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2 years ago

Scale Drawings

1 answer:

4 0

the correct question Part 1) is
A school photo has dimensions of 2 1/4 inches by 2 3/4 inches. What are the dimensions of the school photo if it is enlarged by a scale factor of 7?

we know that
2 1/4 in-------> (2*4+1)/4----> 9/4 in
2 3/4 in-----> (2*4+3)/4-----> 11/4 in

if the scale factor=7
the dimensions of the school photo are
(9/4)*7-----> 63/4 in-----> 15 3/4 in
(11/4)*7----> 77/4 in-----> 19 1/4 in

the answer Part 1) is
the dimensions of the school photo are
15 3/4 in x 19 1/4 in

Part 2) Stephanie drew a picture of her house with her prize rosebush in the front. In her picture, she drew the rosebush 1.5 centimeters tall, and she drew the house 7.5 centimeters tall.

If her rosebush is really 0.75 meter tall and she made her drawing to scale, what scale did she use?

scale factor=measure in the drawing/measure in the actual
scale factor=1.5 cm/0.75 m-----> 2 cm/m
that means
2 cm in the drawing is equal to 1 meter in the actual

if the house in the drawing is 7.5 cm tall
the house in the actual is 7.5/2----> 3.75 m

the answer Part 2) is
the scale is 2 cm/meters

Part 3)A photo of a painting has a scale of 3 inches = 2 feet. If the photo is 7.5 inches long, how many feet long is the painting?

we know that

scale factor=measure in the photo/measure in the painting
measure in the painting=measure in the photo/scale factor
scale factor=3/2---> 1.5 in/ft
measure in the photo=7.5 in

measure in the painting=7.5/1.5----> 5 ft

the answer part 3) is
the painting is 5 ft long

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The arrow is fired with an initial upward velocity of 32ft/s

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1 year ago

Diana sold 336 muffins at the bake sale.Bob sold 287 muffins.Bob estimates that he sold 50 fewer muffins than Diana.how did he e

malfutka [58]

Step-by-step explanation:

Since we have given that

Number of muffins Diana sold at the bake sale = 336

Number of muffins Bob sold at the bake sale = 287

Now, here we are using the method of estimation i.e. rounding the integers to nearest ones.

By estimation, we get

Number of muffins Diana sold at the bake sale = 340

Number of muffins Bob sold at the bake sale = 290

So,

Difference between them is given by

$340-290\\=50$

Hence, Bob sold 50 fewer muffins than Diana.

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1 year ago

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Select the functions that have identical graphs.

shtirl [24]

Answer:

c. 1 and 3

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot each equation.

Please see the attached image below, to find more information about the graph s

The equations are:

1) y = sin (3x + π/6)

2) y = cos (3x - π/6)

3) y = cos (3x - π/3)

Looking at the graphs, we can see that the identical ones

are equations one and three

Correct option:

c. 1 and 3

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2 years ago

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se the function to show that fx(0, 0) and fy(0, 0) both exist, but that f is not differentiable at (0, 0). f(x, y) = 9x2y x4 + y

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Answer:

It is proved that $f_x, f_y$ exixts at (0,0) but not differentiable there.

Step-by-step explanation:

Given function is,

$f(x,y)=\frac{9x^2y}{x^4+y^2}; (x,y)\neq (0,0)$

To show exixtance of $f_x(0,0), f_y(0,0)$ we take,

$f_x(0,0)=\lim_{h\to 0}\frac{f(h+0,k+0)-f(0,0)}{h}=\lim_{h\to 0}\frac{\frac{9h^2k}{h^4+k^2}-0}{h}\\\therefore f_x(0,0)=\lim_{h\to 0}\frac{9hk}{h^4+k^2}=\lim_{h\to 0}\frac{9k}{h^3+\frac{k^2}{h}}=0$ exists.

And,

$f_y(0,0)=\lim_{k\to 0}\frac{f(h,k)-f(0,0)}{k}=\lim_{k\to 0}\frac{9h^2k}{k(h^4+k^2)}=\lim_{k\to 0}\frac{9h^2}{h^4+k^2}=\frac{9}{h^2}$ exists.

To show f(x,y) is not differentiable at the origin cheaking continuity at origin be such that,

$\lim_{(x,y)\to (0,0)}\frac{9x^2y}{x^4+y^2}=\lim_{x\to 0\\ y=mx^2}\frac{9x^2y}{x^4+y^2}=\frac{9x^2\times m x^2}{x^4+m^2x^4}=\frac{9m}{1+m^2}$ where m is a variable.

which depends on various values of m, therefore limit does not exists. So f(x,y) is not continuous at (0,0). Hence it is not differentiable at (0,0).

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2 years ago

Susie has $95 to spend on renting snorkeling gear at the beach. There is a $15 flat service fee to rent the snorkeling gear alon

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Answer:

10 hours

Step-by-step explanation:

We can actually solve this problem simply as if it were an equation instead of an inequality. We have:

15 + 8h ≤ 95

Subtract 15 from both sides:

8h ≤ 95 - 15

8h ≤ 80

Divide by 8 from both sides:

h ≤ 80/8

h ≤ 10

So, the number of hours cannot exceed 10, which means the maximum number of hours Susie can rent is 10 hours.

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1 year ago

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