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3 years ago

Working together, Shawn and Hector can install a tile floor in 6 hours. It would take Shawn 9 hours to do the job alone.

Mathematics

2 answers:

Naya [18.7K]3 years ago

7 0

Is there another part to your question?

Yanka [14]3 years ago

3 0

Hector could do it in 3 hours.
Your question doesn’t really make sense though.

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(a) Write 14 as a decimal.

Yuliya22 [10]

Answer:

0.14

Step-by-step explanation:

14% describes 14 out of 100. It is written as 14 in the numerator and 100 in the denominator of a fraction. A percent is always written as the number over 100 as a fraction. “Out of 100” refers to the decimal place “hundredths.” 14% is 14 hundredths.

3 0

3 years ago

Verify that the given point is on the curve and find the lines that are (a) tangent and (b) normal to the curve at the given poi

lara [203]

For each curve, plug in the given point $(x,y)$ and check if the equality holds. For example:

(I) (2, 3) does lie on $x^2+xy-y^2=1$ since 2^2 + 2*3 - 3^2 = 4 + 6 - 9 = 1.

For part (a), compute the derivative $\frac{\mathrm dy}{\mathrm dx}$ , and evaluate it for the given point $(x,y)$ . This is the slope of the tangent line at the point. For example:

(I) The derivative is

$x^2+xy-y^2=1\overset{\frac{\mathrm d}{\mathrm dx}}{\implies}2x+x\dfrac{\mathrm dy}{\mathrm dx}+y-2y\dfrac{\mathrm dy}{\mathrm dx}=0\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x+y}{2y-x}$

so the slope of the tangent at (2, 3) is

$\dfrac{\mathrm dy}{\mathrm dx}(2,3)=\dfrac74$

and its equation is then

$y-3=\dfrac74(x-2)\implies y=\dfrac74x-\dfrac12$

For part (b), recall that normal lines are perpendicular to tangent lines, so their slopes are negative reciprocals of the slopes of the tangents, $-\frac1{\frac{\mathrm dy}{\mathrm dx}}$ . For example:

(I) The tangent has slope 7/4, so the normal has slope -4/7. Then the normal line has equation

$y-3=-\dfrac47(x-2)\implies y=-\dfrac47x+\dfrac{29}7$

3 0

3 years ago

How many counting numbers have three distinct nonzero digits such that the sum of the three digits is 7?

SOVA2 [1]

Answer:

Step-by-step explanation:

You have 2 conditions.

1. The digits must be different.

2. The digits must add to 7.

There aren't very many

124

142

214

241

412

421

That's it. That's your answer. There are 6 of them

7 0

3 years ago

The formula F=95(K−273.15)+32 converts a temperature from kelvin K to degrees Fahrenheit

DENIUS [597]

F=95(K−273.15)+32

Switch the equation so that F is on the right side:

95(K−273.15)+32 = F

Use the distributive property:

95K + 95(-273.15) + 32 = F

95K - 25949.25 + 32 = F

95K - 25917.25 = F

Add 25917.25 to both sides:

95K = 25917.25 + F

Divide each term by 95:

K = 25917.25 / 95 + F/95

K = (25917.25 + F) /95

7 0

3 years ago

Ashley has already walked 0.5 miles this week, plus she plans to walk 1.5 miles during each trip to school. If she plans to take

alisha [4.7K]

Answer:

Step-by-step explanation:

The slope is 1.5 miles / day

7 0

3 years ago