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3 years ago

The rectangle below is enlarged using a scale factor of 1.5. What will be the new length and width of the rectangle?

Mathematics

1 answer:

Likurg_2 [28]3 years ago

5 0

Answer: length = 4.5 m, width = 3 m

Step-by-step explanation:

When a shape is enlarged using a scale factor, you simply multiply each of the sides by the scale factor.

length = 3 * 1.5 = 4.5 m

width = 2 * 1.5 = 3 m

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Consider the surface f(x,y) = 21 - 4x² - 16y² (a plane) and the point P(1,1,1) on the surface.

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Answer:

A) ( -8, -32 )

Step-by-step explanation:

Given function : f (x,y) = 21 - 4x^2 - 16y^2

point p( 1,1,1 ) on surface

Gradient of F

attached below is the detailed solution

7 0

3 years ago

I dont really understand this

galina1969 [7]

Answer:

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3 years ago

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = $21m^3$

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

<em>Using the volume formula of a cylinder</em>

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

$V = \frac{4}{3}\pi r^3$

Divide both sides by r

$\frac{V}{r} = \frac{4}{3r}\pi r^3$

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

$V = 14$

Hence, the volume of the sphere is 14m³

4 0

3 years ago

Read 2 more answers

PlZ HELP WILL MARK YOU AS THE BRAINLIEST!

defon

Answer:

1. distance = sqrt( (7-7)^2+(2- -8)^2) = 10

2. check out desk (0,0 ) => distance = sqrt( (0- -9)^2+(0-0)^2) = 9

3. last corner ( -3, 4)

4. area = sqrt( (-10- -10)^2+(10-4)^2) x sqrt( (-3- -10)^2+(10-10)^2) = 6x7 =42

5. check desk (0,0), south direction = negative y axis => P_beginning (0,-20), P_end (0,-(20+25)) = (0,-45)

6. A(-2,-1) and B(4,-1) lie in y =-1. AB = sqrt( (-2- 4)^2+(-1- -1)^2) =6

=> area = 3.6x6 =21.6

=> peri = 2x(3.6+6) = 19.2

7. A(-5,4) and B(2,4), AB = sqrt( (-5- 2)^2+(4- -4)^2) = 7 => AB is base

=> p = peri = 7+ 8.3x2 = 23.6

=> area = sqrt[px(p-7)x(p-8.3)x(p-8.3)]

=sqrt[23.6x(23.6-7)x(23.6-8.3)x(23.6-8.3)] = 302.8

5 0

4 years ago

Q : <br> what 1:9 x 6 = ?

kow [346]

Answer:

the answer is $\frac{2}{3}$

Step-by-step explanation:

hope this helps :)

can I get brainliest plz

4 0

3 years ago

Read 2 more answers