r^2 + 2 \pi r h \quad\textsf{(where r is the radius and h is the height)}$

Substitute the given value of h and the found value of r into the formula and solve for SA:

$\implies \sf SA=2 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)^2 + 2 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)(18)$

$\implies \sf SA=2 \pi \left(\dfrac{1715}{18 \pi} \right) + 36 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)$

$\implies \sf SA=\dfrac{1715}{9} + 36 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)$

$\implies \sf SA=813.3908956...$

Therefore, the surface area of the cylinder is 813.4 cm² (nearest tenth)

8 0

2 years ago

Read 2 more answers