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3 years ago

Please answer all three questions for full points.

Mathematics

1 answer:

ludmilkaskok [199]3 years ago

5 0

Answer:

Step-by-step explanation:

1. a) vertical stretch by a factor of 5 and

e) reflection over x-axis

2. c) reflection over the y-axis

e) horizontal shift to the right 4 units

3. c) horizontal shift

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Round 0.0645 g to 2 significant figures: ___ g 0.064 0.06 0.065 0.1

Anna11 [10]

0.065 as 0 doesn't count as a significant number

6 0

4 years ago

Read 2 more answers

Forty square inches of material is available to make a cylindrical; can of tuna and water. What dimensions of the can will give

krek1111 [17]

The dimensions of the can are 1.457 inches and 2.913 inches that will give the most volume

Step-by-step explanation:

Let us revise the rule of surface area and volume of a cylinder

S.A = 2π r h + 2π r²
V = π r² h

Forty square inches of material is available to make a cylindrical; can of tuna and water, we need to find the dimensions of the can that will give the most volume

∵ S.A = 40 inches²

∵ S.A = 2π r h + 2π r²

∴ 2π r h + 2π r² = 40

Let us use this rule to find h in terms of r

- Subtract 2π r² from both sides

∵ 2π r h = 40 - 2 π r²

- Divide both sides by 2π r

∴ $h=\frac{40-2\pi r^{2}}{2\pi r}$

∴ $h=\frac{40}{2\pi r}-\frac{2\pi r^{2}}{2\pi r}$

∴ $h=\frac{20}{\pi r}-r$

∵ V = π r² h

- Substitute h by its value above

∴ $V=\pi r^{2}(\frac{20}{\pi r}-r)$

∴ V = 20 r - π r³

To find the most volume differentiate it with respect to r and equate it by 0 to find the value of r

∵ $\frac{dV}{dr}$ = 20 - 3π r²

∵ $\frac{dV}{dr}$ = 0

∴ 20 - 3π r² = 0

- Add 3π r² to both sides

∴ 20 = 3π r²

- Divide both sides by 3π

∴ r² = 2.122

- Take √ for both sides

∴ r = 1.457 inches

To find h substitute the value of r in the expression of h

∵ $h=\frac{20}{\pi r}-r$

∴ $h=\frac{20}{\pi (1.457)}-(1.457)$

∴ h = 2.913 inches

The dimensions of the can are 1.457 inches and 2.913 inches that will give the most volume

Learn more:

You can learn more about volume of solids in brainly.com/question/6443737

#LearnwithBrainly

3 0

4 years ago

Please help me im new to the site. A soda company had sales of $35,119 million in 2010 and $45,962 million in 2014. Use the Midp

viva [34]

Answer:40533.5

Step-by-step explanation:

Midpoint formula

(35113, 2010) > (X1, Y1)

(45954, 2014) > (X2, Y2)

Plug it into the midpoint formula

4 0

3 years ago

For questions 19-22, write a linear equation with the given information.

podryga [215]

Answer:

19. y = x + 1
20. y = -2/3x - 5
21. y = -1/2x + 7
22. y = 4x - 3

Step-by-step explanation:

19. Passing through (2, 3) and PARALLEL to y = x - 4

Parallel lines have equal slopes:

y = x + b

Use given point to find b:

3 = 2 + b
b = 1

The line is:

y = x + 1

20. Passing through (-6, -1) and PARALLEL 2x + 3y = 3

Rewrite in the slope-intercept form:

2x + 3y = 3
3y = -2x + 3
y = -2/3x + 1

The line have same slope:

y = -2/3x + b
-1 = -2/3(-6) + b
-1 = 4 + b
b = - 5

The line is:

y = -2/3x - 5

21. Passing through (-2, 8) and PERPENDICULAR to y = 2x + 5

Perpendicular lines have negative-reciprocal slopes

The line has the form:

y = -1/2x + b

Find the y-intercept:

8 = -1/2*(-2) + b
8 = 1 + b
b = 7

The line is:

y = -1/2x + 7

22. Passing through (-2, -11) and PERPENDICULAR to x + 4y = 8

Perpendicular lines have negative-reciprocal slopes

Rewrite in slope-intercept form:

x + 4y = 8
4y = -x + 8
y = -1/4x + 2

The line has the form:

y = 4x + b

Find y-intercept:

-11 = 4(-2) + b
-11 = -8 + b
b = -3

The line is:

y = 4x - 3

3 0

3 years ago

Show your work F(x)=5x^2-4x+1 G(x)=3x-2 H(x)=x+1 K(x)= 4x What is (g*h)(x)= What is g(k(x))= What is k(g(0)) =

andre [41]

Answer:

— What is (g × h)(x)?

The answer is 3x²+x-2

— What is g(k(x))?

The answer is 12x - 2 or 2(6x-1)

— What is k(g(0))

The answer is -8

Explanation:

Given these functions —

$f(x) = 5 {x}^{2} - 4x + 1 \\ g(x) = 3x - 2 \\ h(x) = x + 1 \\ k(x) = 4x$

Find (g × h)(x)

$(g \times h)(x) = g(x) \times h(x)$

Substitute g(x) = 3x - 2 and h(x) = x + 1

$(3x - 2) \times (x + 1) \\ (3x - 2)(x + 1)$

Multiply the polynomial.

$3 {x}^{2} + 3x - 2x - 2$

Subtract - 2x out of 3x —

$3 {x}^{2} + x - 2$

Thus, the answer is —

$(g \times h)(x) = 3 {x}^{2} + x - 2$

Find (g(k(x))

Substitute k(x) = 4x in g(x).

$g(x) = 3x - 2 \\ k(x) = 4x$

$g(k(x)) = g(4x)$

$g(4x) = 3(4x) - 2$

Distribute 3 in 4x —

$g(4x) = 12x - 2$

Thus the answer is —

$g(k(x)) = 12x - 2$

Alternative Solution

$g(k(x)) = 2(6x - 1)$

Find k(g(0))

Given two functions — k(x) and g(x)

$k(x) = 4x \\ g(x) = 3x - 2$

Evaluate the value of g(0) as we substitute x = 0 in g(x)

$g(0 ) = 3(0) - 2 \\ g(0) = 0 - 2 \\ g(0) = - 2$

Since we need to find k(g(0)), our currently input is g(0).

From k(x) and g(0) —

$k(x) = 4x \\ g(0) = - 2$

Substitute g(0) = -2 in k(x)

$k(g(0)) = 4(g(0)) \\ k( - 2) = 4( - 2) \\ k( - 2) = - 8$

Thus, the answer is —

$k(g(0)) = - 8$

7 0

3 years ago

Please answer all three questions for full points.​

Please answer all three questions for full points.